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Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.

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Title:
Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.
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Space-time reactor kinetics studies with the University of Florida, SPERT Assembly.
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Diaz, Nils Juan,
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Gainesville FL
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University of Florida
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Subjects / Keywords:
Analyzers ( jstor )
Decay constants ( jstor )
Instrumentation ( jstor )
Kinetics ( jstor )
Neutrons ( jstor )
Pulse duration ( jstor )
Reactivity ( jstor )
Reflectors ( jstor )
Spacetime ( jstor )
Thermal neutrons ( jstor )

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University of Florida
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University of Florida
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Copyright Nils Juan Diaz. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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000955726 ( alephbibnum )
16973836 ( oclc )

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SPACE-TIME REACTOR KINETICS STUDIES WITH THE

UNIVERSITY OF FLORIDA SPERT ASSEMBLY














By

NILS J. DIAZ














A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA
1969







































TO

ZENA















ACKNOWLEDGMENTS


The author wishes to express his sincere appreciation to his

graduate committee for their guidance. Special recognition is due

Dr. M. J. Ohanian, whose encouragement, dedication and detailed

scientific knowledge made this work possible.

The support of the Nuclear Engineering Sciences Department of

the University of Florida throughout the author's graduate work is

greatly appreciated. In particular Dr. R. E. Uhrig's support and

friendship is gratefully recognized.

The author feels fortunate and proud in having studied and worked

with a remarkable scientist and gentleman, Dr. R. B. Perez, now at

Oak Ridge National Laboratory. The author's years of association with

Dr. T. F. Parkinson, now at the University of Missouri, formed the

necessary background for this work.

The continuous assistance of Mr. G. W. Fogle throughout the ex-

perimental program is sincerely appreciated. Mr. L. B. Myers designed

and built the control instrumentation. Mr. R. E. Schoessow was respon-

sible for the design and construction of the assembly. Mr. E. Dugan

and Mr. H. Leydolt aided in the data processing. The cooperation of

the staff of the Nuclear Engineering Sciences Department during the

construction of the facility is acknowledged.

Most of this work was financed under subcontract No. C281 and

C635 with Atomic Energy Division of the Phillips Petroleum Company,








I
under a prime contract with the United States Atomic Energy Commission.

The technical aid of the University of Florida Computing Center in the

development of the computer programs and their financial assistance is

gratefully acknowledged.

Special mention is due Messrs. S. 0. Johnson, R. W. Garner,

G. A. Mortensen and Mrs. M. E. Radd of the Nuclear Safety Research

Branch, Atomic Energy Division, Phillips Petroleum Company for their

continuous assistance and invaluable suggestions throughout the

research program.

To my sister, Miss Lydia Gonzalez, my sincere appreciation for

typing an elegant manuscript from my unintelligible characters.

To the fellow students, who struggled with me to reach the un-

reachable star, my space and time independent friendship.















PREFACE


The text of this dissertation is divided into two related but

essentially independent parts:

Part 1. The University of Florida SPERT Assembly
Design and Calibration -

Part 2. Space-Time Reactor Kinetics Studies with the
University of Florida SPERT Assembly

In Part 1, the design, operational safety and nuclear calibration

of the large-in-one-space dimension, highly multiplicative University

of Florida SPERT Assembly (UFSA) are described. The presentation of

this material is pertinent for a complete understanding of the physical

characteristics of the system to be studied in Part 2 and also because

the system in itself is interesting from the nuclear engineering point

of view. The data acquisition system used for the experimentation is

presented in Chapter IV of this section.

In Part 2, the linear reactor kinetics studies performed with the

UFSA are presented. The space-time dependent distribution of the

neutrons in the assembly, following the introduction of a burst of

neutrons at one end of the core, are studied in the time and in the

frequency domain.

The study of the spatially dependent time profile of the neutron

flux required a large number of figures containing the calculational

and experimental results at different positions in the core. Some

typical figures are included in the main text but most of the recorded

(and calculated) time profiles are included as appendices to the main text.
















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS ..................... ................ ......... iii

PREFACE ............... ............................... ......... v

LIST OF TABLES ................................................. xi

LIST OF FIGURES ................................................ xiii

LIST OF SYMBOLS ................................................ xviii

ABSTRACT .. ........ ....... ..... ........... ..... ............... xix



PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
DESIGN AND CALIBRATION ................. 1

CHAPTER I INTRODUCTION ........................................ 2

CHAPTER II DESCRIPTION OF THE FACILITY ........................ 5

General Features ........................................... 5

Fuel Characteristics ...................................... 9

Mechanical Design .......................................... 10

Moderator Flow Control System .............................. 15

Instrumentation and Interlock System ....................... 22

Fuel Storage ............................................... 27

Neutron Sources .......................................... 30

CHAPTER III OPERATIONAL SAFETY ................................ 32

Introduction ............................................... 32

Initial Loading ............................................ 33















TABLE OF CONTENTS (cont'd)


Page

Operating Limits .......................................... 35

Design Basis Accident Analysis ............................. 39

CHAPTER IV THE DATA ACQUISITION SYSTEM ........................ 45

Introduction ................................................ 45

The Neutron Detector ....................................... 47

The Electronic Instrumentation ............................. 50

The Resolution Time Correction ............................. 54

The Normalization Technique ................................ 61

Comments ....................................... ......... ... 62

CHAPTER V NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL ......... 64

Introduction ............ ................................... 64

Theoretical Notes .......................................... 64

Inverse Multiplication Measurements ........................ 68

Absolute Determination of kf ............................. 73
eff
Conclusions ....................................... ...... .. 75.



PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY ......... 79

CHAPTER I INTRODUCTION ........................................ 80

Statement of the Problem ................................... 80

Description of the Study ................................... 81
















TABLE OF CONTENTS (cont'd)


Page

Nomenclature Used in the Description of
Pulse Propagation Phenomena ............................... 83

CHAPTER II THEORETICAL NOTES .................................. 85

Introduction ................................................ 85

Review of the Literature .................................. 85

The WIGLE Calculational Scheme ............................. 87

Neutron Wave Analysis ................................. .... 89

CHAPTER III DESCRIPTION OF THE MEASUREMENTS ................... 91

Introduction .................................... ........... 91

The Epicadmium Subtraction Method .......................... 92

The Geometrical Arrangement .............................. 94

Synopsis of the Measurements ............................... 97

CHAPTER IV EXPERIMENTAL AND THEORETICAL RESULTS IN THE
TIME DOMAIN ....................................... 100

The Analytical Model ....................................... 100

Flux Traverses ...................................*...... 109

Clean Core Pulse Propagation Measurements ................... 118

Propagation of a Narrow Pulse ............................ 147

Propagation of a Wide Pulse ................................. 148

Pulse Shape vs. Input Pulse Width .......................... 150

Effect of Room Return at Peripheral Detector Positions ..... 152


viii















TABLE OF CONTENTS (cont'd)


Page

CHAPTER V EXPERIMENTAL AND THEORETICAL RESULTS IN
THE FREQUENCY DOMAIN .................................. 156

Introduction ................................................ 156

Method of Analysis ........................................... 157

Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis ......................... 159

CHAPTER VI SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS .............................. 174

Introduction ................................................. 174

The Decay Constant ........................................... 175

The Ratio ksB/ ................. ........... ........ .. ....... 176

The Measured Reactivity and keff Values ...................... 179

CHAPTER VII CONCLUSIONS ........................................ 185

APPENDICES

A CALCULATIONAL PROCEDURES USED IN THE DETERMINATION
OF THE NUCLEAR PARAMETERS AND THE k VALUES ............. 187
eff

B DESCRIPTION OF THE COMPUTER PROGRAMS ...................... 191

C UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT NINETEEN CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC ............ 196

D UFSA Rl CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX AT SEVERAL CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC ............ 235

E UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT FOUR POSITIONS
IN THE CORE FOR A 0.1 MSEC INPUT PULSE .................... 248
















TABLE OF CONTENTS (cont'd)


Page

F UFSA Rl CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A WIDE (10 MSEC) INPUT PULSE ... 253

G UFSA Rl CLEAN CORE
SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF INPUT
PULSE WIDTH .............................................. 255

LIST OF REFERENCES .............................................. 258

BIOGRAPHICAL SKETCH ............................................. 262
















LIST OF TABLES


TABLE Page

I k vs. MODERATOR LEVEL OF UFSA REFLECTED
eff
CORES ....... ............... .... .......... ............. 7

II UFSA INSTRUMENTATION AND CONTROL .......................... 25

III SUMMARY OF 1/M AND PULSED MEASUREMENTS .................... 74

IV INPUT PARAMETERS FOR THE WIGLE CALCULATIONAL
SCHEME ......................................... ............. 104

V TIME STEPS USED FOR THE WIGLE CALCULATIONS ................ 106

VI DELAY TIMES MEASURED ACROSS THE WIDTH OF
THE CORE
0.5 MSEC INPUT PULSE .......................... 119

VII CLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
0.5 MSEC INPUT PULSE WIDTH ................. 127

VIII CLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
1.0 MSEC INPUT PULSE WIDTH ................... 128

IX ASYMPTOTIC PROPAGATION VELOCITY v ........................ 133
p
X DYNAMIC INVERSE RELAXATION LENGTH Kd ...................... 134

XI CHANGES IN THE NUCLEAR PARAMETERS DUE TO
CHANGES IN THE TRANSVERSE BUCKLING ........................ 138

XII THE CALCULATED ASYMPTOTIC VELOCITY OF
PROPAGATION AND DYNAMIC INVERSE RELAXATION
LENGTH vs. CORE HEIGHT
0.5 MSEC INPUT PULSE WIDTH ........................ 146

XIII DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE ............. 148

XIV DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE ............... 149

XV PULSE SHAPES vs. INPUT PULSE WIDTH ........................ 151
















LIST OF TABLES (cont'd)


TABLE Page

XVI THE REAL AND THE IMAGINARY COMPONENTS
OF THE COMPLEX INVERSE RELAXATION LENGTH
0.5 MSEC INPUT PULSE ........................ 164

XVII THE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
1.0 MSEC INPUT PULSE ........................ 165

XVIII THE DECAY CONSTANT AND kB/ VALUES MEASURED
AS A FUNCTION OF INPUT PULSE WIDTH ........................ 180

XIX REGION-WISE DEPENDENCE OF THE REACTIVITY
MEASUREMENTS ............................................. 183














LIST OF FIGURES


FIGURE Page

1 OVERALL VIEW OF THE FACILITY ............................... 6

2A BOTTOM FUEL ROD SPACING SYSTEM ............................. 12

2B BOTTOM FUEL ROD SPACING SYSTEM ............................. 13

3 TOP FUEL ROD SPACING SYSTEM ............................... 14

4 REACTIVITY-CONTROL FLOW SYSTEM ............................ 16

5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE
WEIR APEX ............................................ 18

6 WEIR "BOX" ................................................ 19

7 AIR SYSTEM SCHEMATIC ....................................... 21

8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM ...................... 23

9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT ............... 44

10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS ....... 49

11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM .................. 51

12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM ............. 52

13 TIME PROFILES OF NEUTRON BURST RECORDED BY
CONVENTIONAL ELECTRONIC INSTRUMENTATION AND BY THE
TIME-PICKOFF SYSTEM ....................................... 58

14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME
CORRECTION AS A FUNCTION OF COUNT RATE ..................... 60

15 DETECTOR POSITIONING SCHEME ................... ......... 69

16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL ................. 71

16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT .......... 72


xiii
















LIST OF FIGURES (cont'd)


FIGURE Page

17A DECAY CONSTANT vs. MODERATOR LEVEL ........................ 76

17B kB/k AND k vs. MODERATOR LEVEL ............................ 77

18 THE TOTAL, EPICADMIUM AND THERMAL FLUX 117.44 CM
FROM THE SOURCE ........................................... 95

19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL
ARRANGEMENT PLAN VIEW ................................ 96

20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE ............................................ 102

21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE
WIGLE CALCULATIONAL SCHEME ............................... 103

22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED
INTO THE WIGLE SCHEME ..................................... 107

23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE ............................. 110

23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE ............................. 111

23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA Rl CORE ............................. 112

24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE .................. 113

24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE .................. 114

25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX ................. 116

26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX ............... 117

27A EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE ....................................... 122


xiv















LIST OF FIGURES (cont'd)


FIGURE Page

27B EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA Rl CORE ......................................... 123

27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA Rl CORE ...................................... 124

28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PUSLE ........... 125

28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE ........... 126

29 CALCULATED AND EXPERIMENTAL DELAY TIMES
1.5 MSEC INPUT PULSE .......................... 129

30 CALCULATED AND EXPERIMENTAL DELAY TIMES
1.0 MSEC INPUT PULSE ......................... 130

31 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
0.5 MSEC INPUT PULSE .......................... 131

32 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
1.0 MSEC INPUT PULSE .......................... 132

33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS ..... 139

34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED
BY THE WIGLE CALCULATIONAL SCHEME FOR DIFFERENT
CORE HEIGHTS .............................................. 140

35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ....................................... 141

35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ....................................... 142















LIST OF FIGURES (cont'd)


FIGURE Page

35C THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING ........................................ 143

36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE
HEIGHT .................... ........... ......................... 144

37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS .................................................. 153

37B EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS ............................ ...................... 154

38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
0.5 MSEC INPUT PULSE .................... 160

39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
1.0 MSEC INPUT PULSE .................... 161

40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
0.5 MSEC INPUT PULSE ......................... 162

41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
1.0 MSEC INPUT PULSE ....................... 163

42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED DAMPING COEFFICIENT a ............................. 166

43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED PHASE SHIFT PER UNIT LENGTH ..................... 167

44 THE UFSA Rl CORE p DISPERSION LAW .......................... 169

45 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED (a2 2) ................................... .... 171


xvi
















LIST OF FIGURES (cont'd)


FIGURE Page

46 COMPARISON OF THE THEORETICALLY PREDICTED
AND THE MEASURED 2 a .................................... 172

47 THE UFSA Rl CORE p DISPERSION LAW ..................... 173

48 DECAY CONSTANT vs. AXIAL POSITION ...................... 177

49 kB/2 vs. AXIAL POSITION ................................ 178

50 REACTIVITY (-$) keff vs. AXIAL POSITION ................ 182
eff
Cl Through C19 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE
CORE FOR A 0.5 MSEC INPUT PULSE ....................... 195-213

C20 Through C38 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE CORE
FOR A 1.0 MSEC INPUT PULSE ............................ 214-232

Dl Through D6 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 0.5
MSEC INPUT PULSE ...................................... .. 234-239

D7 Through D12 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 1.0
MSEC INPUT PULSE ........................................ 240-245

El Through E4 TIME PROFILES OF THERMAL NEUTRON
FLUX AT FOUR POSITIONS IN THE CORE FOR A 0.1
MSEC INPUT PULSE ...................................... 247-250

Fl TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A 10.0 MSEC INPUT PULSE ...... 252

G1 Through G2 SHAPE OF THE PROPAGATING PULSE AS A
FUNCTION OF PULSE WIDTH ............................... 254-255


xvii



























Di .........


eff
.........


z .........

a .........
a


p .........

z .........


.........
P





4,


LIST OF SYMBOLS



TRANSVERSE BUCKLING

DELAYED NEUTRON PRECURSOR CONCENTRATION OF THE
ith GROUP

DIFFUSION COEFFICIENT OF THE ith GROUP

FREQUENCY (cps)

EFFECTIVE MULTIPLICATION CONSTANT

NEUTRON LIFETIME

NEUTRON MULTIPLICATION

VELOCITY OF THE ith GROUP

AXIAL COORDINATE

DECAY CONSTANT (IN THE TIME DOMAIN)

DAMPING COEFFICIENT (IN THE FREQUENCY DOMAIN)

EFFECTIVE DELAYED NEUTRON FRACTION

PHASE SHIFT PER UNIT LENGTH

REACTIVITY

COMPLEX INVERSE RELAXATION LENGTH

MACROSCOPIC CROSS SECTION

NEUTRON FLUX


xviii













Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy



SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY


By


Nils J. Diaz


March 1969


Chairman: Dr. M. J. Ohanian
Major Department: Nuclear Engineering Sciences

A large-in-one-space dimension, side reflected, highly multiplica-

tive (keff ~ 0.99) subcritical assembly was designed and calibrated.

The sole purpose of the facility is the experimental investigation of

the dynamic behavior of large reactor cores and to provide a test for

space-time kinetics models presently in use. With this facility the

linear aspects of neutron physics phenomena can be investigated in the

absence of inherent feedback effects. This work was conducted under a

subcontract with the Nuclear Safety Research Branch, Atomic Energy

Division, Phillips Petroleum Company, under a prime contract with the

United States Atomic Energy Commission.

The University of Florida SPERT Assembly (UFSA) is a light-water

moderated subcritical facility fueled by 4.81% enriched U02 pellets

encased in stainless steel tubes of 0.465 inch outside diameter (SPERT

F-l Fuel). The fuel arrays are contained in a rectangular tank, 8 feet


xix










long, 39 inches high, and of variable width. In this study, the core

was 6.5 inches wide and 30 inches high. The effective multiplication

constant of the assembly was determined to be 0.990+.003. The assembly

is equipped with nuclear instrumentation capable of automatic scram

action.

For the kinetics studies, a fast data acquisition system was

developed to handle accurately the very high, time-changing count rate

encountered in the measurements. It essentially consists of a trans-

former-coupled pulse amplifier to produce a fast logic signal at the

input of a multichannel analyzer from the input signal originating in

a long, thin He3 counter. The instrumentation adequately handled count

rates up to 3 x 10 counts/sec at the peak of the pulses. A high degree

of reproducibility and fidelity in following the pulse profiles was

obtained with this instrumentation.

The space-time kinetics studies were performed by analyzing the

propagation of a fast neutron burst introduced at one end of the assem-

bly, in the absence of inherent feedback effects. The experimental

results are compared with the results obtained from the two-group,

space-time dependent, one-dimensional diffusion theory scheme known as

the WIGLE program. A stringent test of the model is provided by a

combined analysis in the time and the frequency domain.

The WIGLE calculational scheme accurately predicts the delay times

and the attenuation of the pulses when a first-flight spatial distribu-

tion is assumed for the fast source. At large distances from the source

WIGLE underpredicts (- 8% in the FWHW) the spreading of the pulse. A

marked sensitivity to small changes in the transverse buckling was

-found for the model, as well as the experiment.

xx










A one-to-one comparison of the predicted and measured values in

the frequency domain was provided by performing identical numerical

Fourier transformations of the WIGLE time profiles and the measured

pulse shapes. The analysis in the frequency domain confirmed the

results obtained in the time domain, although discrepancies past 100
2
cps are found in the ultrasensitive p plane. The agreement in the p

plane, the system's dispersion law, is good up to 200 cps and reasonable

up to 800 cps. Both theory and experiment showed a smooth behavior
2
throughout the frequency range investigated, in both the p and the p

plane.

Spatial effects in large cores are clearly demonstrated in this

work. The determination of the range of applicability of the one-

dimensional scheme requires extending the study to cases in which two-

dimensional effects will be noticeable and the important feedback

effects can be considered.


xxi




































PART 1

THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
DESIGN AND CALIBRATION -















CHAPTER I


INTRODUCTION


The development and construction of large power reactors focused

the attention of industry and of the United States Atomic Energy Com-

mission on the necessity of having reliable reactor dynamics analysis

methods to accurately describe the spatial and temporal behavior of the

neutron flux in these systems. The point-model reactor kinetics calcu-

lations seem to have been adequate for the gross evaluation of the time-

dependent neutron flux during the occurrence of a transient but the

model can be in large error when the physical size of the system and the

magnitude of the perturbation necessitates that spatial effects in the

redistribution of the neutron flux be considered. Preliminary calcula-

tions done by Johnson and Garner using a one-dimensional space-time

kinetics model [1] showed that the space-time dependent scheme predicts

a "destructive zone" much larger than that predicted by point-model

kinetics.

The necessity of experimentally determining the validity of the

various space-time kinetic analysis methods was brought out by Johnson

and Garner [1], and recognized by the USAEC in establishing the Large

Core Dynamics Experimental Program. The primary responsibility for this

program has been vested in the Nuclear Safety Research Branch, Atomic

Energy Division, Phillips Petroleum Company as major contractor for

USAEC.









The Large Core Dynamics Experimental Program is to be performed

in three phases:

Phase I. Pulsed Source Experiments in Subcritical, Multiplying Media,
Large in One-Dimension

The first phase of the experimental program is to be conducted in

a close-to-critical subcritical assembly, 8 feet long, 3 feet deep and

with widths changing from 6.5 inches to 16 inches according to the core

configuration and whether bare or side reflected cores are studied.

The experimental information obtained from studying the pulse

propagation phenomena in this assembly is to be used to test the valid-

ity of current space-time kinetic models in the absence of inherent

feedback effects.

Phase II. Kinetic Behavior for Control-Rod-Induced Power Excursions in
Large, One-Dimensional Cores

A reactor large in one-dimension, 16 feet long, three feet deep

and with varying widths to accommodate different metal/water ratios will

be used to investigate the one-dimensional kinetic behavior of large cores

subjected to a large perturbation. Both non-feedback (low power exper-

iments) and self-shutdown measurements will be conducted.

Phase III. Kinetic Behavior for Control-Rod-Induced Power Excursions
in Large, Two-Dimensional Cores

The same type of measurements performed for the one-dimensional

core will be conducted in a two-dimensional core.

The measurements should provide the necessary information to

establish the validity ranges for one-dimensional models, the basis for

the development of a two-dimensional scheme and as a bridge to the

complex, three-dimensional problem.

Phase II and Phase III of the research program will be performed









at the SPERT IV facility at the National Reactor Testing Site, Idaho.

The appropriate existing experimental equipment, as well as the

extensive kinetics studies conducted by the Nuclear Engineering Sciences

Department at the University of Florida, was conducive to the granting

of a subcontract by the Phillips Petroleum Company so that the basic,

linear kinetics studies of Phase I could be performed at the University

of Florida.

The research to be performed as Phase I of the Large Core Dynamics

Experimental Program can be succinctly defined as the experimental and

analytical determination of the dynamic behavior of the neutron flux in

slightly subcritical water moderated assemblies of SPERT F-l fuel rods.

The facility in which the required measurements for Phase I, Large

Core Dynamics Experimental Program, are to be conducted necessitated a

thorough design and safety analysis. The assemblies are to be close to

critical and the core has a large U235 inventory. The nuclear capabil-

ities of such systems were the object of a detailed study to determine

their operational characteristics under normal and accident conditions.

The flexible mechanical design, the safety instrumentation, the

nuclear evaluation, as well as the experimental calibration of the

first configuration under study constitutes Part 1 of this dissertation.

The reactor kinetics studies performed in the first of the con-

figurations to be studied are dealt with in Part 2 of this manuscript.















CHAPTER II


DESCRIPTION OF THE FACILITY


General Features


The University of Florida Spert Assembly is a light water-

moderated subcritical facility fueled by 4.81% enriched U02 pellets

encased in stainless steel tubes of 0.4655" outside diameter. The fuel

arrays are contained in a rectangular tank, 8 feet long, 39 inches high,

and of variable widths. The system is designed so that both bare and

reflected cores can be studied. Only one reflected core will be dealt

with in Part 2 of this manuscript; information on three reflected cores

is included in this chapter. The .assembly width and fuel spacing may be

varied in order to:

a) have a keff not to exceed 0.99 in all cases to be

considered.

b) accommodate non-moderator/moderator ratios of

0.5, 1.0, and 1.5, respectively.

Shown in Table I are the k eff's as a function of the moderator
eff
height, the fuel spacings, core widths, and total number of fuel ele-

ments for the different reflected cases to be considered. The calcu-

lational procedures used in the determination of the nuclear parameters

and the keff values for the three reflected configurations of the

assembly are described in Appendix A. Only the sides of the assembly

will be reflected. Fig. 1 shows an overall view of the facility.

5




















































DUMP
VALVES


FIG. 1 OVERALL VIEW OF THE FACILITY











TABLE I


keff vs. MODERATOR LEVEL OF UFSA REFLECTED CORES


Calculated Using the AIM6 Code
Core Length = 243.8 cm (96")
Reflector Width = 30.48 cm (12")
Active Fuel Height = 91.4 cm (36")

Metal to Water Ratio = 0.5
Lattice Pitch (in) = 0.7152
Core Width (cm) = 16.35
No. of Fuel Rods = 1206


1.0
0.584
19.28
2132


Moderator Level


Moderator Level
(cm)

20

25

30

35

40

45

50

55

60

65

70

75

80

85

91.4


Effective Multiplication Constant


.7695

.8288

.8715

.9022

.9249

.9420

.9551

.9655

.9738

.9805

.9870

.9906

.9944

.9977

1.0012


.7397

.8028

.8471

.8793

.9032

.9213

.9353

.9465

.9554

.9626

.9686

.9736

.9777

.9813

.9851


.7276

.7941

.8416

.8761

.9020

.9218

.9372

.9494

.9592

.9672

.9738

.9793

.9840

.9880

.9922


1.5
0.5332
25.73
3420









The assemblies are highly multiplicative; this is important for

the extrapolation of the results of the study to critical systems. The

system's subcriticality is attractive because of the inherent safety

of such systems and of the absence of inherent feedback effects.

In order to provide as "clean" a core as possible, a unique control

system which has been successfully used on the UFAPA [2] will be em-

ployed. In this system the reactivity is controlled by adjustment of

the water height in the assembly. The water height is controlled by

the position of two "V"-notched weirs located in a water "box" hydrau-

lically coupled with the assembly through flexible lines. The quantity
5/2
of water discharging through a "V"-notched weir varies as H5/2 (H is the

distance between the apex of the weir and the water level) thus pro-

viding precise control of the moderator height. The hydraulic coupling

assures that under normal operating conditions (with continuous flow)

there will be the same water level in the core and the reflector tanks.

The UFSA subcritical assembly is located in an isolated and

shielded room in the Nuclear Research Field Building, approximately

three miles from the University campus.

The Nuclear Research Field Building consists of four bays, two of

them having shielded rooms for experiments with subcritical and moder-

ating assemblies. The shielded walls consist of stacked concrete block

eight feet high and thirty-eight inches wide covered with plywood to

assure that the blocks remain in place. The ceiling of this single-floor

building is approximately 15 feet above the floor and consists of excel-

sior-filled cement bonded board. Neutron reflection from this ceiling.

over the walls does not constitute a hazard to personnel operating the

accelerator-type neutron source. The access door from the control room









is interlocked with the neutron generator and the subcritical assembly

scram system, as is the door on the only other entrance to the shielded

room from the fuel storage area. Across the front face of the assembly,

a screened wire cage with a lockable door controls access to the core.

While not in use in the assembly the fuel is stored in a room

adjacent to the facility, built entirely for this purpose.

A more complete description of the facility and its characteristics

can be found in the Design and Hazards of the UFSA and its addenda

[3, 4, 5].

The system has been licensed under Atomic Energy Commission SPECIAL

NUCLEAR MATERIAL LICENSE SNM 1050, March 1968. The license allows for

the possession of 5400 fuel rods with a total U235 inventory of 190 kgs.


Fuel Characteristics

The UFSA is fueled with Spert F-l type fuel elements provided by

the Phillips Petroleum Company.

The fuel characteristics are:

Fuel Composition: UO2 in pellet form

U enrichment: 4.81 + .15%
235
Active Fuel Length: 36" + .062"

Active Fuel Diameter: .42" + .0005"

Fuel Tube Material: stainless steel

Fuel Tube Length: 41.625"

Fuel Tube o. d.: .4655" + .0025"









Mechanical Design

The entire assembly can be divided into three components: the

supporting platform and dump tank; the basic core tank and fuel rod

support structure; and the combination core side walls and side

reflector tanks.

The supporting platform is composed of 5 inch steel I-beams, raised

5 feet from the floor level by six steel columns 3 1/2 inches in diam-

eter. The column footings rest within a 6x8x2 foot steel rank which

serves as a reservoir for the continuous water flow system and as a dump

tank. Under normal operating conditions, this represents a minimum

distance of about 4 feet between the bottom of the assembly and the

water surface in the reservoir. This distance is sufficiently large so

that the bottom of the assembly is considered to be unreflected under

all conditions.

All the core and reflector hardware is made of type 5456-H321

aluminum. The bottom of the basic tank is made of a 24x96x3/4 inch plate

bolted to the steel I-bean platform. The underside of the plate is

covered with a .030 inch thick Cadmium sheet. The lower fuel rod sup-

port assembly rests on the plate. The end walls of the basic tank are

made of a 24 x 39 3/4 inch plate and are supported by two 2 1/2 x 2 1/2

x 1/4 inch steel angle braces welded to the I-beam platform. Two four-

inch aluminum channels span the eight foot dimension of the tank, con-

fining the upper fuel rod support system and detector mounts.

The side walls of the basic tank serve also as reflector tanks when

the reflected cores are under study. These tanks have dimensions of

12 x 96 x 37 inches. The arrangement allows one to vary the width of the

core with a sole structural support.









The end walls are permanently covered with Cadmium on the outside

surface while the side walls have movable Cadmium covers to define the

boundaries for the bare and reflected cases. To optimize the number of

neutrons inserted into the assembly by the neutron generator, the accel-

erator target penetrates about 4 inches into the core. A water-tight

port is provided for this purpose. The port can be removed and a blind

flange inserted in its place. Several fuel rods must be taken out, the

number depending on how deep the target goes into the assembly and on the

lattice pitch.

The core section of the assembly consists of an interchangeable

fuel rod spacing system made of 3/4 x 1/2 x 1/8 inch channels, 5/8 x 1/4

inch bars and aluminum shims mounted on the base plate of the tank. The

bars have milled slots to accommodate the .25 inch end tip of the fuel

rod and to set the pitch along the core width. The shims are placed

between the channel bar units to set the pitch along the core length

(96 inches) (see Fig. 2). The top fuel rod spacing system consists of

an aluminum grating. The mesh is determined by the lattice pitch under

study. The grating is made of aluminum bars and spacers, as shown in

Fig. 3. Thus, fuel rod removal along the length of the core is pos-

sible to locate the detector for the experimental measurements.

The one-half inch long rod tip is fully surrounded by aluminum,

with practically no reflecting characteristic, but there is a 7/8 inch

length of rod between the end of the active fuel and the tip which is

surrounded by water. This bottom reflector is unavoidable and will be

considered in the calculations.
























FUEL ROD





c WIDTH
SPACE




WIDTH SPACE
CHANNEL


LENGTH
SPACER
SHIM


FIG. 2A BOTTOM FUEL ROD SPACING SYSTEM





































7~- J


WIDTH SPACER




-WIDTH
CHANNEL
I__ SPACERS


BASE PLATE



CADMIUM


FIG. 2B BOTTOM FUEL ROD SPACING SYSTEM


_ L ___ _~ __


w






S14


ALUMINUM SUPPORT
FRAME


FUEL ROD


CORE WIDTH
FUEL ROD
SPACING
GRATE


CORE LENGTH
/ FUEL ROD
/ SPACING
GRATE


FIG. 3 TOP FUEL ROD SPACING SYSTEM


SPACER







TIE ROD









Moderator Flow Control System

The moderator flow control system of the UFSA can be better des-

cribed by'the water flow schematic shown in Fig. 4. Besides the normal

fill and drain functions for the moderator, it serves as an accurate

reactivity control using adjustable moderator height by continuous flow.

The characteristic components of this system are described below.

A. Storage Tank: A 6 x 8 x 2 foot steel tank located directly

below the assembly will serve as the reservoir for the circulating

light-water moderator and as a dump tank. Normal water heights while

operating will be between 6 and 12 inches. The tank also serves as a

footing for the assembly supports. This arrangement makes a very con-

venient and compact facility.

B. Core and Reflector Tanks: As seen from the flow diagram, water

is pumped from the reservoir to the core and reflector tanks through a

manifold at one end of the assembly and flows from the other end of the

core and reflectors tanks to the weir "box". From the weir "box", water

flows over the weirs back to the storage tank through a flexible line.

The core section is equipped with two normally open solenoid

activated dump valves, 3 inches in diameter, located at each end of the

core. These valves provide the reactor with a fast shutdown safety

system. The reflector tanks have their own 1 1/2 inch normally open

solenoid valves actuated by the same safety system.

Since the quantity of water discharging through a V-notched weir

varies as H5/2 where H is the height of the water level above the apex

of the V-notch, the water level and hence, the reactivity, can be con-

trolled in a precise manner simply by varying the height of the weirs

and the rate of flow of water into the tank. This is accomplished by







WEIRR DRAIN
--- DISTRIBUTION MANIFOLD


ION EXCHANGE BED


m\









PU MPt
CONTROL ORIFICE
VALVE


FIG. 4 REACTIVITY-CONTROL FLOW SYSTEM









an automatically operated pneumatic control valve. A plot of the flow

rate versus the height of the water level above the apex of the weirs

is shown in Fig. 5.

The weir plate is rigidly mounted on a "box" or small tank (see

Fig. 6). The weir "box" is connected to a drive mechanism composed

of the following: guide post, slide block, and drive screw. The guide

post is a 2 inch diameter pipe attached to the support column of the

crane which is used for removal of the reflector tanks. The "box" is

mounted on the guide block which slides along the vertical post and

provides a rigid support for the system and is driven up and down by

means of the drive screw which is fixed at the top of the guide post

support and passes through the guide block. The upper limit of the

position of the weir"box"is controlled by mechanical stops whose posi-

tion is determined as part of the initial start-up procedure for each

configuration to be considered.

The final adjustment of the position of the weir"box"is such that

when the water reaches the moderator level in the assembly corresponding

to k < .99 for a given configuration it will be flowing about 2.0
eff -
inches above the apex of the V-notch weirs. At this design level the

flow rate is 7 gallons per minute with the keff values as given in

Table I for the full fuel loading. After the operating height of the

weir box has been determined for k ff 0.99 in the initial start-up,

stops are inserted to prevent raising the weirs above this height (if

the height is less than the active fuel height). It should also be

pointed out that the orifice in the line limits the pump capacity to a

flow rate which is just sufficient to bring the weirs to full flow. A

further increase in flow rate would cause discharge over the entire

















S 2.8-


j 2.4
1,4

> 2.0

0
< 1.6
r-i

4 1.2 o0
4

S 0.8


0.4


0 I I -_1 1 _I
0 2 4 6 8 10 12

Flow Rate (gpm)


FIG. 5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE WEIR APEX












4



3.5"

._


i.5" O.D. x 1/8 WALL (3)


2" O.D. x 1/8 WALL


FIG. 6 WEIR "BOX"









perimeter of the weir "box" into the drain line effectively preventing

any further increase of the moderator level in the assembly.

The measurement of the water height in the core is accomplished by

fixing a reference mark on the slide block at the same level as the

bottom of the weir within the "box". An accurate scale is provided to

read off the distance between the bottom of the core and the apex of the

weirs. Continuous indication of the moderator level in the core is

provided on the console by means of a recorder calibrated between the

bottom of the active fuel and the maximum moderator height and by a

manometer, connected directly to the core, for precise measurement of

the water level. These two measuring systems insure reproducibility of

the moderator height for the experiments.

The water is pumped out of the storage tank by a constant speed

centrifugal pump which has a "no load" capacity of 20 gal/min. The

control valve is designed to restrict the flow to the maximum design

value of 12 gal/min. A deionization system is provided to keep the

water as pure as possible at all times. The pneumatic flow control

system consists of two differential pressure cells, transmitters, control

valve, and recorder-controller. The strip type chart recorder-con-

troller records both flow rate and moderator level in the core. The

control valve is of the air-to-open type which will close in the case of

air supply loss, stopping the flow into the assembly. The flow diagram

for the air system is shown in Fig. 7. A pressure differential from the

pressure transmitters applied to the recorder-controller allows both

manual and automatic control of the flow rate through the valve operated

by the controller.








SOLENOID
TO INTERLOCK


L WEIR


I I
I I


DIFFERENTIAL
PRESSURE
TRANSMITTER


FROM PUMP


I I


-----. ORIFICE ----. TO CORE


-- WATER

AIR


FLOW
VALVE


FIG. 7 AIR SYSTEM SCHEMATIC


CORE


DUMP
VALVE









Instrumentation and Interlock System

The instrumentation and interlock system of the UFSA has been

discussed extensively in the reports submitted to the Atomic Energy

Commission [3, 4, 5] in conjunction with the license application. More

recently, Mr. L. B. Myers submitted a detail technical report on the

subject [6]. A brief descriptive explanation is given below.

A block diagram of the safety system logic flow in use at the UFSA

subcritical assembly for routine monitoring is shown in Fig. 8. There

are five principal channels of instrumentation:

a. Start-up channel using a He proportional counter, scaler, and

rate meter. The counter is located at the bottom of the core, close to

the geometrical center of the assembly.

b. Log power and period instrument No. 1 channel using a compen-

sated ion chamber (operated uncompensated) as a signal to a Log N

amplifier. The chamber is located along the longitudinal axis of the

assembly, on the bottom of the core some two feet from the neutron

generator end.

c. Period instrument No. 2 channel using a compensated ion chamber

(operated uncompensated) as a signal to a log N amplifier. The chamber

is located along the longitudinal axis of the assembly, on the bottom

of the core, some six feet from the neutron generator end.

d. Linear neutron flux No. 1 channel using an uncompensated ion

chamber as a signal to a micromicroammeter. The chamber is mounted on

the top core support frame, close to the geometrical center of the core.

e. Linear neutron flux No. 2 channel using a compensated ion

chamber (operated uncompensated) to feed a signal to a micromicroammeter.

The chamber is mounted on the top core support frame on the opposite































And Manual 1 And
CKT. SCRAM CKT.

And1 And
CKT. C Y, CKT.

And And
CKT. CKT.


mp CAnd Core Dump And
WidthT. Valve # 2 CKT

Refl. Dump v Pump
Valves


FIG. 8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM









side from the linear channel No. 1.

Items a. through d. are part of the safety amplifier while item f.

is used to display the neutron flux on a console front panel meter.

The safety amplifier monitors the seven continuously varying input

signals and provides a trip signal if any of the input signals fall

outside of acceptable limits. The safety amplifier provides means of

adjusting these limits over a wide range.

The duality of the scram action (see Fig. 8) is a prominent feature

of the safety system. It can be said that no single failure will

invalidate both automatic scram channels. Furthermore, it.has been

determined that no single failure can invalidate both the manual and

automatic scrams. The method of measurement and the function of each

instrumentation and safety channelare shown in Table II (parts A and B).

A series of safety interlocks prevent water from flowing into or

remaining in the assembly unless a proper sequence of events are fol-

lowed and certain conditions are satisfied. The conditions are:

a. The moderator temperature must be > 60F. This is established

by the desire to obtain the experimental data near room temperature con-

ditions. The insertion of water at 32*F will introduce a maximum k of

.00342 (based on the calculated negative temperature coefficient of

reactivity) above the design keff value with no hazards created.

b. The four instrumentation channels must have their high voltage

on.

c. The core width must be smaller than 26 cm.

d. The door to the assembly room must be locked.

e. The start-up channel must count more than 2 counts/sec.

f. The neutron flux, subcritical assembly power level and period










TABLE II


Measured Parameter

a. Low level neutron flux



b. Linear neutron flux


c. Log neutron fluxb


d. Linear neutron flux


e. Reactor period 1


f. Gamma flux



g. Detector power supply
voltage


h. Reactor period 2


UFSA INSTRUMENTATION AND CONTROL
A. NUCLEAR


Method of Measurement

He3 detector pulse discriminatory;
at neutron generator end of core


CICa ammeter; on side of core


CICa log N and period amp; under
core near center line

UIC ammeter; on side of core


CICa log N and period amp


Ion chamber area monitor; on front
of reactor cage


Unijunction transistor oscillator
and relay. Monitor detector
voltage for b, c, d and e

CICa log N and period amp; under
core near center line


Application

Insure source is present before
adding reactivity. Scram on low
count rate

Indicate power level scram on
power

Indicate power level scram on
high power; log N recorder

Indicate reactor power; linear N
recorder

Indicate reactor period; scram on
short period

Criticality monitor for storage
room. Area monitor for reactor
room. Activate evacuation alarm

Scram reactor on low detector
voltage


Indicate reactor period; scram on
short period


To be operated in the uncompensated mode
Common detector and instrument










TABLE II (Continued)


B. NON-NUCLEAR


Measured Parameter

a. Reactor water temper-
ature

b. Reactor water level



c. Reactor door and per-
sonnel



d. Reactor core width




e. Reactor water level


f. Reflector tank water
level (low)

g. Flow control valve
shut


h. Reactor flow


Method of Measurement

Fenwall temperature switch in
inlet line

Barksdale pressure switch mounted
on weir"box"with sensing line
connected to core

Limit switches on doors and push
buttons inside reactor room



Limit switches on reflector tanks




Barnstead pressure switch senses
level in weir box

Float switches in reflector tanks


Limit switch on valve


Differential pressure cell and
pneumatic control

D/P cell and pneumatic system


Application

Scram reactor on low reactor
inlet water temp. (600F)

Scram reactor if water level in
core exceeds top of weir height


Scram system and shut down neutron
gun if reactor doors are opened
or interior switches are acti-
vated

Prohibit filling reflector tanks
when distance between tanks
exceeds widest reflected core
width

Stops pump when water reaches llcm
below weir apex

Indicates water is filling reflec-
tor tanks

Requires closing valve before
starting pump


Control flow rate.
record flow rate


Indicate and


Indicate and record water level


i. Reactor water level









must be as specified under Operating Limits in this report.

g. After a normal start-up, the water height in the core must be

within 0.5" of the level set by the position of the weirs.


Fuel Storage

The large amount of fuel needed for the experimental program

required a detailed criticality analysis of the fuel storage area.

Criticality considerations of the fuel storage arrangements follow the

Atomic Energy Commission regulations regarding the subject. Three dif-

ferent criteria were used to calculate the effective multiplication of

the fuel storage area to assure that the array will remain subcritical

under the worst circumstances. The methods and the corresponding con-

ditions are outlined below.

The fuel storage array consists of three slabs of air-spaced fuel

pins, separated by a minimum distance of 54 inch face to center. The

fuel is stored in steel baskets containing 308 pins per basket. Two

sets of 1/4 inch thick plastic plates, located at the bottom and top of

each basket, drilled to properly position the fuel rods. The charac-

teristics of the fuel slab are:

Slab Width = 3.73 in = 9.46 cm (corresponds to 7 fuel pins in

transverse direction)

Slab length = 14 ft

Height = 3 ft (active fuel height)

a. Multiregion-multigroup calculation

The effective multiplication factor of the fuel storage array con-

sisting of three slabs (3.73 inch wide, 14 ft long and 3 ft wide) which

are 54 inch apart (face to face) was computed for the case of flooding









the storage area to the level of the active fuel height. A 2-foot

reflector on both sides was used to represent an infinite reflector.

No reflector was considered on the ends, but the contribution of this

to the system would be small. The calculation was done using four

groups and seven regions and followed the method outlined in Appendix

A of this thesis. The following configuration, which is symmetric about

the indicated center line, was assumed:


3.73"


Water


24"


Fuel Water


Under these water-moderated and reflected conditions, a keff =

0.79 was obtained

b. Solid angle criterion for slabs

To determine the interaction between the fuel storage slabs in the

proposed 3-slab array, the solid angle criterion established in 10 CFR,

Part 70, 70.52, paragraph (b) was used. This establishes the maximum









total solid angle subtended by any unit in the array to be 6 steradians

if the effective multiplication factor for the individual slabs is less

than 0.3, as is the cese here.

From 10 CFR 70.52 (d) (2) (i) the minimum required separation dis-

tance, i.e., center of one slab to face of adjacent slab, is obtained

from:
S cross sectional area
3 steradians =
(separation distance)2

1/2
This gives, separation distance = ( x 3 ) = 3.74 ft.

We propose to establish a minimum distance between faces of adja-

cent slabs of 4.5 ft. This gives a total solid angle for the center

slab of 3.88 steradian, which is well below the established criteria.

c. Comparison with Clark's criteria

For 5% enriched, 0.4 inch diameter uranium oxide rods with a 190.13

gm/liter U-235 concentration (compared to 4.81% enriched, 0.42 inch

diameter uranium oxide rods with a 200 gm/liter U-235 concentration in

our case) the following data is obtained from pp. 39 and 59, respectively,

of DP-1014:
-2
Width of Slab (cm) Buckling (cm2)
Critical Safe Critical Safe
11.2 10.4 0.014945 0.015912

It should be noted that the slab widths quoted on page 39 of DP-1014

are for an infinite water-moderated and reflected slab. From the buck-

ling values given, the critical width of the infinite water-moderated

unreflected slab is 25.7 cm; the corresponding safe width is 24.9 cm.

When twice the reflector savings for the latter case as given on page

59 of DP-1014 is subtracted, a safe width for the infinite, water-










moderated reflected slab of 10.44 cm is obtained consistent with the

10.4 cm value.

Thus the slab width of 9.46 cm proposed by us compares favorably

from the safety viewpoint with the safe width for an infinite, water-

moderated and reflected slab and is considerably narrower than the safe

width for an infinite, water-moderated and unreflected slab. Within the

present context it should also be pointed out that as indicated on page

54 of the Design and Hazards Report [3], no flooding of the storage area

seems possible from natural causes.


Neutron Sources

Two types of neutron sources were used throughout this work.

1) Two Pu-Be sources mounted in an aluminum cylinder which can be

driven remotely through a plastic pipe from a shielded box located in

one corner of the facility room to underneath the center of the core.

Neon lights provide indication at the console of the position of the

sources. These sources, which have a combined yield of ~ 3.2 x 106

n/sec are used for start-ups and for the inverse multiplication meas-

urements.

2) A Texas Nuclear Neutron Generator which is used in continuous

mode for static measurements and in the pulsing mode for the pulse

propagation measurements. The generator is of the Cockcroft-Walton

type, TNC Model 150-1H with continuously variable high voltage from

0-150 kv and has been modified to obtain larger currents by removing

the einzel lenses and installing a new 22 electrode accelerator tube and

gap lense. Pre- and post-acceleration beam deflection produces sharp,

low-residual pulses.






31


The accelerator was used with a 4-5 curie tritium target.

The position of the target can be changed to keep the source

centered on the target-end of the assembly for any given moderator

level.















CHAPTER III


OPERATIONAL SAFETY


Introduction


The University of Florida SPERT Assembly, due to its large size,

enriched uranium-oxide fuel and nuclear potentialities required a

thorough study of its capabilities, operational characteristics, initial

loading procedures and of the behavior of the assembly under accident

conditions. The study was part of the requirements established by the

Division of Material Licensing of the USAEC prior to the granting of an

operating license.

Legally, a subcritical assembly has to comply with regulations

under 10 CFR Part 70 "Licensing of Special Nuclear Materials" since no

self-sustaining nuclear reaction is envisioned. In the case of the

UFSA, however, the Commission felt-that certain technical sections of

10 CFR Part 50, which deals with nuclear reactor licensing, should apply

and serve as a guide for the design and the safety analysis.

The basic philosophies employed in the design of the system were:

a) The UFSA facility has been designed to remain subcritical under

normal operating conditions.

b) The safety instrumentation (see Part 1, Chapter I) has been

designed such that a single failure will not invalidate both the manual

and automatic scram and will not cause subsequent failures.

c) The design basis accidents were postulated on a single failure
32









criterion.

d) Operating limits have been set to delineate the normal oper-

ating ranges of the assembly.

e) Initial loading procedures have been established to determine

the safe operating multiplication factor of each configuration.

A series of administrative controls are necessarily applied to all

segments of the experimental program and strictly enforced.


Initial Loading

A series of calculations were done to determine which of the two

following schemes should be employed for the initial loading of UFSA:

I) Step loading of the fuel from the center out, accompanied by

step increases in water level with the usual inverse multiplication

determination.

II) Loading all the fuel into the dry tank and proceeding with a

careful evaluation of the multiplication as a function of water level.

Since the UFSA core is very loosely coupled as far as the lumped

reactivity parameter is concerned, the second method was selected due to

the fact that a better determination of the multiplication was possible

from a basic moderator height-zero loading inverse counts determination.

The slope of the keff vs. water height curve has a slope substantially

smoother than the keff vs. per cent fuel loading (full water height)

curve.

The moderator level control system in operation at the facility

provides a extremely reliable and safe mode of adjusting the water level

without safety compromises.

The following regulations were followed for the initial fuel









loading, and will be followed for subsequent cores:

1) After the fuel has been loaded, prior to each new incremental

change in the water level, the water is drained completely and the weir

(and water level scram) adjusted to prevent a level increase beyond the

desired value.

2) The first three measurements of the inverse multiplication are

obtained at water heights of approximately 20 cm, 25 cm, and 30 cm above

the bottom of the active fuel. As shown in Table I, the maximum kff

calculated for a water height of 30 cm is 0.87. Subsequent filling

increments are not to exceed the least of the following:

a. An increase in water height of 10 cm.

b. An increase in water height which, by extrapolation of the

inverse multiplication curve, would increase the keff by one-half of the

amount required to make the assembly delayed critical.

c. An increase in water height which would, by extrapolation of

the inverse multiplication curve, result in a k of 0.990. For values
eff
of keff above 0.95, the keff of the assembly are also determined by

pulsed source techniques.

3) At each filling step, the measured k effof the assembly is

compared with the calculated value. If significant deviations of the

experimental values from the calculated keff vs. water height curves

occur, the experiments are to be discontinued, and a detailed analysis

of the results obtained performed. If it is determined that the dimen-

sions of the assembly should be changed in order to achieve the desired

keff at maximum water height, the University of Florida will apply for

and obtain written approval from the Atomic.Energy Division of the

Phillips Petroleum Company before such changes are made.










Operating Limits

A description of the operating limits of the subcritical assembly,

including the basis for such limits ate listed below.

Effective Multiplication Factor

Specification: the maximum allowable keff will be 0.985+.005.

The absolute value of keff as well as the slope of the keff vs. water
eff eff
height will be carefully measured so as not to exceed the limiting value.

Basis: the upper limit of kf = 0.985+.005 is established by:
eff
the accuracy with which keff can be measured, the reported [7] differ-

ences between calculations and experiments in similar cores and the value

of the multiplication factor required to make a meaningful study of the

dynamic properties of large cores. Comparison [7] between 29 calcula-

tions and the corresponding critical experiments (on cores similar to

the UFSA) established that an overestimate of keff is generally made; the

standard deviation for these cases was + 0.00175 and the maximum under-

stimate of the multiplication was for a case yielding keff = 0.9966, a

0.34% deviation.

The absolute value of keff will be determined for water levels
eff
yielding a keff >.95 by pulsed techniques independently of the inverse

multiplication measurements. The method to be used is the Garelis-

Russell[8] method which, when appropriate corrections are made for the

reflector, has been shown to give good results. In this method both
1-keff(l-8) keffB
a = and -- are determined; then keff may be. obtained by

independently obtaining $ or A. Since of the two parameters 8 changes

the most slowly with keff, it is valid to use a value based on theoret-

ical calculations.









Reactivity Addition Rate

Specification: the reactivity addition rate is controlled by the

water flow rate into the subcritical assembly. The maximum flow is fixed

to be 12 gpm. At this maximum flow rate, the rates of addition of water,

and consequently or reactivity, computed between water heights of 30 and

45 cm. are:


0.5332"


Lattice Pitch

0.584"


0.7152"


Rate of increase of
water level 0.0435 0.0439 0.0431

Ak/cm 0.0093 0.00865 0.008

Ak/sec 0.0004 0.0038 0.000344

$/sec 0.057 0.054 0.049

It should be noted that these reactivity addition rates are a large

overstimate compared to the calculated rates at keff- .98.

Basis: the maximum rate of addition of reactivity was established

by the calculated values of keff vs. water height and the maximum flow

rate. The values specified above constitute an upper limit in the

region of interest and are considered to be safe under circumstances.

The flow rate is a function of the capacity of the pump, the ori-

fice and the pneumatic control valve and cannot exceed 12 gpm.

Reactivity Removal Rate

Specification: a conservative value for the reactivity removal

rate is taken from the slope of the keff vs. water height curves near

the maximum designed k -, values. Since no difference is detected for
err
the scram times of the three configurations, only one rate of removal

will be specified, corresponding to the smallest slope.










Drain rate, including the system

reaction time ................... 2.65 cm/sec

Rate of removal of reactivity ....... 0.00037 Ak/cm

....... 0.00098 Ak/sec

....... 0.140 $/sec

it should be noted that the value of Ak/cm used to specify the reac-

tivity removal rate is 20 times smaller than the corresponding value

specified for the reactivity insertion rate.

Basis: the rate of drainage from the assembly established the

reactivity removal rate. Consistent with the approach taken when

specifying the reactivity, the time to drain 45 cm of water from the

assembly was measured to establish a lower limit on the rate of de-

crease of water height. Even under these extreme assumptions, i.e.,

using the maximum slope of the keff vs. water height curve for the

insertion rate, the small calculated slope around k ef=.99 for the

removal rate and the reduced pressure head, the reactivity removal rate

is three times larger than the insertion rate.

Subcritical Assembly Power Level and Power Level Scram

Specification:

Power Level ........................ 0.5 watt

Power Level Scram ................... 1.0 watt

Basis: with the maximum source strength available and with k -e
eff
0.985 the maximum average power was calculated to be .130 watts by

taking into account the spatial dependence of the flux and a steady

source at one end.

Assuming that a reactivity accident occurs, based on the maximum

reactivity addition rate specified above, the design basis accident









predicts that from a keff of 0.993 it would take approximately 15

seconds to double the power level. Even if the power level indicator

were not to scram the system until the power level reached 10 kw,

assuming a one second delay time to actuate the scram, the power would

increase to only 69 kw by the time the scram actually begins. Based on

the reactivity removal rate described above, the power level would then

decrease rapidly to a very low value.

Period Scram

Specification:

Period scram ........................ 15 sec

Basis: A positive period will be obtained in the subcritical assem-

bly for any addition of reactivity beyond a given steady state condition.

If the maximum reactivity insertion rate of 0.05 $/sec is considered,

the initial positive period is about 50 sec and decreases monotonically

with time. The period channel has been determined to respond reliably

to periods = 50 sec. Originally, the period scram was set at 50 sec but

repeated scrams caused by the start-up of the neutron generator forced

the reduction of the scram period to 15 sec for operational reasons.

Average Neutron Flux and Neutron Flux Scram

Specification:

Ave neutron flux for

most reactive core .................. 1.5 x 105 n/cm2 sec
C 2
Neutron flux scram .................. 3.0 x 105 n/cm sec

Basis: the above are based on the average power calculated for the

assembly. Doubling of the flux will occur when 0.75 $ worth of reac-

tivity is added to the system from any design subcriticality level.

Under these conditions, even at the maximum keff status, the facility
ef f










will still be subcritical and the instrumentation will have sufficient

time to scram the system before accidental criticality occurs.


Design Basis Accident Analysis

Two types of accidents have been postulated to occur in conjunction

with the UFSA experimental program. The design basis accident analysis

will deal with the following two cases: a) a dropped fuel rod accident

in which a fuel rod is broken releasing the fission products accumulated

during previous operation of the assembly; b) an accidental criticality

resulting in a power excursion. It will be shown below that the poten-

tial consequences of either accident are well within the radiation dose

limits specified by Title 10 CFR Part 20.

Dropped Fuel Rod Accident

For the purposes of this analysis, it is assumed that a dropped

fuel rod results in a broken pin releasing the accumulated fission pro-

ducts. The following bases have been established to calculate the

radiation dose from such an accident:

a. It is stipulated that the assembly has been operated continu-

ously for 200 hr at an average power level of 0.065 watt. It should be

noted that this is a conservative value since the assembly will not be

operated on a continuous basis; the 200 hours of operating time for each

configuration is essentially spread over a period of several weeks.

b. The assembly contains 1200 rods. Since the actual loadings for

the three reflected cases are 1206, 2132 and 3430 rods respectively, this

will result in conservative results.

c. The peak to space-averaged flux ratio during operation is a

maximum of 120, with the rod at peak flux contributing 1/10 of the









total power of the assembly.

d. The fuel rod subjected to the specified highest specific power

is broken open and the fuel is completely fragmented, releasing 100% of

the gaseous fission products.

e. The iodine (in elementary form) diffuses uniformly throughout

the 18' x 32' x 15' room to calculate the on-site internal dose. The

off-site dose was calculated using the very conservative Pasqual's

principle of atmospheric diffusion.

The fission products inventory was calculated by means of the RSAC

code [9]. The results indicated that the iodine isotopes were the only

significant contributor to the inhalation dose. Using the active worker
-4 3
breathing rate of 3.47 x 10 m /sec specified in 10 CFR 20, a person

remaining in the room would accumulate a thyroid dose of 0.023 mr for

each minute he remains in the room, after the hottest rod breaks open.

The total dose to a person that inhales all of the iodine contained in

the rod would be 0.2 r. The established radiation safeguards at the

University of Florida require the personnel to abandon the area imme-

diately and notify the Radiation Safety Officer. The maximum time

required to evacuate the assembly and the fuel storage area is 10 sec

with 30 sec needed to evacuate the entire building; these times have

been measured during practice evacuation of the building.

The off-site total inhalation dose, calculated assuming the iodine

is released in one puff with zero wind velocity, cloud inverted con-

dition, were typically:









Distance'from site (m) Total dose (mrem)

200 4.5 x 104

500 2 x 104
1000 7 x 10-6

The direct radiation dose from all the fission products of the

irradiated fuel elements is calculated to be 1.3 mr/hr.

Accidental Criticality and Subsequent Power Excursion

Accidental criticality and a subsequent power excursion could occur

only by the uncontrolled addition of water to the assembly and gross

error in the calculations and/or procedures. The occurrence of such an

accident is highly improbably and would require:

a. Setting a core width corresponding to the 1.5 metal/water ratio

and proceed to install the fuel spacer system for the 0.5 metal/water

ratio, load the fuel under these conditions and disregard small water

height increments and 1/M measurements. To do this, several administra-

tive rules would have to be wilfully ignored.

and/or

b. Improper setting of the following: the weir height, the water

height scram system for any configuration and a gross error in the

calculations causing criticality at about half the design core height

(91.44 cm). It should be noted that the calculational method used to

predict that keff values has been tested successfully against the

results of 29 different critical assemblies [7].

and/or

c. An obstructed 2 inch line from the core to the weir drain

system and a simultaneous failure of the water height scram together

with the referred to error in the calculations.









d. Violation by the facility operator of the administrative

procedures requiring a visual check of the assembly before start-up and

continuous attention to the control console instrumentation to determine

the status of the assembly at all times.

The consequences of such an accident were determined by assuming

the following:

1. The assembly is initially at a steady state power level of 10

watts (normal average power is .065 watt).

2. Water flows into the system at the maximum rate of 12 gpm.

3. The reactivity addition rate is 0.05 $/sec. This rate is

larger than the calculated rate (.04 $/sec) for the case discussed

above and more than that calculated to occur near critical for properly

loaded assembly.

4. The power scram is set, through calibration or other error, at

10 kw. Corresponding error settings occur for the neutron flux and

period scram.

5. A scram occurs 1 sec after a power level of 10 kw is reached.

This time has been determined as the elapsed time from the initiation

of a scram signal to the opening of the dump valves.

6. No feedback effects are considered. This is a good approxima-

tion to our case due to the low power levels involved and again is a

conservative assumption.

The calculations were made using the IREKIN code, described in

reference [10]. IREKIN numerically solves the point model kinetics

equations.

Starting with the assembly one dollar subcritical (ke = .993),
and proceeding with the described excursion, the accident would yield
and proceeding with the described excursion, the accident would yield










a peak power of 69 kw, the total energy release is 0.5 Mwsec. The

power vs. time behavior of the assembly for the postulated power excur-

sion is shown in Fig. 9.

The combined neutron and gamma dose to the operator is 1.5 rem

assuming that: the energy release is instantaneous, all neutrons have

an energy of 1 MeV and there is no attenuation in the assembly. The

proper RBE factors were taken into consideration.

It is concluded that, even if such an improbable accident would

occur, the hazards to personnel and the general population are not

significant.







7x104


3 -At t=0: k eff=0.993, Power=0
Ramp Insertion of .05$/sec
2 Scram 1 sec after 10 kw
Scram Rate = .14$/sec
Total Energy Release=0.5Mwse


Time secss)


FIG. 9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT















CHAPTER IV


THE DATA ACQUISITION SYSTEM


Introduction


In the delicate and laborious task of performing nuclear experi-

ments the most common source of difficulties and errors lies in the

acquisition of the data. Modern nuclear instrumentation with its excel-

lent time-energy resolution has enhanced detection sensitivity to the

extent that deviations previously masked by the poorer resolution of the

equipment are easily distinguishable. The major problem now lies in the

degree of reproducibility of the results. Although in general the in-

strumentation is very reliable the enhanced sensitivity demands contin-

ual standardization for the sake of reproducibility.

The "brain" of the data acquisition system for pulsed neutron

measurements is the multichannel analyzer (MCA) which is now available

with a large number of data channels and narrower channel widths for

increased time resolution. In general, the mode of data acquisition

for a pulsing experiment differs from that of many other types of

nuclear experiments. In particular, neutron interactions with a suitable

detector are fed into the analyzer while it is time-sweeping. Ideally

every neutron interaction should be counted regardless of the ampli-

tude of the collected pulse. This implies that the linear signal

originated at the neutron detector should be converted to a logic .signal

so that its probability of being recorded is independent of its amplitude.

45









Logic signals have fixed amplitude-shape characteristic and convey

information by their presence, absence of time relationship with

respect to a reference signal. Only gamma and noise discrimination

are necessary; this process will inherently eliminate the counting of

weak neutron interactions.

The process of registering events whose density per unit time

varies considerably requires an electronic system with extremely high

time resolution and a broad frequency response. Typically the counting

rates at the peak of the neutron burst in pulsed neutron measurements

vary from 10 to > 10 event/sec. This high, time-varying count rate

caused drastic losses in conventional instrumentation due to pulse

pile-up and circuit induced distortion when the dynamic range of the

circuit is exceeded causing a net amplitude shift in excess of that

tolerable by the system. The alternative modus operandi is to use low

count rates so that resolution losses are minimized; this, however,

increases the probability of systematic errors due to much longer run-

ning times.

The count rates encountered during the initial experiments with a

He counter close to the neutron generator target in the SPERT assembly

exceeded 10 event/sec at the peak. Saturation effects were observed

in modular instrumentation incorporating the latest F.E.T. preamplifier

and double-delay line pulse shaping amplifier at about 105 event/sec.

The fast pulse train caused a drop in the base voltage of the Field

Effect Transistor which prevented further counting until a significant

reduction in the count rate allowed the voltage to recover. Changing

to a fast scintillation prototype preamplifier improved the situation

somewhat. However, if the potential count rate in the UFSA assembly









were efficiently handled with few losses the actual running time of a

particular experiment could be reduced to a few minutes. This possi-

bility forced the development of the ultra-fast instrumentation chan-

nels used in this work.

The electronic counting system used throughout the experimentation

used a transformer-coupled pulse amplifier to produce a fast logic sig-

nal to the input of the MCA from a slower input signal originating in a

He counter. The system has superior counting and stability character-

istics. The resolution time of the system is practically nil compared

to that of the MCA. In general, data acquisition times were reduced

to a few minutes; in that time it was possible to obtain, at most of

the detector locations, the following counting statistics:

Peak Channel Counts: 217

Counting Time: 2 10 minutes

No. of data channels: 1024

Channel Width: 20 micro sec

Pulse repetition rate: 30 hz

Noise Level: 40 event/min

Background Level: 140 event/min


The Neutron Detector

The neutron detectors used throughout the experimental program were
3
proportional counters filled with He The counters are of the Texlium

variety made by Texas Nuclear Corporation and were specially built to

conform to the UFSA core grid. Detectors of this type have been



1. The assistance of Mr. Joel B. Ayers of ORTEC, Inc.,who suggested
this electronic instrumentation is gratefully acknowledged.









preferred over the BF3 variety at the University of Florida because of

the larger neutron absorption cross section and operational reliability.
3
He undergoes the following reaction

He3 + n H3 + p + 0.764 Mev.

The cross section for this reaction is 5327 + 10 barn at v = 2200
-- o
10 3
m/sec compared to 3840 + 11 barn for B He follows a 1/v law in the

energy range from 0 to 200 kev. The pulse heights yielded by a He3

filled counter are proportional to the energy of the neutrons plus 764

kev. The reaction has been used for neutron spectroscopy from the 100

kev to 2 Mev energy range. Gamma discrimination can be easily accom-

plished by the use of a biased integral discriminator.

The detectors were long and thin and each took the place of a fuel

element in the core. The active length of the counter is slightly less

than the active length of the fuel. Two one atmosphere (predominantly

thermal detection) and one ten atmosphere (more responsive to higher

energy neutrons) detectors were used in the experimental program. A

sketch of the physical characteristics of the counters is shown in

Fig. 10. The thin, long cylindrical shape enhances the time character-

istics'of the counter. Although normally a 1 atmosphere He detector

operates with a bias voltage of 1000 volt, the minimum input pulse

voltage requirement of the pulse transformer was such that the operating

voltage of the counters had to be raised to 1200 volt. At this

voltage the slope of the counts vs. high voltage curve was about 8% per

100 volt; therefore very stable, low ripple high voltage supplies were

used to insure reproducibility of the detector response.













HV BNC Connector


.- 5.1 25"-4


ive Volume Stoinless Casing







*: . * *
.247"




4- 33" 2.375"


40.5" 0.5" ---


FIG. 10 PHYSICAL CHARACTERISTICS OF THE He NEUTRON COUNTERS










The Electronic Instrumentation

A block diagram of the instrumentation used in the pulse propaga-

tion experiments is shown in Figs. 11 and 12. Two independent data

acquisition systems with a common start-stop clock are necessary to

carry out the measurements: (1) a system connected to a movable detec-

tor that obtains the time profile of the propagating pulse at a given

position and (2) the all important normalizing detector, fixed at one

position. Two 1 atmosphere He3 detectors with the characteristics de-

scribed above were used for these purposes. The system is essentially

composed of signal transmitting devices and data registering and

handling units.

The movable detector data acquisition system (MDDAS) consists of:

1. Detector High Voltage Power Supply

The high voltage power supply was an ultrastable FLUKE 405 B with

superior stability and negligible ripple. Manufacturer's specifications

state the stability at .005% per hour and the ripple at less than 1 my

RMS.

2. ORTEC Model 260 Time-Pickoff unit, with 3000 volt isolation

The time-pickoff units are normally used to detect the time of

arrival of a detected particle, usually with subnanosecond precision..

The use of this characteristic and the electronic arrangement shown in

Figs. 11 and 12 permitted the counting of neutron events with excellent

time resolution. To our knowledge this is the first time that the time-

pickoff units have been used for this application.

Briefly, the system operates as follows: the primary of a toroidal

transformer, having a bandpass for very high frequencies only, is

inserted between the detector and the bias power supply. Fast














4-RTC I
LORTEC 260 TIME-PICKOFFj


FIG. 11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM













4I 2_ I

ORTEC 260 TIME-PICKOFFJ


FIG. 12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM









components of the detector signal will actuate a wide band transistor

amplifier and tunnel diode discriminator from the secondary of the

transformer. A line driver buffer is also provided. The power and

control bias are provided by the ORTEC 403 Time Pickoff Control.

3. Modified ORTEC 403 Time Pickoff-Control

The 403 Time-Pickoff Control provides control and fan-out buf-

fering for time derivation units such as the 260 Time Pickoff Unit.

The fan-out buffer accepts the fast negative logic signal from the 260

unit and provides either fast negative or slower positive logic output

signals.

The 403 Time-Pickoff Control had to be modified to make its out-

put signal compatible with the input requirements of the 212 Pulsed

Neutron Logic Unit used with the MCA. The 212 plug-in unit requires

pulses with rise times longer than 50 nsec while the positive output

from the 403 control unit has a rise time ~ 10 nsec. Furthermore, the

positive logic signal from the 403 control has a 0.5 microsec pulse

width which is too wide for the time resolution required. Therefore

two modifications were made: a capacitor2 (C12) was changed from 270

pf to 68 pf reducing the pulse width to 0.12 microsec and an inductor

coil (Ll) was removed from the system changing the rise time to 50

nsec.

The modifications made the system compatible with the input

requirements of the MCA and avoided overdriving the analyzer.





2. Refer to ORTEC, Inc. "Instruction Manual for 403 Time-Pickoff
Control."









4. Technical Measurement Corp. 1024 Multichannel Analyzer

(MCA) and Data Handling Units

The time analysis of the pulse and the corresponding data output

are obtained from the following coupled instrumentation:

Pulsed Neutron Logic Unit, TMC Model 212

Digital Computer Unit, TMC Model CN1024

Data Output Unit, TMC Model 220C

Digital Recorder, Hewlett-Packard Model 561B

Binary Tape Perforator, Tally Model 420

A trigger from an external pulse generator starts the sweep of the

analyzer as controlled by the pulsed neutron logic unit and initiates

the burst at the accelerator. The 212 has variable channel widths from

10 to 2560 microsec. The full 1024 channels were used in all the meas-

urements. The storage capacity of the CN1024 is 217 counts. Both

printed paper tape and perforated binary tape were obtained as output.

5. ORTEC 430 Scaler

For some of the flux traverses and the 1/M measurements, the

integral counts were recorded in a 10 Mhz scaler.

The normalizing detector data acquisition system (NDDAS) consists

of the same components as the movable detection system except that a

256 multichannel analyzer, TMC Model CN110 was used for data handling

and the integral counts were accumulated in an ORTEC 429 Scaler, modi-

fied for 7 Mhz counting rate.


The Resolution Time Correction

The resolution time of the pulsed neutron data acquisition system

was the parameter under consideration while searching for a well-matched









and fast electronic instrumentation set-up. Some of the findings were

surprising and may explain some of the discrepancies found in previous

pulse propagation and neutron wave experiments which used an acceler-

ator type neutron source. In these experiments it has been customary

to increase the neutron yield of the genetator as the movable detector

is positioned farther away from the source to keep running times within

tolerable limits. The count rate at the movable detector is then

maintained at a level which has been determined to be acceptable; how-

ever the normalizing detector usually fixed in a position close to

the source (normally at the "thermalizing tank" if one is used) may

then be exposed to count rates beyond the capabilities of the detector

and the associated instrumentation. Since the movable detector signal

was always fed into an analyzer, saturation effects could be easily

detected; the signal from the normalizing counter, however, was always

being fed into a scaler where saturation effects may go unnoticed since

a time profile is not available.

During most of the present work, two MCA's were available and the

phenomenon described above was observed and count rates throughout the

experimental program limited to those permissible by the time charac-

teristics of the counting system.

The experimental program being carried out with the UFSA subcrit-

ical calls for the one to one comparison between theoretically calcu-

lated and experimentally determined time profiles of the neutron flux

as a function of space. The shape of the pulse, rather than conven-

tional integral parameters extracted from it, is therefore the signif-

icant and required information. For this reason the influence of the

resolution time correction on the shape of the pulse came under close









scrutiny.

The resolution time of several, submicrosecond preamplifier-linear

amplifier combinations was shown to be a function of the mode of opera-

tion and of the count rate. For this type of instrumentation, there is

a significant difference between the resolution time as determined by a

steady-state technique (two source method) and a dynamic method (maximum

count rate method [11]), the latter method yielding a much larger reso-

lution time.

For the instrumentation finally chosen to carry out the pulsed

experiments in this work no significant difference was found between

the results of the two methods. Furthermore the pulse transformer-

amplifier combination behaves like an ideal non-paralyzing system. The

resolution time of the overall data acquisition system was found to be

primarily determined by the multichannel analyzer.

As a matter of illustration, when the system depicted below was

used the resolution time changed from -0.24 microsec as determined

under low count rate steady-state conditions to -8 microsec as deter-

mined under high count rate, pulsing mode conditions.









Shown in Fig. 13 are two time profiles obtained at the same posi-

tion in the UFSA core for the same count rate. The conventional

preamplifier-linear aLaplifier system shown above was used to obtain one

of the profiles and the instrumentation selected for this work was used

to obtain the other. Both were corrected for resolution time losses

with the best available value for the resolution time. The distortion

observed in the pulse shape obtained with the conventional preamplifier-

linear amplifier system is non-linear due to the count-rate dependent

resolution time. It should be noted that the count rate near the peak

of the pulse was less than 105 count sec. The conventional system

response "flattens out" when it reaches complete saturation in this

case above 105 count sec. Saturation effects are not observed in the

pulse transformer system until the count rate exceeds 3.3 x 10 count

sec. An erroneous resolution time correction, or one which used a

resolution time that does not characterize the system throughout the

range of count rates will change the shape of the neutron pulse and

consequently affect any analysis done on the pulse shape obtained.

As pointed out by Bierman, Garlid and Clark [11], in a pulsing

experiment it is necessary to determine whether the counting system

has the characteristics of a purely non-paralyzing system or those

of a mixture of paralyzing and non-paralyzing systems. Using the

method described by Bierman and co-workers, it was established that

the data acquisition system being used in the present work is, as

close as can be determined, non-paralyzing. The resolving time of the

system is essentially determined by the width of the input pulse to the

analyzer and the MCA characteristics.

It should be noted that for a wide range of count rates, depending





58



40












30


Conventional








Time-Pickoff
20












10






30 microsec between channels




SI I I I I I I I l I !
0 4 12 16 24 32 40 48 56

Channel Number


FIG. 13 TIME PROFILES OF NEUTRON BURST RECORDED BY CONVENTIONAL
ELECTRONIC INSTRUMENTATION AND BY THE TIME-PICKOFF SYSTEM










on the magnitude of the resolving time, it is not necessary to prop-

erly identify the counting system since no significant difference in

the corrected counts are observed when using the paralyzing or non-

paralyzing correction. This is shown in Fig. 14.

The resolution time correction for the UFSA data acquisition

system is then given by:

No
N = o
T Noxtr
1-
CWxTrs

where

NT = true number of events in a given channel

N = observed number of events in a given channel

tr = resolution time of the system

CW = channel width

Trs = number of sweeps of the analyzer

and, for a non-paralyzing system

tr = reciprocal of the maximum observable count rate

Using this method the following resolution or resolving time fac-

tors were determined:

A) MDDAS including 1024 Multichannel Analyzer

tr = 0.31 + .015 microsec

B) MDDAS excluding Multichannel Analyzer

tr 0.20 + .01 microsec

C) NDDAS including 256 Multichannel Analyzer

tr = 0.56 + .02 microsec

D) NDDAS excluding Multichannel Analyzer

tr 0.20 + .01 microsec




I-w


700




600




- 500



0
z 400

S-- Non-paralizable


o 300 Paralizable
u /

") 0 80% non-paralizable
S20% paralizable

- i 200




100





0 100 200 300 400 500 600 700 800 900 1000

True Count Rate NT (x 103)


FIG. 14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME CORRECTION AS A FUNCTION
OF COUNT RATE









The Normalization Technique

The analysis of a pulse propagation experiment will yield informa-

tion on the velocity of propagation, the attenuation and pulse shape as

a function of position of a propagating disturbance. To determine the

attenuation or relative amplitude of the pulse at different positions

in an assembly, the data must be normalized to a fixed reference so

that variations in the source strength, data acquisition time, etc.,

can be properly accounted for. The usual technique requires accumulating

integral counts in a scaler for each measurement and reducing all meas-

urements to the fixed reference afterwards. As was mentioned previously,

the resolution time correction can have a significant effect on the nor-

malizing factor since widely differing count rates are employed. It is

extremely hard, if not impossible, to obtain a proper resolution time

correction based on integral counts determined from a time-varying count

rate.

Two methods of normalization and their relative merits are discussed

below.

The Integral Count Method is the normally employed method of nor-

malization. The total counts accumulated with the NDDAS for all runs

is referred to a predetermined one, with the normalizing detector in a

fixed position while the movable detector changes position.

The Analyzer Method, which is essentially the same as the above

except that the counts arising from the normalizing detector are stored

as a function of time in a multichannel analyzer. The average of a

series of ratios obtained by dividing the corrected channel counts by

the corresponding channel counts of a predetermined measurement gives

the normalizing factor.









The Analyzer Method is intrinsically more accurate than the

Integral Count Method because it permits an "exact" correction for

resolution time losses by the use of the expression previously given

applied to the recorded time profile. The correction for the integral

counts is, on the other hand, inaccurate since the count rate is con-

tinuously changing and no base exists for a resolution time correction.

It was found, however, that as long as the count rate near the

peak of the pulse is kept well within the capabilities of the NDDAS no

significant difference is observed in the results of the two methods.

This is due to the fact that ratios are being taken in both cases; this

tends to minimize whatever differences there might be. Thus, it is

concluded that with proper care the Integral Method is adequate whenever

an analyzer is not available for normalization purposes.

It should be noted that an "effective" resolution time can be used

to improve the results of the Integral Method. This "effective" reso-

lution time can be found by forcing the normalizing ratio obtained from

two runs by the Integral Method to match the normalizing ratio obtained

from the Analyzer Method for the same two runs by adjusting the reso-

lution time correction applied to the integral counts.


Comments

Certain inconsistencies in the results of the first few experi-

ments prompted a careful inspection of the multichannel analyzer modus

operandi. For the sake of completeness the significant findings are

listed below.

A) Operation with the 10 microsec channel width (selected by the

settings of the 212 plug-in-unit) proves to be unreliable due to insta-

bilities in the clock and gating circuits. Channel widths of 20









microsec or longer are stable.

B) The address current setting of the CN1024 is extremely criti-

cal, markedly so for high count rates.

C) An optimum pulse into the analyzer should have a rise time of

50 nanosec, a total width of .1 microsec and an amplitude of 3-5

volt.

D) Above noise level, the discriminator setting of the 212 logic

unit becomes irrelevant when a constant pulse height is used as input.

E) Reproducibility tests were performed on the analyzer with the

neutron generator in continuous mode.

The statistical analysis of the channel counts gave:

72% were less than 1 from the mean

25% were between 1 and 2 from the mean

3% were between 2 and 3 from the mean

The system is statistically well-behaved.















CHAPTER V


NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL


Introduction


The nuclear calibration of the University of Florida SPERT Assem-

bly was performed prior to the space-time kinetics studies. The cali-

bration involved conventional inverse multiplication measurements,

absolute keff determination by pulsing techniques and comparison with

multigroup-multiregion diffusion theory calculations. The Garelis-

Russell technique was employed to determine ka/I and this result used to

calculate keff by coupling it with the experimentally determined decay

constant and the theoretically calculated effective delayed neutron

fraction. During this phase of the experimentation, "spatial effects"

were noted in both a and k8/t. These effects and other interesting

kinetic phenomena involving these basic reactor parameters were con-

sidered worthy of further study and were investigated during the main

part of the research. They are discussed in Part 2, Chapter V. In

this section the results pertinent to the necessary calibration of the

system are given.


Theoretical Notes

The Inverse Multiplication Method

Under ideal conditions, usually met only in small-fast assemblies,

the reactivity can be represented by
64










1 k 1
~ M or 1 k /M
k M 1

where M is the net neutron multiplication in the assembly with a

centrally located source. In practice, the multiplication is obtained

from the ratio of multiplied to unmultiplied counts with a centrally

located source. The unmultiplied counts are obtained with the fissile

material removed and all other conditions undisturbed. In water-

moderated cores it is difficult to match neutron spectra for multiplied

and unmultiplied counts and deviations from the ideal M are to be ex-

pected. If possible, a search for detector locations should be con-

ducted so as to obtain curves that follow the expected behavior of l/M.

Even if k can not be directly inferred from the 1/M determination, the

curve of reciprocal count rate vs. the parameter that controls reac-

tivity (fuel loading or moderator height or % control rod withdrawal)

is a useful guide for safely approaching criticality if a well-behaved

curve can be obtained.

The inverse multiplication curve can be obtained as a function of

moderator height by first obtaining a series of unmultiplied counts at

various water levels and the multiplied counts as the water level is

raised with the assembly originally air-spaced. Sensitivity to geo-

metrical configuration (source-detector-water level) requires an empir-

ical determination of "well-behaved" detector positions.

Reactivity Measurements by the Pulsing Technique

The pulsed-neutron technique has been used successfully for several

years to measure reactivity. The transient neutron density following a

burst of neutrons is used to determine the reactivity of the system by

either the Simmons and King method [12], Sjostrand's area ratio method









[13], Gozani's extrapolated area-ratio analysis [14] or the Garelis-

Russel technique [8]. In all these techniques it is essential that a

fundamental spatial distribution of the neutrons be established for a

correct determination of the decay constant and, therefore, the reac-

tivity of the system.

The Sirmons and King method established that a value for the

reactivity can be obtained directly if a prompt fundamental decay con-

stant can be measured at delayed critical. The value of a at delayed

critical determines B/k and if these parameters are assumed constant

over the reactivity range of interest a value of a can be obtained. The

technique has given good results up to ~ $20 subcritical in small mul-

tiplicative systems. The method strongly depends on being able to

establish the prompt fundamental decay mode; it suffers from the incon-

venient necessity of a delayed critical measurement and the assumed

constancy of B/k throughout the ranges of reactivity.

The Sjostrand method improves the Simmons and King method in that

the delayed critical measurement is no longer necessary but the results

are shadowed by the strong influence of higher spatial harmonics. The

method is based on the premise that the impulse response curve of the

system is dominated by the prompt fundamental mode.

Gozani's treatment is a significant improvement over Sjostrand's

method. Gozani proposed the extraction of the fundamental mode of

prompt neutron decay from the impulse response curve and the extrapola-

tion of this curve to zero time. The reactivity in dollars can be found

by integrating under this curve; the method is independent of the pres-

ence of higher prompt spatial modes.

The Garelis-Russelltechnique, similar to Gozani's extrapolated










area-ratio method, is of practical value because of its intrinsic

elimination of the effect of prompt higher harmonics. This method,

which was used in the present work, was postulated originally for a

repetitively pulsed (with a delta function source in time), bare,

monoenergetic reactor but has proven to be of broader application.

Garelis and Russellpostulate, that for the conditions specified above:

1/R 1/R
fNp exp((k3B/)t)dt = fNpdt + Nd/R

where

Np = prompt contribution to the neutron density

Nd = delayed contribution to the neutron density

R = pulsing rate

The following conditions should be satisfied for the correct ap-

plication of the method.

a) R>>X, where A is the decay constant of the shortest lived

precursor group.

b) R >> a, where a is the prompt fundamental decay constant.

c) The system must be pulsed a sufficient number of times so that

exp (masn/R) << exp (-as /R), where m + 1 is the total number of pulses

and the a are the roots of the inhour equation.
sn
d) The prompt root dominates the decay.

The Garelis-Russelltreatment permits the determination of p ($)

when all the above conditions are satisfied, by the relation:


P ($) = k -

An absolute value of p is obtained by the use of a calculated effective

delayed neutron fraction. Garelis has discussed the use of the method

in reflected systems; the technique seems to be of practical value in









these systems [15].

Becker and Quisenberry were able to compute a correction [16] for

the observed spatial dependence of the reactivity in two-region systems

by recognizing the differences in the spatial distributions of prompt

and delayed neutrons. Their excellent comparative study of the above

techniques emphasized the need for their recommended spatial correction

unless the neutron detector is properly positioned to minimize this

correction.

The study of Garlid and Bierman [17] correctly points out that in

very large systems "an asymptotic spatial distribution cannot be estab-

lished before the pulse has decayed away, since the asymptotic mode is

one that is uniform everywhere in space." They proceed to apply a

combination of first flight, age, and time-dependent diffusion theory

to the study of pulsed measurements in large aqueous media; their con-

clusion is that their measured apparent decay constant is a good ap-

proximation to the asymptotic value and that pulsed measurements in very

large multiplying systems may also give good results.


Inverse Multiplication Measurements

The safe approach to the design value of k <.99 was undertaken
eff -
with the conventional 1/M measurements until k 0.95 and then by both

the 1/M and the pulsing technique.

To establish detector positions free from geometrical effects

(source-detector-water level), six different locations were used until

a water level of 60 cm (k .98) was reached and four locations afterwards.

Two of the detector locations, the closest to the neutron source, failed

to describe the multiplication of the system. Shown in Fig. 15 are the




SI VV I,














GRID POSITION

134 101 84 1 59 42

----- B 0-- '-b - *- i--
0 c- TNC
- -- DO- ,- 4' 5
WEIRS F 2 4 5, GENERATOR
Ho- I i S
HI ------, I HG ,
1 0_-_,l 6
ro


- 241.61
DISTANCE IN CM.


FIG. 15 DETECTOR POSITIONING SCHEME









locations employed for these measurements and for the absolute keff

determination by pulsing. Two 1 cu, centrally located Pu-Be sources

were used for these measurements.

The measurements were performed in the following sequence:

a) Unmultiplied counts vs. water level were obtained from a water

level of 20 cm to 91.4 cm above the bottom of the active fuel in steps

of 5 cm.

b) The fuel was loaded in the assembly in the presence of two

centrally located Pu-Be sources, with proper monitoring.

c) Multiplied counts vs. water level were obtained from a water

level of 20 cm in 5 cm steps until an effective multiplication factor

<.99 was reached. This procedure follows the criteria established for

Initial Loading of the assembly, Part 2, Chapter III of this work; the

5 cm steps were more conservative increments than those specified for

the Initial Loading of the assembly.

The results of these measurements are shown in Figs. 16 (A, B).

All the curves were well behaved in the sense that none "nose-dived."

Position 2 and 4 failed to properly describe the multiplication of the

assemblies because of their nearness to the source. Position 1 seems

to overestimate the multiplication, mainly because the unmultiplied

count rate was extremely low at this position thus an apparently high

ratio of multiplied/unmultiplied counts was obtained. A detector more

sensitive to high energy neutrons was used in locations 1 and 6.

It should be noted that when the inverse multiplication is plotted

vs. 1/H2 the predictions become quite linear much earlier than when

plotted versus H. Better predictions are therefore made with the 1/H2

curves but the approach can become less conservative by underestimating




w w







.6


.5 \ R Core
.5
o Position No 1
\ No2
A No 3
.4 \ No 4
SNo 5
.r-
A\ No 6
U\ \ \ o

S3 \\ \
*.3













0
( .2\\ \ < e








--4-
20 30 40 50 60 70 80

Moderator Level (cm)


FIG. 16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL




w


V I


w


Moderator Level (cm)


30.5


4 8 12 16

(1/Moderator Level)2 x 10-4 (cm-2)


FIG. 16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT










the multiplication.

Shown in Table III are the values estimated for keff for the four
eff
locations that seemed to represent the system best. Position 3 gives

a lower limit and Position 1 an upper bound. No attempt was made to

establish the error associated with measured keff but it is believed

that the 0.99 value obtained at the last water level is within +.005

of the true value.


Absolute Determination of keff

After an estimated value of keff >.95 was obtained from the 1/M
eff -
measurements, an independent determination of k was required by the

operating license at every new increment in the moderator level (as

determined by the criteria established in Part 1, Chapter 3). The

technique chosen for this determination was the Garelis-Russellmethod

of measuring kB/W and a simultaneous determination of the prompt funda-

mental decay constant.

Different detector locations were used to determine the influence

of the source and of higher order harmonics contamination. Strong

"spatial effects" were observed in both a and kS/P. This phenomena will

be discussed in detail in Part 2, Chapter V because of its importance.

A seemingly true fundamental decay constant and "spaced-converged"

kB/ were obtained at large distances from the source and were used to

determine the reactivity of the system.

A Fortran IV, IBM 360 computer program named UNIPUL was coded to

perform a unified analysis of the pulsed neutron data (see Appendix B).

The program calculates the decay constant using Peierl's statistical

analysis [18] and kB/k using the Garelis-Russellapproach after the data













TABLE III


SUMMARY OF 1/M AND PULSED MEASUREMENTS


UFSA RI Core
0.5 M/W Ratio
16.35 cm wide reflected core

INVERSE MULTIPLICATION
Moderatora keff
eff


Height (cm) Pos. 1 Pos. 3


PULSED EXP
keffb


Pos. 5 Pos. 6


20 .415 .481 .425

25 .744 .629 .705

30 .867 .737 .824

35 .914 .794 .881

40 .944 .84 .908

45 .9612 .873 .934

50 .973 .895 .950

55 .98 .918 .962

60 .985 .936 .973

65 .9891 .95 .980

70 .9925 .96 .9853

75 .9949 .971 .989

80

85

91.4

Above bottom of active fuel
Averaged from 3 detector positions


.581

.771

.865

.900

.927

.946

.961

.969

.971

.979

.986

.990


.948+.01

.965+.007

.972+.006

.9796+.005

.9855+.004

.990+.003


PREDICTED
keff


.7675

.8287

.871

.9022

.925

.9419

.955

.9655

.974

.980

.986

.9906

.9944

.9976

1.00117









has been resolution time corrected and background subtracted. A "pure"

delayed neutron background is statistically calculated and used to

determine kB/t. The data can be normalized to a reference detector

position for the analysis of the pulse propagation measurements in the

time and in the frequency domain. A Fourier analysis of the pulse can

also be performed if required.

Shown in Fig. 17 (A, B) are the experimentally determined a, kBg/

and k as a function of moderator height obtained by averaging results

from three chosen detector locations in the "asymptotic" region. The

results are summarized, together with the 1/M measurements and theoreti-

cally calculated values in Table III. The excellent agreement between

the experimental and theoretical results should be considered somewhat

fortuitous. The calculations were done following the method outlined

in Appendix A. Some later calculations [19] done by the Phillips

Petroleum Co.,showed more disagreement, especially at low water levels.

The last calculations tried to account for the fact that there is a

fissionable reflector above each experimental moderator height. This

fact was disregarded in the calculational results shown in this work.

The agreement at the 75 cm water level is good for all calculational

methods.


Conclusions

The University of Florida SPERT Assembly has been operated for

several months with very few operational problems. The system has

proven to be extremely reliable and the instrumentation has performed

adequately. The calibration of the system has established that mean-

ingful values for the reactivity can be obtained when applying the













N


R1 Core


N.


N
N


-0


I S I I


i i i I I


0 60 70 r


Moderator Level (cm)


FIG. 17A DECAY CONSTANT vs. MODERATOR LEVEL


w


w


1200


1000 C


800


400 k


200 -


05
5


* g t




w


210 -


I I I


' "I


I I I I I


Moderator Level (cm)


FIG. 17B k8/W AND k vs. MODERATOR LEVEL


w


R1 Core


1.00




0.99




0.98




0.97 ;




0.96




0.95


200 1


190 L


0 o


.J


4=-


/


170 1-


160 1-


~1
d/


150


d


I I









Garelis-Russelltechnique to a reflected slab assembly when proper care

is taken. Agreement between calculated and experimentally determined

values of the reactivity is termed excellent but since only one case

has been studied judgement on the overall applicability of the technique

to this type of reactor configurations should be reserved until the

other assemblies to be studied in the UFSA facility are duly analyzed.

It should be pointed out that multiple detector positions are necessary

to establish when an asymptotic decay constant is obtained, and that the

value of k/ is affected by the input pulse width. As mentioned previ-

ously, a more detailed analysis of the pulsed neutron reactivity meas-

urements is conducted later in this thesis.




































PART 2

SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY




Full Text
rLUX (RELATIVE UNITS)
FIG. 23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
112


FLUX (RELATIVE UNITS)
FIG. G1 SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF PULSE WIDTH
- EXPERIMENTAL -
256


FLUX (RELATIVE UNITS
TIME (MSEC)
FIG- E4 TIME PROFILE' OF THERMAL NEUTRON FLUX 142-8E3 CM FROM THE SOURCE
252


41
Distncfrom sit (m)
200
500
1000
The direct radiation dose from all the fission products of the
irradiated fuel elements is calculated to be 1.3 mr/hr.
Accidental Criticality and Subsequent Power Excursion
Accidental criticality and a subsequent power excursion could occur
only by the uncontrolled addition of water to the assembly and gross
error in the calculations and/or procedures. The occurrence of such an
accident is highly improbably and would require:
a. Setting a core width corresponding to the 1.5 metal/water ratio
and proceed to install the fuel spacer system for the 0.5 metal/water
ratio, load the fuel under these conditions and disregard small water
height increments and 1/M measurements. To do this, several administra
tive rules would have to be wilfully ignored.
and/or
b. Improper setting of the following: the weir height, the water
height scram system for any configuration and a gross error in the
calculations causing criticality at about half the design core height
(91.44 cm). It should be noted that the calculational method used to
predict that values has been tested successfully against the
results of 29 different critical assemblies [7].
and/or
c. An obstructed 2 inch line from the core to the weir drain
system and a simultaneous failure of the water height scram together
with the referred to error in the calculations.
Total dose (mrem)
4.5 x lO-4
2 x 10"4
7 x 10-6


36
Reactivity Addition Rate
Specification: the reactivity addition rate is controlled by the
water flow rate into the subcritical assembly. The maximum flow is fixed
to be 12 gpm. At this maximum flow rate, the rates of addition of water,
and consequently or reactivity, computed between water heights of 30 and
45 cm. are:
Lattice Pitch
0.5332"
0.584"
0.7152"
Rate of increase of
water level
0.0435
0.0439
0.0431
Ak/cm
0.0093
0.00865
0.008
Ak/sec
0.0004
0.0038
0.000344
$/sec
0.057
0.054
0.049
It should be noted that these reactivity addition rates are a large
overstimate compared to the calculated rates at k^^ ~ .98.
Basis: the maximum rate of addition of reactivity was established
by the calculated values of k^^ vs. water height and the maximum flow
rate. The values specified above constitute an upper limit in the
region of interest and are considered to be safe under circumstances.
The flow rate is a function of the capacity of the pump, the ori
fice and the pneumatic control valve and cannot exceed 12 gpm.
Reactivity Removal Rate
Specification: a conservative value for the reactivity removal
rate is taken from the slope of the k ^ vs. water height curves near
the maximum desiened k values. Since no difference is detected for
w err
the scram times of the three configurations, only one rate of removal
will be specified, corresponding to the smallest slope.


165
TABLE XVII
THE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
- 1.0 MSEC INPUT PULSE -
FREQUENCY a (cm"1) ? (rad/cm)
(cps)
Theory
Exp
Theory
. Exp
0
.02444
.02346
,
10
.02330
.02324
.001500
.001499
20
.02343
.02344
.002987
.002980
30
.02365
.02361
.004438
.004427
40
.02394
.02393
.005963
.005951
50
.02429
.02437
.007338
.007319
60
.02469
.02484
.008655
.008623
70
.02512
.02535
.009920
.009864
80
.02558
.02597
.01115
.01104
100
.02665
.02724
.01343
.01320
120
.02775
.02861
.01559
.01516
140
.02883
.03004
.01739
.01688
160
.02995
.03148
.01918
.01846
180
.03111
.03292
.02081
.01995
200
.03220
.03438
.02230
.02129
200
.03330
.03577
.02380
.02257
240
.03444
.03714
.02515
.02377
260
.03547
.03834
.02640
.02493
280
.03650
.03959
.02770
.02605
300
.03764
.04068
.02883
.02712
350
.04013
.04288
.03160
.02925
400
.04246
.04465
.03409
.03138
450
.04496
.04896
.03634
.03362
500
.04708
.05121
.03840
.03568
550
.04920
.05420
.04031
.03771
600
.05122
.05625
.04200
.03814
650
.05329
.05813
.04363
.03881
700
.05528
.06113
.04501
.04008
750
.05746
.06276
.04638
.04389
800
.06000
.06396
.04777
.04848
900
.06530
.06692
.05230
.05410


148
TABLE XIII
DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE
DISTANCE TO
SOURCE (cm)
PEAK AT
Theory
(msec)
Exp
FWHM
Theory
(msec)
ExP
53.9
0.60
0.580
1.35
1.62
79.3
1.08
1.06
2.06
2.28
130.2
2.27
2.26
3.20
3.51
142.9
2.50
2.53
3.47
3.75
Significant discrepancies between theoretical and experimental
pulse shapes were noted in the region where source effects are still
noticeable; in contrast, excellent agreement was found in this region
for the 0.5 and 1.0 msec input pulse cases. Deep in the asymptotic
region the measured pulse shapes are identical to those determined for
the 0.5 and 1.0 msec input pulses.
The results are somewhat inconclusive, however, since near the
source the measured pulse shapes appeared wider than the corresponding
shapes for the 0.5 and 1.0 msec input pulsed, although they occur
earlier in time. Unfortunately, the assembly was dismantled before
these comparisons were completed. The observed discrepancies deserve
further experimental study.
It should also be noted that noticeable oscillations were observed
in the WIGLE results in the spatial region close to the source.
Propagation of Wide Pulse
A series of measurements were also made in the clean core with a
10 msec wide input pulse. This pulse is much wider than the


55
and fast electronic instrumentation set-up. Some of the findings were
surprising and may explain some of the discrepancies found in previous
pulse propagation and neutron wave experiments which used an acceler
ator type neutron source. In these experiments it has been customary
to increase the neutron yield of the genetator as the movable detector
is positioned farther away from the source to keep running times within
tolerable limits. The count rate at the movable detector is then
maintained at a level which has been determined to be acceptable; how
ever the normalizing detector usually fixed in a position close to
the source (normally at the "thermalizing tank" if one is used) may
then be exposed to count rates beyond the capabilities of the detector
and the associated instrumentation. Since the movable detector signal
was always fed into an analyzer, saturation effects could be easily
detected; the signal from the normalizing counter, however, was always
being fed into a scaler where saturation effects may go unnoticed since
a time profile is not available.
During most of the present work, two MCA's were available and the
phenomenon described above was observed and count rates throughout the
experimental program limited to those permissible by the time charac
teristics of the counting system.
The experimental program being carried out with the UFSA subcrit-
ical calls for the one to one comparison between theoretically calcu
lated and experimentally determined time profiles of the neutron flux
as a function of space. The shape of the pulse, rather than conven
tional integral parameters extracted from it, is therefore the signif
icant and required information. For this reason the influence of the
resolution time correction on the shape of the pulse came under close


FLUX (RELATIVE UNITS)
FIG C32 TIME PROFILE OF THERMAL NEUTRON FLUX 155-53 CM FROM THE SOURCE
228


158
time domain were transformed to the frequency domain, with identical
numerical and fitting procedures, setting a firm basis for a one-to-
one comparison.
The following interesting numerical problems are worthy of note:
a) To determine to what extent the numerical transformation is
affected by the accuracy of the operations of the IBM 360 computer,
sample problems were run in single precision (4 byte words) and double
precision (8 byte words) using the MORWIG program. No differences were
found in the results up to the sixth significant figure, but the double
precision computations consumed almost twice the amount of time as
the single precision ones.
b) Initially, the results of every third WIGLE time calculation
was punched on cards for the comparison in the time domain and for the
input to the Fourier transformation code. Less than 250 time points,
with time increments of up to 150 microsec, were available for each space
point. The numerical transformation performed on these results was
somewhat unsatisfactory since not all the amplitude and phase curves
2
were smooth and in the p plane the scattering of points was significant.
The WIGLE calculations were then performed again, with smaller time in
crements, carried farther in time and every time step punched for input
to the MORWIG program. A total of 997 and 998 points respectively were
now available for the Fourier transformation for the 0.5 and 1.0 msec
input pulse cases. The largest time increment was 32 microsec. The
calculation was carried to about 19.2 msec after the initiation of the
pulse. A significant improvement was noted in the results of the numer
ical transformation. The results were smooth throughout up to ~ 800
cps, where a certain amount of scattering was observed.


Observed Count Rate
FIG. 14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME CORRECTION AS A FUNCTION
OF COUNT RATE


101
"effective" core height is very close to 76 cm. The transverse leakage
was taken into account in the WIGLE scheme by changing the absorption
2
cross section of the fast and the thermal group with the proper D^B^
obtained from the above calculations.
The aluminum port in which the target section of the accelerator
is located created a large void in the source section of the core.
Shown in Fig. 20 is a plan and front view of this arrangement. To mock-
up the physical situation as closely as possible the input to the WIGLE
code consisted of parameters for two different types of regions: one
for the normal core and one for the region depicted in Fig. 20. The
parameters calculated for the UFSA core were then volume-weighted
together with two group parameters for aluminum and light water as a
first approximation to the parameters in the source region (Region 1 in
the calculations).
In Fig. 21 the type of material, number of mesh points and the
mesh spacing used in the calculations is shown. Table IV shows the
value of the parameters for Region 1 and for Regions 2, 3, 4, 5 respec
tively. Before the final runs were made the importance of the mesh
spacing was investigated by running two identical cases with 166 and 99
mesh points respectively. No difference was found between results of
these two cases.
The choice of time increments was more critical. When time steps
of 5 ysec were used in the vicinity of the time where the value of the
4
fast source was changed from 10 to 0 severe oscillations developed at
the first space point. To avoid this problem, time steps of 0.2 to 0.5
ysec were employed in this time region and the magnitude of the source
was reduced in two steps; first to one-half the original value and then-


CHAPTER II
DESCRIPTION OF THE FACILITY
General Features
The University of Florida Spert Assembly is a light water
moderated subcritical facility fueled by 4.81% enriched U0£ pellets
encased in stainless steel tubes of 0.4655" outside diameter. The fuel
arrays are contained in a rectangular tank, 8 feet long, 39 inches high,
and of variable widths. The system is designed so that both bare and
reflected cores can be studied. Only one reflected core will be dealt
with in Part 2 of this manuscript; information on three reflected cores
is included in this chapter. The .assembly width and fuel spacing may be
varied in order to:
a) have a k not to exceed 0.99 in all cases to be
eff
considered.
b) accommodate non-moderator/moderator ratios of
0.5, 1.0, and 1.5, respectively.
Shown in Table I are the k _'s as a function of the moderator
eff
height, the fuel spacings, core widths, and total number of fuel ele
ments for the different reflected cases to be considered. The calcu-
lational procedures used in the determination of the nuclear parameters
and the k^^ values for the three reflected configurations of the
assembly are described in Appendix A. Only the sides of the assembly
will be reflected. Fig. 1 shows an overall view of the facility.
5


LIST OF FIGURES (cont'd)
FIGURE Page
35C THE SENSITIVITY OF THE ONE-DIMENSIONAL, TOO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 143
36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE
HEIGHT 144
37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS 153
37B EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS 154
38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE 160
39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE 161
40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE 162
41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE 163
42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED DAMPING COEFFICIENT a 166
43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED PHASE SHIFT PER UNIT LENGTH 5 167
44 THE UFSA R1 CORE p DISPERSION LAW 169
45 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED (a2 £2) 171
xvi


CHAPTER V
NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL
Introduction
The nuclear calibration of the University of Florida SPERT Assem
bly was performed prior to the space-time kinetics studies. The cali
bration involved conventional inverse multiplication measurements,
absolute k^.,. determination by pulsing techniques and comparison with
multigroup-multiregion diffusion theory calculations. The Garelis-
Russell technique was employed to determine kg/l and this result used to
calculate ke^ by coupling it with the experimentally determined decay
constant and the theoretically calculated effective delayed neutron
fraction. During this phase of the experimentation, "spatial effects"
were noted in both a and kg/£. These effects and other interesting
kinetic phenomena involving these basic reactor parameters were con
sidered worthy of further study and were investigated during the main
part of the research. They are discussed in Part 2, Chapter V. In
this section the results pertinent to the necessary calibration of the
system are given.
Theoretical Notes
The Inverse Multiplication Method
Under ideal conditions, usually met only in small-fast assemblies,
the reactivity can be represented by
64


TABLE V
TIME STEPS USED FOR THE WIGLE CALCULATIONS
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
Input Pulse Width = 0.5 msec
Time Step
(Microsec)
2
4
1
5
1
2
5
10
25
50
To Time
Step No.
40
140
160
170
205
235
315
415
655
795
Time Step
(Microsec)
To Time
Step No.
Input Pulse Width = 1.0 msec
3
5
1
.5
1
2
5
10
25
50
30
210
220
230
265
295
375
475
695
834
106


59
on the magnitude of the resolving time, it is not necessary to prop
erly identify the counting system since no significant difference in
the corrected counts are observed when using the paralyzing or non
paralyzing correction. This is shown in Fig. 14.
The resolution time correction for the UFSA data acquisition
system is then given by:
N.
N =
T N0xtr
1
CWxTrs
where
N^, = true number of events in a given channel
N = observed number of events in a given channel
tr = resolution time of the system
CW = channel width
Trs = number of sweeps of the analyzer
and, for a non-paralyzing system
tr = reciprocal of the maximum observable count rate
Using this method the following resolution or resolving time fan
tors were determined:
A) MDDAS including 1024 Multichannel Analyzer
tr = 0.31 + .015 microsec
B) MDDAS excluding Multichannel Analyzer
tr 0.20 + .01 microsec
C) NDDAS including 256 Multichannel Analyzer
tr = 0.56 + .02 microsec
D) NDDAS excluding Multichannel Analyzer
tr 0.20 + .01 microsec


FLUX (RELATIVE UNITS)
FIG- C24 TIME PROFILE OF THERMAL NEUTRON FLUX 53-8G CM FROM THE SOURCE
220


260
30. M. A. Perks, "FREAK A Fast Reactor Multigroup Kinetics Program,"
ANL-7050 (1965).
31. R. W. Garner, private communication (1968).
32. S. Kaplan, 0. J. Marlower and J. Bewick, "Application of
Synthesis Techniques to Problems Involving Time Dependance,"
Nuc. Sci. Eng., 18, 163 (1964).
33. J. B. Yasinsky and A. F. Henry, "Some Numerical Experiments
Concerning Space-Time Reactor Kinetics Behavior, Nuc. Sci. Eng.,
22, 171 (1965).
34. W. M. Stacey, Jr., "A Variational Multichannel Space-Time
Synthesis Method for Nonseparable Reactor Transients," Nuc. Sci.
Eng., 34, 45 (1968).
35. A.Foderaro and H. L. Garabedian, "Two Group Reactor Kinetics,"
Nuc. Sci. Eng., 14, 22 (1962).
36. K. 0. Ott, "Quasistatic Treatment of Spatial Phenomena in Reactor
Dynamics," Nuc. Sci. Eng., 26, 559 (1966).
37. K. 0. Ott and D. A. Meneley, "Accuracy of the Quasistatic Treat
ment of Spatial Reactor Kinetics," Proceedings of the Brookhaven
Conference on Industrial Needs and Academic Research in Reactor
Kinetics, BNL 50117 (T-497) (1968).
38. A. F. Henry, "The Application of Reactor Kinetics to the Analysis
of Experiments," Nuc. Sci. Eng., _3, 52 (1958).
39. C. D. Kylstra and R. E. Uhrig, "Spatially Dependent Transfer
Function of Nuclear Systems," Nuc. Sci. Eng., 22, 191 (1965).
40. S. R. Kavipurapu, "Energy and Spatially Dependent Impulse Response
and Transfer Function of Nuclear Systems, Unpublished Ph.D.
Dissertation, University of Florida (1964).
41. A. M. Weinberg and H.. C. Schweinler, "Theory of Oscillating
Absorber in a Chain Reactor," Physical Review, 74, 851 (1948).
42. R. B. Perez and R. E. Uhrig, "Propagation of Neutron Waves in
Moderating Media," NuC. Sci. Eng., 17, 90 (1963).
43. M. N. Moore, "The Determination of Reactor Dispersion Laws from
Modulated Neutron Experiments," Nuc. Sci. Eng., 21, 565 (1965).
44. R. L. Brehm, "Analysis of Neutron Wave Experiments," Proceedings
of the Symposium on Neutron Noise, Waves, and Pulse Propagation,
AEC Symposium Series No. 9 (1967).


31
The accelerator was used with a 4-5 curie tritium target.
The position of the target can be changed to keep the source
centered on the target-end of the assembly for any given moderator
level


FLUX (RELATIVE UNITS)
FIG- C17 TIME PROFILE OF THERMAL NEUTRON FLUX PCS-46 CM FROM THE SOURCE


82
of this work. The subcritical assembly consists of a square array of
4.8% enriched UC^ SPERT F-l fuel elements moderated by light water and
with essentially an infinite light water reflector on the sides. The
core is 243 cm long, 16.35 cm wide, has an effective height of 76 cm
with 30.5 cm wide side reflectors. The effective multiplication con
stant of the assembly has been determined to be 0.990+.003.
A fast, reliable set of electronic instrumentation was developed
and used to record the very high, time-varying count rate as a function
of position in the core of the assembly. A technique was developed to
subtract the contribution of epicadmium neutrons from the recorded
time profile of the neutron flux.
The study of the pulse propagation phenomena was conducted in a
two-fold manner: in the time and in the frequency domain. The study
in the time domain consisted of several sections, focusing the attention
on basic aspects of the space and time dependence of propagating dis
turbances. The following aspects were investigated:
a) The propagation of 0.5 and 1.0 msec wide input pulse intro
duced at one end of the assembly. This investigation constituted the
main part of the research; it involved a detailed comparison of the
experimental results with the predictions of the WIGLE calculational
scheme. The sensitivity of the one-dimensional model to small varia
tions in the transverse leakage was also investigated.
b) Static flux traverses were conducted to determine the steady-
state neutron distribution in the asymptotic region. Dynamic flux
traverses were performed to determine whether any propagation occurs in
the transverse direction.
c) The effect that the input pulse width has on the propagation


APPENDIX E
UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT FOUR POSITIONS IN THE CORE
FOR A 0.1 MSEC INPUT PULSE


47
were efficiently handled with few losses the actual running time of a
particular experiment could be reduced to a few minutes. This possi
bility forced the development of the ultra-fast instrumentation chan
nels used in this work.
The electronic counting system^" used throughout the experimentation
used a transformer-coupled pulse amplifier to produce a fast logic sig
nal to the input of the MCA from a slower input signal originating in a
3
He counter. The system has superior counting and stability character
istics. The resolution time of the system is practically nil compared
to that of the MCA. In general, data acquisition times were reduced
to a few minutes; in that time it was possible to obtain, at most of
the detector locations, the following counting statistics:
ol7
Peak Channel Counts:
Counting Time:
No. of data channels:
Channel Width:
Pulse repetition rate:
Noise Level:
Background Level:
2-10 minutes
1024
20 micro sec
30 hz
40 event/min
140 event/min
The Neutron Detector
The neutron detectors used throughout the experimental program were
3
proportional counters filled with He The counters are of the Texlium
variety made by Texas Nuclear Corporation and were specially built to
conform to the UFSA core grid. Detectors of this type have been
1. The assistance of Mr. Joel B. Ayers of ORTEC, Inc.,who suggested
this electronic instrumentation is gratefully acknowledged.


86
methods presently in use are:
a) Direct solution of the multigroup, space-time diffusion
equations, referred to as the "exact" method. This method constitutes
a benchmark for the other techniques. The most prominent of these
calculational schemes are:
1) WIGLE, a two-group, one-dimensional space-time diffusion
theory computer program [24, 27, 28].
2) TWIGLE, a two-dimensional version of WIGLE [29].
3) FREAK, a fast reactor multigroup kinetics code [30].
4) A four-group, one-dimensional space-time diffusion theory
computer program [31] developed by the Phillips Petroleum Co.
b) Flux Synthesis methods, which used the idea that the flux
shapes which occur during a transient can be bracketed by a set of
shape functions [32, 33, 34].
c) Conventional Modal methods, exemplified by the Foderaro-
Garabedian technique [35] in which the flux is expanded in terms of
the eigenfunctions of the wave equation (Helmholtz modes).
d) The Quasistatic approach of Ott [36, 37], a more sophisticated
"factorizing" technique (the flux is factorized into an amplitude and
a shape function). Use is made of the fact that the time dependence
of the shape function is less important than the time dependence of
the amplitude function.
e) The Adiabatic approximation [38], a "factorizing" technique
in which, besides ignoring the time dependence of the shape function,
no distinction is made between the prompt and delayed neutron sources.
Other related studies, on a somewhat different context,were performed
by Kystra and Uhrig [39] and by Kavipurapu [40]. They studied the


SPACE-TIME REACTOR KINETICS STUDIES WITH THE
UNIVERSITY OF FLORIDA SPERT ASSEMBLY
By
NILS J. DIAZ
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1969


179
pulse.
Tabulated in Table XVIII are values of kg/5 determined using the
Garelis-Russell technique on pulses arising from widely differing input
pulses; the measurements were made at one position far from the neutron
source. The effect of the finite pulse width on kg/5, is significant.
An analysis of the results shown in Fig. 49 points to the fact that at
very large distances from the source a value of kg/5- close to the one
that would be obtained from a delta function input pulse is obtained.
Some comments on observed facts about the Garelis-RusseU tech
nique are pertinent. A dominant factor in the determination of kg/5, is
the delayed neutron background, which is strongly dependent on the
repetition rate of the neutron generator (which should be determined
very accurately). Meaningful values of kg/5, are obtained far from the
source for not too wide input pulses. A correction on the determined
kg/5, values to account for the finite width of the input pulses was
developed by G. A. Mortensen, Nuclear Safety Division, Phillips
Petroleum Co. [48] after the experimental observation of the phenomena.
The suggested method was applied to several of the cases under consid
eration but an overcorrection seems to result; the "corrected" values
keep changing drastically at long distances from the source where the
influence of the input pulse is negligible. Further work in this cor
rection should improve the results.
The Measured Reactivity and kef£ Values
The reactivity in dollars is obtained, following the Garelis-
Russell method, by the expression
P($) -
a
kg/5,
- 1


PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
- DESIGN AND CALIBRATION -


90
^0(r, f) = A1(J (f) Q23 (r2, r3, B^)
exp {[-o^Cf, B) + i (f, b£)]z}
where:
A1q specifies the source condition.
2
Q23 (r2> r3> B ) specifies the transverse space dependence.
and are respectively the real and imaginary components of
the complex inverse relaxation length.
The Fourier transform (r, f) of the unit impulse response
(r, t) is the transfer function of the system. Therefore the ampli
tude and phase curves obtained from a numerical Fourier transformation
of the pulse propagation data corresponds to those measured directly
by the wave experiment.
It should be mentioned that, although most common nomenclature
refers to the pulse propagation phenomena and/or the neutron wave
propagation as "thermal" neutron propagation because of the "close-to-
thermal" source employed and the characteristics of the media studied,
there is no such "pure" phenomena in a multiplying medium. The dis
turbance propagates whether it started as a "fast" or "thermal" pulse
and quickly losses memory of its origin (specially in water moderated
media). The only difference between inserting a thermal or a fast
burst of neutrons lies in the spatial distribution.of source neutrons.
The thermal source will appear essentially localized at the point of
insertion while the fast source neutrons will penetrate deep into the
assembly.


FLUX (RELATIVE UNITS)
FIG- C20 TIME PROFILE OF THERMAL NEUTRON FLUX
3-0 CM FROM THE SOURCE


180
TABLE XVIII
THE DECAY CONSTANT AND kg/A VALUES
MEASURED AS A FUNCTION OF INPUT PULSE WIDTH
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Clean Core
0.5 M/W Ration
16.35 cm wide reflected core
PULSE
WIDTH
(msec)
a
(sec
k8/£
(sec
0.1
511+10
213+4
0.5
488+11
202+5
1.0
501+6
193+5
2.0
503+8
183+7
3.0
51.0+4
172+9
4.0
523+16
169+9
5.0
494+6
144+10
6.0
504+5
136+10
7.0
505+5
126+9
8.0
522+17
118+11
9.0
524+13
111+8
10.0
496+16
108+9


This dissertation was prepared under the direction of the chairman
of the candidate's supervisory committee and has been approved by all
members of that committee. It was submitted to the Dean of the College
of Engineering and to the Graduate Council, and was approved as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
March 1969
Dean, Graduate School
Supervisory Committee:
Chairman


188
Determination of the Four Group Parameters
A four-group diffusion approach was used to calculate the effective
multiplication factor of the six UFSA configurations to be studied as
Phase I of the large core dynamics experimental program. The calcula
tion of the parameters was performed by the Nuclear Safety Research
Branch of the Phillips Petroleum Company [31].
The four energy groups were divided as follows:
Group 1 8.21 X 105 107 EV
Group 2 5.53 X 103 8.21 X 105 EV
Group 3 0.532 5.53 X 103 EV
Group 4 0 0.532 EV.
To obtain the four-group constants, the following sequence of cal
culations was performed for each of the six cases mentioned.
1. Fast group (groups 1-3) constants were calculated by the PHROG
[50] computer program. These calculations include resonance integral
and Dancoff correction calculations as provided by the RAVEN [51] cal-
culational scheme.
2. Thermal constants were calculated by the TOTEM [52] computer
program.
The constants used for the core object of this work are given
below. It should be mentioned that the procedure described was also
employed to determine the two-group parameters used for the WIGLE
calculations.


VALVE
FIG. 7 AIR SYSTEM SCHEMATIC


P'LX (RELATIVE UNITS)
FIG*. C12 TIME PROFILE OF THERMAL NEUTRON FLUX 145-BB CM FROM THE SOURCE


192
General
A set of computer programs was coded for the data processing and
the analysis of the results of the pulsed measurements.^ The programs
were written for the IBM 360-50 computer, with the exception of
MULTIPLOT which was coded for the IBM 1800 computer.
UNIPUL
The FORTRAN IV, IBM 360 computer program UNIPUL is used for a
unified processing of the data obtained from conventional pulsing or
pulse propagation measurements. A complete description of the program
and the input requirements are available in Ref. 54.
The main operations of UNIPUL are:
1. Resolution time correction of the data, using a non-paralyzing
counting correction.
2. Statistical determination of the neutron background. If the
system under study is multiplicative, the delayed neutron background
is calculated and stored in COMMON for the calculation of k8/JL.
3. Determination of the fundamental decay constant using Peierl's
statistical method [18]. The decay constants can be calculated at dif
ferent waiting times from the peak of the pulse to determine the time
convergence. The a's are stored in COMMON for the reactivity determina
tion.
4. The background is subtracted from the data. A test is made to
find if any channel has a negative number of counts. If a few channels
have negative counts, their value is set to zero. The number of
1. The cooperation of Dr. M. J. Ohanian in the coding of these
programs is gratefully acknowledged.


120
were conducted to investigate the propagation, throughout the core, of
0.5 and 1.0 msec input pulses. As mentioned in the previous section,
particular aspects of the propagation phenomena investigated are dealt
with separately.
The experimental technique used has already been described.
Briefly, the time profile of the normalized thermal neutron flux is
obtained at selected positions by the integral count method of normal
ization and the epicadmium subtraction technique. Nineteen detector
positions were used for these measurements. For each pulse width two
runs were made at each position, except at the far end of the core where
data acquisition times became significantly longer. Most of the ex
perimental errors assigned to the data were obtained by analyzing the
results of these two measurements.
Following the nomenclature developed by Doshi and Miley [20] at
the University of Illinois, the delay times t^, the dynamic inverse
relaxation length k^, the asymptotic velocity of propagation v the
full-width at half-maximum (FWHM) of the propagating pulse and the
pulse shapes will be analyzed to describe the propagation character
istics of a neutron burst in the very close to critical assembly. The
experimental results are presented together with the calculated values.
It should be noted that practically all the figures showing the
pulse shapes were plotted using a Calcomp plotter which is part of the
IBM 1800 Computer facility in the Nuclear Engineering Sciences Depart
ment at the University of Florida. The data is plotted in a continuous
manner and the points are superimposed later for convenience.' Typi
cally the experimental pulse shapes were plotted from 333 time steps;
the corresponding calculational results have 231-245 time steps.


FLUX (RELATIVE UNITS)
FIG C31 TIME PROFILE OF THERMAL NEUTRON FLUX 142-09 CM FROM THE SOURCE
227


138
TABLE XI
CHANGES IN THE NUCLEAR PARAMETERS
DUE TO CHANGES IN THE TRANSVERSE BUCKLING
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
WIGLE X-Section
(cm )
Reactor
Height (cm)
Estimated
k ,,
eff
Vertical
Buckling
(cm-2)
S
70.0
.986
20.14
E-04
.054671
.12223
72.5
.988
18.78
E-04
.054526
.122207
76
.990
17.08
E-04
.054345
.12217
77.5
.992
16.43
E-04
.054277
.122158
80.0
.995
15.42
E-04
.054169
.122137
85.0
.998
13.66
E-04
.053981
.122096


40
total power of the assembly.
d. The fuel rod subjected to the specified highest specific power
is broken open and the fuel is completely fragmented, releasing 100% of
the gaseous fission products.
e. The iodine (in elementary form) diffuses uniformly throughout
the 18 x 32 x 15 room to calculate the on-site internal dose. The
off-site dose was calculated using the very conservative Pasqual's
principle of atmospheric diffusion.
The fission products inventory was calculated by means of the RSAC
code [9]. The results indicated that the iodine isotopes were the only
significant contributor to the inhalation dose. Using the active worker
breathing rate of 3.47 x 10 in /sec specified in 10 CFR 20, a person
remaining in the room would accumulate a thyroid dose of 0.023 mr for
each minute he remains in the room, after the hottest rod breaks open.
The total dose to a person that inhales all of the iodine contained in
the rod would be 0.2 r. The established radiation safeguards at the
University of Florida require the personnel to abandon the area imme
diately and notify the Radiation Safety Officer. The maximum time
required to evacuate the assembly and the fuel storage area is 10 sec
with 30 sec needed to evacuate the entire building; these times have
been measured during practice evacuation of the building.
The off-site total inhalation dose, calculated assuming the iodine
is released in one puff with zero wind velocity, cloud inverted con
dition, were typically:


210
200
190
180
170
160
150
O 0.5 msec input pulse width
O 1.0 msec input pulse width x)
'O
c/
/
/
/
X '
p
p"
if
/
/
9'
M M O* C?.. ' 1
__ .Q o
o o
-Q-
UFSA Ri Clean Core
12.72 cm between data points
? i ill I l
6 20 34 48
I I i 1 t ! I I I
62 76 90 104 118 132
Position Number
49 vs. AXIAL POSITION
178


53
components of the detector signal will actuate a wide band transistor
amplifier and tunnel diode discriminator from the secondary of the
transformer. A line driver buffer is also provided. The power and
control bias are provided by the ORTEC 403 Time Pickoff Control.
3. Modified ORTEC 403 Time Pickoff-Control
The 403 Time-Pickoff Control provides control and fan-out buf
fering for time derivation units such as the 260 Time Pickoff Unit.
The fan-out buffer Accepts the fast negative logic signal from the 260
unit and provides either fast negative or slower positive logic output
signals.
The 403 Time-Pickoff Control had to be modified to make its out
put signal compatible with the input requirements of the 212 Pulsed
Neutron Logic Unit used with the MCA. The 212 plug-in unit requires
pulses with rise times longer than 50 nsec while the positive output
from the 403 control unit has a rise time ~ 10 nsec. Furthermore, the
positive logic signal from the 403 control has a 0.5 microsec pulse
width which is too wide for the time resolution required. Therefore
2
two modifications were made: a capacitor (C12) was changed from 270
pf to 68 pf reducing the pulse width to 0.12 microsec and an inductor
coil (LI) was removed from the system changing the rise time to 50
nsec.
The modifications made the system compatible with the input
requirements of the MCA and avoided overdriving the analyzer.
2. Refer to ORTEC, Inc. "Instruction Manual for 403 Time-Pickoff
Control."


FLUX (RELATIVE UNITS)
FIG. 23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
110


Decay Constant (sec
FIG. 48 DECAY CONSTANT VS. AXIAL POSITION
177


84
Asymptotic Velocity of Propagation
The asymptotic velocity of propagation, v is defined as the
inverse of the slope of the delay time vs. distance curve in the
asymptotic region.
The Asymptotic Dynamic Inverse Relaxation Length
The asymptotic dynamic inverse relaxation length, k^, is defined
as the inverse of the distance required for the amplitude of the pulses
to attenuate by a factor e.
The Damping Coefficient of the Neutron Wave
The damping coefficient of the neutron wave, a, is a measure of
the exponential attenuation of the amplitude of the wave for a given
frequency. The damping coefficient is determined from the amplitudes
of the zeroth Fourier moment by numerical transformation for each
frequency of interest.
The Phase-Shift per Unit Length
The phase-shift per unit length of path, £, is determined from
the phase angles of the zeroth Fourier moment by numerical transforma
tion for each frequency of interest.
The damping coefficient and the phase shift per unit length of
path are the real and the imaginary components of the complex inverse
relaxation length, p, respectively.
It should be noted that in this work pulse and wave propagation
from the "conventional" viewpoint, i.e., propagation of a residual
disturbance rather than the propagation of a pulse or wave front, is
being studied.


FLUX (RELATIVE UNITE)
TIME (MSEC)
TIME FRCFILE CF THERMAL NEUTRON FLUX
FI CL- C6
B6-5S CM FROM THE SDJRCE
mu)


REGION NO.
1
2
3
A
5
6
MATERIAL NO.
2
1
1
1
1
1
NO. OF MESH POINTS
12
9
A
7
6A
1
MESH SIZE (cm)
.9916
1.0
1.179
1.8166
3.17905
2.777
MESH POINT NO.
DETECTOR POSITION
13
25
32
36
AO
AA
A8
52
56
60
6A
68
72
76
80
8A
88
92
96
NO.
6
13
20
27
3A
A1
A8
55
62
69
76
83
90
97
10 A
111
118
125
132
FIG. 21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE WIGLE CALCULATIONAL
SCHEME


FIG. 9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT


Amplitude (Relative Units)
FIG. 39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE -


FLUX (RELATIVE UNITS)
TIME (MSEC)
FIG* El
TIME PROFILE OF THERMAL NEUTRON FLUX
53*BS CM FROM THE SOURCE


APPENDIX B
DESCRIPTION OF THE COMPUTER PROGRAMS
UNIPUL
MORE
MORWIG
ALXILS
MULTIPLOT


Flux (Relative Units)
131
FIG. 31 AMPLITUDE ATTENUATION OF THE THERMAL NEUTRON FLUX
- 0.5 MSEC INPUT PULSE -


42
d. Violation by the facility operator of the administrative
procedures requiring a visual check of the assembly before start-up and
continuous attention to the control console instrumentation to determine
the status of the assembly at all times.
The consequences of such an accident were determined by assuming
the following:
1. The assembly is initially at a steady state power level of 10
watts (normal average power is .065 watt).
2. Water flows into the system at the maximum rate of 12 gpm.
3. The reactivity addition rate is 0.05 $/sec. This rate is
larger than the calculated rate (.04 $/sec) for the case discussed
above and more than that calculated to occur near critical for properly
loaded assembly.
4. The power scram is set, through calibration or other error, at
10 kw. Corresponding error settings occur for the neutron flux and
period scram.
5. A scram occurs 1 sec after a power level of 10 kw is reached.
This time has been determined as the elapsed time from the initiation
of a scram signal to the opening of the dump valves.
6. No feedback effects are considered. This is a good approxima
tion to our case due to the low power levels involved and again is a
conservative assumption.
The calculations were made using the IREKIN code, described in
reference [10]. IREKIN numerically solves the point model kinetics
equations.
Starting with the assembly one dollar subcritical (ke^ = .993),
and proceeding with the described excursion, the accident would yield


kg/£ (sec
FIG. 17B kg/i, AND k vs. MODERATOR LEVEL


173
looo
>
FIG. 47- THE UFSA R1 CORE p2 DISPERSION LAW


87
space dependent reactor transfer function, within the framework of a
combination of time-dependent Fermi-Age and diffusion thories.
A parallel field of study has been the neutron wave technique
[41, 42, 43]. A major improvement in the neutron wave field was
achieved when Moore proved [25] that the pulsed technique is equivalent
to the neutron wave method when the pulsed data is analyzed in the
Fourier transform plane. The work by Booth [26] confirmed this simpli
fying and time-saving approach to the powerful but time-consuming neu
tron wave measurements.
The study of multiplying media by neutron wave (or pulse) propaga
tion has not been developed as extensively as in non-multiplying media.
Brehm made a very elegant analysis of the problem, showing the excita
tion of slowing down modes whose relaxation lengths he was able to
compute [44]. Dunlap and Perez studied the dispersion law of a heavy
water-moderated, natural uranium assembly [45].
To date, no complete analysis of a pulse propagation experiment,
i.e., in the time and in the frequency domain is available in the
literature.
The WIGLE Calculational Scheme
The version of the WIGLE code used for the calculations performed
in this work is an IBM 360 version of the WIGLE-40 program described
by Radd [27]. The following description is extracted from Ref. 27.
WIGLE is a one-dimensional, two-energy-group, time-dependent dif
fusion program. It calculates the space-time behavior of the neutron
flux in a reactor during a transient. The calculation is restricted
to one-dimensional slab geometry with zero gradient or zero flux


FLUX (RELATIVE UNITS)
1-0
FIG* FI PROPAGATION OF A PULSE WIDER THAN THE SYSTEM PROPAGATION TIME
- EXPERIMENTAL -
254


FLUX (RELATIVE UNITS)
FIG' E2
TIME PRDFILE OF THERMAL NEUTRON FLUX
73-30 CM FROM THE SOURCE


LIST OF TABLES
TABLE Page
Ik vs. MODERATOR LEVEL OF UFSA REFLECTED
eff
CORES 7
II UFSA INSTRUMENTATION AND CONTROL 25
III SUMMARY OF 1/M AND PULSED MEASUREMENTS 74
IVINPUT PARAMETERS FOR THE WIGLE CALCULATIONAL
SCHEME 104
V TIME STEPS USED FOR THE WIGLE CALCULATIONS 106
VIDELAY TIMES MEASURED ACROSS THE WIDTH OF
THE CORE
- 0.5 MSEC INPUT PULSE 119
VIICLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
- 0.5 MSEC INPUT PULSE WIDTH 127
VIIICLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
- 1.0 MSEC INPUT PULSE WIDTH 128
IX ASYMPTOTIC PROPAGATION VELOCITY v 133
P
X DYNAMIC INVERSE RELAXATION LENGTH k, 134
a
XICHANGES IN THE NUCLEAR PARAMETERS DUE TO
CHANGES IN THE TRANSVERSE BUCKLING 138
XIITHE CALCULATED ASYMPTOTIC VELOCITY OF
PROPAGATION AND DYNAMIC INVERSE RELAXATION
LENGTH vs. CORE HEIGHT
- 0.5 MSEC INPUT PULSE WIDTH 146
XIII DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE 148
XIV DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE 149
XV PULSE SHAPES vs. INPUT PULSE WIDTH 151
xi


136
in which the largest number of counts was recorded and in many in
stances is not the best value for the location of the peak. The values
quoted in Tables VII and VIII represent refined values obtained by
inspection of the experimental data.
c) The Input Pulse Width
d) The Experimental and Theoretical FWHM
e) The Location with Respect to the Source is given in the
figure title.
A comparison between the theoretical and experimental pulse shapes
reveals the following:
a) Shapes agree very closely in the spatial region dominated by
the neutron source.. Small discrepancies start to show up near P41.
b) Past P41 the theoretical pulses become consistently narrower
than the experimental one. As discussed above, the other main charac
teristics describing the propagation of the pulses are well matched.
Discussion of the Clean Core Results
The fact that good agreement was found between the theoretical and
experimental results deserves some elabotation since the agreement may
seem fortuitous.
The calculational scheme used to obtain the WIGLE input parameters
is well established. The parameters are therefore considered to be as
reliable as the present state of the art permits. The main uncertainty
as far as the calculational model is concerned is in the allocation of
a transverse buckling.
To investigate the sensitivity of the two-group, one-dimensional
model to changes in the transverse buckling (incorporated into the
WIGLE scheme as a change in the absorption cross-section) a series of


FLUX (RELATIVE UNITS)
FIG- D12 TIME PRDFILE OF FAST NEUTRON FLUX 101-03 CM FROM THE SOURCE


FLUX (RELATIVE UNITS)
FIG* C21 TIME PROFILE GF THERMAL NEUTRON FLUX
15-71 CM FROM THE SCURCE


PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY


19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
Exp
O

s=
20
FIG. 45
Frequency
COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED (cx2-£2)
171


10
Mechanical Design
The entire assembly can be divided into three components: the
supporting platform and dump tank; the basic core tank and fuel rod
support structure; and the combination core side walls and side
reflector tanks.
The supporting platform is composed of 5 inch steel I-beams, raised
5 feet from the floor level by six steel columns 31/2 inches in diam
eter. The column footings rest within a 6x8x2 foot steel rank which
serves as a reservoir for the continuous water flow system and as a dump
tank. Under normal operating conditions, this represents a minimum
distance of about 4 feet between the bottom of the assembly and the
water surface in the reservoir. This distance is sufficiently large so
that the bottom of the assembly is considered to be unreflected under
all conditions.
All the core and reflector hardware is made of type 5456-H321
aluminum. The bottom of the basic tank is made of a 24x96x3/4 inch plate
bolted to the steel I-bean platform. The underside of the plate is
covered with a .030 inch thick Cadmium sheet. The lower fuel rod sup
port assembly rests on the plate. The end walls of the basic tank are
made of a 24 x 39 3/4 inch plate and are supported by two 2 1/2 x 2 1/2
x 1/4 inch steel angle braces welded to the I-beam platform. Two four-
inch aluminum channels span the eight foot dimension of the tank, con
fining the upper fuel rod support system and detector mounts.
The side walls of the basic tank serve also as reflector tanks when
the reflected cores are under study. These tanks have dimensions of
12 x 96 x 37 inches. The arrangement allows one to vary the width of the
core with a sole structural support.


FLUX (RELATIVE UNITS)
FIG* C13 TIME PROFILE DF THERMAL NEUTRDN FLUX 155-53 CM FROM THE SOURCE


92
by the pump or the low operating average power level of the system
( 0.13 watt). The large volume of circulating water aided in main
taining the temperature constant. In one 14-hour period of operation
the temperature change was about 1C.
The Epicadmium Subtraction Method
The use of a thermalizing tank and the cadmium difference method
is widespread for pulse propagation measurements. In the particular
case of the UFSA assembly this technique is not pertinent, since the
primary reason for the measurement was to test the analytical model
under stringent, viz. non-asymptotic, conditions; furthermore, with
the WIGLE model it is possible to account for the spatial and energy
dependence of the fast source rather well within a two-energy group,
slab geometry scheme. Therefore, no thermalizing tank was used and no
cadmium plate was inserted between the source and the assembly.
3
The He detectors used for the measurements respond to epicadmium
neutrons, although with decreasing efficiency of detection as the
neutron energy increases. Therefore, to obtain a true basis of compar
ison between the model and experiment, the contribution of the
epicadmium neutrons was subtracted from the time profile recorded by
the detector.
The thermal and epicadmium neutron time profiles measured in the
assembly do not differ significantly in shape in the asymptotic region
but show significant differences in the time scale, the relative atten
uation and the shapes near the source. Although the detectors used
are about ten times more efficient for detecting thermal neutrons, the
epicadmium flux is much larger than the thermal flux throughout the
system and, in particular, close to the source. Therefore, the


GRID POSITION
WEIRS
FIG. 15 DETECTOR POSITIONING SCHEME


70
locations employed for these measurements and for the absolute
determination by pulsing. Two 1 cu, centrally located Pu-Be sources
were used for these measurements.
The measurements were performed in the following sequence:
a) Unmultiplied counts vs. water level were obtained from a water
level of 20 cm to 91.4 cm above the bottom of the active fuel in steps
of 5 cm.
b) The fuel was loaded in the assembly in the presence of two
centrally located Pu-Be sources, with proper monitoring.
c) Multiplied counts vs. water level were obtained from a water
level of 20 cm in 5 cm steps until an effective multiplication factor
<_.99 was reached. This procedure follows the criteria established for
Initial Loading of the assembly, Part 2, Chapter III of this work; the
5 cm steps were more conservative increments than those specified for
the Initial Loading of the assembly.
The results of these measurements are shown in Figs. 16 (A, B).
All the curves were well behaved in the sense that none "nose-dived."
Position 2 and 4 failed to properly describe the multiplication of the
assemblies because of their nearness to the source. Position 1 seems
to overestimate the multiplication, mainly because the unmultiplied
count rate was extremely low at this position thus an apparently high
ratio of multiplied/unmultiplied counts was obtained. A detector more
sensitive to high energy neutrons was used in locations 1 and 6.
It should be noted that when the inverse multiplication is plotted
2
vs. 1/H the predictions become quite linear much earlier than when
2
plotted versus H. Better predictions are therefore made with the 1/H
curves but the approach can become less conservative by underestimating


151
TABLE XV
PULSE SHAPES VS. INPUT PULSE WIDTH
UFSA Rl Core
0.5 H/W Ratio
16.35 cm wide reflected
core
INPUT PULSE
PEAK AT
FWHM
WIDTH (msec)
(msec)
(msec!
.1
2.53
3.75
.5
2.65
3.69
1.0
3.04
3.69
2.0
3.79
4.20
3.0
4.39
4.68
4.0
4.72
5.28
5.0
6.02
5.95
6.0
6.97
6.70
7.0
7.67
7.40
8.0
8.62
8.30
9.0
9.67
9.20
10.0
10.22
10.5


Amplitude (Relative Units)
160
FIG. 38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE -


30
moderated reflected slab of 10.44 cm is obtained consistent with the
10.4 cm value.
Thus the slab width of 9.46 cm proposed by us compares favorably
from the safety viewpoint with the safe width for an infinite, water
moderated and reflected slab and is considerably narrower than the safe
width for an infinite, water-moderated and unreflected slab. Within the
present context it should also be pointed out that as indicated on page
54 of the Design and Hazards Report [3], no flooding of the storage area
seems possible from natural causes.
Neutron Sources
Two types of neutron sources were used throughout this work.
1) Two Pu-Be sources mounted in an aluminum cylinder which can be
driven remotely through a plastic pipe from a shielded box located in
one corner of the facility room to underneath the center of the core.
Neon lights provide indication at the console of the position of the
sources. These sources, which have a combined yield of 3.2 x 10^
n/sec are used for start-ups and for the inverse multiplication meas
urements .
2) A Texas Nuclear Neutron Generator which is used in continuous
mode for static measurements and in the pulsing mode for the pulse
propagation measurements. The generator is of the Cockcroft-Walton
type, TNC Model 150-1H with continuously variable high voltage from
0-150 kv and has been modified to obtain larger currents by removing
the einzel lenses and installing a new 22 electrode accelerator tube and
gap lense. Pre- and post-acceleration beam deflection produces sharp,
low-residual pulses.


43
a peak power of 69 kw, the total energy release is 0.5 Mwsec. The
power vs. time behavior of the assembly for the postulated power excur
sion is shown in Fig. 9.
The combined neutron and gamma dose to the operator is 1.5 rem
*
assuming that: the energy release is instantaneous, all neutrons have
an energy of 1 MeV and there is no attenuation in the assembly. The
proper RBE factors were taken into consideration.
It is concluded that, even if such an improbable accident would
occur, the hazards to personnel and the general population are not
significant.


88
boundary conditions. Up to six delayed neutron groups can be con
sidered in the calculations. The feedback subroutine may be used to
introduce arbitrary changes in the reactor parameters, either for
inherent feedback or for other time-dependent variations.
The basic equations solved by the WIGLE program are as follows:
D1 v*l Z1 h + X1 (vi:f *1 + vZf2 4>2) (1 Y1B)
1 1 3*1
+ E i + si = ^-ir
1=1 1
(1)
VD2 V2 E2<*>2 + x2 ^vEf1 ^1 + vZf2 ^ y2B^
1 i 92
+ S + Cl 6) C2iXi + S, = (2)
3C
Xi Cli + Y1 Bi vEfl *1
li
3t
3C
Xi C21 + Y2 Bi vEf2 ^2 = "3t
2i
(3a)
(i = 1, 2, ..., I)
(3b)
The number (I) of delayed neutron groups may be 0, 1, or 6. 6 can
be 1 or 0. When 5=1 and = y2> these equations are the conventional,
two-group, time-dependent diffusion equations. .
The time-dependent equations, and those equations necessary to
represent the inherent feedback effects if they are considered, are
reduced to finite (time) difference equations and numerically solved.
WIGLE can handle up to 60 regions, 251 mesh, points and 999 time steps.


145
evaluation of the nuclear parameters.
The asymptotic propagation velocity and dynamic inverse relaxation
length as a.function of core height ar shown in Table XII. As ex
pected, the velocity of propagation and the attenuation decrease as
criticality is approached.
The above analysis puts the good agreement between experiment and
theory on a firmer footing. When the observed phenomenon is very sen
sitive to small variations in system characteristics the probability
that fortuitous agreement may be obtained between theory and experi
ment diminishes with the degree of sensitivity.
Comments on the Fast Group Results
The following comments are pertinent regarding the fast group
results as calculated by the two-group WIGLE model:
1. The curve of delay times vs. distance remains flatter than
the corresponding curve for the thermal group near the source region;
it then bends rapidly to yield the same asymptotic velocity of propaga
tion as that of the thermal group.
2. The fast group flux peaks between positions P6 and P13; this
has been confirmed experimentally. In contrast the thermal group flux
peaks at P6. The asymptotic inverse relaxation length of the fast
group is, as expected, identical to the one determined for the thermal
group.
3. The fast group pulse profiles are slightly wider than those
for the thermal group.
The time profiles from the cadmium-covered detector measurements,
which were used to determine the thermal group pulse profiles by the
epicadmium subtraction method were compared with the calculated fast


155
distance of 5 cm from the outer wall. At the far end of the assembly
the reflected pulse "propagated" into the assembly, attenuating and
dispersing with distance to the end wall. This pulse quickly dissi
pated into the.assembly with no significant effect on the measurements


APPENDIX D
UFSA R1 CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX
AT SEVERAL CORE POSITIONS
FOR INPUT PULSES OF 0.5 AND 1.0 MSEC


190
N0G ( Ef)i<¡>i(r)
s(r) = z L-
i=l X
where X is the eigenvalue. The code then sets and solves a set of
finite difference equations.


Water Level Above Weir Apex (cm)
Flow Rate (gpm)
FIG. 5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE WEIR APEX


APPENDIX A
CALCULATIONAL PROCEDURES USED IN THE
DETERMINATION OF THE NUCLEAR PARAMETERS
AND THE k VALUES
eff


FLUX (RELATIVE UNITS)
FIG* C36 TIME PROFILE OF THERMAL NEUTRON FLUX E0G-4S CM FROM THE SOURCE
232


FLUX (RELATIVE UNITS)
1-0
0*9
0-E3
0-7
0-G
0 *5
0-4
0-3
ft
I
0-
0-1
T
0
3
3 4
=F
5
RIFS 30-1
PEAK AT 0-430 MSECS
pulse: width = o-s msecs
THEORY FWHM = 0-747 MSEC
EXP- FWHM = 0-750 MSEC
to
OJ
0
9
f
10
TIME (MSEIO
FIG- D2
TIME PROFILE OF FAST NEUTRON FLUX 38-43 CM FROM THE SOURCE
UVJ1


FLUX (RELATIVE UNITS)
FIG* C37 TIME PROFILE OF THERMAL NEUTRON FLUX 219*17 CM FROM THE SOURCE
233


54
4. Technical Measurement Corp. 1024 Multichannel Analyzer
(MCA) and Data Handling Units
The time analysis of the pulse and the corresponding data output
are obtained from the following coupled instrumentation:
Pulsed Neutron Logic Unit, TMC Model 212
Digital Computer Unit, TMC Model CN1024
Data Output Unit, TMC Model 220C
Digital Recorder, Hewlett-Packard Model 561B
Binary Tape Perforator, Tally Model 420
A trigger from an external pulse generator starts the sweep of the
analyzer as controlled by the pulsed neutron logic unit and initiates
the burst at the accelerator. The 212 has variable channel widths from
10 to 2560 microsec. The full 1024 channels were used in all the meas
urements. The storage capacity of the CN1024 is 2^ counts. Both
printed paper tape and perforated binary tape were obtained as output.
5. ORTEC 430 Scaler
For some of the flux traverses and the 1/M measurements, the
integral counts were recorded in a 10 Mhz scaler.
The normalizing detector data acquisition system (NDDAS) consists
of the same components as the movable detection system except that a
256 multichannel analyzer, TMC Model CN110 was used for data handling
and the integral counts were accumulated in an ORTEC 429 Scaler, modi
fied for 7 Mhz counting rate.
The Resolution Time Correction
The resolution time of the pulsed neutron data acquisition system
was the parameter under consideration while searching for a well-matched


FLUX (RELATIVE UNITS)
FIG* C19 TIME PROFILE OF THERMAL NEUTRON FLUX 031-QQ CM FROM THE SOURCE


104
TABLE IV
INPUT PARAMETERS FOR THE WIGLE
CALCULATIONAL SCHEME
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
CORE
Region Regions
1
2,3,4,5,6
ALUMINUM
WATER
D^(cm) 1
.5211
1.06379
1.9338
1.1370
EaiCcnf1)
.055588
.054350
.000228
.000589
Ir^(cm
.02116
.025224
.000159
.0483
vEfl(cm-1)
.003247
.007337
.00
.00
D2(cm-^)
.2895
.20809
3.6078
.14938
Ia2(cm-1)
.4234
.12217
.01048
.019242
vlfzicm-^)
.10027
.22662
.00
.00
[l/v^3(cm ^sec)
5647E-7
3324E-7
[l/v2](cm "'sec)
.3324E-7
.3324E-5
Note: Thermal group
: 0-0.53
ev

Fast group:
0.53 ev
- 10.0 MeV
V


78
Garelis-RusseHtechnique to a reflected slab assembly when proper care
is taken. Agreement between calculated and experimentally determined
values of the reactivity is termed excellent but since only one case
has been studied judgement on the overall applicability of the technique
to this type of reactor configurations should be reserved until the
other assemblies to be studied in the UFSA facility are duty analyzed.
It should be pointed out that multiple detector positions are necessary
to establish when an asymptotic decay constant is obtained, and that the
value of k£/Jl is affected by the input pulse width. As mentioned previ
ously, a more detailed analysis of the pulsed neutron reactivity meas
urements is conducted later in this thesis.


5 (rad/cm)
169
FIG. 44 THE UFSA R1 CORE p DISPERSION LAW


CHAPTER VII
CONCLUSIONS
The space-time kinetics behavior of a large-in-one-space dimension,
side-reflected, highly multiplicative (k^^ ~ 0.99) subcritical assembly
has been studied by the use of the pulse propagation technique. The
experimental results were used to test the predictions of the one
dimensional two-group, space-time diffusion theory calculational scheme
(WIGLE). The analysis of both the theoretically predicted and experi
mentally measured results was performed in the time as well as the fre
quency domain.
The comparison of theory and experiment in the time domain shows
good agreement. WIGLE accurately predicted the delay times and the
attenuation of the peak of the pulse when a first flight kernel was used
to describe the spatial distribution of the fast source. At large dis
tances from the source the time profiles predicted by WIGLE are con
sistently narrower than the measured pulse shapes. The sensitivity of
the one-dimensional model to small changes in the transverse buckling
was studied; WIGLE (and experiment) showed a large sensitivity to these
changes. These results point to the necessity of obtaining the best pos
sible estimate of the nuclear parameters to be used in space-time ki
netics calculations.
The comparison of theory and experiment in the sensitive frequency
domain confirms the good agreement found in the time domain. The
185


CHAPTER III
OPERATIONAL SAFETY
Introduction
The University of Florida SPERT Assembly, due to its large size,
enriched uranium-oxide fuel and nuclear potentialities required a
thorough study of its capabilities, operational characteristics, initial
loading procedures and of the behavior of the assembly under accident
conditions. The study was part of the requirements established by the
Division of Material Licensing of the USAEC prior to the granting of an
operating license.
Legally, a subcritical assembly has to comply with regulations
under 10 CFR Part 70 "Licensing of Special Nuclear Materials" since no
self-sustaining nuclear reaction is envisioned. In the case of the
UFSA, however, the Commission felt that certain technical sections of
10 CFR Part 50, which deals with nuclear reactor licensing, should apply
and serve as a guide for the design and the safety analysis.
The basic philosophies employed in the design of the system were:
a) The UFSA facility has been designed to remain subcritical under
normal operating conditions.
b) The safety instrumentation (see Part 1, Chapter I) has been
designed such that a single failure will not invalidate both the manual
and automatic scram and will not cause subsequent failures.
c) The design basis accidents were postulated on a single failure
32


FLUX (RELATIVE UNITS)
TIME (MSEC)
TIME PROFILE OF FAST NEUTRON FLUX 53-SB CM FROM THE SOURCE
FIG* D9
(JILO


40
30
20
10
58
Conventional
24 32
Channel Number
IG. 13 TIME PROFILES OF NEUTRON BURST RECORDED BY CONVENTIONAL
ELECTRONIC INSTRUMENTATION AND BY THE TIME-PICKOFF SYSTEM


FLUX (RELATIVE UNITE)
FIG. 273 EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE TJFSA R1 CORE
123


FLUX (RELATIVE UNITS)
FIG* D8
TIME PROFILE OF FAST NEUTRON FLUX 41*15 EM FROM THE SOURCE
243


22
Instrumentation and Interlock System
The instrumentation and interlock system of the UFSA has been
discussed extensively in the reports submitted to the Atomic Energy
Commission [3, 4, 5] in conjunction with the license application. More
recently, Mr. L. B. Myers submitted a detail technical report on the
subject [6]. A brief descriptive explanation is given below.
A block diagram of the safety system logic flow in use at the UFSA
subcritical assembly for routine monitoring is shown in Fig. 8. There
are five principal channels of instrumentation:
3
a. Start-up channel using a He proportional counter, scaler, and
rate meter. The counter is located at the bottom of the core, close to
the geometrical center of the assembly.
b. Log power and period instrument No. 1 channel using a compen
sated ion chamber (operated uncompensated) as a signal to a Log N
amplifier. The chamber is located along the longitudinal axis of the
assembly, on the bottom of the core some two feet from the neutron
generator end.
c. Period instrument No. 2 channel using a compensated ion chamber
(operated uncompensated) as a signal to a log N amplifier. The chamber
is located along the longitudinal axis of the assembly, on the bottom
of the core, some six feet from the neutron generator end.
d. Linear neutron flux No. 1 channel using an uncompensated ion
chamber as a signal to a micromicroammeter. The chamber is mounted on
the top core support frame, close to the geometrical center of the core.
e. Linear neutron flux No. 2 channel using a compensated ion
chamber (operated uncompensated) to feed a signal to a micromicroammeter.
The chamber is mounted on the top core support frame on the opposite


CHAPTER II
THEORETICAL NOTES
Introduction
The main concern of this work has been the experimental investiga
tion of space-time kinetics effects on a large core subjected to a
perturbation; the basic aspects of the neutron physics phenomena were
studied. The analysis of the experiment has been conducted in both
the time and the frequency domain. The theoretical model used for
comparison with experiment, in the time and the frequency domain, was
the two-group, space-time dependent diffusion equations numerically
solved by the WIGLE code [24]. A one-to-one comparison of theory and
experiment was performed in the time domain. For the corresponding
study in the frequency domain both the WIGLE and experimental time
profiles as a function of position were analyzed into its wave compo
nents by a numerical Fourier transformation; this method was suggested
by Moore [25] and confirmed by Booth [26]. In this work only the
zeroth Fourier moment is analyzed; the amplitude and phase angle of
the zeroth Fourier moment correspond to those measured by the conven
tional neutron wave experiment.
Review of the Literature
A considerable amount of theoretical effort has been devoted to
the space-time kinetics problem in nuclear reactors. The more important
85


FLUX (RELATIVE UNITS)
FIG- C18 TIME PROFILE OF THERMAL NEUTRON FLUX 219-17 CM FROM THE SOURCE
214


FLUX (RELATIVE UNITS)
FIG- C38 TIME PROFILE OF THERMAL NEUTRON FLUX E31-8B CM FROM THE SOURCE
234


61
The Normalization Technique
The analysis of a pulse propagation experiment will yield informa
tion on the velocity of propagation, the attenuation and pulse shape as
a function of position of a propagating disturbance. To determine the
attenuation or relative amplitude of the pulse at different positions
in an assembly, the data must be normalized to a fixed reference so
that variations in the source strength, data acquisition time, etc.,
can be properly accounted for. The usual technique requires accumulating
integral counts in a scaler for each measurement and reducing all meas
urements to the fixed reference afterwards. As was mentioned previously,
the resolution time correction can have a significant effect on the nor
malizing factor since widely differing count rates are employed. It is
extremely hard, if not impossible, to obtain a proper resolution time
correction based on integral counts determined from a time-varying count
rate.
Two methods of normalization and their relative merits are discussed
below.
The Integral Count Method is the normally employed method of nor
malization. The total counts accumulated with the NDDAS for all runs
is referred to a predetermined one, with the normalizing detector in a
fixed position while the movable detector changes position.
The Analyzer Method, which is essentially the same as the above
except that the counts arising from the normalizing detector are stored
as a function of time in a multichannel analyzer. The average of a
series of ratios obtained by dividing the corrected channel counts by
the corresponding channel counts of a predetermined measurement gives
the normalizing factor.


175
yielded the decay constants at different times after the pulse and
computed a value of p ($), as well as absolute p and k^^ using a
calculated fc>ef£ for each decay constant.
The Decay Constant
A series of decay constants were obtained by analyzing the tail
of the pulse at increasing times from the peak. The convergence of the
decay constant in time was sought, before background is reached, and
the value that gave the least deviation according to Peierls statis
tical analysis was considered to give the decay constant at that posi
tion.
The decay constants determined close to the source decreased
monotonically as the fitting was performed farther away in time from
the peak. Once the "asymptotic" source region, as defined in the pulse
propagation measurements, was reached, an apparent decay constant was
found at each position. This decay constant is observed to converge
or to vary very slowly with respect to time and decreased in magnitude
as the distance to the source increased. At large distances from the
source a fundamental decay constant is observed, seemingly when an
asymptotic distribution of the neutrons is established in the assembly,
more than 9 msec after the burst.
An analysis of the time-space behavior of the neutron flux (ref. .
Fig. 28) reveals that, indeed, more than 9 msec are required for the
assembly to achieve an asymptotic neutron distribution. Therefore,
only at large distances from the source can a true fundamental decay
constant be measured; prior to P83 (142.9 cm) background is reached
before a uniform spatial distribution is established.


FLUX (RELATIVE UNITS)
FIG- C22 TIME PROFILE OF THERMAL NEUTRON FLUX
2B-43 CM FROM THE SOURCE
218


UX (RELATIVE: UNITS)
FIG C4 TIME PROFILE OF THERMAL NEUTRON FLUX 4115 EM FROM THE SOURCE


24
side from the linear channel No. 1.
Items a. through d. are part of the safety amplifier while item f.
is used to display the neutron flux on a console front panel meter.
The safety amplifier monitors the seven continuously varying input
signals and provides a trip signal if any of the input signals fall
outside of acceptable limits. The safety amplifier provides means of
adjusting these limits over a wide range.
The duality of the scram action (see Fig. 8) is a prominent feature
of the safety system. It can be said that no single failure will
invalidate both automatic scram channels. Furthermore, it has been
determined that no single failure can invalidate both the manual and
automatic scrams. The method of measurement and the function of each
instrumentation and safety channel are shown in Table II (parts A and B).
A series of safety interlocks prevent water from flowing into or
remaining in the assembly unless a proper sequence of events are fol
lowed and certain conditions are satisfied. The conditons are:
a. The moderator temperature must be >_ 60F. This is established
by the desire to obtain the experimental data near room temperature con
ditions. The insertion of water at 32F will introduce a maximum k of
.00342 (based on the calculated negative temperature coefficient of
reactivity) above the design k^^ value with no hazards created.
b. The four instrumentation channels must have their high voltage
on.
c. The core width must be smaller than 26 cm.
d. The door to the assembly room must be locked.
e. The start-up channel must count more than 2 counts/sec.
f. The neutron flux, subcritical assembly power level and period


CHAPTER I
INTRODUCTION
The development and construction of large power reactors focused
the attention of industry and of the United States Atomic Energy Com
mission on the necessity of having reliable reactor dynamics analysis
methods to accurately describe the spatial and temporal behavior of the
neutron flux in these systems. The point-model reactor kinetics calcu-
lations seem to have been adequate for the gross evaluation of the time-
dependent neutron flux during the occurrence of a transient but the
model can be in large error when the physical size of the system and the
magnitude of the perturbation necessitates that spatial effects in the
redistribution of the neutron flux be considered. Preliminary calcula
tions done by Johnson and Garner using a one-dimensional space-time
kinetics model [1] showed that the space-time dependent scheme predicts
a "destructive zone" much larger than that predicted by point-model
kinetics.
The necessity of experimentally determining the validity of the
various space-time kinetic analysis methods was brought out by Johnson
and Garner [1], and recognized by the USAEC in establishing the Large
Core Dynamics Experimental Program. The primary responsibility for this
program has been vested in the Nuclear Safety Research Branch, Atomic
Energy Division, Phillips Petroleum Company as major contractor for
USAEC.
2


FLUX (RELATIVE UNITS)
FIG- C25 TIME PROFILE OF THERMAL NEUTRON FLUX
EG-58 CM FROM THE SOURCE
221


- 14
ALUMINUM SUPPORT
FIG. 3 TOP FUEL ROD SPACING SYSTEM


35
Operating Limits
A description of the operating limits of the subcritical assembly,
including the basis for such limits ate listed below.
Effective Multiplication Factor
Specification: the maximum allowable will be 0.985+.005.
The absolute value of k as well as the slope of the k vs. water
eff r eff
height will be carefully measured so as not to exceed the limiting value.
Basis: the upper limit of kg^^ = 0.985+.005 is established by:
the accuracy with which k^^ can be measured, the reported [7] differ
ences between calculations and experiments in similar cores and the value
of the multiplication factor required to make a meaningful study of the
dynamic properties of large cores. Comparison [7] between 29 calcula
tions and the corresponding critical experiments (on cores similar to
the UFSA) established that an overestimate of kg^^ is generally made; the
standard deviation for these cases was + 0.00175 and the maximum under-
stimate of the multiplication was for a case yielding kg^^ = 0.9966, a
0.34% deviation.
The absolute value of k will be determined for water levels
eff
yielding a k^^ >.95 by pulsed techniques independently of the inverse
multiplication measurements. The method to be used is the Garelis-
Russell[8] method which, when appropriate corrections are made for the
reflector, has been shown to give good results. In this method both
l-keff(l-$) keff8
a = and are determined; then ke££ may be. obtained by
independently obtaining B or L Since of the two parameters 8 changes
the most slowly with k^^, it is valid to use a value based on theoret
ical calculations.


FLUX (RELATIVE UNITS)
FIG C14 TIME PROFILE OF THERMAL NEUTRON FLUX IBS-31 CM FROM THE SOURCE


133
"asymptotic region of the assembly. In this region a linear rela
tionship between delay times and distance from the source exists.
The asymptotic velocity of propagation for the clean UFSA core is
given in Table IX.
TABLE IX
ASYMPTOTIC PROPAGATION VELOCITY v
P
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm reflected core
Input Pulse
Width (msec)
Theory
vp (m/sec)
Experiment
0.5
456
448+9
1.0
456
452+7
It should be mentioned that the asymptotic velocity of propaga
tion is independent of the assumed distribution of the source. When
a localized source in space was introduced into the WIGLE scheme the
results yielded the same asymptotic velocity as the calculations with
a spatially distributed source. This is to be expected since v^ is a
characteristic of the system and has been defined in a region removed
from source effects.
The Dynamic Inverse Relaxation Length
. The dynamic inverse relaxation length, k^, is defined as the
inverse of the distance required for the amplitude of the pulses to
attenuate by a factor e. is determined by the relationship between
the logarithm of the magnitude of the peak of the propagating pulses
and distance in the "asymptotic" region where this relationship is
linear.


Flux (Relative Units)
140
FIG. 34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED BY
THE WICLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS


TABLE OF CONTENTS (cont'd)
Operating Limits
Design Basis Accident Analysis
CHAPTER IV THE DATA ACQUISITION SYSTEM
Introduction .
The Neutron Detector
The Electronic Instrumentation
The Resolution Time Correction ..
The Normalization Technique
Comments
CHAPTER V NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL
Introduction
Theoretical Notes
Inverse Multiplication Measurements
Absolute Determination of k
eff
Conclusions
Page
35
39
45
45
47
50
54
61
62
64
64
64
68
73
75,
PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY 79
CHAPTER I INTRODUCTION 80
Statement of the Problem 80
Description of the Study 81
vii


FLUX (RELATIVE UNITS)
FIG- C34 TIME PROFILE OF THERMAL NEUTRON FLUX 181-03 CM FROM THE SOURCE
230


125
e
!=>
0)
>
te
t-H
Pi
X
d
iH
tn
Position Number
FIG. 28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE


UX (RELATIVE UNITS)
FIG- C8
TIME PROFILE GF THERMAL NEUTRGN FLUX
35"01 CM FROM THE SOURCE


17
an automatically operated pneumatic control valve. A plot of the flow
rate versus the height of the water level above the apex of the weirs
is shown in Fig. 5.
The weir plate is rigidly mounted on a "box" or small tank (see
Fig. 6). The weir "box" is connected to a drive mechanism composed
of the following: guide post, slide block, and drive screw. The guide
post is a 2 inch diameter pipe attached to the support column of the
crane which is used for removal of the reflector tanks. The "box" is
mounted on the guide block which slides along the vertical post and
provides a rigid support for the system and is driven up and down by
means of the drive screw which is fixed at the top of the guide post
support and passes through the guide block. The upper limit of the
position of the weir"box"is controlled by mechanical stops whose posi
tion is determined as part of the initial start-up procedure for each
configuration to be considered.
The final adjustment of the position of the weir"box"is such that
when the water reaches the moderator level in the assembly corresponding
to *99 for a given configuration it will be flowing about 2.0
inches above the apex of the V-notch weirs. At this design level the
flow rate is ~ 7 gallons per minute with the k^^ values as given in
Table I for the full fuel loading. After the operating height of the
weir box has been determined for kg^^ <^0.99 in the initial start-up,
stops are inserted to prevent raising the weirs above this height (if
the height is less than the active fuel height). It should also be
pointed out that the orifice in the line limits the pump capacity to a
flow rate which is just sufficient to bring the weirs to full flow. A
further increase in flow rate would cause discharge over the entire


9
8
7
6
5
4
3
2
1
O
163
Position Number
. 41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE -


TABLE OF CONTENTS (cont'd)
Page
Nomenclature Used in the Description of
Pulse Propagation Phenomena 83
CHAPTER II THEORETICAL NOTES 85
Introduction 85
Review of the Literature 85
The WIGLE Calculational Scheme 87
Neutron Wave Analysis 89
CHAPTER III DESCRIPTION OF THE MEASUREMENTS 91
Introduction 91
The Epicadmium Subtraction Method 92
The Geometrical Arrangement 94
Synopsis of the Measurements 97
CHAPTER IV EXPERIMENTAL AND THEORETICAL RESULTS IN THE
TIME DOMAIN 100
The Analytical Model 100
Flux Traverses 109
Clean Core Pulse Propagation Measurements 118
Propagation of a Narrow Pulse 147
Propagation of a Wide Pulse 148
Pulse Shape vs. Input Pulse Width 150
Effect of Room Return at Peripheral Detector Positions 152
viii


FLUX (RELATIVE UNITS)
1-0
0*3
0-E3
0*7
0-S
0*5
0-4
0*3
0-3
0-1
RIFS 41-1
PEAK AT 0-340 MSECS
PULSE WIDTH =0-5 MSECS
THEGRY FWHM = 1-7BS MSECS
EXP- FWHM = 1*710 MSECS
to
u>
MO
10
TIME (MSE:C)
TIME PROFILE OF FAST NEUTRDN FLUX 66-5B CM FRDM THE SOURCE
FIG- D4


TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
PREFACE V
LIST OF TABLES xi
LIST OF FIGURES xiii
LIST OF SYMBOLS xviii
ABSTRACT xix
i '
PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
- DESIGN AND CALIBRATION 1
CHAPTER I INTRODUCTION 2
CHAPTER II DESCRIPTION OF THE FACILITY 5
General Features .. 5
Fuel Characteristics 9
Mechanical Design 10
Moderator Flow Control System 15
Instrumentation and Interlock System 22
Fuel Storage 27
Neutron Sources 30
CHAPTER III OPERATIONAL SAFETY 32
Introduction 32
Initial Loading 33
vi


FLUX (RELATIVE UNITS)
FIG- D5
TIME PROFILE OF FAST NEUTRON FLUX 79-30 CM FROM THE SOURCE
240


99
the Johnson criterion [25] a wide, 10 msec square pulse was introduced
into the assembly. Three selected positions were used for these meas
urements.
Pulse Propagation vs. Pulse Width
During the experimentation described above, the observation was
made that narrow input pulses will yield the same pulse shape in the
asymptotic region, with the peaks displaced in time. To gain an
insight into this predicted occurrence, measurements were taken at one
detector location (P83) with input pulse widths of 0.1, 0.5, 1.0, 2.0,
3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 and 10.0 msec.
Effect of Room Return at Peripheral Detector Positions
The effect of neutrons reflected from the concrete walls on the
measurements was investigated by recording pulse shapes at peripheral
detector positions. The measurements were done with and without a
shield of borated paraffin in the region in which the detector was
located.


FLUX (RELATIVE UNITS)
FIG- C28 TIME PROFILE OF THERMAL NEUTRON FLUX 104-73 CM FROM THE SOURCE
224


:~LUX (RELATIVE UNITS)
R1REFREF7G
PEAK AT 0-4S0 MSECS
PULSE WIDTH = 05 MSECS
EXP" FWHV1 = 0-570 MSECS
UNSHIELDED SHIELDED
M
Ui
-C~
4

3 4 5 S 7
a
8
CJ
10
TIME (MSEC)
FIG- 37B EFFECT DF ROOM RETURN AT PERIPHERAL DETECTOR POSITIONS


63
microsec or longer are stable.
B) The address current setting of the CN1024 is extremely criti
cal, markedly so for high count rates.
C) An optimum pulse into the analyzer should have a rise time of
50 nanosec, a total width of .1 microsec and an amplitude of 3-5
volt.
D) Above noise level, the discriminator setting of the 212 logic
unit becomes irrelevant when a constant pulse height is used as input.
E) Reproducibility tests were performed on the analyzer with the
neutron generator in continuous mode.
The statistical analysis of the channel counts gave:
72% were less than 1 from the mean
25% were between 1 and 2 from the mean
3% were between 2 and 3 from the mean
The system is statistically well-behaved.


189
UFSA R1 CORE PARAMETERS
0.5 M/W ratio
16.35 cm wide reflected core
Group
1
2
3
4
D
1.6079
0.94239
0.61401
0.20809
^a
0.0035411
0.0023701
0.23109
0.20809
Zr
0.090927
0.096727
0.084015
_
vlf
0.0068929
0.0012609
0.015301
0.22662
1/v
5.25 Ox 10-10
2.637 x 10"9
1.843 x 10~7
3.324 x 10"6
_3
Void Coefficient of Reactivity: 3.14 x 10 Ak/% void
Temperature Coefficient of Reactivity: 1.03 x 10 ^ Ak/C
Determination of k
eff
Using the constants tabulated above, eigenvalue calculations were
performed with the AIM-6 computer code [53].
' AIM-6 is a multigroup, multiregion, one-dimensional diffusion
theory code that has been widely used for criticality calculations.
The code will handle as many as 18 energy groups, 101 space points
and 20 regions. Basically, the code solves the equation
- D^Vir) + 4 4(r) = x^ir) + ^ E j+i j(r)
i J-q s
1 < i < NOG < 18. NOG = number of groups
The symbols follow conventional notation and
X* = the integral of the fission spectrum over the lethargy range
represented by group i.


97
penetrated 10 cm into the core. The purpose of this arrangement was
to increase the solid angle subtended by the target in the assembly to
augment the number of neutrons going into the system and to reduce the
number of unscattered fast neutrons dispersing into the room and
creating a shielding problem.
Synopsis of the Measurements
Flux .Traverses
A series of flux traverses were done on the assembly to determine
the flux shapes across the width and the height of the assembly. The
traverses were done dynamically and statically.
Static traverses were performed with Indium foils at a distance of
66.6 cm from the neutron source. Measurements were done on the width
and height of the assembly with the neutron generator in the continuous
mode for a period of 6 hours to achieve the saturation activity of the
foils. The foils were 5 mil thick, 7/16" in diameter, and 99.97+%
Indium.
Dynamic traverses were performed across the width of the core at 41,
54, 130 cm from the neutron source with the generator in the pulsing
mode to determine whether any propagation occurs in the tranverse
3
direction. The long He detectors were used for the measurements,
which employed pulse widths of 0.5 and 1.0 msec as input.
Clean Core Pulse Propagation Measurements
A whole series of measurements using narrow, square, fast bursts
of neutrons as a disturbance were carried out to determine the most
important characteristics of the pulse propagation phenomena. Most
of the measurements utilized the entire length of the assembly. Certain


LIST OF FIGURES (cont'd)
FIGURE Page
46 COMPARISON OF THE THEORETICALLY PREDICTED
AND THE MEASURED 2 a F, ... 172
47 THE UFSA R1 CORE p2 DISPERSION LAW 173
48 DECAY CONSTANT vs. AXIAL POSITION 177
49 kB/A vs. AXIAL POSITION 178
50 REACTIVITY (-$) k f vs. AXIAL POSITION 182
Cl Through C19 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE
CORE FOR A 0.5 MSEC INPUT PULSE 195-213
C20 Through C38 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE CORE
FOR A 1.0 MSEC INPUT PULSE 214-232
Dl Through D6 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 0.5
MSEC INPUT PULSE 234-239
D7 Through D12 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 1.0
MSEC INPUT PULSE 240-245
El Through E4 TIME PROFILES OF THERMAL NEUTRON
FLUX AT FOUR POSITIONS IN THE CORE FOR A 0.1
MSEC INPUT PULSE 247-250
FI TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A 10.0 MSEC INPUT PULSE 252
G1 Through G2 SHAPE OF THE PROPAGATING PULSE AS A
FUNCTION OF PULSE WIDTH 254-255
xvii


66
[13], Gozani's extrapolated area-ratio analysis [14] or the Garelis-
Russel technique [8]. In all these techniques it is essential that a
fundamental spatial distribution of the neutrons be established for a
correct determination of the decay constant and, therefore, the reac
tivity of the system.
The Simmons and King method established that a value for the
reactivity can be obtained directly if a prompt fundamental decay con
stant can be measured at delayed critical. The value of a at delayed
critical determines B/£ and if these parameters are assumed constant
over the reactivity range of interest a value of a can be obtained. The
technique has given good results up to $20 subcritical in small mul
tiplicative systems. The method strongly depends on being able to
establish the prompt fundamental decay mode; it suffers from the incon
venient necessity of a delayed critical measurement and the assumed
constancy of 8/£ throughout the ranges of reactivity.
The Sjostrand method improves the Simmons and King method in that
the delayed critical measurement is no longer necessary but the results
are shadowed by the strong influence of higher spatial harmonics. The
method is based on the premise that the impulse response curve of the
system is dominated by the prompt fundamental mode.
Gozani's treatment is a significant improvement over Sjostrand's
method. Gozani proposed the extraction of the fundamental mode of
prompt neutron decay from the impulse response curve and the extrapola
tion of this curve to zero time. The reactivity in dollars can be found
by integrating under this curve; the method is independent of the pres
ence of higher prompt spatial modes.
The Garelis-Russell technique, similar to Gozani's extrapolated


152
"characteristic asymptotic" pulse shape already exists. Characteristic
"dumbbell" shapes are observed however until the HWHM ^ propagation time.
For wider input pulses, the "propagating" pulses are unable to achieve
the smooth shape observed for narrower pulses. Still, a certain
spatial "re-arrangement" of the shape occurs, as was discussed above
for the 10 msec input pulse.

Effect of Room Return at Peripheral Detector Positions
At positions farthest removed from the source, it was observed
that a secondary peak was occurring at times corresponding to the input
pulse width. This was also observed at peripheral positions in the
reflector tanks. To prove that neutrons reflected from the concrete
walls were the cause of this secondary peak, measurements were made at
the outer edge of the reflector tanks with the neutron detector
shielded by borated paraffin placed outside the reflector tank and with
the detector unshielded.
The results of these measurements are shown in Fig. 37A. A
pronounced peak at M).5 msec was found when the detector was not
shielded from the walls and practically disappeared when about 6" of
borated paraffin was placed between the reflector tank and the concrete
wall. The input pulse width was 0.5 msec. Shown in Fig. 37B is the
result of subtracting the "shielded" pulse from the "unshielded" one.
A sharp 0.5 msec pulse is obtained. The "early" peaks are therefore
blamed on fast neutrons reflected from the walls.
The penetration of these neutrons into the reflectors was analyzed
by positioning a detector at increasing distances from the outer reflec
tor tank wall. It was found that the effect was negligible at a


FLUX (RELATIVE UNITS)
FIG- C15 TIME PROFILE OF THERMAL NEUTRON FLUX 181-03 CM FROM THE SOURCE


TABLE OF CONTENTS (cont'd)
Page
F UFSA R1 CLEAN CORE
TIME PROFILES OF THEKMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A WIDE (10 MSEC) INPUT PULSE ... 253
G UFSA R1 CLEAN CORE
SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF INPUT
PULSE WIDTH 255
LIST OF REFERENCES 258
BIOGRAPHICAL SKETCH 262
x


Flux (Relative Units)
R1 Clean Core
66.6 cm from the source
In Foil Activation
FIG. 26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX
117


Reactivity (-$)
FIG. 50 REACTIVITY (-$) AND k .. VS. AXIAL POSITION
eff
Effective Multiplication Factor


108
configuration of the source and the assembly. The planar nature of the
source was confirmed experimentally by obtaining pulse propagation data
across the width of the core close to and far from the source.
The removal cross-section for the uncollided source neutrons in
region 1 was chosen to be the removal cross-section of neutrons from
the fast group in that region as obtained from the two-group scheme
(ref. Table IV). For regions 2,3,4 and 5 the corresponding removal
cross-section was taken to be the removal cross-section of neutrons
from the fast group in the four-group scheme.
It should be noted that the results are not sensitive to the value
of the removal cross-section in region 1. The above choice of the
\
removal cross-section for the remainder of the assembly is consistent
with the overall calculational scheme used and with the value deter
mined empirically for 14 Mev neutrons in light water.
This choice of a first-flight source gave calculational results
in surprinsingly good agreement with experiment, particularly for the
delay times and the spatial attenuation. The predicted pulse shapes
are somewhat narrower than the pulse shapes obtained from experiment.
No significant differences between the results of the localized sources
case mentioned above and a point kernel source distribution were ob
served. The point kernel source distribution underpredicts the pene
tration of the first collision fast neutrons into the assembly.
At this point a few comments on the energy distribution of the
source neutrons are pertinent. A pure tritium target bombarded with a
beam of monoenergetic deuteron ions will produce essentially mono-
energetic neutrons, since the relationship between the energy of the
ions, the neutron energy and the angle of emission is unique. However,


FIG. 10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS


146
TABLE XII
THE CALCULATED ASYMPTOTIC VELOCITY OF PROPAGATION AND
DYNAMIC INVERSE RELAXATION LENGTH VS. CORE HEIGHT
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
Core
Kd
V
Height
(cm)
Q
(cm X)
P
(msec )
70
0.03565
571
72.5
0.03233
506
76
0.03027
456
77.5
0.02772
435
80
0.02515
397
85
0.02047
321


WEIR SYSTEM
6
CORE TANK
REFLECTOR
TANK
RESERVOIR
DUMP
VALVES
FIG. 1 OVERALL VIEW OF THE FACILITY


FLUX (RELATIVE UNITS)
FIG* D7
TIME PROFILE OF FAST NEUTRON FLUX 15-71 CM FROM THE SOURCE
in in


75
has been resolution time corrected and background subtracted. A "pure"
delayed neutron background is statistically calculated and used to
determine k$/£. The data can be normalized to a reference detector
position for the analysis of the pulse propagation measurements in the
time and in the frequency domain. A Fourier analysis of the pulse can
also be performed if required.
Shown in Fig. 17 (A, B) are the experimentally determined a, kg/i,
and k as a function of moderator height obtained by averaging results
from three chosen detector locations in the "asymptotic" region. The
results are summarized, together with the 1/M measurements and theoreti
cally calculated values in Table III. The excellent agreement between
the experimental and theoretical results should be considered somewhat
fortuitous. The calculations were done following the method outlined
in Appendix A. Some later calculations [19] done by the Phillips
Petroleum Co.,showed more disagreement, especially at low water levels.
The last calculations tried to account for the fact that there is a
fissionable reflector above each experimental moderator height. This
fact was disregarded in the calculational results shown in this work.
The agreement at the 75 cm water level is good for all calculational
methods.
Conclusions
The University of Florida SPERT Assembly has been operated for
several months with very few operational problems. The system has
proven to be extremely reliable and the instrumentation has performed
adequately. The calibration of the system has established that mean
ingful values for the reactivity can be obtained when applying the


Delay Time (msec)
130
ft
ft
FIG. 30 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.0 MSEC INPUT PULSE -


Flux (Relative Units)
FIG. 25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX
116


261
45. J. H. Dunlap and R. B. Perez, "Dispersion Law for a Subcritical
Assembly," Proceedings of the Symposium on Neutron Noise, Waves,
and Pulse Propagation, AEC Symposium Series No. 9 (1967).
46. CORA, an improved version of the IMP computer program. IMP is
described in IDO-17199.
47. S. 0. Johnson, SPERT PROJECT Quarterly Progress Report, Philips
Petroleum Co., IDO-17123, 43 (1966).
48. G. Mortensen, private communication (1968).
49. A. E. Waltar and L. Ruby, "Interpretation of Pulsed-Source Experi
ments in a Reflected Reactor," Internal Report, Department of
Nuclear Engineering, University of California (1964).
50. PHROG is a Phillips-Hanford revision of GAM-1 (G. D. Joanou and
J. S. Dudek, GAM-1, GA-1850 (1961).
51. F. J. Wheeler, "RAVEN, A Computer Package for Evaluating Resolved
and Unresolved Resonance Absorption Including Pin Shadowing,"
IDO-17212 (1964).
52. TOTEM links the TOPIC and TEMPEST codes for calculating thermal
constants (G. E. Putnam, TOPIC, IDO-16968 (1964), and R. H. Shudde
and J. Dyer, TEMPEST II, TID-18284 (1961)).
53. H. P. Flatt and D. C. Bailer, "AIM-6, A Multigroup, One-Dimensional
Diffusion Equation Code (1961).
54. N. J. Diaz and M. J. Ohanian, "UNIPUL, A Unified Data Processing
Program for Pulsed Measurements," Internal Report, University of
Florida (1969).
55. M. J. Ohanian, "MORE, A Conventional Fourier Transform Program for
Pulsed Measurements," Internal Report, University of Florida (1969).
56. M. J. Ohanian, "MORWIG, A Conventional Fourier Transform Program
with Variable Time Increments," Internal Report, University of
Florida (1969).
57. N. J. Diaz, "ALXILS, A Linear Least-Squares Program for the Fitting
of Alpha and Xi," Internal Report, University of Florida (1969).


119
TABLE VI
DELAY TIMES MEASURED ACROSS THE WIDTH OF THE CORE
- 0.5 MSEC INPUT PULSE -
UFSA R1 core
0.5 M/W ratio
16.35 cm wide reflected core
Delay Times (msec)
Position Distance to Distance to the source
No Core Center (cm) 53.9 cm 130.2 cm
A
7.27
.860
2.42
B
5.45
.830
2.51
C
3.63
.830
2.48
D
1.82
.830
2.45
E.
0.0
.830
2.42
F-
3.63
.830
2.54
G
5.45
.830
2.42
H
7.27
.860
2.51
I
10.9
.860
2.42
RE1
12.5
.890
2.45
RE2
14.3
.920
2.48
RE3
16.1
.950

RE4
17.9
.920
2.57
RE5
28.9
.920

RE6
31.8

2.45
RE7
34.3
.890



105
to zero with 2-5 ysec (10 time steps) between the two steps. It was
also observed that a long time after the input pulse was cut-off oscil
lations developed at spatial points close to the source when time
imcrements larger than 50 ysec were used.
The time increments used for the 0.5 and 1.0 msec input pulse
problems are shown in Table V. Stable operation of the code was ob
tained with these time steps. Running times were of the order of 20
minutes in the UF IBM 360-50.
The main problem in establishing a fair comparison between the
calculational and experimental results lies in an adequate physical
description of the spatial distribution of the external fast source.
For example, when calculations were done with a spatially localized,
1 cm wide source placed at the physical location of the neutron target
(Fig. 20) the calculated pulse shapes were found to agree reasonably
well with experiment but the peaks of the pulses were delayed by 50 to
500 microsec with respect to the experimental values. Furthermore the
calculations predicted a much sharper attenuation of the peak of the
pulse near the source, although predicting an asymptotic relaxation
length in agreement with experimental results. Therefore, a careful
study was undertaken to obtain the "best" description of the spatial
distribution of the source.
The best approximation to the source that could logically be
assumed based on physical grounds was that of a spatial distribution
I Z
given by a first-flight kernel of the form e r where £r is the removal
cross-section for source neutrons. The distribution used is shown in
Fig. 22. The choice of a plane source kernel is reasonable especially
at points a few cm removed from the source due to the physical


FLUX (RELATIVE UNITS)
X
FIG* C9 time PROFILE CF THERMAL NEUTRON FLUX 104-73 CM FROM THE SOURCE


LIST OF SYMBOLS
TRANSVERSE BUCKLING
DELAYED NEUTRON PRECURSOR CONCENTRATION OF THE
ith GROUP
DIFFUSION COEFFICIENT OF THE ith GROUP
FREQUENCY (cps)
EFFECTIVE MULTIPLICATION CONSTANT
NEUTRON LIFETIME
NEUTRON MULTIPLICATION
VELOCITY OF THE ith GROUP
AXIAL COORDINATE
DECAY CONSTANT (IN THE TIME DOMAIN)
DAMPING COEFFICIENT (IN THE FREQUENCY DOMAIN)
EFFECTIVE DELAYED NEUTRON FRACTION
PHASE SHIFT PER UNIT LENGTH
REACTIVITY .
COMPLEX INVERSE RELAXATION LENGTH
MACROSCOPIC CROSS SECTION
NEUTRON FLUX
xviii


TABLE VIII
CLEAN CORE PULSE PROPAGATION STUDIES
EXPERIMENTAL AND THEORETICAL RESULTS
- 1.0 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ration
16.35 cm wide reflected core
POSITION
DISTANCE TO
PEAK
AT (msec)
FWHM
(msec)
PEAK
COUNTS3
NO
SOURCE (cm)
Theory
Exp
Theory
Exp
Theory
6
3
1.000
0.97+.03
1.020
0.930+.06
48.25
56.5+1.5
13
15.71
1.000
1.00+.03
1.065
0.960+.06
47.62
56.7+1.7
20
28.43
1.00
1.03+.03
1.140
1.080+.06
36.52
37.9+.9
27
41.15
1.046
1.04+.03
1.365
1.290+.06 .
23.60
29.6+1.6
34
53.86
1.215
1.19+.03
1.620
1.62+.06
14.99
14.9+.2
41
66.58
1.410
1.33+.03
1.875
1.92+.06
9.720
10.1+.3
48
79.30
1.630
1.65+.06
2.175
2.19+.06
6.431
6.43+.05
55
92.01
1.880
1.81+.06
2.468
2.49+.09
4.332
4.32+.04
62
104.73
2.150
2.10+.06
2.760
2.82+.09
2.955
3.11+.04
69
117.44
2.420
2.41+.06
3.030
3.12+.09
2.041
2.15+.05
76
130.16
2.725
2.71+.06
3.315
3.45+.09
1.423
1.41+.02
83
142.88
3.025
3.01+.06
3.585
3.69+.09
1.000
1.00+.03
90
155.60
3.275
3.30+.06
3.750
3.96+.09
0.7070
0.663+.01
97
168.31
3.575
3.58+.06
3.945
4.29+.09
0.5019
0.489+.009
104
181.03
3.850
3.85+.06
4.110
4.44+.12
0.3553
0.356+.007
111
193.74
4.075
4.10+.08
4.185
4.59+.12
0.2471
0.254+.003
118
206.46
4.275
4.30+.08
4.200
4.56+.12
0.1640
0.184+.003
125
219.17
4.425
4.475+.09
4.275
4.53+.12
0.0962
0.121+.0025
132
231.88
4.500
4.600+.12
4.275
4.56+.15
0.0369
0.0585+.00012
a Normalized to Position 83
k Errors assigned from the deviation from the mean of two measurements except for the last 5 space
points. This error is usually larger than the counting statistics error. The error of the last 5
points was calculated from counting statistics.
128


164
TABLE XVI
THE REAL AND THE
IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION
LENGTH
- 0.5 MSEC INPUT PULSE -
FREQUENCY
a (cm
'1)
5
(rad/cm)
(cps)
Theory
Exp
Theory
Exp
0
.02286
.02248
10
.02290
.02254
.001557
.001558
20
.02305
.02270
.003095
.003098
30
.02328
.02296
.004595
.004600
40
.02359
.02331
.006046
.006054
50
.02396
.02373
.007435
.007451
60
.02438
.02423
.008765
.008780
70
.02483
.02476
.01004
.01006
80
.02532
.02536
.01128
.01124
100
.02640
.02663
.01358
.01349
120
.02755
.02797
.01563
.01541
140
.02866
.02937
.01753
.01714
160
.02986
.03081
.01932
.01868
180
.03101
.03223
.02092
.02026
200
.03215
.03359
.02244
.02148
220
.03330
.03495
.02391
.02278
240
.03442
.03627
.02521
.02396
260
.03545
.03757
.02650
.02508
280
.03658
.03878
.02775
.02619
300
.03766
.04002
.02883
.02726
350
.04028
.04285
.03153
.02979
400
.04272
.04576
.03401
.03213
450
.04505
.04813
.03627
.03434
500
.04724
.05018
.03841
.03661
550
.04941
.05272
.04037
.03803
600
.05146
.05475
.04224
.04060
650
.05344
.05754
.04391
.04138
700
.05534
.05934
.04550
.04234
750
.05727
.06095
.04695
.04118
800
.05910
.06237
.04829
.04425
900
.06276
.06852
.05091
.05150
1000
.06636
.07404
.0530
.05650


APPENDIX F
UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT THREE POSITIONS IN THE CORE
FOR A WIDE (10 MSEC) INPUT PULSE


CHAPTER IV
THE DATA ACQUISITION SYSTEM
Introduction
In the delicate and laborious task of performing nuclear experi
ments the most common source of difficulties and errors lies in the
acquisition of the data. Modern nuclear instrumentation with its excel
lent time-energy resolution has enhanced detection sensitivity to the
extent that deviations previously masked by the poorer resolution of the
equipment are easily distinguishable. The major problem now lies in the
degree of reproducibility of the results. Although in general the in
strumentation is very reliable the enhanced sensitivity demands contin
ual standardization for the sake of reproducibility.
The "brain" of the data acquisition system for pulsed neutron
measurements is the multichannel analyzer (MCA) which is now available
with a large number of data channels and narrower channel widths for
increased time resolution. In general, the mode of data acquisition
for a pulsing experiment differs from that of many other types of
nuclear experiments. In particular, neutron interactions with a suitable
detector are fed into the analyzer while it is time-sweeping. Ideally
every neutron interaction should be counted regardless of the ampli
tude of the collected pulse. This implies that the linear signal
originated at the neutron detector should be converted to a logic signal
so that its probability of being recorded is independent of its amplitude
45


FLUX (RELATIVE UNITS)
FIG. 35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING
142


FLUX (RELATIVE UNITS)
FIG- Cl
TIME PROFILE OF THERMAL NEUTRON FLUX 3-0 CM FROM THE SOURCE


55
Sr1' >rhf r 1 -k'1/M
where M is the net neutron multiplication in the assembly with a
centrally located source. In practice, the multiplication is obtained
from the ratio of multiplied to unmultiplied counts with a centrally
located source. The unmultiplied counts are obtained with the fissile
material removed and all other conditions undisturbed. In water
moderated cores it is difficult to match neutron spectra for multiplied
and unmultiplied counts and deviations from the ideal M are to be ex
pected. If possible, a search for detector locations should be con
ducted so as to obtain curves that follow the expected behavior of 1/M.
Even if k can not be directly inferred from the 1/M determination, the
curve of reciprocal count rate vs. the parameter that controls reac
tivity (fuel loading or moderator height or % control rod withdrawal)
is a useful guide for safely approaching criticality if a well-behaved
curve can be obtained.
The inverse multiplication curve can be obtained as a function of
moderator height by first obtaining a series of unmultiplied counts at
various water levels and the multiplied counts as the water level is
raised with the assembly originally air-spaced. Sensitivity to geo
metrical configuration (source-detector-water level) requires an empir
ical determination of "well-behaved" detector positions.
Reactivity Measurements by the Pulsing Technique
The pulsed-neutron technique has been used successfully for several
years to measure reactivity. The transient neutron density following a
burst of neutrons is used to determine the reactivity of the system by
either the Simmons and King method [12], Sjostrand's area ratio method


28
the storage area to the level of the active fuel height. A 2-foot
reflector on both sides was used to represent an infinite reflector.
No reflector was considered on the ends, but the contribution of this
to the system would be small. The calculation was done using four
groups and seven regions and followed the method outlined in Appendix
A of this thesis. The following configuration, which is symmetric about
the indicated center line, was assumed:
54"
Water
24" -
Water
Under these water-moderated and reflected conditions, a k =
eff
0.79 was obtained
b. Solid angle criterion for slabs
To determine the interaction between the fuel storage slabs in the
proposed 3-slab array, the solid angle criterion established in 10 CFR,
Part 70, 70.52, paragraph (b) was used. This establishes the maximum


ACKNOWLEDGMENTS
The author wishes to express his sincere appreciation to his
graduate committee for their guidance. Special recognition is due
Dr. M. J. Ohanian, whose encouragement, dedication and detailed
scientific knowledge made this work possible.
The support of the Nuclear Engineering Sciences Department of
the University of Florida throughout the authors graduate work is
greatly appreciated. In particular Dr. R. E. Uhrigs support and
friendship is gratefully recognized.
The author feels fortunate and proud in having studied and worked
with a remarkable scientist and gentleman, Dr. R. B. Perez, now at
Oak Ridge National Laboratory. The author's years of association with
Dr. T. F. Parkinson, now at the University of Missouri, formed the
necessary background for this work.
The continuous assistance of Mr. G. W. Fogle throughout the ex
perimental program is sincerely appreciated. Mr. L. B. Myers designed
and built the control instrumentation. Mr. R. E. Schoessow was respon
sible for the design and construction of the assembly. Mr. E. Dugan
and Mr. H. Leydolt aided in the data processing. The cooperation of
the staff of the Nuclear Engineering Sciences Department during the
construction of the facility is acknowledged.
Most of this work was financed under subcontract No. C281 and
C635 with Atomic Energy Division of the Phillips Petroleum Company,
iii


118
long detector in one position and rotating the fuel elements that
surround it. The narrow core (6.5 in wide) is obviously very suscep
tible to this effect and to the exact centering of the neutron source
whose location could not be determined to better than 0.5 cm accuracy.
Dynamic Flux'Traverses
Dynamic flux traverses across the width of the core and reflector
were carried out at distances of 41, 54, and 130 cm from the source.
As mentioned above, these measurements are important since the theoret
ical model is one-dimensional and planar propagation is conceptually
desirable.
Shown in Table VI are the "peaking times" obtained for several
positions across the width of the core and side reflectors. The exper
iment was performed with both 0.5 and 1.0 msec input pulses. Only the
results for the 0.5 msec input pulse are shown. The results for the
1 msec case display the same behavior. All the peaks occurred well
within the experimental accuracy. Comparison of pulse shapes at dif
ferent positions across the core and reflector revealed no differences
in the basic shapes. Near the outer wall of the reflector a secondary
pulse, which peaked at a time corresponding to the input pulse width,
was observed. It was confirmed experimentally that this was due to
neutron reflections from the walls of the facility room.
From the pulse propagation measurements, reactivity data was also
obtained. These results are analyzed in Part 2, Chapter VI.
Clean Cor Pulse Propagation Measurements
The main portion of the research propagation measurements in the
clean, cold, side-reflected assembly. These most detailed experiments


193
channels is now reduced to an odd number of points terminating where
the background has been determined to start.
5. Determination of the ratio kf3/£ following the Garelis-Russel
method. Simpson's integration is used for the pulse and the Regula-
Falsi iterative method is used to find the root.
6. The data is normalized according to a selected normalization
scheme (see Part I, Chapter IV). The normalized data can be punched
in cards for further analysis.
7. If a neutron wave type analysis is desired, a numerical
Fourier transformation is performed and the amplitude and phase of the
pulse for each frequency selected is printed and punched for further
processing.
UNIPUL was used to process the pulse data punched in cards from
original perforated paper tape (at the IBM 1800 computer of the
Department of Nuclear Engineering Sciences, University of Florida);
the paper tape is the output of the multichannel analyzer used in the
experimentation.
MORE
The FORTRAN IV, IBM 360 computer program MORE performs a conven
tional numerical Fourier transformation of the pulse neutron data
(zeroth moment only) for the analysis of the experiment in the fre
quency domain. The transformation used equal time steps, a maximum
of 1023 time points and Simpson's integration scheme. An odd number
of points are required by the program. Thermal neutron data can be
entered directly as input or the total and epicadmium neutron flux
are required to obtain the thermal flux by subtraction.


FLUX (RELATIVE UNITS)
FIG* C23 TIME PROFILE OF THERMAL NEUTRON FLUX 41*15 CM FROM THE SOURCE
219


FLUX (RELATIVE UNITE)
FIG. 36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE HEIGHT


27
must be as specified under Operating Limits in this report.
g. After a normal start-up, the water height in the core must be
within 0.5" of the level set by the position of the weirs.
Fuel Storage
The large amount of fuel needed for the experimental program
required a detailed criticality analysis of the fuel storage area.
Criticality considerations of the fuel storage arrangements follow the
Atomic Energy Commission regulations regarding the subject. Three dif
ferent criteria were used to calculate the effective multiplication of
the fuel storage area to assure that the array will remain subcritical
under the worst circumstances. The methods and the corresponding con
ditions are outlined below.
The fuel storage array consists of three slabs of air-spaced fuel
pins, separated by a minimum distance of 54 inch face to center. The
fuel is stored in steel baskets containing 308 pins per basket. Two
sets of 1/4 inch thick plastic plates, located at the bottom and top of
each basket, drilled to properly position the fuel rods. The charac
teristics of the fuel slab are:
Slab Width = 3.73 in = 9.46 cm (corresponds to 7 fuel pins in
transverse direction)
Slab length = 14 ft
Height = 3 ft (active fuel height)
a. Multiregion-multigroup calculation
The effective multiplication factor of the fuel storage array con
sisting of three slabs (3.73 inch wide, 14 ft long and 3 ft wide) which
are 54 inch apart (face to face) was computed for the case of flooding


APPENDIX C
UFSA Rl-CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT NINETEEN CORE POSITIONS
FOR INPUT PULSES OF 0.5 AND 1.0 MSEC


195
the pulses. A CALCOMP plotter is used in connection with the 1800
computer for the actual plotting of the pulse. The program is capable
of normalizing to the peak counts of a reference pulse for the super
position of related time profiles.


98
aspects of pulse propagation phenomena were studied using a few or a
single detector location in the clean core; these measurements will be
discussed separately from the main part of the research as complementary
experiments. .
Pulse propagation measurements across the entire length of the
core were conducted with input pulse widths of 0.5 and 1.0 msec. The
time profile of the thermal neutron flux was obtained by the cadmium
subtraction method at nineteen locations in the core. The first
detector position was 3 cm from the neutron target and measurements
were taken every 12.72 cm thereafter. The data thus obtained was then
analyzed in the time domain.
With the exception of the measurements at the last four detector
locations, 2^ or 2^ counts were accumulated in the peak channel of
the analyzer and two measurements conducted at each position. The full
1024 available channels of the analyzer were used. The channel width
was 20 microsec with an intrinsic 10 microsec storage dead time giving
an effective time between channels of 30 microsec. Running times
varied from 3 minutes close to the source to two hours at the position
farthest from the source.
Propagation of a Narrow Pulse
To test the analytical model under more severe conditions, a
narrow, 100 microsec wide input pulse was introduced into the assembly
and the pulse profile recorded at a few detector locations. The exper
iment is identical to the one described above except that fewer detec
tor locations were employed.
Propagation of a Wide Pulse
To illustrate the propagation characteristics of a pulse violating


Flux (Relative Units)
132
FIG. 32 AMPLITUDE ATTENUATION OF THE THERMAL NEUTRON FLUX
- 1.0 MSEC INPUT PULSE -


FLUX (RELATIVE UNITS)
FID- C26 TIME PROFILE OF THERMAL NEUTRON FLUX 73-30 CM FROM THE SOURCE


FLUX (RELATIVE UNITS)
1-0
0*9
0-9
0-7
I
,*2 .
* '
\
THERM--5- 34 '
PEAK AT 0-950 MSE.'CS
PULSE WIDTH = 0-55 MSECS
THECRY FWHM = 1-3559 MSECS
....... EXP- FWHM = 1-470 MSECS
0-G
I
S
s
0-55
0-4
0*3
03
0-1
0 1
*
%
9
%
hO
O
{1
V
******
***.
-i-
-L.
*"****..*
....[
10
3
4 5
TIME (MSECD
9
FIG- C5
TIME PRDFILE GF THERMAL NEUTRGN FLUX
53 BS GM FRDM THE SOURCE


3
The Large Core Dynamics Experimental Program is to be performed
in three phases:
Phase I. Pulsed Source Experiments in Subcritical, Multiplying Media,
Large in One-Dimension
The first phase of the experimental program is to be conducted in
a close-to-critical subcritical assembly, 8 feet long, 3 feet deep and
with widths changing from 6.5 inches to 16 inches according to the core
configuration and whether bare or side reflected cores are studied.
The experimental information obtained from studying the pulse
propagation phenomena in this assembly is to be used to test the valid
ity of current space-time kinetic models in the absence of inherent
feedback effects.
Phase II. Kinetic Behavior for Control-Rod-Induced Power Excursions in
Large, One-Dimensional Cores
A reactor large in one-dimension, 16 feet long, three feet deep
and with varying widths to accommodate different metal/water ratios will
be used to investigate the one-dimensional kinetic behavior of large cores
subjected to a large perturbation. Both non-feedback (low power exper
iments) and self-shutdown measurements will be conducted.
Phase III. Kinetic Behavior for ContrOl-Rod-Induced Power Excursions
in Large, Two-Dimensional Cores
The same type of measurements performed for the one-dimensional
core will be conducted in a two-dimensional core.
The measurements should provide the necessary information to
establish the validity ranges for one-dimensional models, the basis for
the development of a two-dimensional scheme and as a bridge to the
complex, three-dimensional problem.
Phase II and Phase III of the research program will be performed


FLUX (RELATIVE UNITS)
FID* C30 time PROFILE OF THERMAL NEUTRON FLUX ISO*IB CM FROM THE SOURCE
226


TABLE II
UFSA INSTRUMENTATION AND CONTROL
A. NUCLEAR
Measured Parameter
Method of Measurement
Application
a. Low level neutron flux
He detector pulse discriminator;
at neutron generator end of core
Insure source is present before
adding reactivity. Scram on low
count rate
b. Linear neutron flux
c. Log neutron flux*5
CICa ammeter; on side of core
Indicate power level scram on
power
3.
CIC log N and period amp; under
core near center line
Indicate power level scram on
high power; log N recorder
d. Linear neutron flux
UIC ammeter; on side of core
Indicate reactor power; linear N
recorder
e. Reactor period lc
CIC log N and period amp
Indicate reactor period; scram on
short period
f. Gamma flux
g. Detector power supply
voltage
h. Reactor period 2
Ion chamber area monitor; on front
of reactor cage
Unijunction transistor oscillator
and relay. Monitor detector
voltage for b, c, d and e
CICa log N and period amp; under
core near center line
Criticality monitor for storage
room. Area monitor for reactor
room. Activate evacuation alarm
Scram reactor on low detector
voltage
Indicate reactor period; scram on
short period
N3
cn
*
a
b
To be operated in the uncompensated mode
Common detector and instrument


CHAPTER VI
SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS
Introduction
A resume of pulsed-neutron reactivity measurements was presented
in Part 2, Chapter V of this work. During the nuclear calibration of
the UFSA assembly certain "spatial" effects were observed in the deter
mination of the reactivity of the long assembly. In this chapter these
effects are investigated.
The pulse propagation measurements performed in the UFSA R1 clean
core were analyzed using the Garelis-RusseUtechnique [8] to determine
the ratio kB/,; the "fundamental" decay constant was obtained by ap
plying Peierls statistical analysis to the tail of the pulse and the
effective delayed neutron fraction was calculated and assumed constant
with respect to reactivity. A strong "spatial" dependence of the
measurements conducted along the center line of the core was observed.
An asymptotic spatial distribution was obtained long times after the
pulse; at these times only the positions farthest from the neutron
source had not reached background level. The Garelis-Russell technique
was found to be very sensitive to the finite width of the input pulse.
A computer program, UNIPUL, was coded and used to perform the
Garelis-RusseU type analysis on the impulse response curves determined
as a function of position in the UFSA R1 core. The same program
174


12
FIG. 2A BOTTOM FUEL ROD SPACING SYSTEM


8
The assemblies are highly multiplicative; this is important for
the extrapolation of the results of the study to critical systems. The
system's subcriticality is attractive because of the inherent safety
of such systems and of the absence of inherent feedback effects.
In order to provide as "clean" a core as possible, a unique control
system which has been successfully used on the UFAPA [2] will be em
ployed. In this system the reactivity is controlled by adjustment of
the water height in the assembly. The water height is controlled by
the position of two "V"-notched weirs located in a water "box" hydrau
lically coupled with the assembly through flexible lines. The quantity
5/2
of water discharging through a "V"-notched weir varies as H (H is the
distance between the apex of the weir and the water level) thus pro
viding precise control of the moderator height. The hydraulic coupling
assures that under normal operating conditions (with continuous flow)
there will be the same water level in the core and the reflector tanks.
The UFSA subcritical assembly is located in an isolated and
shielded room in the Nuclear Research Field Building, approximately
three miles from the University campus.
The Nuclear Research Field Building consists of four bays, two of
them having shielded rooms for experiments with subcritical and moder
ating assemblies. The shielded walls consist of stacked concrete block
eight feet high and thirty-eight inches wide covered with plywood to
assure that the blocks remain in place. The ceiling of this single-floor
building is approximately 15 feet above the floor and consists of excel
sior-filled cement bonded board. Neutron reflection from this ceiling .
over the walls does not constitute a hazard to personnel operating the
accelerator-type neutron source. The access door from the control room


89
Neutron Wave Analysis
The neutron wave technique has proven to be a very powerful method
of determining the deficiences a model has in predicting propagation
phenomena or in establishing the "quality" of the results from a corre
sponding experiment.
The study of the space-time data in the frequency domain "looks"
at the overall behavior of the asymptotic spatial region of the assem
bly with parameters that include information on all spatial points for
each frequency of interest. The comparison of the predicted and meas
ured real and imaginary components of the complex inverse relaxation
length, 5, is therefore a more comprehensive evaluation of the discrep
ancies than the point-wise comparison in the time domain. The analysis
in the 6^ plane is an especially stringent test of the model and the
experimental data.
In this work, the comparisons in the frequency domain were made
by numerically determining the zeroth Fourier moment of the data meas
ured in the time domain. This method was suggested by Moore.^
Moore expressed Fourier moments of the space-time data as
. n -2-rrift .
i|>n(r, f) = / dt t e ij>(r, t)
(A)
where iKr, t) is the neutron pulse at space point r as a function of
time, t, and f is the frequency in cycles per second.
The fundamental space and energy mode propagating through the
medium is given by:
1. The author acknowledges Dr. M. N. Moore for several enlightening
discussions on the subject of neutron waves propagation.


A one-to-one comparison of the predicted and measured values in
the frequency domain was provided by performing identical numerical
Fourier transformations of the WIGLE time profiles and the measured
pulse shapes. The analysis in the frequency domain confirmed the
results obtained in the time domain, although discrepancies past 100
2
cps are found in the ultrasensitive p plane. The agreement in the p
plane, the system's dispersion law, is good up to 200 cps and reasonable
up to 800 cps. Both theory and experiment showed a smooth behavior
2
throughout the frequency range investigated, in both the p and the p
plane.
Spatial effects in large cores are clearly demonstrated in this
work. The determination of the range of applicability of the one
dimensional scheme requires extending the study to cases in which two-
dimensional effects will be noticeable and the important feedback
effects can be considered.
xxi


LIST OF FIGURES (contd)
FIGURE Page
27B EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 123
27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 124
28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PUSLE 125
28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE 126
29 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.5 MSEC INPUT PULSE 129
30 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.0 MSEC INPUT PULSE 130
31 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
- 0.5 MSEC INPUT PULSE 131
32 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
- 1.0 MSEC INPUT PULSE 132
33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS 139
34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED
BY THE WIGLE CALCULATIONAL SCHEME FOR DIFFERENT
CORE HEIGHTS 140
35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 141
35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 142
xv


FLUX (RELATIVE UNITS)
TIME PROFILE OF THERMAL NEUTRON FLUX 130IS CM FROM THE SOURCE
FID- E3


flux (relative: units)
1-0 +
0-0
0-0
0-7-
0-G
0-5
0-4
0-3
V

UNSHIELDED
ft
*
ft
*
ft
ft
f
ft

ft

I \
/****'*?>> A A**
fit'* y?
\a^ f
* y
&
4
a-
§r
SHIELDED
r
%
*h
? rw
i n:
r
&
5.
2f.\
0-1
i
i
a
if /
f/
-UJ
*H\ft
/
VA
Vni1
n\
NORMALIZED TO
R1REFREF7G
pulse: width = 0-5 msecs
EXP- FWHM = 3-570 MSECS
V**4<

10
0
J.
4
G
7
B
3
TIME (MSEC)
FIG- 37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR POSITIONS
153


67
area-ratio method, is of practical value because of its intrinsic
elimination of the effect of prompt higher harmonics. This method,
which was used in the present work, was postulated originally for a
repetitively pulsed (with a delta function source in time), bare,
monoenergetic reactor but has proven to be of broader application.
Garelis and Russellpostulate, that for the conditions specified above:
1/R 1/R
.fNp exp( (k|3/£,) t)dt = £Npdt + Nj/R
where
Np = prompt contribution to the neutron density'
= delayed contribution to the neutron density
R = pulsing rate
The following conditions should be satisfied for the correct ap
plication of the method.
a) R>>X, where X is the decay constant of the shortest lived
precursor group.
b) R a, where a is the prompt fundamental decay constant.
c) The system must be pulsed a sufficient number of times so that
exp (magn/R) << exp (-agn/R) where m + 1 is the total number of pulses
and the agn are the roots of the inhour equation.
d) The prompt root dominates the decay.
The Garelis-RusseUtreatment permits the determination of p ($)
when all the above conditions are satisfied, by the relation:
($) =
k e/£
- 1
An absolute value of p is obtained by the use of a calculated effective
delayed neutron fraction. Garelis has discussed the use of the method
in reflected systems; the technique seems to be of practical value in


FLUX IRELATIVE UNITS)
FIG* 18 THE TOTALtEPICADMIUM AND THERMAL FLUX 117-44 CM FROM THE SOURCE


13
I
FIG. 2B BOTTOM FUEL ROD SPACING SYSTEM


7
TABLE I
keff vs. MODERATOR LEVEL OF UFSA REFLECTED CORES
Calculated Using the AIM6 Code
Core Length = 243.8 cm (96")
Reflector Width = 30.48 cm (12")
Active Fuel Height = 91.4 cm (36")
Metal to Water Ratio = 0.5
Lattice Pitch (in) = 0.7152
Core Width (cm) = 16.35
No. of Fuel Rods = 1206
1.0
0.584
19.28
2132
1.5
0.5332
25.73
3420
Moderator Level
(cm)
20
25
30
35
40
45
50
55
60
65
70
75
80
85
Effective Multiplication Constant
.7695
.7397
. 7276
.8288
.8028
.7941
.8715
.8471
.8416
.9022
.8793
.8761
.9249
.9032
.9020
.9420
.9213
.9218
.9551
.9353
.9372
.9655
.9465
.9494
.9738
.9554
.9592
.9805
.9626
.9672
.9870
.9686
.9738
.9906
.9736
.9793
.9944
.9777
.9840
.9977
.9813
.9880
1.0012
.9851
.9922
91.4


109
the (d,t) reaction rapidly becomes contaminated with the (d,d) reaction
due to the accumulation of the deuteron beam on target. After ~ 600
microamp-hr per unit area of accumulated beam on target the original
neutron yield from the (d,t) reaction has dropped to half of its
original value while (d,d) neutrons account for 1% of the neutron
beam. After ~ 2000 microamp-hr per unit area of accumulated bean on
target, the number of (d,d) neutrons has increased to 2%; this .repre
sents a detectable contamination, and may have some effect on the
removal cross-section of source neutrons. In the present case, how
ever, due to the coarse energy mesh used in the calculation scheme the
effect is not considered to be important.
Typical results obtained with the WIGLE code are shown in Fig. 23
(A, B, C) for a 0.5 msec input pulse. The general characteristics of
the pulse propagation phenomena are clearly displayed. The calculated
spatial distribution of the neutrons as a function of time is shown for
times of 1,2,3,5,7 and 9 msec in Fig. 24 (A, B). The spatial dispersion
increases with time while the pulse attenuates severely in time and
space.
The WIGLE results are discussed simultaneously with the results of
the clean core measurements.
Flux Traverses
Static and dynamic flux traverses were obtained in the clean core
to establish the following:
a) The asymptotic steady-state flux shapes in the transverse
direction.
b) The planar propagation of the neutron pulse. This is extremely


Flux (Relative Units)
126
UFSA R1 Clean Core
12.716 cm between points
Position Number
FIG. 28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE


CHAPTER IV
EXPERIMENTAL AND THEORETICAL RESULTS
IN THE TIME DOMAIN
The Analytical Model
The analytical results were obtained using an IBM 360 version of
the WIGLE code^ supplied by the Phillips Petroleum Company, and made
operative on the IBM 360-50 at the University of Florida. Certain modi
fications were made to WIGLE to obtain punched card output of the time
profile at selected spatial points. In this manner, the pulse shapes
at the detector positions corresponding to the experimental measurements
were readily available for direct comparison with experiment.
The WIGLE scheme, being a one-dimensional model, requires that the
transverse leakage be taken into account by the proper adjustment of
the parameters. The two-group nuclear parameters for WIGLE were obtained
by the procedure outlined in Appendix A. The eigenvalue, three-di
mensional flux shapes and the bucklings were obtained from the CORA [46]
computer program. The core width was set at 16.35 cm, the reflector
width at 30.5 cm and the reactor height at 76 cm. The experimental
measurements were made with 75 cm of water above the bottom of the ac
tive fuel but there was a small water reflector at the bottom; thus the
1. The author is indebted to Mrs. M. E. Radd, Nuclear Safety Research
Branch, Phillips Petroleum Company, for her valuable cooperation in
familiarizing the author in the use of the WIGLE code.
100


50
The Electronic Instrumentation
A block diagram of the instrumentation used in the pulse propaga
tion experiments is shown in Figs. 11 and 12. Two independent data
acquisition systems with a common start-stop clock are necessary to
carry out the measurements: (1) a system connected to a movable detec
tor that obtains the time profile of the propagating pulse at a given
position and (2) the all important normalizing detector, fixed at one
3
position. Two 1 atmosphere He detectors with the characteristics de
scribed above were used for these purposes. The system is essentially
composed of signal transmitting devices and data registering and
handling units.
The movable detector data acquisition system (MDDAS) consists of:
1. Detector High Voltage Power Supply
The high voltage power supply was an ultrastable FLUKE 405 B with
superior stability and negligible ripple. Manufacturer's specifications
state the stability at .005% per hour and the ripple at less than 1 mv
RMS.
2. ORTEC Model 260 Time-Pickoff unit, with 3000 volt isolation
The time-pickoff units are normally used to detect the time of
arrival of a detected particle, usually with subnanosecond precision..
The use of this characteristic and the electronic arrangement shown in
Figs. 11 and 12 permitted the counting of neutron events with excellent
time resolution. To our knowledge this is the first time that the time-
pickoff units have been used for this application.
Briefly, the system operates as follows: the primary of a toroidal
transformer, having a bandpass for very high frequencies only, is
inserted between the detector and the bias power supply. Fast


Delay Times (msec)
139
FIG. 33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULA!IONAL SCHEME FOR DIFFERENT CORE HEIGHTS


38
predicts that from a k^^ of 0.993 it would take approximately 15
seconds to double the power level. Even if the power level indicator
were not to scram the system until the power level reached 10 kw,
assuming a one second delay time to actuate the scram, the power would
increase to only 69 kw by the time the scram actually begins. Based on
the reactivity removal rate described above, the power level would then
decrease rapidly to a very low value.
Period Scram
Specification;
Period scram 15 sec
Basis; A positive period will be obtained in the subcritical assem
bly for any addition of reactivity beyond a given steady state condition.
If the maximum reactivity insertion rate of 0.05 $/sec is considered,
the initial positive period is about 50 sec and decreases monotonically
with time. The period channel has been determined to respond reliably
to periods = 50 sec. Originally, the period scram was set at 50 sec but
repeated scrams caused by the start-up of the neutron generator forced
the reduction of the scram period to 15 sec for operational reasons.
Average Neutron Flux and Neutron Flux Scram
Specification:
Ave neutron flux for
5 2
most reactive core 1.5 x 10 n/cm sec
5 2
Neutron flux scram 3.0 x 10 n/cm sec
Basis: the above are based on the average power calculated for the
assembly. Doubling of the flux will occur when 0.75 $ worth of reac
tivity is added to the system from any design subcriticality level.
Under these conditions, even at the maximum k^^ status, the facility


LIST OF FIGURES
FIGURE Page
1 OVERALL VIEW OF THE FACILITY .. 6
2A BOTTOM FUEL ROD SPACING SYSTEM 12
2B BOTTOM FUEL ROD SPACING SYSTEM 13
3 TOP FUEL ROD SPACING SYSTEM 14
4 REACTIVITY-CONTROL FLOW SYSTEM 16
5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE
WEIR APEX 18
6 WEIR "BOX 19
7 AIR SYSTEM SCHEMATIC 21
8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM 23
9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT 44
10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS 49
11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM 51
12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM 52
13 TIME PROFILES OF NEUTRON BURST RECORDED BY
CONVENTIONAL ELECTRONIC INSTRUMENTATION AND BY THE
TIME-PICKOFF SYSTEM 58
14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME
CORRECTION AS A FUNCTION OF COUNT RATE 60
15 DETECTOR POSITIONING SCHEME 69
16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL 71
16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT 72
xiii


.WEIR DRAIN
DISTRIBUTION MANIFOLD
PUMP
FIG. 4 REACTIVITY-CONTROL FLOW SYSTEM
CONTROL
VALVE
-0
ORIFICE


62
The Analyzer Method is intrinsically more accurate than the
Integral Count Method because it permits an "exact" correction for
resolution time, losses by the use of the expression previously given
applied to the recorded time profile. The correction for the integral
counts is, on the other hand, inaccurate since the count rate is con
tinuously changing and no base exists for a resolution time correction.
It was found, however, that as long as the count rate near the
peak of the pulse is kept well within the capabilities of the NDDAS no
significant difference is observed in the results of the two methods.
This is due to the fact that ratios are being taken in both cases; this
tends to minimize whatever differences there might be. Thus, it is
concluded that with proper care the Integral Method is adequate whenever
an analyzer is not available for normalization purposes.
It should be noted that an "effective" resolution time can be used
to improve the results of the Integral Method. This "effective" reso
lution time can be found by forcing the normalizing ratio obtained from
two runs by the Integral Method to match the normalizing ratio obtained
from the Analyzer Method for the same two runs by adjusting the reso
lution time correction applied to the integral counts.
Comments
Certain inconsistencies in the results of the first few experi
ments prompted a careful inspection of the multichannel analyzer modus
operandi. For the sake of completeness the significant findings are
listed below.
A) Operation with the 10 microsec channel width (selected by the
settings of the 212 plug-in-unit) proves to be unreliable due to insta
bilities in the clock and gating circuits. Channel widths of 20


157
Method of Analysis
The following method of analysis was applied to the calculated
and measured results of the UFSA R1 clean core space-time studies:
1. A conventional zeroth moment Fourier transformation was
performed on the experimental data. The numerical integration employed
Simpson's rule of integration. Equal time steps (30 microsec) were
used throughout this analysis. The number of data points varied from
500 to 800, depending on where a stable neutron background was reached,
as determined by an statistical analysis performed in the UNIPUL pro
gram. A computer code, MORE, was coded for this purpose.^"
2. A conventional zeroth moment Fourier transformation was
performed on the space-time results obtained from the WIGLE calcula
tions. It should be recalled that the WIGLE calculation employs a
series of time increments in different time intervals. To conform to
this scheme Simpson's rule of integration with different time incre
ments was used for each time interval. Trapezoidal integration was
used to bridge the gap between the different time intervals. A computer
program, MORWIG, was coded for this purpose.
3. The amplitudes and phases of the zeroth Fourier moment as a
function of frequency, obtained from the MORE and MORWIG numerical
transformation, were least-squares fitted to obtain the damping coef
ficient and the phase shift per unit length for the frequencies of
interest.
In this manner, the theoretical and experimental results in the
1. The MORE and MORWIG programs were coded by Dr. M. J. Ohanian,
University of Florida.


83
phenomena was studied.
The space-time data was also analyzed in the frequency domain by
numerically obtaining the amplitude and phase of the zeroth Fourier
moment of the pulse. The experimentally determined dispersion law of
the system is compared to that predicted by the WIGLE scheme. The
results of the WIGLE calculations performed for the analysis in the
time domain were Fourier analyzed so that a one-to-one comparison could
be performed.
Space dependent effects on reactivity measurements were studied
by analyzing the pulsed data using the Garelis-Russellmodel.
Nomenclature- Used in the Description of Pulse
Propagation Phenomena
A series of directly measurable or inferred parameters are used
to describe the pulse propagation phenomena, in the time and in the
frequency domain. The most important of these parameters are defined
below. The pulse shapes and the conventional full-width-at-half-
maximum also form part of the analysis.
Delay Time
The delay time, t^, is defined as the time displacement of the
peak of the pulse from a reference position to the position under con
sideration. In this work all delay times are referred to zero time;
this corresponds physically to the initiation of the pulse at the
neutron generator.
Propagation Time
The propagation time of a narrow pulse in the assembly is defined
as the delay time between two extreme positions in the assembly.


68
these systems [15].
Becker and Quisenberry were able to compute a correction [16] for
the observed spatial dependence of the reactivity in two-region systems
by recognizing the differences in the spatial distributions of prompt
andjdelayed neutrons. Their excellent comparative study of the above
techniques emphasized the need for their recommended spatial correction
unless the neutron detector is properly positioned to minimize this
correction.
The study of Garlid and Bierman [17] correctly points out that in
very large systems "an asymptotic spatial distribution cannot be estab
lished before the pulse has decayed away, since the asymptotic mode is
one that is uniform everywhere in space." They proceed to apply a
combination of first flight, age, and time-dependent diffusion theory
to the study of pulsed measurements in large aqueous media; their con
clusion is that their measured apparent decay constant is a good ap
proximation to the asymptotic value and that pulsed measurements in very
large multiplying systems may also give good results.
Inverse Multiplication Measurements
The safe approach to the design value of k^^ <^99 was undertaken
with the conventional 1/M measurements until k ~0.95 and then by both
eff
the 1/M and the pulsing technique.
To establish detector positions free from geometrical effects
(source-detector-water level), six different locations were used until
a water level of 60 cm (k ~ .98) was reached and four locations afterwards
Two of the detector locations, the closest to the neutron source, failed
to describe the multiplication of the system. Shown in Fig. 15 are the


FLUX (RELATIVE UNITS)
FIG. 23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
111


181
Using a calculated value of = 0.0079 for this assembly configura
tion, the absolute value of the reactivity p, is obtained. The cor
responding value of k^, is then found by the relation
k =
eff 1 + p
Shown in Fig. 50 are the measured absolute reactivity and ke££ as a
function of position in the lattice. It is obvious from what has been
said above regarding the behavior of a and kg/£, that a meaningful
value for either k ,, or p cannot be obtained in this case until 143
cm separate the source and detector. The assigned value of k^^ was
0.990+.003. This value compares very favorably with a value of
0.990+.0025 found by inverse multiplication measurements and a calcu
lated value of 0.9906. Although the agreement obtained could be some
what fortuitous, it can be said that a representative value of the
reactivity was found. It seems that, if proper care is taken, the
pulsed reactivity measurements will yield good results in large multi
plying media.
Region-wise Dependence of the Reactivity Measurements
Becker and Quisenberry, as well as Waltar and Ruby [49] have
pointed out the spatial dependence of pulsed source reactivity measure
ments in two-media systems. Differences in the measured reactivity can
be present whether the detector is located in the core or in the reflec
tor.
A series of pulsed source traverses were conducted across the UFSA
R1 clean core and reflectors, at three different distances from the
source. No differences were found for this core in the reactivity
measured in the core or in the reflector. Shown in Table XIX is a


102
16.35
i r
i i
i i
K?.5-h
i i
-^pss
in
co
r\
-1
vJ
m
m
co
i
\o
FIG. 20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE


194
MORE punches in cards the amplitude and phase of the zeroth
Fourier moment of the pulse for input to the ALXILS program. A com
plete description of the program and input requirements can be found
in Ref. 55.
MORWIG
The MORWIG program is a version of the MORE code written to
perform a numerical Fourier transformation on a pulse with unequal
time steps. It is intended specifically for the neutron wave type
analysis of the space-time data calculated by the WIGLE scheme. See
Ref. 56 for a complete description.
ALXILS
The FORTRAN IV, IBM 360 program ALXILS performs a least-squares
fit of the amplitudes and phases obtained from the Fourier transforma
tion performed by either the MORE of the MORWIG program. A linear
least-squares scheme is- used. The values of ALPHA are obtained by fit
ting the log amplitude vs. distance for each frequency. The values of
XI are obtained by a linear fit of the phase angle vs. distance. The
channel chopping technique is used to determine the convergence of a
and £ in space. The weighting of the points can be set to (1/observed
value) or to equal weights. Statistical quantities determining the
"goodness of the fit" are calculated for each fit. A complete descrip
tion can be found in Reg. 57.
MULTIPLOT
The FORTRAN IV, IBM 1800 computer program MULTIPLOT used the out
put of the UNIPUL and/or the WIGLE codes to plot the time profiles of


FLUX (RELATIVE UNITS)
FIG- DIO TIME PROFILE OF FAST NEUTRON FLUX EG-58 CM FROM THE SOURCE


57
Shown in Fig. 13 are two time pi-ofiles obtained at the same posi
tion in the UFSA core for the same count rate. The conventional
preamplifier-linear amplifier system shown above was used to obtain one
of the profiles and the instrumentation selected for this work was used
to obtain the other. Both were corrected for resolution time losses
with the best available value for the resolution time. The distortion
observed in the pulse shape obtained with the conventional preamplifier-
linear amplifier system is non-linear due to the count-rate dependent
resolution time. It should be noted that the count rate near the peak
of the pulse was less than 10^ count sec. The conventional system
response "flattens out" when it reaches complete saturation in this
case above 10^ count sec. Saturation effects are not observed in the
pulse transformer system until the count rate exceeds 3.3 x 10^ count
sec. An erroneous resolution time correction, or one which used a
resolution time that does not characterize the system throughout the
range of count rates will change the shape of the neutron pulse and
consequently affect any analysis done on the pulse shape obtained.
As pointed out by Bierman, Garlid and Clark [11], in a pulsing
experiment it is necessary to determine whether the counting system
has the characteristics of a purely non-paralyzing system or those
of a mixture of paralyzing and non-paralyzing systems. Using the
method described by Bierman and co-workers, it was established that
the data acquisition system being used in the present work is, as
close as can be determined, non-paralyzing. The resolving time of the
system is essentially determined by the width of the input pulse to the
analyzer and the MCA characteristics.
It should be noted that for a wide range of count rates, depending


176
Shown in. Fig. 48 are the experimentally determined decay constants
as a function of position in the assembly, for a 0.5 and 1.0 msec input
pulse. As distance to the source increased, more "waiting" time was
available to extract the decay constant. The values found past P83 are
believed to represent the fundamental decay constant of the assembly.
It should be noted that the instantaneous decay constant at dif
ferent times after the pulse was calculated for all the detector posi
tions in the assembly, using the WIGLE code. The results agree closely
with those measured experimentally at different times after the peak.
The two-group, space-time dependent model describes well the observed
phenomena.
The Ratio k8/5,
The Garelis-RusseUtechnique was applied to the two-medium system
referred to as the UFSA R1 core. The measured kg/5, values, determined
as a function of distance from the source, showed a "spatial" depend
ence. This was somewhat surprising since the detector was supposedly
located to minimize the Becker-Quisenberry correction [16] and a more
uniform value of kg/5, was expected. Although the model lacks a good
energy representation of the system being studied such a strong spatial
variation in kg/5, was not expected.
Shown in Fig. 49 are the measured kg/5, values for input pulses of
0.5 and 1.0 msec. A prominent feature is the noticeable difference
between the results obtained with the two different, finite width
input pulses. Attention was focused on the sensitivity of the Garelis-
RusselLmodel to the finite input pulse widths use in the experiments.
As mentioned previously, the model utilizes a delta function input


74
TABLE III
SUMMARY OF 1/M AND PULSED MEASUREMENTS
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
INVERSE MULTIPLICATION PULSED EXP PREDICTED
Moderator3 keff k0ffb keff
Height (cm) Pos. 1 Pos. 3 Pos. 5 Pos. 6
20
.415
.481
.425
.581
.7675
25
.744
.629
.705
.771
.8287
30
.867 .
.737
.824
.865
.871
35
.914
.794
.881
.900
.9022
40
.944
.84
.908
.927
.925
45
.9612
.873
.934
.946
.9419
50
.973
.895
.950
.961
.948+.01
.955
55
.98
.918
.962
.969
.965+.007
.9655
60
.985
.936
.973
.971
.972+.006
.974
65
.9891
.95
.980
.979
.9796+.005
.980
70
.9925
.96
.9853
.986
.9855+.004
.986
75
.9949
.971
.989
.990
.990+.003
.9906
80
.9944
85
.9976
91.4
1.00117
Above
bottom of ,
active fuel
Averaged from 3 <
detector positions


135
The Full Width at Half-Maximm (FWHM)
The FWHM is defined as the time-width of the pulse at half the
peak amplitude. The FWHM is one of the parameters conventionally used
to compare pulse shapes and is therefore included in this study.
An analysis of the experimental and calculated values of the FWHM
tabulated in Tables VII and VIII showed the following.
a) Close to the source, theory predicts slightly larger FWHM
values than experiment, the difference decreasing with distance from
the source. As discussed above the discrepancy near the source is due
to difficulties in adequately describing the void region behind the
source.
b) Between P27 and P34 the FWHM are practically identical.
c) Past P34 the experimentally determined FWHM becomes increasing
ly larger than the WIGLE prediction. The maximum difference is about
350 microsec which corresponds to ~ 8% of the experimental value.
The agreement is still considered to be very good.
The Flux Shapes
A detailed comparison of the theoretical and experimental flux
shapes obtained for the UFSA assembly was also made.
Plots of the time profiles of the thermal flux at each detector
position are included in Appendix C for the 0.5 and the 1.0 msec wide
source pulses. The peaks are normalized to unity.
The following information is supplied in each figure:
a) Identifying Run Number
b) Location of the Experimental Peak in Time
This parameter is determined directly by a computer routine which is
part of the plotter program. The routine simply finds the time channel


15
Moderator Flow Control System
The moderator flow control system of the UFSA can be better des
cribed by'the water flow schematic shown in Fig. 4. Besides the normal
fill and drain functions for the moderator, it serves as an accurate
reactivity control using adjustable moderator height by continuous flow.
The characteristic components of this system are described below,
A. Storage Tank: A 6 x 8 x 2 foot steel tank located directly
below the assembly will serve as the reservoir for the circulating
light-water moderator and as a dump tank. Normal water heights while
operating will be between 6 and 12 inches. The tank also serves as a
footing for the assembly supports. This arrangement makes a very con
venient and compact facility.
B. Core and Reflector Tanks: As seen from the flow diagram, water
is pumped from the reservoir to the core and reflector tanks through a
manifold at one end of the assembly and flows from the other end of the
core and reflectors tanks to the weir "box". From the weir "box", water
flows over the weirs back to the storage tank through a flexible line.
The core section is equipped with two normally open solenoid
activated dump valves, 3 inches in diameter, located at each end of the
core. These valves provide the reactor with a fast shutdown safety
system. The reflector tanks have their own 1 1/2 inch normally open
solenoid valves actuated by the same safety system.
Since the quantity of water discharging through a V-notched weir
5/2
varies as H where H is the height of the water level above the apex
of the V-notch, the water level and hence, the reactivity, can be con
trolled in a precise manner simply by varying the height of the weirs
and the rate of flow of water into the tank. This is accomplished by


TABLE VII
CLEAN CORE PULSE PROPAGATION STUDIES
EXPERIMENTAL AND THEORETICAL RESULTS
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ration
16.35 cm wide reflected core
POSITION
DISTANCE TO
PEAK
AT (msec)
FWHM
(msec)
PEAK
COUNTS3
NO
SOURCE (cm)
Theory
Exp
Theory
Exp
Theory
Expb
6
3
0.500
0.50+.01
0.542
0.540+.03
81.22
94.8+6
13
15.71
0.501
050+.01
0.615
0.540+.03
72.68
81.9+5
20
28.43
0.504
0.52+.01
0.779
0.779+.03
48.13
49.9+.8
27
41.15
0.635
0.63+.01
1.098
1.080+.03
27.35
32.7+1.6
34
53.86
0.840
0.82+.03
1.398
1.470+.06
16.37
16.5+.4
41
66.58
1.060
1.04+.03
1.766
1.800+.06
10.27
10.6+.5
48
79.30
1.300
1.28+.03
2.055
2.13+.06
6.65
6.4+.3
55
92.01
1.560
1.50+.04
2.355
2.52+.09
4.42
4.39+.11
62
104.73
1.840
1.82+.04
2.655
2.82+.09
3.00
2.97+.10
69
117.44
2.125
2.11+.04
2.925
3.11+.09
2.055
2.03+.06
76
130.16
2.400
2.40+.05
3.195
3.42+.09
1.427
1.53+.07
83
142.88
2.700
2.65+.06
3.465
3.72+.09
1.000
1.00+.005
90
155.60
3.000
2.96+.06
3.735
3.90+.12
0.7056
0.7062+.03
97
168.31
3.300
3.29+.06
3.900
4.17+.12
0.5000
0.5065+.02
104
181.03
3.570
3.50+.06
4.050
4.38+.12
0.3534
0.362+.007
111
193.74
3.810
3.85+.08
4.125
4.44+.12
0.2460
0.2512+.005
118
206.46
4.000
4.00+.08
4.200
4.47+.12
0.1630
0.1764+.004
125
219.17
4.150
4.18+.08
4.200
4.47+.15
0.0957
0.1161+.0035
132
231.88
4.210
4.21+.09
4.200
4.53+.15
0.0367
0.0437+.003
a Normalized to Position 83
b Errors assigned from the deviation from the mean of two measurements except for the last 5 space
points. This error is usually larger than the counting statistics error. The error of the last 5
points was calculated from counting statistics.
127


149
characteristic propagation time (^3.7 msec) across the assembly of a
narrow (0.5 msec) pulse. It should be recalled that the Johnson
criterion [47]postulates that to be able to observe spatially dependent
effects, the HWHM of the input pulse should be smaller than the charac
teristic propagation time across the assembly. For example, the experi
ments of Miley and co-workers at the University of Illinois [20, 21, 22]
showed that for an initially asymptotic very wide input pulse no shape
changes were observed as the pulse "propagated" across the assembly.
The pulse shapes resulting from these measurements at three posi
tions in the assembly are shown in Appendix F. The delay times, the
FWHM and area under the pulses, normalized to unity at the first posi
tion, are given below in Table XIV.
TABLE XIV
DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE
DISTANCE TO
SOURCE (cm)
PEAK AT
(msec)
FWHM
(msec)
AREA UNDER
THE CURVE
41.2
10.07
10.1
1.0
79.3
10.17
10.7
1.15
142.9
10.22
10.5
0.92
From these results it seems that, although the delay times between
the recorded peaks are quite small a certain "rearrangement" of the
initially non-asymptotic pulse takes place. Close to the source the
pulse is practically square, at a distance of 79 cm it has widened some
what and at large distances from the source the pulse seems to be trying
to achieve the normal "dumbbell" shape. Johnson's criterion appears to


73
the multiplication.
Shown in Table III are the values estimated for k for the four
eff
locations that seemed to represent the system best. Position 3 gives
a lower limit and Position 1 an upper bound. No attempt was made to
establish the error associated with measured k but it is believed
eff
that the 0.99 value obtained at the last water level is within +.005
of the true value.
Absolute Determination of kef£
After an estimated value of k >.95 was obtained from the 1/M
eft
measurements, an independent determination of k was required by the
operating license at every new increment in the moderator level (as
determined by the criteria established in Part 1, Chapter 3). The
technique chosen for this determination was the Garelis-Russell method
of measuring k3/& and a simultaneous determination of the prompt funda
mental decay constant.
Different detector locations were used to determine the influence
of the source and of higher order harmonics contamination. Strong
"spatial effects" were observed in both a and k3/£. This phenomena will
be discussed in detail in Part 2, Chapter V because of its importance.
A seemingly true fundamental decay constant and "spaced-converged"
kS/i were obtained at large distances from the source and were used to
determine the reactivity of the system.
A Fortran IV, IBM 360 computer program named UNIPUL was coded to
perform a unified analysis of the pulsed neutron data (see Appendix B).
The program calculates the decay constant using Peierl's statistical
analysis [18] and k8/£ using the Garelis-Russellapproach after the data


56
scrutiny.
The resolution time of several, submicrosecond preamplifier-linear
amplifier combinations was shown to be a function of the mode of opera
tion and of the count rate. For this type of instrumentation, there is
a significant difference between the resolution time as determined by a
steady-state technique (two source method) and a dynamic method (maximum
count rate method [11]), the latter method yielding a much larger reso
lution time.
For the instrumentation finally chosen to carry out the pulsed
experiments in this work no significant difference was found between
the results of the two methods. Furthermore the pulse transformer-
amplifier combination behaves like an ideal non-paralyzing system. The
resolution time of the overall data acquisition system was found to be
primarily determined by the multichannel analyzer.
As a matter of illustration, when the system depicted below was
used the resolution time changed from -0.24 microsec as determined
under low count rate steady-state conditions to 8 microsec as deter
mined under high count rate, pulsing mode conditions.
ORTEC 410
Linear Amo
ORTEC 429
Scaler


4
at the SPERT IV facility at the National Reactor Testing Site, Idaho.
The appropriate existing experimental equipment, as well as the
extensive kinetics studies conducted by the Nuclear Engineering Sciences
Department at the University of Florida, was conducive to the granting
of a subcontract by the Phillips Petroleum Company so that the basic,
linear kinetics studies of Phase I could be performed at the University
of Florida.
The research to be performed as Phase I of the Large Core Dynamics
Experimental Program can be succinctly defined as the experimental and
analytical determination of the dynamic behavior of the neutron flux in
slightly subcritical water moderated assemblies of SPERT F-l fuel rods.
The facility in which the required measurements for Phase I, Large
Core Dynamics Experimental Program, are to be conducted necessitated a
thorough design and safety analysis. The assemblies are to be close to
critical and the core has a large U235 inventory. The nuclear capabil
ities of such systems were the object of a detailed study to determine
their operational characteristics under normal and accident conditions.
The flexible mechanical design, the safety instrumentation, the
nuclear evaluation, as well as the experimental calibration of the
first configuration under study constitutes Part 1 of this dissertation.
The reactor kinetics studies performed in the first of the con
figurations to be studied are dealt with in Part 2 of this manuscript.


Page 2 of 2
Internet Distribution Consent Agreement
In reference to the following dissertation:
AUTHOR: Diaz,Nils
TITLE: Space-time reactor kinetics studies with the University of Florida SPERT
Assembly, (record number: 955726)
PUBLICATION DATE: 1969
i. K\vW A. as copyright holder for the aforementioned
dissertation, hereby grant specific and limited archive and distribution rights to the Board of Trustees of
the University of Florida and its agents. I authorize the University of Florida to digitize and distribute
the dissertation described above for nonprofit, educational purposes via the Internet or successive
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5/28/2008


Frequency
FIG. 46 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED 2 a K
172


FLUX (RELATIVE UNITS)
FIG- D3
TIME PROFILE OF FAST NEUTRON FLUX 53-BG EM FROM THE SOURCE
238


37
Drain rate, including the system
reaction time 2.65 cm/sec
Rate of removal of reactivity 0.00037 Ak/cm
0.00098 Ak/sec
0.140 $/sec
it should be noted that the value of Ak/cm used to specify the reac
tivity removal rate is ~ 20 times smaller than the corresponding value
specified for the reactivity insertion rate.
Basis: the rate of drainage from the assembly established the
reactivity removal rate. Consistent with the approach taken when
specifying the reactivity, the time to drain 45 cm of water from the
assembly was measured to establish a lower limit on the rate of de
crease of water height. Even under these extreme assumptions, i.e.,
using the maximum slope of the k^^ vs. water height curve for the
insertion rate, the small calculated slope around k^^.99 for the
removal rate and the reduced pressure head, the reactivity removal rate
is three times larger than the insertion rate.
Subcritical Assembly Power Level and Power Level Scram
Specification:
Power Level 0.5 watt
Power Level Scram 1.0 watt
Basis: with the maximum source strength available and with k^^ =
0.985 the maximum average power was calculated to be .130 watts by
taking into account the spatial dependence of the flux and a steady
source at one end.
Assuming that a reactivity accident occurs, based on the maximum
reactivity addition rate specified above, the design basis accident


34
loading, and will be followed for subsequent cores:
1) After the fuel has been loaded, prior to each new incremental
change in the water level, the water is drained completely and the weir
(and water level scram) adjusted to prevent a level increase beyond the
desired value.
2) The first three measurements of the inverse multiplication are
obtained at water heights of approximately 20 cm, 25 cm, and 30 cm above
the bottom of the active fuel. As shown in Table I, the maximum k
eff
calculated for a water height of 30 cm is 0.87. Subsequent filling
increments are not to exceed the least of the following:
a. An increase in water height of 10 cm.
b. An increase in water height which, by extrapolation of the
inverse multiplication curve, would increase the kg^^ by one-half of the
amount required to make the assembly delayed critical.
c. An increase in water height which would, by extrapolation of
the inverse multiplication curve, result in a kg_^ of 0.990. For values
of k^^ above 0.95, the k^^ of the assembly are also determined by
pulsed source techniques.
3) At each filling step, the measured kej£ of the assembly is
compared with the calculated value. If significant deviations of the
experimental values from the calculated kg^^ vs. water height curves
occur, the experiments are to be discontinued, and a detailed analysis
of the results obtained performed. If it is determined that the dimen
sions of the assembly should be changed in order to achieve the desired
ke^ at maximum water height, the University of Florida will apply for
and obtain written approval from the Atomic.Energy Division of the
Phillips Petroleum Company before such changes are made.


94
however for the fast group. Although the results for the epicadmium
flux obtained in these measurements will be presented, they should be
looked on with the reservation that the energy-dependent neutron
counting statistics invalidate the one-to-one comparison with calcu-
lational results. The epicadmium flux was obtained primarily for the
necessary correction of the time profiles. The analysis of the thermal
neutron group is duly emphasized.
Shown in Fig. 18 is a typical plot of the total and epicadmium
time profiles recorded in the experiment and the thermal pulse shape
obtained by subtraction. The magnitude of the correction is space-
dependent, since no constant thermal/fast ratio (as detected by the
counter) was observed. The correction varied from 3-10% of the total
flux values.
The Geometrical Arrangement
Shown in Fig. 19 is a plan view of the source-subcritical assembly
arrangement used throughout this work. The detector positions used for
the measurements are clearly indicated. The numbers shown correspond
to the positions of fuel pins with respect to the end of the assembly
facing the neutron generator. There were 7 grid-holes between detector
positions, giving a distance of 12.72 cm between data points. Through
out the rest of this report the positions of the data points will be
referred to as PXX, where XX is the grid-hole number at which the data
was recorded, i.e., P41 refers to position number 41 starting from the
front face of the assembly. A total of 134 rows of fuel pins were in
the assembly. Data was taken at nineteen spatial points for the main
part of the research. The target assembly of the neutron generator


FLUX (RELATIVE UNITS)
FIG. 35C THE SENSITIVITY OF THE ONE-DIMENSICNAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING
143


FLUX (RELATIVE UNITS)
FIG- D6
TIME PROFILE OF FAST NEUTRON FLUX 133-7-4 CM FROM THE SOURCE


FLUX (RELATIVE UNITS)
FIG* G2 SHAPE DF THE PROPAGATING PULSE AS A FUNCTION OF PULSE WIDTH
- EXPERIMENTAL -
257


FLUX (RELATIVE UNITS)
FIG C33 TIME PROFILE OF THERMAL NEUTRON FLUX IBB*31 CM FROM THE SOURCE


Chapter v
EXPERIMENTAL AND THEORETICAL
RESULTS IN THE FREQUENCY DOMAIN
Introduction
The results of the pulse propagation measurements and of the space
time-dependent WIGLE calculations were analyzed in the sensitive Fourier
transform plane. This neutron wave type analysis probes into the defi-
ciences of the model and/or the experimental data that the analysis in
the time domain might fail to reveal. In this study the analysis is
performed with the sole intention of testing the model and not to ex
tract parameters.
The WIGLE predicted time profiles of the propagating disturbance as
a function of space and the pulse propagation data were Fourier analyzed
in an identical manner; the amplitude and phase angle of the zeroth
Fourier moment thus obtained were least-squares fitted (log amplitude vs.
z and phase angle vs. z for each frequency of interest) yielding the
damping coefficient, a, and the phase shift per unit length, £. The
predicted and measured dispersive characteristics of the system are then
2
compared in the p and p plane.
The neutron wave analysis was applied to both the 0.5 and 1.0 msec
input pulse space-time measurements and calculations.
156


TO
ZENA


FLUX (RELATIVE UNITS)
NORMALIZED TD
THERM-5- 20
PULSE WIDTH = 0-5 MSECS
TIME CM;
E)
FIG. 27A EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
122


FLUX (RELATIVE UNITS)
FIG- C35 TIME PROFILE OF THERMAL NEUTRON FLUX 193-74 CM FROM THE SOURCE
231


FLUX (RELATIVE UNITS)
FIG* C27 TIME PROFILE OF THERMAL NEUTRON FLUX 32-01 CM FROM THE SOURCE
223


183
TABLE XIX
REGION-WISE DEPENDENCE OF THE REACTIVITY MEASUREMENTS
Measurement across the core width
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm wide reflected core
POSITION
NO
DISTANCE TO
CORE CENTER
(cm)
a
, -Is
vsec )
k B/i
(sec
P
k
eff
A
7.27
508
205
.01169
.9884
B
5.45
504
2C7
.01132
.9888
C
3.63
497
208
.01102
.9891
D
1.82
505
207
.01137
.9887
E
0.0
517
203
.01227
.9878
F
3.63
504
209
.01119
.9889
G
5.45
510
206
.01168
.9884
H
7.27
503
207
.01124
.9889
I
10.9
512
203
.01205
.9881
RE2
14.3
501
205
.01147
.9887
RE4
17.9
490
199
.01154
.9886
RE6
31.8
474
187
.01214
.9886


29
total solid angle subtended by any unit in the array to be 6 steradians
if the effective multiplication factor for the individual slabs is less
than 0.3, as is the case here.
From 10.CFR 70.52 (d) (2) (i) the minimum required separation dis
tance, i.e., center of one slab to face of adjacent slab, is obtained
from:
3 steradians =
cross sectional area
2
(separation distance)
14 x 3
This gives, separation distance = ( ^) = 3.74 ft.
We propose to establish a minimum distance between faces of adja
cent slabs of 4.5 ft. This gives a total solid angle for the center
slab of 3.88 steradian, which is well below the established criteria,
c. Comparison with Clarks criteria
For 5% enriched, 0.4 inch diameter uranium oxide rods with a 190.13
gm/liter U-235 concentration (compared to 4.81% enriched, 0.42 inch
diameter uranium oxide rods with a 200 gm/liter U-235 concentration in
our case) the following data is obtained from pp. 39 and 59, respectively,
of DP-1014:
Width of Slab (cm)
Critical Safe
11.2 10.4
_2
Buckling (cm )
Critical Safe
0.014945 0.015912
It should be noted that the slab widths quoted on page 39 of DP-1014
are for an infinite water-moderated and reflected slab. From the buck
ling values given, the critical width of the infinite water-moderated
unreflected slab is 25.7 cm; the corresponding safe width is 24.9 cm.
When twice the reflector savings for the latter case as given on page
59 of DP-1014 is subtracted, a safe width for the infinite, water-


52
FIG. 12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM


115
important since the one-dimensional WIGLE calculations cannot account
for transverse propagation of a disturbance.
Static Flux Traverses
Shown in Figs.25 and 26 are the mapped steady-state fluxes across
the height and the width of the core respectively, at a distance of
66.6 cm from the neutron source. This location was chosen because'the
delay time and attenuation of the pulses showed it to be at the begin
ning of the "asymptotic region", viz. the region in which both the
velocity of propagation and the relaxation length have reached their
asymptotic values. Both flux maps were done with Indium foils and
appropriate corrections were applied to account for self-shielding and
interference (shadowing) effects between foils.
The fluxes calculated from four-group diffusion theory using the
AIM-6 code are displayed together with the experimental data. A cosine
fit was made on the vertical flux and is shown as a solid line in
Fig. 25; the fit obtained was excellent. The analysis of the results
in this direction gives an extrapolation distance between 5 and 7 cm.
The results were not as consistent across the width of the core.
A sophisticated aluminum foil holder was built to permit the location
of the foils between two rows of fuel; the foils were inserted in slots
parallel to the axis of the assembly. Due to the mechanical difficulty
of positioning the foils in the assembly, the physical impossibility of
having them perfectly horizontal and the arduous, significant correction
due to the short distance between foils, only one irradiation was per
formed. When all this is taken into account the results look reason
able. It was found that the bowing of the fuel rods affected these
measurements significantly. This was determined by positioning the


114
FIG. 24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE
13
12
11
10
9
8
7
6
5
4
3
2
1
0


147
group pulse shapes. Several typical examples are shown in Appendix
D. The following features were observed:
1. The calculated pulse shapes are delayed in time in comparison
to the measured shapes throughout most of the length of the assembly.
2. The measured and calculated attenuation of the peaks is in
poor agreement.
3. The measured and calculated pulse shapes are practically
identical.
The validity of the comparison between theory and experiment in
this instance is not clear, however. The main question is whether the
experimental measurement corresponds to the fast group used in the
calculations, since the sensitivity of the detector rapidly diminishes
with increasing neutron energies. Therefore the conclusions based on
the above comparison must be taken with some reservation, until a more
detailed study can be conducted.
Propagation of a Narrow Pulse
A series of measurements were made in the clean core utilizing a
100 microsec wide input pulse. Only 4 positions along the longitudinal
axis were studied. The purpose of these measurements was to obtain a
qualitative idea of how well the WIGLE scheme can predict the space-
time kinetic behavior of a system perturbed by a very narrow pulse.
From the experimental viewpoint the narrow input pulse resulted in
much poorer count rates, thus requiring longer data acquisition times.
Listed below are the calculated and measured FWHM and delay times
for these measurements; the pulse shapes at the different positions
are included in Appendix E.


flux (relative units)
TIME PROFILE OF THERMAL NEUTRON FLUX 15*71 EM FROM THE SOURE'E
FIG- C2


PREFACE
The text of this dissertation is divided into two related but
essentially independent parts:
Part 1. The University of Florida SPERT Assembly
- Design and Calibration -
Part 2. Space-Time Reactor Kinetics Studies with the
University of Florida SPERT Assembly
In Part 1, the design, operational safety and nuclear calibration
of the large-in-one-space dimension, highly multiplicative University
of Florida SPERT Assembly (UFSA) are described. The presentation of
this material is pertinent for a complete understanding of the physical
characteristics of the system to be studied in Part 2 and also because
the system in itself is interesting from the nuclear engineering point
of view. The data acquisition system used for the experimentation is
presented in Chapter IV of this section.
In Part 2, the linear reactor kinetics studies performed with the
UFSA are presented. The space-time dependent distribution of the
neutrons in the assembly, following the introduction of a burst of
neutrons at one end of the core, are studied in the time and in the
frequency domain.
The study of the spatially dependent time profile of the neutron
flux required a large number of figures containing the calculational
and experimental results at different positions in the core. Some
typical figures are included in the main text but most of the recorded
(and calculated) time profiles are included as appendices to the main text
v


APPENDIX G
UFSA R1 CLEAN CORE
SHAPE OF THE PROPAGATING PULSE
AS A FUNCTION OF INPUT PULSE WIDTH
Pulse Width (msec) = 0.1,0.5,1.0,2.0,3.0,
4.0,5.0,6.0,7.0,8.0,
9.0,10.0


LIST OF TABLES (cont'd)
TABLE Page
XVITHE REAL AND THE IMAGINARY COMPONENTS
OF THE COMPLEX INVERSE RELAXATION LENGTH
- 0.5 MSEC INPUT PULSE 164
XVIITHE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
- 1.0 MSEC INPUT PULSE 165
XVIIITHE DECAY CONSTANT AND kB/i VALUES MEASURED
AS A FUNCTION OF INPUT PULSE WIDTH 180
XIXREGION-WISE DEPENDENCE OF THE REACTIVITY
MEASUREMENTS 183
xii


FLUX (RELATIVE. UNITS)
FIG D1
TIME PROFILE OF FAST NEUTRON FLUX 1571 CM FROM THE SOURCE


TABLE OF CONTENTS (contd)
Page
CHAPTER V EXPERIMENTAL AND THEORETICAL RESULTS IN
THE FREQUENCY DOMAIN 156
Introduction 156
Method of Analysis ... 157
Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis 159
CHAPTER VI SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS 174
Introduction ... 174
The Decay Constant 175
The Ratio kS/& 176
The Measured Reactivity and ke^ Values 179
CHAPTER VII CONCLUSIONS 185
APPENDICES
A CALCULATIONAL PROCEDURES USED IN THE DETERMINATION
OF THE NUCLEAR PARAMETERS AND THE k _ VALUES 187
eff
B DESCRIPTION OF THE COMPUTER PROGRAMS 191
C UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT NINETEEN CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC 196
D UFSA R1 CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX AT SEVERAL CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC 235
E UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT FOUR POSITIONS
IN THE CORE FOR A 0.1 MSEC INPUT PULSE 248
ix


81
is the experimental verification of present space-time kinetics
models and to guide the development of new calculational techniques.
Phase I of the Large Core Dynamics Experimental Program is being
conducted at the University of Florida SPERT Assembly, under Subcon
tracts C281 and C635 with the Phillips Petroleum Co. This part of the
program will provide the most fundamental neutron physics type of in
formation as the redistribution characteristics of the neutron flux in
a close-to-critical assembly are studied in the absence of inherent
feedback effects. The adequacy of basic parts of the analytical models
can be tested accurately by concentrating on the neutron physics
problem.
In this work, the propagation of a narrow, non-asymptotic neutron
burst is studied in the time and in the frequency domain. The experi
mental results are compared with results obtained from the two-group,
space-time dependent, one-dimensional diffusion theory calculational
scheme known as the WIGLE program [24]. A stringent test of the model
is provided by a combined analysis in the time and frequency domain.
Clean, unambiguous experimental information will be shown demonstrating
the presence of spatial effects in large cores.
Description of the Study
Pulse propagation phenomena in a large-in-one-space dimension side
reflected core were studied by introducing a fast neutron burst through
one face of the assembly. A Cockcroft-Walton (TNC) type generator was
employed to produce square neutron pulses of selected widths using the
(d,t) neutron reaction.
The assembly which was studied is described in detail in Part 1


113
FIG. 24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE


46
Logic signals have fixed amplitude-shape characteristic and convey
information by their presence, absence of time relationship with
respect to a reference signal. Only gamma and noise discrimination
are necessary; this process will inherently eliminate the counting of
weak neutron interactions.
The process of registering events whose density per unit time
varies considerably requires an electronic system with extremely high
time resolution and a broad frequency response. Typically the counting
rates at the peak of the neutron burst in pulsed neutron measurements
vary from 10^ to > 10^ event/sec. This high, time-varying count rate
caused drastic losses in conventional instrumentation due to pulse
pile-up and circuit induced distortion when the dynamic range of the
circuit is exceeded causing a net amplitude shift in excess of that
tolerable by the system. The alternative modus operandi is to use low
count rates so that resolution losses are minimized; this, however,
increases the probability of systematic errors due to much longer run
ning times.
The count rates encountered during the initial experiments with a
3
He counter close to the neutron generator target in the SPERT assembly
exceeded 10^ event/sec at the peak. Saturation effects were observed
in modular instrumentation incorporating the latest F.E.T. preamplifier
and double-delay line pulse shaping amplifier at about 10"* event/sec.
The fast pulse train caused a drop in the base voltage of the Field
Effect Transistor which prevented further counting until a significant
reduction in the count rate allowed the voltage to recover. Changing
to a fast scintillation prototype preamplifier improved the situation
somewhat. However, if the potential count rate in the UFSA assembly


FLUX (RELATIVE UNITS)
FIG- C29 TIME PROFILE OF THERMAL NEUTRON FLUX 117-44 CM FROM THE SOURCE


FLUX (RELATIVE UNITS)
FIG- C16 TIME PROFILE OF THERMAL NEUTRON FLUX 133-74 CM FROM THE SOURCE
212


BIOGRAPHICAL SKETCH
Nils J. Diaz was born in Moron, Cuba on April 7, 1938. He was
graduated in June, 1955 from LaSalle High School in Havana, Cuba. In
July, I960, he obtained the degree of Professional Mechanical Engine
ering from the University of Villanova, Havana, Cuba, with honors* He
worked as a plant design engineer from January, 1960 to April, 1961
and also as instructor of Machine and Plant Design at the University of
Villanova for two semesters after his graduation. He arrived in the
United States in October, 1961 and worked as a machine designer until
September, 1962. He then entered the Graduate School of the University
of Florida and received a Master of Science in Engineering in June, 1964.
He held a graduate assistantship and a Fellowship from the Organization
of American States until December, 1965. From January, 1966 to date he
held a Junior Faculty appointment, as an Engineering Assistant, in the
Nuclear Engineering Sciences Department of the University of Florida,
while working toward the degree of Doctor of Philosophy.
Nils J. Diaz is married to the former Zena G. Gonzalez and is the
father of three children, Nils, Ariadne, and Aliene. He is a member of
the American Nuclear Society and the Society of the SIGMA XI.
262


159
Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis
To determine the effect that the input pulse width could have on
the results of the wave analysis, the study was performed for both the
0.5 and 1.0 msec input pulse cases. These experimental and theoretical
results in the time domain were presented in Part 2, Chapter IV of this
work.
Shown in Figs. 38 through 41 are the amplitude and phase of the ex
perimental data obtained by numerical Fourier transformation, for both
the 0.5 and the 1.0 msec input pulses. The results for the 0.5 msec
case are consistently "smoother" than those for the 1.0 msec case. In
the 0.5 msec case the results "blow-up" past 1000 cps while the 1 msec
case seems to be good only to 800 cps. The behavior of the amplitude and
phase is as expected. The data was still good in a frequency region were
most wave type measurements in multiplying media reported to date had
already broken down. For example the experiments of Dunlap were only
good to ~ 250 cps [23]. Undoubtedly, the frequency content of the nar
row, fast burst is superior to the smeared pulse that is normally ob
tained if a thermalizing tank is used. The wave analysis on the WIGLE
space-time results showed an identical behavior throughout the fre
quency range.
The real and the imaginary components of the complex inverse
relaxation length are shown for both theory and experiment in Tables
XVI and XVII, for the 0.5 and the 1.0 msec input pulses respectively.
A graphical comparison of these results is shown in Figs. 42 and 43.
The following comments are pertinent:
a) A distinct but not significant difference is found between the
results of the 0.5 and the 1.0 msec cases in both theory and experiment.


134
The attenuation of the amplitude of the peaks for the UFSA assem
bly were shown in Figs. 31 and 32; the normalized peak values were
tabulated in Tables VII and VIII. Again excellent agreement was ob
tained between theory and experiment, not only in the asymptotic region
but throughout most of the assembly. The first two data points (P6 and
P13) are considerably larger in magnitude than the values predicted by
WIGLE. This is probably caused by an undercorrection for the epicadmium
flux detected at these positions and by not accounting for the signifi
cant neutron streaming in the large void created by the aluminum port
in which the target is located. Position 27 is probably the only "bad"
data point and no explanation has been found for its behavior since
four consecutive runs were made at that position and all four showed
identical behavior. The WIGLE results reflect the influence of end
effects more markedly than experiment. It should be noted that reflec
tions from the concrete walls in the assembly room are significant at
peripheral detector positions.
TABLE X
DYNAMIC INVERSE RELAXATION LENGTH <.
d
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm wide reflected core
Input Pulse
Width (msec)
Theory
Experiment
0.5
.03025
.0297+.0012
1.0
.03025
.0301+.0010


Inverse Multiplication
Moderator Level (cm)
FIG. 16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL


Delay Time (msec)
129

FIG. 29 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 0.5 MSEC INPUT PULSE -


184
list of the decay constants, kg/£, p and ke^ measured across the core
and side reflector at a distance of 130.2 cm from the source.
The core-reflector configuration investigated is too narrow to
observe any transverse propagation of the pulse; consequently no dif
ference in the value of the reactivity was measured across the system.
The value of a and of kg/£ obtained near the outer edge of the reflector
was low compared to the other values but somehow compensated each other
to maintain p approximately constant.


39
will still be subcritical and the instrumentation will have sufficient
time to scram the system before accidental criticality occurs.
Design Basis Accident Analysis
Two types of accidents have been postulated to occur in conjunction
with the UFSA experimental program. The design basis accident analysis
will deal with the following two cases: a) a dropped fuel rod accident
in which a fuel rod is broken releasing the fission products accumulated
during previous operation of the assembly; b) an accidental criticality
resulting in a power excursion. It will be shown below that the poten
tial consequences of either accident are well within the radiation dose
limits specified by Title 10 CFR Part 20.
Dropped Fuel Rod Accident
For the purposes of this analysis, it is assumed that a dropped
fuel rod results in a broken pin releasing the accumulated fission pro
ducts. The following bases have been established to calculate the
radiation dose from such an accident:
a. It is stipulated that the assembly has been operated continu
ously for 200 hr at an average power level of 0.065 watt. It should be
noted that this is a conservative value since the assembly will not be
operated on a continuous basis; the 200 hours of operating time for each
configuration is essentially spread over a period of several weeks.
b. The assembly contains 1200 rods. Since the actual loadings for
the three reflected cases are 1206, 2132 and 3430 rods respectively, this
will result in conservative results.
c. The peak to space-averaged flux ratio during operation is a
maximum of 120, with the rod at peak flux contributing 1/10 of the


SPACE-TIME REACTOR KINETICS STUDIES WITH THE
UNIVERSITY OF FLORIDA SPERT ASSEMBLY
By
NILS J. DIAZ
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1969

TO
ZENA

ACKNOWLEDGMENTS
The author wishes to express his sincere appreciation to his
graduate committee for their guidance. Special recognition is due
Dr. M. J. Ohanian, whose encouragement, dedication and detailed
scientific knowledge made this work possible.
The support of the Nuclear Engineering Sciences Department of
the University of Florida throughout the authors graduate work is
greatly appreciated. In particular Dr. R. E. Uhrigs support and
friendship is gratefully recognized.
The author feels fortunate and proud in having studied and worked
with a remarkable scientist and gentleman, Dr. R. B. Perez, now at
Oak Ridge National Laboratory. The author's years of association with
Dr. T. F. Parkinson, now at the University of Missouri, formed the
necessary background for this work.
The continuous assistance of Mr. G. W. Fogle throughout the ex
perimental program is sincerely appreciated. Mr. L. B. Myers designed
and built the control instrumentation. Mr. R. E. Schoessow was respon
sible for the design and construction of the assembly. Mr. E. Dugan
and Mr. H. Leydolt aided in the data processing. The cooperation of
the staff of the Nuclear Engineering Sciences Department during the
construction of the facility is acknowledged.
Most of this work was financed under subcontract No. C281 and
C635 with Atomic Energy Division of the Phillips Petroleum Company,
iii

under a prime contract with the United States Atomic Energy Commission.
The technical aid of the University of Florida Computing Center in the
development of the computer programs and their financial assistance is
gratefully acknowledged.
Special mention is due Messrs. S. 0. Johnson, R. W. Garner,
G. A. Mortensen and Mrs. M. E. Radd of the Nuclear Safety Research
Branch, Atomic Energy Division, Phillips Petroleum Company for their
continuous assistance and invaluable suggestions throughout the
research program.
To my sister, Miss Lydia Gonzalez, my sincere appreciation for.
typing an elegant manuscript from my unintelligible characters.
To the fellow students, who struggled with me to reach the un
reachable star, my space and time independent friendship.
iv

PREFACE
The text of this dissertation is divided into two related but
essentially independent parts:
Part 1. The University of Florida SPERT Assembly
- Design and Calibration -
Part 2. Space-Time Reactor Kinetics Studies with the
University of Florida SPERT Assembly
In Part 1, the design, operational safety and nuclear calibration
of the large-in-one-space dimension, highly multiplicative University
of Florida SPERT Assembly (UFSA) are described. The presentation of
this material is pertinent for a complete understanding of the physical
characteristics of the system to be studied in Part 2 and also because
the system in itself is interesting from the nuclear engineering point
of view. The data acquisition system used for the experimentation is
presented in Chapter IV of this section.
In Part 2, the linear reactor kinetics studies performed with the
UFSA are presented. The space-time dependent distribution of the
neutrons in the assembly, following the introduction of a burst of
neutrons at one end of the core, are studied in the time and in the
frequency domain.
The study of the spatially dependent time profile of the neutron
flux required a large number of figures containing the calculational
and experimental results at different positions in the core. Some
typical figures are included in the main text but most of the recorded
(and calculated) time profiles are included as appendices to the main text
v

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
PREFACE V
LIST OF TABLES xi
LIST OF FIGURES xiii
LIST OF SYMBOLS xviii
ABSTRACT xix
i '
PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
- DESIGN AND CALIBRATION 1
CHAPTER I INTRODUCTION 2
CHAPTER II DESCRIPTION OF THE FACILITY 5
General Features .. 5
Fuel Characteristics 9
Mechanical Design 10
Moderator Flow Control System 15
Instrumentation and Interlock System 22
Fuel Storage 27
Neutron Sources 30
CHAPTER III OPERATIONAL SAFETY 32
Introduction 32
Initial Loading 33
vi

TABLE OF CONTENTS (cont'd)
Operating Limits
Design Basis Accident Analysis
CHAPTER IV THE DATA ACQUISITION SYSTEM
Introduction .
The Neutron Detector
The Electronic Instrumentation
The Resolution Time Correction ..
The Normalization Technique
Comments
CHAPTER V NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL
Introduction
Theoretical Notes
Inverse Multiplication Measurements
Absolute Determination of k
eff
Conclusions
Page
35
39
45
45
47
50
54
61
62
64
64
64
68
73
75,
PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY 79
CHAPTER I INTRODUCTION 80
Statement of the Problem 80
Description of the Study 81
vii

TABLE OF CONTENTS (cont'd)
Page
Nomenclature Used in the Description of
Pulse Propagation Phenomena 83
CHAPTER II THEORETICAL NOTES 85
Introduction 85
Review of the Literature 85
The WIGLE Calculational Scheme 87
Neutron Wave Analysis 89
CHAPTER III DESCRIPTION OF THE MEASUREMENTS 91
Introduction 91
The Epicadmium Subtraction Method 92
The Geometrical Arrangement 94
Synopsis of the Measurements 97
CHAPTER IV EXPERIMENTAL AND THEORETICAL RESULTS IN THE
TIME DOMAIN 100
The Analytical Model 100
Flux Traverses 109
Clean Core Pulse Propagation Measurements 118
Propagation of a Narrow Pulse 147
Propagation of a Wide Pulse 148
Pulse Shape vs. Input Pulse Width 150
Effect of Room Return at Peripheral Detector Positions 152
viii

TABLE OF CONTENTS (contd)
Page
CHAPTER V EXPERIMENTAL AND THEORETICAL RESULTS IN
THE FREQUENCY DOMAIN 156
Introduction 156
Method of Analysis ... 157
Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis 159
CHAPTER VI SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS 174
Introduction ... 174
The Decay Constant 175
The Ratio kS/& 176
The Measured Reactivity and ke^ Values 179
CHAPTER VII CONCLUSIONS 185
APPENDICES
A CALCULATIONAL PROCEDURES USED IN THE DETERMINATION
OF THE NUCLEAR PARAMETERS AND THE k _ VALUES 187
eff
B DESCRIPTION OF THE COMPUTER PROGRAMS 191
C UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT NINETEEN CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC 196
D UFSA R1 CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX AT SEVERAL CORE
POSITIONS FOR INPUT PULSES OF 0.5 AND 1.0 MSEC 235
E UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX AT FOUR POSITIONS
IN THE CORE FOR A 0.1 MSEC INPUT PULSE 248
ix

TABLE OF CONTENTS (cont'd)
Page
F UFSA R1 CLEAN CORE
TIME PROFILES OF THEKMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A WIDE (10 MSEC) INPUT PULSE ... 253
G UFSA R1 CLEAN CORE
SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF INPUT
PULSE WIDTH 255
LIST OF REFERENCES 258
BIOGRAPHICAL SKETCH 262
x

LIST OF TABLES
TABLE Page
Ik vs. MODERATOR LEVEL OF UFSA REFLECTED
eff
CORES 7
II UFSA INSTRUMENTATION AND CONTROL 25
III SUMMARY OF 1/M AND PULSED MEASUREMENTS 74
IVINPUT PARAMETERS FOR THE WIGLE CALCULATIONAL
SCHEME 104
V TIME STEPS USED FOR THE WIGLE CALCULATIONS 106
VIDELAY TIMES MEASURED ACROSS THE WIDTH OF
THE CORE
- 0.5 MSEC INPUT PULSE 119
VIICLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
- 0.5 MSEC INPUT PULSE WIDTH 127
VIIICLEAN CORE PULSE PROPAGATION STUDIES EXPERIMENTAL
AND THEORETICAL RESULTS
- 1.0 MSEC INPUT PULSE WIDTH 128
IX ASYMPTOTIC PROPAGATION VELOCITY v 133
P
X DYNAMIC INVERSE RELAXATION LENGTH k, 134
a
XICHANGES IN THE NUCLEAR PARAMETERS DUE TO
CHANGES IN THE TRANSVERSE BUCKLING 138
XIITHE CALCULATED ASYMPTOTIC VELOCITY OF
PROPAGATION AND DYNAMIC INVERSE RELAXATION
LENGTH vs. CORE HEIGHT
- 0.5 MSEC INPUT PULSE WIDTH 146
XIII DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE 148
XIV DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE 149
XV PULSE SHAPES vs. INPUT PULSE WIDTH 151
xi

LIST OF TABLES (cont'd)
TABLE Page
XVITHE REAL AND THE IMAGINARY COMPONENTS
OF THE COMPLEX INVERSE RELAXATION LENGTH
- 0.5 MSEC INPUT PULSE 164
XVIITHE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
- 1.0 MSEC INPUT PULSE 165
XVIIITHE DECAY CONSTANT AND kB/i VALUES MEASURED
AS A FUNCTION OF INPUT PULSE WIDTH 180
XIXREGION-WISE DEPENDENCE OF THE REACTIVITY
MEASUREMENTS 183
xii

LIST OF FIGURES
FIGURE Page
1 OVERALL VIEW OF THE FACILITY .. 6
2A BOTTOM FUEL ROD SPACING SYSTEM 12
2B BOTTOM FUEL ROD SPACING SYSTEM 13
3 TOP FUEL ROD SPACING SYSTEM 14
4 REACTIVITY-CONTROL FLOW SYSTEM 16
5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE
WEIR APEX 18
6 WEIR "BOX 19
7 AIR SYSTEM SCHEMATIC 21
8 UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM 23
9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT 44
10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS 49
11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM 51
12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM 52
13 TIME PROFILES OF NEUTRON BURST RECORDED BY
CONVENTIONAL ELECTRONIC INSTRUMENTATION AND BY THE
TIME-PICKOFF SYSTEM 58
14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME
CORRECTION AS A FUNCTION OF COUNT RATE 60
15 DETECTOR POSITIONING SCHEME 69
16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL 71
16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT 72
xiii

LIST OF FIGURES (contd)
FIGURE Page
17A DECAY CONSTANT vs. MODERATOR LEVEL 76
17B kS/£ AND k vs. MODERATOR LEVEL 77
18 THE TOTAL, EPICADMIUM AND THERMAL FLUX 117.44 CM
FROM THE SOURCE 95
19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL
ARRANGEMENT PLAN VIEW 96
20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE 102
21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE
WIGLE CALCULATIONAL SCHEME 103
22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED
INTO THE WIGLE SCHEME 107
23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE 110
23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE Ill
23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE 112
24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE 113
24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE 114
25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX 116
26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX 117
21k EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 122
xiv

LIST OF FIGURES (contd)
FIGURE Page
27B EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 123
27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 124
28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PUSLE 125
28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE 126
29 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.5 MSEC INPUT PULSE 129
30 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.0 MSEC INPUT PULSE 130
31 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
- 0.5 MSEC INPUT PULSE 131
32 AMPLITUDE ATTENUATION OF THE THERMAL FLUX
- 1.0 MSEC INPUT PULSE 132
33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS 139
34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED
BY THE WIGLE CALCULATIONAL SCHEME FOR DIFFERENT
CORE HEIGHTS 140
35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 141
35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 142
xv

LIST OF FIGURES (cont'd)
FIGURE Page
35C THE SENSITIVITY OF THE ONE-DIMENSIONAL, TOO GROUP,
SPACE-TIME KINETICS SCHEME TO CHANGES IN THE
TRANSVERSE BUCKLING 143
36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE
HEIGHT 144
37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS 153
37B EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR
POSITIONS 154
38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE 160
39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE 161
40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE 162
41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE 163
42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED DAMPING COEFFICIENT a 166
43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED PHASE SHIFT PER UNIT LENGTH 5 167
44 THE UFSA R1 CORE p DISPERSION LAW 169
45 COMPARISON OF THE THEORETICALLY PREDICTED AND THE
MEASURED (a2 £2) 171
xvi

LIST OF FIGURES (cont'd)
FIGURE Page
46 COMPARISON OF THE THEORETICALLY PREDICTED
AND THE MEASURED 2 a F, ... 172
47 THE UFSA R1 CORE p2 DISPERSION LAW 173
48 DECAY CONSTANT vs. AXIAL POSITION 177
49 kB/A vs. AXIAL POSITION 178
50 REACTIVITY (-$) k f vs. AXIAL POSITION 182
Cl Through C19 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE
CORE FOR A 0.5 MSEC INPUT PULSE 195-213
C20 Through C38 TIME PROFILES OF THE THERMAL
NEUTRON FLUX AT NINETEEN POSITIONS IN THE CORE
FOR A 1.0 MSEC INPUT PULSE 214-232
Dl Through D6 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 0.5
MSEC INPUT PULSE 234-239
D7 Through D12 TIME PROFILES OF THE FAST NEUTRON
FLUX AT SIX POSITIONS IN THE CORE FOR A 1.0
MSEC INPUT PULSE 240-245
El Through E4 TIME PROFILES OF THERMAL NEUTRON
FLUX AT FOUR POSITIONS IN THE CORE FOR A 0.1
MSEC INPUT PULSE 247-250
FI TIME PROFILES OF THERMAL NEUTRON FLUX AT THREE
POSITIONS IN THE CORE FOR A 10.0 MSEC INPUT PULSE 252
G1 Through G2 SHAPE OF THE PROPAGATING PULSE AS A
FUNCTION OF PULSE WIDTH 254-255
xvii

LIST OF SYMBOLS
TRANSVERSE BUCKLING
DELAYED NEUTRON PRECURSOR CONCENTRATION OF THE
ith GROUP
DIFFUSION COEFFICIENT OF THE ith GROUP
FREQUENCY (cps)
EFFECTIVE MULTIPLICATION CONSTANT
NEUTRON LIFETIME
NEUTRON MULTIPLICATION
VELOCITY OF THE ith GROUP
AXIAL COORDINATE
DECAY CONSTANT (IN THE TIME DOMAIN)
DAMPING COEFFICIENT (IN THE FREQUENCY DOMAIN)
EFFECTIVE DELAYED NEUTRON FRACTION
PHASE SHIFT PER UNIT LENGTH
REACTIVITY .
COMPLEX INVERSE RELAXATION LENGTH
MACROSCOPIC CROSS SECTION
NEUTRON FLUX
xviii

Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
By
Nils J. Diaz
March 1969
Chairman: Dr. M. J. Ohanian
Major Department: Nuclear Engineering Sciences
A large-in-one-space dimension, side reflected, highly multiplica
tive (kgff ~ 0.99) subcritical assembly was designed and calibrated.
The sole purpose of the facility is the experimental investigation of
the dynamic behavior of large reactor cores and to provide a test for
space-time kinetics models presently in use. With this facility the
linear aspects of neutron physics phenomena can be investigated in the
absence of inherent feedback effects. This work was conducted under a
subcontract with the Nuclear Safety Research Branch, Atomic Energy
Division, Phillips Petroleum Company, under a prime contract with the
United States Atomic Energy Commission.
The University of Florida SPERT Assembly (UFSA) is a light-water
moderated subcritical facility fueled by 4.81% enriched UC^ pellets
encased in stainless steel tubes of 0.465 inch outside diameter (SPERT
F-l Fuel). The fuel arrays are contained in a rectangular tank, 8 feet
xix

long, 39 inches high, and of variable width. In this study, the core
was 6.5 inches wide and 30 inches high. The effective multiplication
constant of the assembly was determined to be 0.990jK003. The assembly
is equipped with nuclear instrumentation capable of automatic scram
action.
For the kinetics studies, a fast data acquisition system was
developed to handle accurately the very high, time-changing count rate
encountered in the measurements. It essentially consists of a trans
former-coupled pulse amplifier to produce a fast logic signal at the
input of a multichannel analyzer from the input signal originating in
3
a long, thin He counter. The instrumentation adequately handled count
rates up to 3 x 10^ counts/sec at the peak of the pulses. A high degree
of reproducibility and fidelity in following the pulse profiles was
obtained with this instrumentation.
The space-time kinetics studies were performed by analyzing the
propagation of a fast neutron burst introduced at one end of the assem
bly, in the absence of inherent feedback effects. The experimental
results are compared with the results obtained from the two-group,
space-time dependent, one-dimensional diffusion theory scheme known as
the WIGLE program. A stringent test of the model is provided by a
combined analysis in the time and the frequency domain.
Tiie WIGLE calculational scheme accurately predicts the delay times
and the attenuation of the pulses when a first-flight spatial distribu
tion is assumed for the fast source. At large distances from the source
WIGLE underpredicts (~ 8% in the FWHW) the spreading of the pulse. A
marked sensitivity to small changes in the transverse buckling was
'found for the model, as well as the experiment.
xx

A one-to-one comparison of the predicted and measured values in
the frequency domain was provided by performing identical numerical
Fourier transformations of the WIGLE time profiles and the measured
pulse shapes. The analysis in the frequency domain confirmed the
results obtained in the time domain, although discrepancies past 100
2
cps are found in the ultrasensitive p plane. The agreement in the p
plane, the system's dispersion law, is good up to 200 cps and reasonable
up to 800 cps. Both theory and experiment showed a smooth behavior
2
throughout the frequency range investigated, in both the p and the p
plane.
Spatial effects in large cores are clearly demonstrated in this
work. The determination of the range of applicability of the one
dimensional scheme requires extending the study to cases in which two-
dimensional effects will be noticeable and the important feedback
effects can be considered.
xxi

PART 1
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
- DESIGN AND CALIBRATION -

CHAPTER I
INTRODUCTION
The development and construction of large power reactors focused
the attention of industry and of the United States Atomic Energy Com
mission on the necessity of having reliable reactor dynamics analysis
methods to accurately describe the spatial and temporal behavior of the
neutron flux in these systems. The point-model reactor kinetics calcu-
lations seem to have been adequate for the gross evaluation of the time-
dependent neutron flux during the occurrence of a transient but the
model can be in large error when the physical size of the system and the
magnitude of the perturbation necessitates that spatial effects in the
redistribution of the neutron flux be considered. Preliminary calcula
tions done by Johnson and Garner using a one-dimensional space-time
kinetics model [1] showed that the space-time dependent scheme predicts
a "destructive zone" much larger than that predicted by point-model
kinetics.
The necessity of experimentally determining the validity of the
various space-time kinetic analysis methods was brought out by Johnson
and Garner [1], and recognized by the USAEC in establishing the Large
Core Dynamics Experimental Program. The primary responsibility for this
program has been vested in the Nuclear Safety Research Branch, Atomic
Energy Division, Phillips Petroleum Company as major contractor for
USAEC.
2

3
The Large Core Dynamics Experimental Program is to be performed
in three phases:
Phase I. Pulsed Source Experiments in Subcritical, Multiplying Media,
Large in One-Dimension
The first phase of the experimental program is to be conducted in
a close-to-critical subcritical assembly, 8 feet long, 3 feet deep and
with widths changing from 6.5 inches to 16 inches according to the core
configuration and whether bare or side reflected cores are studied.
The experimental information obtained from studying the pulse
propagation phenomena in this assembly is to be used to test the valid
ity of current space-time kinetic models in the absence of inherent
feedback effects.
Phase II. Kinetic Behavior for Control-Rod-Induced Power Excursions in
Large, One-Dimensional Cores
A reactor large in one-dimension, 16 feet long, three feet deep
and with varying widths to accommodate different metal/water ratios will
be used to investigate the one-dimensional kinetic behavior of large cores
subjected to a large perturbation. Both non-feedback (low power exper
iments) and self-shutdown measurements will be conducted.
Phase III. Kinetic Behavior for ContrOl-Rod-Induced Power Excursions
in Large, Two-Dimensional Cores
The same type of measurements performed for the one-dimensional
core will be conducted in a two-dimensional core.
The measurements should provide the necessary information to
establish the validity ranges for one-dimensional models, the basis for
the development of a two-dimensional scheme and as a bridge to the
complex, three-dimensional problem.
Phase II and Phase III of the research program will be performed

4
at the SPERT IV facility at the National Reactor Testing Site, Idaho.
The appropriate existing experimental equipment, as well as the
extensive kinetics studies conducted by the Nuclear Engineering Sciences
Department at the University of Florida, was conducive to the granting
of a subcontract by the Phillips Petroleum Company so that the basic,
linear kinetics studies of Phase I could be performed at the University
of Florida.
The research to be performed as Phase I of the Large Core Dynamics
Experimental Program can be succinctly defined as the experimental and
analytical determination of the dynamic behavior of the neutron flux in
slightly subcritical water moderated assemblies of SPERT F-l fuel rods.
The facility in which the required measurements for Phase I, Large
Core Dynamics Experimental Program, are to be conducted necessitated a
thorough design and safety analysis. The assemblies are to be close to
critical and the core has a large U235 inventory. The nuclear capabil
ities of such systems were the object of a detailed study to determine
their operational characteristics under normal and accident conditions.
The flexible mechanical design, the safety instrumentation, the
nuclear evaluation, as well as the experimental calibration of the
first configuration under study constitutes Part 1 of this dissertation.
The reactor kinetics studies performed in the first of the con
figurations to be studied are dealt with in Part 2 of this manuscript.

CHAPTER II
DESCRIPTION OF THE FACILITY
General Features
The University of Florida Spert Assembly is a light water
moderated subcritical facility fueled by 4.81% enriched U0£ pellets
encased in stainless steel tubes of 0.4655" outside diameter. The fuel
arrays are contained in a rectangular tank, 8 feet long, 39 inches high,
and of variable widths. The system is designed so that both bare and
reflected cores can be studied. Only one reflected core will be dealt
with in Part 2 of this manuscript; information on three reflected cores
is included in this chapter. The .assembly width and fuel spacing may be
varied in order to:
a) have a k not to exceed 0.99 in all cases to be
eff
considered.
b) accommodate non-moderator/moderator ratios of
0.5, 1.0, and 1.5, respectively.
Shown in Table I are the k _'s as a function of the moderator
eff
height, the fuel spacings, core widths, and total number of fuel ele
ments for the different reflected cases to be considered. The calcu-
lational procedures used in the determination of the nuclear parameters
and the k^^ values for the three reflected configurations of the
assembly are described in Appendix A. Only the sides of the assembly
will be reflected. Fig. 1 shows an overall view of the facility.
5

WEIR SYSTEM
6
CORE TANK
REFLECTOR
TANK
RESERVOIR
DUMP
VALVES
FIG. 1 OVERALL VIEW OF THE FACILITY

7
TABLE I
keff vs. MODERATOR LEVEL OF UFSA REFLECTED CORES
Calculated Using the AIM6 Code
Core Length = 243.8 cm (96")
Reflector Width = 30.48 cm (12")
Active Fuel Height = 91.4 cm (36")
Metal to Water Ratio = 0.5
Lattice Pitch (in) = 0.7152
Core Width (cm) = 16.35
No. of Fuel Rods = 1206
1.0
0.584
19.28
2132
1.5
0.5332
25.73
3420
Moderator Level
(cm)
20
25
30
35
40
45
50
55
60
65
70
75
80
85
Effective Multiplication Constant
.7695
.7397
. 7276
.8288
.8028
.7941
.8715
.8471
.8416
.9022
.8793
.8761
.9249
.9032
.9020
.9420
.9213
.9218
.9551
.9353
.9372
.9655
.9465
.9494
.9738
.9554
.9592
.9805
.9626
.9672
.9870
.9686
.9738
.9906
.9736
.9793
.9944
.9777
.9840
.9977
.9813
.9880
1.0012
.9851
.9922
91.4

8
The assemblies are highly multiplicative; this is important for
the extrapolation of the results of the study to critical systems. The
system's subcriticality is attractive because of the inherent safety
of such systems and of the absence of inherent feedback effects.
In order to provide as "clean" a core as possible, a unique control
system which has been successfully used on the UFAPA [2] will be em
ployed. In this system the reactivity is controlled by adjustment of
the water height in the assembly. The water height is controlled by
the position of two "V"-notched weirs located in a water "box" hydrau
lically coupled with the assembly through flexible lines. The quantity
5/2
of water discharging through a "V"-notched weir varies as H (H is the
distance between the apex of the weir and the water level) thus pro
viding precise control of the moderator height. The hydraulic coupling
assures that under normal operating conditions (with continuous flow)
there will be the same water level in the core and the reflector tanks.
The UFSA subcritical assembly is located in an isolated and
shielded room in the Nuclear Research Field Building, approximately
three miles from the University campus.
The Nuclear Research Field Building consists of four bays, two of
them having shielded rooms for experiments with subcritical and moder
ating assemblies. The shielded walls consist of stacked concrete block
eight feet high and thirty-eight inches wide covered with plywood to
assure that the blocks remain in place. The ceiling of this single-floor
building is approximately 15 feet above the floor and consists of excel
sior-filled cement bonded board. Neutron reflection from this ceiling .
over the walls does not constitute a hazard to personnel operating the
accelerator-type neutron source. The access door from the control room

9
is interlocked with the neutron generator and the subcritical assembly
scram system, as is the door on the only other entrance to the shielded
room from the fuel storage area. Across the front face of the assembly,
a screened wire cage with a lockable door controls access to the core.
While not in use in the assembly the fuel is stored in a room
adjacent to the facility, built entirely for this purpose.
A more complete description of the. facility and its characteristics
can be found in the Design and Hazards of the UFSA and its addenda
[3, 4, 5],
The system has been licensed under Atomic Energy Commission SPECIAL
NUCLEAR MATERIAL LICENSE SNM 1050, March 1968. The license allows for
the possesion of 5400 fuel rods with a total U235 inventory of 190 kgs.
Fuel Characteristics
The UFSA is fueled with Spert F-l type fuel elements provided by
the Phillips Petroleum Company.
The fuel characteristics are:
Fuel Composition: UO^ in pellet form
U235 enr:*-c^linent: 4.81 + .15%
Active Fuel Length: 36" + .062"
Active Fuel Diameter: .42" + .0005"
Fuel Tube Material: stainless steel
Fuel Tube Length: 41.625"
Fuel Tube o. d.: .4655" + .0025"

10
Mechanical Design
The entire assembly can be divided into three components: the
supporting platform and dump tank; the basic core tank and fuel rod
support structure; and the combination core side walls and side
reflector tanks.
The supporting platform is composed of 5 inch steel I-beams, raised
5 feet from the floor level by six steel columns 31/2 inches in diam
eter. The column footings rest within a 6x8x2 foot steel rank which
serves as a reservoir for the continuous water flow system and as a dump
tank. Under normal operating conditions, this represents a minimum
distance of about 4 feet between the bottom of the assembly and the
water surface in the reservoir. This distance is sufficiently large so
that the bottom of the assembly is considered to be unreflected under
all conditions.
All the core and reflector hardware is made of type 5456-H321
aluminum. The bottom of the basic tank is made of a 24x96x3/4 inch plate
bolted to the steel I-bean platform. The underside of the plate is
covered with a .030 inch thick Cadmium sheet. The lower fuel rod sup
port assembly rests on the plate. The end walls of the basic tank are
made of a 24 x 39 3/4 inch plate and are supported by two 2 1/2 x 2 1/2
x 1/4 inch steel angle braces welded to the I-beam platform. Two four-
inch aluminum channels span the eight foot dimension of the tank, con
fining the upper fuel rod support system and detector mounts.
The side walls of the basic tank serve also as reflector tanks when
the reflected cores are under study. These tanks have dimensions of
12 x 96 x 37 inches. The arrangement allows one to vary the width of the
core with a sole structural support.

11
The end walls are permanently covered with Cadmium on the outside
surface while the side walls have movable Cadmium covers to define the
boundaries for the bare and reflected cases. To optimize the number of '
neutrons inserted into the assembly by the neutron generator, the accel
erator target penetrates about 4 inches into the core. A water-tight
port is provided for this purpose. The port can be removed and a blind
flange inserted in its place. Several fuel rods must be taken out, the
number depending on how deep the target goes into the assembly and on the.
lattice pitch.
The core section of the assembly consists of an interchangeable
fuel rod spacing system made of 3/4 x 1/2 x 1/8 inch channels, 5/8 x 1/4
inch bars and aluminum shims mounted on the base plate of the tank. The
bars have milled slots to accommodate the .25 inch end tip of the fuel
rod and to set the pitch along the core width. The shims are placed
between the channel bar units to set the pitch along the core length
(96 inches) (see Fig. 2). The top fuel rod spacing system consists of
an aluminum grating. The mesh is determined by the lattice pitch under
study. The grating is made of aluminum bars and spacers, as shown in
Fig. 3. Thus, fuel rod removal along the length of the core is pos
sible to locate the detector for the experimental measurements.
The one-half inch long rod tip is fully surrounded by aluminum,
with practically no reflecting characteristic, but there is a 7/8 inch
length of rod between the end of the active fuel and the tip which is
t
surrounded by water. This bottom reflector is unavoidable and will be
considered in the calculations.

12
FIG. 2A BOTTOM FUEL ROD SPACING SYSTEM

13
I
FIG. 2B BOTTOM FUEL ROD SPACING SYSTEM

- 14
ALUMINUM SUPPORT
FIG. 3 TOP FUEL ROD SPACING SYSTEM

15
Moderator Flow Control System
The moderator flow control system of the UFSA can be better des
cribed by'the water flow schematic shown in Fig. 4. Besides the normal
fill and drain functions for the moderator, it serves as an accurate
reactivity control using adjustable moderator height by continuous flow.
The characteristic components of this system are described below,
A. Storage Tank: A 6 x 8 x 2 foot steel tank located directly
below the assembly will serve as the reservoir for the circulating
light-water moderator and as a dump tank. Normal water heights while
operating will be between 6 and 12 inches. The tank also serves as a
footing for the assembly supports. This arrangement makes a very con
venient and compact facility.
B. Core and Reflector Tanks: As seen from the flow diagram, water
is pumped from the reservoir to the core and reflector tanks through a
manifold at one end of the assembly and flows from the other end of the
core and reflectors tanks to the weir "box". From the weir "box", water
flows over the weirs back to the storage tank through a flexible line.
The core section is equipped with two normally open solenoid
activated dump valves, 3 inches in diameter, located at each end of the
core. These valves provide the reactor with a fast shutdown safety
system. The reflector tanks have their own 1 1/2 inch normally open
solenoid valves actuated by the same safety system.
Since the quantity of water discharging through a V-notched weir
5/2
varies as H where H is the height of the water level above the apex
of the V-notch, the water level and hence, the reactivity, can be con
trolled in a precise manner simply by varying the height of the weirs
and the rate of flow of water into the tank. This is accomplished by

.WEIR DRAIN
DISTRIBUTION MANIFOLD
PUMP
FIG. 4 REACTIVITY-CONTROL FLOW SYSTEM
CONTROL
VALVE
-0
ORIFICE

17
an automatically operated pneumatic control valve. A plot of the flow
rate versus the height of the water level above the apex of the weirs
is shown in Fig. 5.
The weir plate is rigidly mounted on a "box" or small tank (see
Fig. 6). The weir "box" is connected to a drive mechanism composed
of the following: guide post, slide block, and drive screw. The guide
post is a 2 inch diameter pipe attached to the support column of the
crane which is used for removal of the reflector tanks. The "box" is
mounted on the guide block which slides along the vertical post and
provides a rigid support for the system and is driven up and down by
means of the drive screw which is fixed at the top of the guide post
support and passes through the guide block. The upper limit of the
position of the weir"box"is controlled by mechanical stops whose posi
tion is determined as part of the initial start-up procedure for each
configuration to be considered.
The final adjustment of the position of the weir"box"is such that
when the water reaches the moderator level in the assembly corresponding
to *99 for a given configuration it will be flowing about 2.0
inches above the apex of the V-notch weirs. At this design level the
flow rate is ~ 7 gallons per minute with the k^^ values as given in
Table I for the full fuel loading. After the operating height of the
weir box has been determined for kg^^ <^0.99 in the initial start-up,
stops are inserted to prevent raising the weirs above this height (if
the height is less than the active fuel height). It should also be
pointed out that the orifice in the line limits the pump capacity to a
flow rate which is just sufficient to bring the weirs to full flow. A
further increase in flow rate would cause discharge over the entire

Water Level Above Weir Apex (cm)
Flow Rate (gpm)
FIG. 5 FLOW RATE vs. HEIGHT OF WATER LEVEL ABOVE WEIR APEX

19
FIG. 6 WEIR "BOX"

20
perimeter of the weir "box" into the drain line effectively preventing
any further increase of the moderator level in the assembly.
The measurement of the water height in the core is accomplished by
fixing a reference mark on the slide block at the same level as the
bottom of the weir within the "box". An accurate scale is provided to
read off the distance between the bottom of the core and the apex of the
weirs. Continuous indication of the moderator level in the core is
provided on the console by means of a recorder calibrated between the
bottom of the active fuel and the maximum moderator height and by a
manometer, connected directly to the core, for precise measurement of
the water level. These two measuring systems insure reproducibility of
the moderator height for the experiments.
The water is pumped out of the storage tank by a constant speed
centrifugal pump which has a "no load" capacity of 20 gal/min. The
control valve is designed to restrict the flow to the maximum design
value of 12 gal/min. A deionization system is provided to keep the
water as pure as possible at all times. The pneumatic flow control
system consists of two differential pressure cells, transmitters, control
valve, and recorder-controller. The strip type chart recorder-con
troller records both flow rate and moderator level in the core. The
control valve is of the air-to-open type which will close in the case of
air supply loss, stopping the flow into the assembly. The flow diagram
for the air system is shown in Fig. 7. A pressure differential from the
pressure transmitters applied to the recorder-controller allows both
manual and automatic control' of the flow rate through the valve operated
by the controller.

VALVE
FIG. 7 AIR SYSTEM SCHEMATIC

22
Instrumentation and Interlock System
The instrumentation and interlock system of the UFSA has been
discussed extensively in the reports submitted to the Atomic Energy
Commission [3, 4, 5] in conjunction with the license application. More
recently, Mr. L. B. Myers submitted a detail technical report on the
subject [6]. A brief descriptive explanation is given below.
A block diagram of the safety system logic flow in use at the UFSA
subcritical assembly for routine monitoring is shown in Fig. 8. There
are five principal channels of instrumentation:
3
a. Start-up channel using a He proportional counter, scaler, and
rate meter. The counter is located at the bottom of the core, close to
the geometrical center of the assembly.
b. Log power and period instrument No. 1 channel using a compen
sated ion chamber (operated uncompensated) as a signal to a Log N
amplifier. The chamber is located along the longitudinal axis of the
assembly, on the bottom of the core some two feet from the neutron
generator end.
c. Period instrument No. 2 channel using a compensated ion chamber
(operated uncompensated) as a signal to a log N amplifier. The chamber
is located along the longitudinal axis of the assembly, on the bottom
of the core, some six feet from the neutron generator end.
d. Linear neutron flux No. 1 channel using an uncompensated ion
chamber as a signal to a micromicroammeter. The chamber is mounted on
the top core support frame, close to the geometrical center of the core.
e. Linear neutron flux No. 2 channel using a compensated ion
chamber (operated uncompensated) to feed a signal to a micromicroammeter.
The chamber is mounted on the top core support frame on the opposite

NO
00
FIG. 8
UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM

24
side from the linear channel No. 1.
Items a. through d. are part of the safety amplifier while item f.
is used to display the neutron flux on a console front panel meter.
The safety amplifier monitors the seven continuously varying input
signals and provides a trip signal if any of the input signals fall
outside of acceptable limits. The safety amplifier provides means of
adjusting these limits over a wide range.
The duality of the scram action (see Fig. 8) is a prominent feature
of the safety system. It can be said that no single failure will
invalidate both automatic scram channels. Furthermore, it has been
determined that no single failure can invalidate both the manual and
automatic scrams. The method of measurement and the function of each
instrumentation and safety channel are shown in Table II (parts A and B).
A series of safety interlocks prevent water from flowing into or
remaining in the assembly unless a proper sequence of events are fol
lowed and certain conditions are satisfied. The conditons are:
a. The moderator temperature must be >_ 60F. This is established
by the desire to obtain the experimental data near room temperature con
ditions. The insertion of water at 32F will introduce a maximum k of
.00342 (based on the calculated negative temperature coefficient of
reactivity) above the design k^^ value with no hazards created.
b. The four instrumentation channels must have their high voltage
on.
c. The core width must be smaller than 26 cm.
d. The door to the assembly room must be locked.
e. The start-up channel must count more than 2 counts/sec.
f. The neutron flux, subcritical assembly power level and period

TABLE II
UFSA INSTRUMENTATION AND CONTROL
A. NUCLEAR
Measured Parameter
Method of Measurement
Application
a. Low level neutron flux
He detector pulse discriminator;
at neutron generator end of core
Insure source is present before
adding reactivity. Scram on low
count rate
b. Linear neutron flux
c. Log neutron flux*5
CICa ammeter; on side of core
Indicate power level scram on
power
3.
CIC log N and period amp; under
core near center line
Indicate power level scram on
high power; log N recorder
d. Linear neutron flux
UIC ammeter; on side of core
Indicate reactor power; linear N
recorder
e. Reactor period lc
CIC log N and period amp
Indicate reactor period; scram on
short period
f. Gamma flux
g. Detector power supply
voltage
h. Reactor period 2
Ion chamber area monitor; on front
of reactor cage
Unijunction transistor oscillator
and relay. Monitor detector
voltage for b, c, d and e
CICa log N and period amp; under
core near center line
Criticality monitor for storage
room. Area monitor for reactor
room. Activate evacuation alarm
Scram reactor on low detector
voltage
Indicate reactor period; scram on
short period
N3
cn
*
a
b
To be operated in the uncompensated mode
Common detector and instrument

TABLE II (Continued)
B. NON-NUCLEAR
Measured Parameter
a. Reactor water temper
ature
Method of Measurement
Fenwall temperature switch in
inlet line
b. Reactor water level
c. Reactor door and per
sonnel
Barksdale pressure switch mounted
on weir"box"with sensing line
connected to core
Limit switches on doors and push
buttons inside reactor room
d. Reactor core width
Limit switches on reflector tanks
e. Reactor water level Barnstead pressure switch senses
level in weir box
f. Reflector tank water Float switches in reflector tanks
level (low)
g. Flow control valve Limit switch on valve
shut
h. Reactor flow Differential pressure cell and
pneumatic control
i. Reactor water level D/P cell and pneumatic system
Application
Scram reactor on low reactor
inlet water temp. (60F)
Scram reactor if water level in
core exceeds top of weir height
Scram system and shut down neutron
gun if reactor doors are opened
or interior switches are acti
vated
Prohibit filling reflector tanks
when distance between tanks
exceeds widest reflected core
width
Stops pump when water reaches 11cm
below weir apex
Indicates water is filling reflec
tor tanks
Requires closing valve before
starting pump
Control flow rate. Indicate and
record flow rate
Indicate and record water level

27
must be as specified under Operating Limits in this report.
g. After a normal start-up, the water height in the core must be
within 0.5" of the level set by the position of the weirs.
Fuel Storage
The large amount of fuel needed for the experimental program
required a detailed criticality analysis of the fuel storage area.
Criticality considerations of the fuel storage arrangements follow the
Atomic Energy Commission regulations regarding the subject. Three dif
ferent criteria were used to calculate the effective multiplication of
the fuel storage area to assure that the array will remain subcritical
under the worst circumstances. The methods and the corresponding con
ditions are outlined below.
The fuel storage array consists of three slabs of air-spaced fuel
pins, separated by a minimum distance of 54 inch face to center. The
fuel is stored in steel baskets containing 308 pins per basket. Two
sets of 1/4 inch thick plastic plates, located at the bottom and top of
each basket, drilled to properly position the fuel rods. The charac
teristics of the fuel slab are:
Slab Width = 3.73 in = 9.46 cm (corresponds to 7 fuel pins in
transverse direction)
Slab length = 14 ft
Height = 3 ft (active fuel height)
a. Multiregion-multigroup calculation
The effective multiplication factor of the fuel storage array con
sisting of three slabs (3.73 inch wide, 14 ft long and 3 ft wide) which
are 54 inch apart (face to face) was computed for the case of flooding

28
the storage area to the level of the active fuel height. A 2-foot
reflector on both sides was used to represent an infinite reflector.
No reflector was considered on the ends, but the contribution of this
to the system would be small. The calculation was done using four
groups and seven regions and followed the method outlined in Appendix
A of this thesis. The following configuration, which is symmetric about
the indicated center line, was assumed:
54"
Water
24" -
Water
Under these water-moderated and reflected conditions, a k =
eff
0.79 was obtained
b. Solid angle criterion for slabs
To determine the interaction between the fuel storage slabs in the
proposed 3-slab array, the solid angle criterion established in 10 CFR,
Part 70, 70.52, paragraph (b) was used. This establishes the maximum

29
total solid angle subtended by any unit in the array to be 6 steradians
if the effective multiplication factor for the individual slabs is less
than 0.3, as is the case here.
From 10.CFR 70.52 (d) (2) (i) the minimum required separation dis
tance, i.e., center of one slab to face of adjacent slab, is obtained
from:
3 steradians =
cross sectional area
2
(separation distance)
14 x 3
This gives, separation distance = ( ^) = 3.74 ft.
We propose to establish a minimum distance between faces of adja
cent slabs of 4.5 ft. This gives a total solid angle for the center
slab of 3.88 steradian, which is well below the established criteria,
c. Comparison with Clarks criteria
For 5% enriched, 0.4 inch diameter uranium oxide rods with a 190.13
gm/liter U-235 concentration (compared to 4.81% enriched, 0.42 inch
diameter uranium oxide rods with a 200 gm/liter U-235 concentration in
our case) the following data is obtained from pp. 39 and 59, respectively,
of DP-1014:
Width of Slab (cm)
Critical Safe
11.2 10.4
_2
Buckling (cm )
Critical Safe
0.014945 0.015912
It should be noted that the slab widths quoted on page 39 of DP-1014
are for an infinite water-moderated and reflected slab. From the buck
ling values given, the critical width of the infinite water-moderated
unreflected slab is 25.7 cm; the corresponding safe width is 24.9 cm.
When twice the reflector savings for the latter case as given on page
59 of DP-1014 is subtracted, a safe width for the infinite, water-

30
moderated reflected slab of 10.44 cm is obtained consistent with the
10.4 cm value.
Thus the slab width of 9.46 cm proposed by us compares favorably
from the safety viewpoint with the safe width for an infinite, water
moderated and reflected slab and is considerably narrower than the safe
width for an infinite, water-moderated and unreflected slab. Within the
present context it should also be pointed out that as indicated on page
54 of the Design and Hazards Report [3], no flooding of the storage area
seems possible from natural causes.
Neutron Sources
Two types of neutron sources were used throughout this work.
1) Two Pu-Be sources mounted in an aluminum cylinder which can be
driven remotely through a plastic pipe from a shielded box located in
one corner of the facility room to underneath the center of the core.
Neon lights provide indication at the console of the position of the
sources. These sources, which have a combined yield of 3.2 x 10^
n/sec are used for start-ups and for the inverse multiplication meas
urements .
2) A Texas Nuclear Neutron Generator which is used in continuous
mode for static measurements and in the pulsing mode for the pulse
propagation measurements. The generator is of the Cockcroft-Walton
type, TNC Model 150-1H with continuously variable high voltage from
0-150 kv and has been modified to obtain larger currents by removing
the einzel lenses and installing a new 22 electrode accelerator tube and
gap lense. Pre- and post-acceleration beam deflection produces sharp,
low-residual pulses.

31
The accelerator was used with a 4-5 curie tritium target.
The position of the target can be changed to keep the source
centered on the target-end of the assembly for any given moderator
level

CHAPTER III
OPERATIONAL SAFETY
Introduction
The University of Florida SPERT Assembly, due to its large size,
enriched uranium-oxide fuel and nuclear potentialities required a
thorough study of its capabilities, operational characteristics, initial
loading procedures and of the behavior of the assembly under accident
conditions. The study was part of the requirements established by the
Division of Material Licensing of the USAEC prior to the granting of an
operating license.
Legally, a subcritical assembly has to comply with regulations
under 10 CFR Part 70 "Licensing of Special Nuclear Materials" since no
self-sustaining nuclear reaction is envisioned. In the case of the
UFSA, however, the Commission felt that certain technical sections of
10 CFR Part 50, which deals with nuclear reactor licensing, should apply
and serve as a guide for the design and the safety analysis.
The basic philosophies employed in the design of the system were:
a) The UFSA facility has been designed to remain subcritical under
normal operating conditions.
b) The safety instrumentation (see Part 1, Chapter I) has been
designed such that a single failure will not invalidate both the manual
and automatic scram and will not cause subsequent failures.
c) The design basis accidents were postulated on a single failure
32

33
criterion.
d) Operating limits have been set to delineate the normal oper
ating ranges of the assembly.
e) Initial loading procedures have been established to determine
the safe operating multiplication factor of each configuration.
A series of administrative controls are necessarily applied to all
segments of the experimental program and strictly enforced.
Initial Loading
A series of calculations were done to determine which of the two
following schemes should be employed for the initial loading of UFSA:
I) Step loading of the fuel from the center out, accompanied by
step increases in water level with the usual inverse multiplication
determination.
II) Loading all the fuel into the dry tank and proceeding with a
careful evaluation of the multiplication as a function of water level.
Since the UFSA core is very loosely coupled as far as the lumped
reactivity parameter is concerned, the second method was selected due to
the fact that a better determination of the multiplication was possible
from a basic moderator height-zero loading inverse counts determination.
The slope of the kg^^ vs. water height curve has a slope substantially
smoother than the kg^^ vs. per cent fuel loading (full water height)
curve.
The moderator level control system in operation at the facility
provides a extremely reliable and safe mode of adjusting the water level
without safety compromises.
The following regulations were followed for the initial fuel

34
loading, and will be followed for subsequent cores:
1) After the fuel has been loaded, prior to each new incremental
change in the water level, the water is drained completely and the weir
(and water level scram) adjusted to prevent a level increase beyond the
desired value.
2) The first three measurements of the inverse multiplication are
obtained at water heights of approximately 20 cm, 25 cm, and 30 cm above
the bottom of the active fuel. As shown in Table I, the maximum k
eff
calculated for a water height of 30 cm is 0.87. Subsequent filling
increments are not to exceed the least of the following:
a. An increase in water height of 10 cm.
b. An increase in water height which, by extrapolation of the
inverse multiplication curve, would increase the kg^^ by one-half of the
amount required to make the assembly delayed critical.
c. An increase in water height which would, by extrapolation of
the inverse multiplication curve, result in a kg_^ of 0.990. For values
of k^^ above 0.95, the k^^ of the assembly are also determined by
pulsed source techniques.
3) At each filling step, the measured kej£ of the assembly is
compared with the calculated value. If significant deviations of the
experimental values from the calculated kg^^ vs. water height curves
occur, the experiments are to be discontinued, and a detailed analysis
of the results obtained performed. If it is determined that the dimen
sions of the assembly should be changed in order to achieve the desired
ke^ at maximum water height, the University of Florida will apply for
and obtain written approval from the Atomic.Energy Division of the
Phillips Petroleum Company before such changes are made.

35
Operating Limits
A description of the operating limits of the subcritical assembly,
including the basis for such limits ate listed below.
Effective Multiplication Factor
Specification: the maximum allowable will be 0.985+.005.
The absolute value of k as well as the slope of the k vs. water
eff r eff
height will be carefully measured so as not to exceed the limiting value.
Basis: the upper limit of kg^^ = 0.985+.005 is established by:
the accuracy with which k^^ can be measured, the reported [7] differ
ences between calculations and experiments in similar cores and the value
of the multiplication factor required to make a meaningful study of the
dynamic properties of large cores. Comparison [7] between 29 calcula
tions and the corresponding critical experiments (on cores similar to
the UFSA) established that an overestimate of kg^^ is generally made; the
standard deviation for these cases was + 0.00175 and the maximum under-
stimate of the multiplication was for a case yielding kg^^ = 0.9966, a
0.34% deviation.
The absolute value of k will be determined for water levels
eff
yielding a k^^ >.95 by pulsed techniques independently of the inverse
multiplication measurements. The method to be used is the Garelis-
Russell[8] method which, when appropriate corrections are made for the
reflector, has been shown to give good results. In this method both
l-keff(l-$) keff8
a = and are determined; then ke££ may be. obtained by
independently obtaining B or L Since of the two parameters 8 changes
the most slowly with k^^, it is valid to use a value based on theoret
ical calculations.

36
Reactivity Addition Rate
Specification: the reactivity addition rate is controlled by the
water flow rate into the subcritical assembly. The maximum flow is fixed
to be 12 gpm. At this maximum flow rate, the rates of addition of water,
and consequently or reactivity, computed between water heights of 30 and
45 cm. are:
Lattice Pitch
0.5332"
0.584"
0.7152"
Rate of increase of
water level
0.0435
0.0439
0.0431
Ak/cm
0.0093
0.00865
0.008
Ak/sec
0.0004
0.0038
0.000344
$/sec
0.057
0.054
0.049
It should be noted that these reactivity addition rates are a large
overstimate compared to the calculated rates at k^^ ~ .98.
Basis: the maximum rate of addition of reactivity was established
by the calculated values of k^^ vs. water height and the maximum flow
rate. The values specified above constitute an upper limit in the
region of interest and are considered to be safe under circumstances.
The flow rate is a function of the capacity of the pump, the ori
fice and the pneumatic control valve and cannot exceed 12 gpm.
Reactivity Removal Rate
Specification: a conservative value for the reactivity removal
rate is taken from the slope of the k ^ vs. water height curves near
the maximum desiened k values. Since no difference is detected for
w err
the scram times of the three configurations, only one rate of removal
will be specified, corresponding to the smallest slope.

37
Drain rate, including the system
reaction time 2.65 cm/sec
Rate of removal of reactivity 0.00037 Ak/cm
0.00098 Ak/sec
0.140 $/sec
it should be noted that the value of Ak/cm used to specify the reac
tivity removal rate is ~ 20 times smaller than the corresponding value
specified for the reactivity insertion rate.
Basis: the rate of drainage from the assembly established the
reactivity removal rate. Consistent with the approach taken when
specifying the reactivity, the time to drain 45 cm of water from the
assembly was measured to establish a lower limit on the rate of de
crease of water height. Even under these extreme assumptions, i.e.,
using the maximum slope of the k^^ vs. water height curve for the
insertion rate, the small calculated slope around k^^.99 for the
removal rate and the reduced pressure head, the reactivity removal rate
is three times larger than the insertion rate.
Subcritical Assembly Power Level and Power Level Scram
Specification:
Power Level 0.5 watt
Power Level Scram 1.0 watt
Basis: with the maximum source strength available and with k^^ =
0.985 the maximum average power was calculated to be .130 watts by
taking into account the spatial dependence of the flux and a steady
source at one end.
Assuming that a reactivity accident occurs, based on the maximum
reactivity addition rate specified above, the design basis accident

38
predicts that from a k^^ of 0.993 it would take approximately 15
seconds to double the power level. Even if the power level indicator
were not to scram the system until the power level reached 10 kw,
assuming a one second delay time to actuate the scram, the power would
increase to only 69 kw by the time the scram actually begins. Based on
the reactivity removal rate described above, the power level would then
decrease rapidly to a very low value.
Period Scram
Specification;
Period scram 15 sec
Basis; A positive period will be obtained in the subcritical assem
bly for any addition of reactivity beyond a given steady state condition.
If the maximum reactivity insertion rate of 0.05 $/sec is considered,
the initial positive period is about 50 sec and decreases monotonically
with time. The period channel has been determined to respond reliably
to periods = 50 sec. Originally, the period scram was set at 50 sec but
repeated scrams caused by the start-up of the neutron generator forced
the reduction of the scram period to 15 sec for operational reasons.
Average Neutron Flux and Neutron Flux Scram
Specification:
Ave neutron flux for
5 2
most reactive core 1.5 x 10 n/cm sec
5 2
Neutron flux scram 3.0 x 10 n/cm sec
Basis: the above are based on the average power calculated for the
assembly. Doubling of the flux will occur when 0.75 $ worth of reac
tivity is added to the system from any design subcriticality level.
Under these conditions, even at the maximum k^^ status, the facility

39
will still be subcritical and the instrumentation will have sufficient
time to scram the system before accidental criticality occurs.
Design Basis Accident Analysis
Two types of accidents have been postulated to occur in conjunction
with the UFSA experimental program. The design basis accident analysis
will deal with the following two cases: a) a dropped fuel rod accident
in which a fuel rod is broken releasing the fission products accumulated
during previous operation of the assembly; b) an accidental criticality
resulting in a power excursion. It will be shown below that the poten
tial consequences of either accident are well within the radiation dose
limits specified by Title 10 CFR Part 20.
Dropped Fuel Rod Accident
For the purposes of this analysis, it is assumed that a dropped
fuel rod results in a broken pin releasing the accumulated fission pro
ducts. The following bases have been established to calculate the
radiation dose from such an accident:
a. It is stipulated that the assembly has been operated continu
ously for 200 hr at an average power level of 0.065 watt. It should be
noted that this is a conservative value since the assembly will not be
operated on a continuous basis; the 200 hours of operating time for each
configuration is essentially spread over a period of several weeks.
b. The assembly contains 1200 rods. Since the actual loadings for
the three reflected cases are 1206, 2132 and 3430 rods respectively, this
will result in conservative results.
c. The peak to space-averaged flux ratio during operation is a
maximum of 120, with the rod at peak flux contributing 1/10 of the

40
total power of the assembly.
d. The fuel rod subjected to the specified highest specific power
is broken open and the fuel is completely fragmented, releasing 100% of
the gaseous fission products.
e. The iodine (in elementary form) diffuses uniformly throughout
the 18 x 32 x 15 room to calculate the on-site internal dose. The
off-site dose was calculated using the very conservative Pasqual's
principle of atmospheric diffusion.
The fission products inventory was calculated by means of the RSAC
code [9]. The results indicated that the iodine isotopes were the only
significant contributor to the inhalation dose. Using the active worker
breathing rate of 3.47 x 10 in /sec specified in 10 CFR 20, a person
remaining in the room would accumulate a thyroid dose of 0.023 mr for
each minute he remains in the room, after the hottest rod breaks open.
The total dose to a person that inhales all of the iodine contained in
the rod would be 0.2 r. The established radiation safeguards at the
University of Florida require the personnel to abandon the area imme
diately and notify the Radiation Safety Officer. The maximum time
required to evacuate the assembly and the fuel storage area is 10 sec
with 30 sec needed to evacuate the entire building; these times have
been measured during practice evacuation of the building.
The off-site total inhalation dose, calculated assuming the iodine
is released in one puff with zero wind velocity, cloud inverted con
dition, were typically:

41
Distncfrom sit (m)
200
500
1000
The direct radiation dose from all the fission products of the
irradiated fuel elements is calculated to be 1.3 mr/hr.
Accidental Criticality and Subsequent Power Excursion
Accidental criticality and a subsequent power excursion could occur
only by the uncontrolled addition of water to the assembly and gross
error in the calculations and/or procedures. The occurrence of such an
accident is highly improbably and would require:
a. Setting a core width corresponding to the 1.5 metal/water ratio
and proceed to install the fuel spacer system for the 0.5 metal/water
ratio, load the fuel under these conditions and disregard small water
height increments and 1/M measurements. To do this, several administra
tive rules would have to be wilfully ignored.
and/or
b. Improper setting of the following: the weir height, the water
height scram system for any configuration and a gross error in the
calculations causing criticality at about half the design core height
(91.44 cm). It should be noted that the calculational method used to
predict that values has been tested successfully against the
results of 29 different critical assemblies [7].
and/or
c. An obstructed 2 inch line from the core to the weir drain
system and a simultaneous failure of the water height scram together
with the referred to error in the calculations.
Total dose (mrem)
4.5 x lO-4
2 x 10"4
7 x 10-6

42
d. Violation by the facility operator of the administrative
procedures requiring a visual check of the assembly before start-up and
continuous attention to the control console instrumentation to determine
the status of the assembly at all times.
The consequences of such an accident were determined by assuming
the following:
1. The assembly is initially at a steady state power level of 10
watts (normal average power is .065 watt).
2. Water flows into the system at the maximum rate of 12 gpm.
3. The reactivity addition rate is 0.05 $/sec. This rate is
larger than the calculated rate (.04 $/sec) for the case discussed
above and more than that calculated to occur near critical for properly
loaded assembly.
4. The power scram is set, through calibration or other error, at
10 kw. Corresponding error settings occur for the neutron flux and
period scram.
5. A scram occurs 1 sec after a power level of 10 kw is reached.
This time has been determined as the elapsed time from the initiation
of a scram signal to the opening of the dump valves.
6. No feedback effects are considered. This is a good approxima
tion to our case due to the low power levels involved and again is a
conservative assumption.
The calculations were made using the IREKIN code, described in
reference [10]. IREKIN numerically solves the point model kinetics
equations.
Starting with the assembly one dollar subcritical (ke^ = .993),
and proceeding with the described excursion, the accident would yield

43
a peak power of 69 kw, the total energy release is 0.5 Mwsec. The
power vs. time behavior of the assembly for the postulated power excur
sion is shown in Fig. 9.
The combined neutron and gamma dose to the operator is 1.5 rem
*
assuming that: the energy release is instantaneous, all neutrons have
an energy of 1 MeV and there is no attenuation in the assembly. The
proper RBE factors were taken into consideration.
It is concluded that, even if such an improbable accident would
occur, the hazards to personnel and the general population are not
significant.

FIG. 9 POWER vs. TIME FOR THE DESIGN BASIS ACCIDENT

CHAPTER IV
THE DATA ACQUISITION SYSTEM
Introduction
In the delicate and laborious task of performing nuclear experi
ments the most common source of difficulties and errors lies in the
acquisition of the data. Modern nuclear instrumentation with its excel
lent time-energy resolution has enhanced detection sensitivity to the
extent that deviations previously masked by the poorer resolution of the
equipment are easily distinguishable. The major problem now lies in the
degree of reproducibility of the results. Although in general the in
strumentation is very reliable the enhanced sensitivity demands contin
ual standardization for the sake of reproducibility.
The "brain" of the data acquisition system for pulsed neutron
measurements is the multichannel analyzer (MCA) which is now available
with a large number of data channels and narrower channel widths for
increased time resolution. In general, the mode of data acquisition
for a pulsing experiment differs from that of many other types of
nuclear experiments. In particular, neutron interactions with a suitable
detector are fed into the analyzer while it is time-sweeping. Ideally
every neutron interaction should be counted regardless of the ampli
tude of the collected pulse. This implies that the linear signal
originated at the neutron detector should be converted to a logic signal
so that its probability of being recorded is independent of its amplitude
45

46
Logic signals have fixed amplitude-shape characteristic and convey
information by their presence, absence of time relationship with
respect to a reference signal. Only gamma and noise discrimination
are necessary; this process will inherently eliminate the counting of
weak neutron interactions.
The process of registering events whose density per unit time
varies considerably requires an electronic system with extremely high
time resolution and a broad frequency response. Typically the counting
rates at the peak of the neutron burst in pulsed neutron measurements
vary from 10^ to > 10^ event/sec. This high, time-varying count rate
caused drastic losses in conventional instrumentation due to pulse
pile-up and circuit induced distortion when the dynamic range of the
circuit is exceeded causing a net amplitude shift in excess of that
tolerable by the system. The alternative modus operandi is to use low
count rates so that resolution losses are minimized; this, however,
increases the probability of systematic errors due to much longer run
ning times.
The count rates encountered during the initial experiments with a
3
He counter close to the neutron generator target in the SPERT assembly
exceeded 10^ event/sec at the peak. Saturation effects were observed
in modular instrumentation incorporating the latest F.E.T. preamplifier
and double-delay line pulse shaping amplifier at about 10"* event/sec.
The fast pulse train caused a drop in the base voltage of the Field
Effect Transistor which prevented further counting until a significant
reduction in the count rate allowed the voltage to recover. Changing
to a fast scintillation prototype preamplifier improved the situation
somewhat. However, if the potential count rate in the UFSA assembly

47
were efficiently handled with few losses the actual running time of a
particular experiment could be reduced to a few minutes. This possi
bility forced the development of the ultra-fast instrumentation chan
nels used in this work.
The electronic counting system^" used throughout the experimentation
used a transformer-coupled pulse amplifier to produce a fast logic sig
nal to the input of the MCA from a slower input signal originating in a
3
He counter. The system has superior counting and stability character
istics. The resolution time of the system is practically nil compared
to that of the MCA. In general, data acquisition times were reduced
to a few minutes; in that time it was possible to obtain, at most of
the detector locations, the following counting statistics:
ol7
Peak Channel Counts:
Counting Time:
No. of data channels:
Channel Width:
Pulse repetition rate:
Noise Level:
Background Level:
2-10 minutes
1024
20 micro sec
30 hz
40 event/min
140 event/min
The Neutron Detector
The neutron detectors used throughout the experimental program were
3
proportional counters filled with He The counters are of the Texlium
variety made by Texas Nuclear Corporation and were specially built to
conform to the UFSA core grid. Detectors of this type have been
1. The assistance of Mr. Joel B. Ayers of ORTEC, Inc.,who suggested
this electronic instrumentation is gratefully acknowledged.

preferred over the BF^ variety at the University of Florida because of
the larger neutron absorption cross section and operational reliability.
3
He undergoes the following reaction
He^ + n H^ + p + 0.764 Mev.
The cross section for this reaction is 5327 + 10 barn at v = 2200
o
10 3
m/sec compared to 3840 +.11 barn for B He follows a 1/v law in the
3
energy range from 0 to 200 kev. The pulse heights yielded by a He
filled counter are proportional to the energy of the neutrons plus 764
kev. The reaction has been used for neutron spectroscopy from the 100
kev to 2 Mev energy range. Gamma discrimination can be easily accom
plished by the use of a biased integral discriminator.
The detectors were long and thin and each took the place of a fuel
element in the core. The active length of the counter is slightly less
than the active length of the fuel. Two one atmosphere (predominantly
thermal detection) and one ten atmosphere (more responsive to higher
energy neutrons) detectors were used in the experimental program. A
sketch of the physical characteristics of the counters is shown in
Fig. 10. The thin, long cylindrical shape enhances the time character-
3
istics of the counter. Although normally a 1 atmosphere He detector
operates with a bias voltage of 1000 volt, the minimum input pulse
voltage requirement of the pulse transformer was such that the operating
voltage of the counters had to be raised to 1200 volt. At this
voltage the slope of the counts vs. high voltage curve was about 8% per
100 volt; therefore very stable, low ripple high voltage supplies were
used to insure reproducibility of the detector response.

FIG. 10 PHYSICAL CHARACTERISTICS OF THE He3 NEUTRON COUNTERS

50
The Electronic Instrumentation
A block diagram of the instrumentation used in the pulse propaga
tion experiments is shown in Figs. 11 and 12. Two independent data
acquisition systems with a common start-stop clock are necessary to
carry out the measurements: (1) a system connected to a movable detec
tor that obtains the time profile of the propagating pulse at a given
position and (2) the all important normalizing detector, fixed at one
3
position. Two 1 atmosphere He detectors with the characteristics de
scribed above were used for these purposes. The system is essentially
composed of signal transmitting devices and data registering and
handling units.
The movable detector data acquisition system (MDDAS) consists of:
1. Detector High Voltage Power Supply
The high voltage power supply was an ultrastable FLUKE 405 B with
superior stability and negligible ripple. Manufacturer's specifications
state the stability at .005% per hour and the ripple at less than 1 mv
RMS.
2. ORTEC Model 260 Time-Pickoff unit, with 3000 volt isolation
The time-pickoff units are normally used to detect the time of
arrival of a detected particle, usually with subnanosecond precision..
The use of this characteristic and the electronic arrangement shown in
Figs. 11 and 12 permitted the counting of neutron events with excellent
time resolution. To our knowledge this is the first time that the time-
pickoff units have been used for this application.
Briefly, the system operates as follows: the primary of a toroidal
transformer, having a bandpass for very high frequencies only, is
inserted between the detector and the bias power supply. Fast

51
FIG. 11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM

52
FIG. 12 NORMALIZING DETECTOR DATA ACQUISITION SYSTEM

53
components of the detector signal will actuate a wide band transistor
amplifier and tunnel diode discriminator from the secondary of the
transformer. A line driver buffer is also provided. The power and
control bias are provided by the ORTEC 403 Time Pickoff Control.
3. Modified ORTEC 403 Time Pickoff-Control
The 403 Time-Pickoff Control provides control and fan-out buf
fering for time derivation units such as the 260 Time Pickoff Unit.
The fan-out buffer Accepts the fast negative logic signal from the 260
unit and provides either fast negative or slower positive logic output
signals.
The 403 Time-Pickoff Control had to be modified to make its out
put signal compatible with the input requirements of the 212 Pulsed
Neutron Logic Unit used with the MCA. The 212 plug-in unit requires
pulses with rise times longer than 50 nsec while the positive output
from the 403 control unit has a rise time ~ 10 nsec. Furthermore, the
positive logic signal from the 403 control has a 0.5 microsec pulse
width which is too wide for the time resolution required. Therefore
2
two modifications were made: a capacitor (C12) was changed from 270
pf to 68 pf reducing the pulse width to 0.12 microsec and an inductor
coil (LI) was removed from the system changing the rise time to 50
nsec.
The modifications made the system compatible with the input
requirements of the MCA and avoided overdriving the analyzer.
2. Refer to ORTEC, Inc. "Instruction Manual for 403 Time-Pickoff
Control."

54
4. Technical Measurement Corp. 1024 Multichannel Analyzer
(MCA) and Data Handling Units
The time analysis of the pulse and the corresponding data output
are obtained from the following coupled instrumentation:
Pulsed Neutron Logic Unit, TMC Model 212
Digital Computer Unit, TMC Model CN1024
Data Output Unit, TMC Model 220C
Digital Recorder, Hewlett-Packard Model 561B
Binary Tape Perforator, Tally Model 420
A trigger from an external pulse generator starts the sweep of the
analyzer as controlled by the pulsed neutron logic unit and initiates
the burst at the accelerator. The 212 has variable channel widths from
10 to 2560 microsec. The full 1024 channels were used in all the meas
urements. The storage capacity of the CN1024 is 2^ counts. Both
printed paper tape and perforated binary tape were obtained as output.
5. ORTEC 430 Scaler
For some of the flux traverses and the 1/M measurements, the
integral counts were recorded in a 10 Mhz scaler.
The normalizing detector data acquisition system (NDDAS) consists
of the same components as the movable detection system except that a
256 multichannel analyzer, TMC Model CN110 was used for data handling
and the integral counts were accumulated in an ORTEC 429 Scaler, modi
fied for 7 Mhz counting rate.
The Resolution Time Correction
The resolution time of the pulsed neutron data acquisition system
was the parameter under consideration while searching for a well-matched

55
and fast electronic instrumentation set-up. Some of the findings were
surprising and may explain some of the discrepancies found in previous
pulse propagation and neutron wave experiments which used an acceler
ator type neutron source. In these experiments it has been customary
to increase the neutron yield of the genetator as the movable detector
is positioned farther away from the source to keep running times within
tolerable limits. The count rate at the movable detector is then
maintained at a level which has been determined to be acceptable; how
ever the normalizing detector usually fixed in a position close to
the source (normally at the "thermalizing tank" if one is used) may
then be exposed to count rates beyond the capabilities of the detector
and the associated instrumentation. Since the movable detector signal
was always fed into an analyzer, saturation effects could be easily
detected; the signal from the normalizing counter, however, was always
being fed into a scaler where saturation effects may go unnoticed since
a time profile is not available.
During most of the present work, two MCA's were available and the
phenomenon described above was observed and count rates throughout the
experimental program limited to those permissible by the time charac
teristics of the counting system.
The experimental program being carried out with the UFSA subcrit-
ical calls for the one to one comparison between theoretically calcu
lated and experimentally determined time profiles of the neutron flux
as a function of space. The shape of the pulse, rather than conven
tional integral parameters extracted from it, is therefore the signif
icant and required information. For this reason the influence of the
resolution time correction on the shape of the pulse came under close

56
scrutiny.
The resolution time of several, submicrosecond preamplifier-linear
amplifier combinations was shown to be a function of the mode of opera
tion and of the count rate. For this type of instrumentation, there is
a significant difference between the resolution time as determined by a
steady-state technique (two source method) and a dynamic method (maximum
count rate method [11]), the latter method yielding a much larger reso
lution time.
For the instrumentation finally chosen to carry out the pulsed
experiments in this work no significant difference was found between
the results of the two methods. Furthermore the pulse transformer-
amplifier combination behaves like an ideal non-paralyzing system. The
resolution time of the overall data acquisition system was found to be
primarily determined by the multichannel analyzer.
As a matter of illustration, when the system depicted below was
used the resolution time changed from -0.24 microsec as determined
under low count rate steady-state conditions to 8 microsec as deter
mined under high count rate, pulsing mode conditions.
ORTEC 410
Linear Amo
ORTEC 429
Scaler

57
Shown in Fig. 13 are two time pi-ofiles obtained at the same posi
tion in the UFSA core for the same count rate. The conventional
preamplifier-linear amplifier system shown above was used to obtain one
of the profiles and the instrumentation selected for this work was used
to obtain the other. Both were corrected for resolution time losses
with the best available value for the resolution time. The distortion
observed in the pulse shape obtained with the conventional preamplifier-
linear amplifier system is non-linear due to the count-rate dependent
resolution time. It should be noted that the count rate near the peak
of the pulse was less than 10^ count sec. The conventional system
response "flattens out" when it reaches complete saturation in this
case above 10^ count sec. Saturation effects are not observed in the
pulse transformer system until the count rate exceeds 3.3 x 10^ count
sec. An erroneous resolution time correction, or one which used a
resolution time that does not characterize the system throughout the
range of count rates will change the shape of the neutron pulse and
consequently affect any analysis done on the pulse shape obtained.
As pointed out by Bierman, Garlid and Clark [11], in a pulsing
experiment it is necessary to determine whether the counting system
has the characteristics of a purely non-paralyzing system or those
of a mixture of paralyzing and non-paralyzing systems. Using the
method described by Bierman and co-workers, it was established that
the data acquisition system being used in the present work is, as
close as can be determined, non-paralyzing. The resolving time of the
system is essentially determined by the width of the input pulse to the
analyzer and the MCA characteristics.
It should be noted that for a wide range of count rates, depending

40
30
20
10
58
Conventional
24 32
Channel Number
IG. 13 TIME PROFILES OF NEUTRON BURST RECORDED BY CONVENTIONAL
ELECTRONIC INSTRUMENTATION AND BY THE TIME-PICKOFF SYSTEM

59
on the magnitude of the resolving time, it is not necessary to prop
erly identify the counting system since no significant difference in
the corrected counts are observed when using the paralyzing or non
paralyzing correction. This is shown in Fig. 14.
The resolution time correction for the UFSA data acquisition
system is then given by:
N.
N =
T N0xtr
1
CWxTrs
where
N^, = true number of events in a given channel
N = observed number of events in a given channel
tr = resolution time of the system
CW = channel width
Trs = number of sweeps of the analyzer
and, for a non-paralyzing system
tr = reciprocal of the maximum observable count rate
Using this method the following resolution or resolving time fan
tors were determined:
A) MDDAS including 1024 Multichannel Analyzer
tr = 0.31 + .015 microsec
B) MDDAS excluding Multichannel Analyzer
tr 0.20 + .01 microsec
C) NDDAS including 256 Multichannel Analyzer
tr = 0.56 + .02 microsec
D) NDDAS excluding Multichannel Analyzer
tr 0.20 + .01 microsec

Observed Count Rate
FIG. 14 THE PARALIZING, NON-PARALIZING SYSTEM RESOLUTION TIME CORRECTION AS A FUNCTION
OF COUNT RATE

61
The Normalization Technique
The analysis of a pulse propagation experiment will yield informa
tion on the velocity of propagation, the attenuation and pulse shape as
a function of position of a propagating disturbance. To determine the
attenuation or relative amplitude of the pulse at different positions
in an assembly, the data must be normalized to a fixed reference so
that variations in the source strength, data acquisition time, etc.,
can be properly accounted for. The usual technique requires accumulating
integral counts in a scaler for each measurement and reducing all meas
urements to the fixed reference afterwards. As was mentioned previously,
the resolution time correction can have a significant effect on the nor
malizing factor since widely differing count rates are employed. It is
extremely hard, if not impossible, to obtain a proper resolution time
correction based on integral counts determined from a time-varying count
rate.
Two methods of normalization and their relative merits are discussed
below.
The Integral Count Method is the normally employed method of nor
malization. The total counts accumulated with the NDDAS for all runs
is referred to a predetermined one, with the normalizing detector in a
fixed position while the movable detector changes position.
The Analyzer Method, which is essentially the same as the above
except that the counts arising from the normalizing detector are stored
as a function of time in a multichannel analyzer. The average of a
series of ratios obtained by dividing the corrected channel counts by
the corresponding channel counts of a predetermined measurement gives
the normalizing factor.

62
The Analyzer Method is intrinsically more accurate than the
Integral Count Method because it permits an "exact" correction for
resolution time, losses by the use of the expression previously given
applied to the recorded time profile. The correction for the integral
counts is, on the other hand, inaccurate since the count rate is con
tinuously changing and no base exists for a resolution time correction.
It was found, however, that as long as the count rate near the
peak of the pulse is kept well within the capabilities of the NDDAS no
significant difference is observed in the results of the two methods.
This is due to the fact that ratios are being taken in both cases; this
tends to minimize whatever differences there might be. Thus, it is
concluded that with proper care the Integral Method is adequate whenever
an analyzer is not available for normalization purposes.
It should be noted that an "effective" resolution time can be used
to improve the results of the Integral Method. This "effective" reso
lution time can be found by forcing the normalizing ratio obtained from
two runs by the Integral Method to match the normalizing ratio obtained
from the Analyzer Method for the same two runs by adjusting the reso
lution time correction applied to the integral counts.
Comments
Certain inconsistencies in the results of the first few experi
ments prompted a careful inspection of the multichannel analyzer modus
operandi. For the sake of completeness the significant findings are
listed below.
A) Operation with the 10 microsec channel width (selected by the
settings of the 212 plug-in-unit) proves to be unreliable due to insta
bilities in the clock and gating circuits. Channel widths of 20

63
microsec or longer are stable.
B) The address current setting of the CN1024 is extremely criti
cal, markedly so for high count rates.
C) An optimum pulse into the analyzer should have a rise time of
50 nanosec, a total width of .1 microsec and an amplitude of 3-5
volt.
D) Above noise level, the discriminator setting of the 212 logic
unit becomes irrelevant when a constant pulse height is used as input.
E) Reproducibility tests were performed on the analyzer with the
neutron generator in continuous mode.
The statistical analysis of the channel counts gave:
72% were less than 1 from the mean
25% were between 1 and 2 from the mean
3% were between 2 and 3 from the mean
The system is statistically well-behaved.

CHAPTER V
NUCLEAR CALIBRATION OF THE UFSA SUBCRITICAL
Introduction
The nuclear calibration of the University of Florida SPERT Assem
bly was performed prior to the space-time kinetics studies. The cali
bration involved conventional inverse multiplication measurements,
absolute k^.,. determination by pulsing techniques and comparison with
multigroup-multiregion diffusion theory calculations. The Garelis-
Russell technique was employed to determine kg/l and this result used to
calculate ke^ by coupling it with the experimentally determined decay
constant and the theoretically calculated effective delayed neutron
fraction. During this phase of the experimentation, "spatial effects"
were noted in both a and kg/£. These effects and other interesting
kinetic phenomena involving these basic reactor parameters were con
sidered worthy of further study and were investigated during the main
part of the research. They are discussed in Part 2, Chapter V. In
this section the results pertinent to the necessary calibration of the
system are given.
Theoretical Notes
The Inverse Multiplication Method
Under ideal conditions, usually met only in small-fast assemblies,
the reactivity can be represented by
64

55
Sr1' >rhf r 1 -k'1/M
where M is the net neutron multiplication in the assembly with a
centrally located source. In practice, the multiplication is obtained
from the ratio of multiplied to unmultiplied counts with a centrally
located source. The unmultiplied counts are obtained with the fissile
material removed and all other conditions undisturbed. In water
moderated cores it is difficult to match neutron spectra for multiplied
and unmultiplied counts and deviations from the ideal M are to be ex
pected. If possible, a search for detector locations should be con
ducted so as to obtain curves that follow the expected behavior of 1/M.
Even if k can not be directly inferred from the 1/M determination, the
curve of reciprocal count rate vs. the parameter that controls reac
tivity (fuel loading or moderator height or % control rod withdrawal)
is a useful guide for safely approaching criticality if a well-behaved
curve can be obtained.
The inverse multiplication curve can be obtained as a function of
moderator height by first obtaining a series of unmultiplied counts at
various water levels and the multiplied counts as the water level is
raised with the assembly originally air-spaced. Sensitivity to geo
metrical configuration (source-detector-water level) requires an empir
ical determination of "well-behaved" detector positions.
Reactivity Measurements by the Pulsing Technique
The pulsed-neutron technique has been used successfully for several
years to measure reactivity. The transient neutron density following a
burst of neutrons is used to determine the reactivity of the system by
either the Simmons and King method [12], Sjostrand's area ratio method

66
[13], Gozani's extrapolated area-ratio analysis [14] or the Garelis-
Russel technique [8]. In all these techniques it is essential that a
fundamental spatial distribution of the neutrons be established for a
correct determination of the decay constant and, therefore, the reac
tivity of the system.
The Simmons and King method established that a value for the
reactivity can be obtained directly if a prompt fundamental decay con
stant can be measured at delayed critical. The value of a at delayed
critical determines B/£ and if these parameters are assumed constant
over the reactivity range of interest a value of a can be obtained. The
technique has given good results up to $20 subcritical in small mul
tiplicative systems. The method strongly depends on being able to
establish the prompt fundamental decay mode; it suffers from the incon
venient necessity of a delayed critical measurement and the assumed
constancy of 8/£ throughout the ranges of reactivity.
The Sjostrand method improves the Simmons and King method in that
the delayed critical measurement is no longer necessary but the results
are shadowed by the strong influence of higher spatial harmonics. The
method is based on the premise that the impulse response curve of the
system is dominated by the prompt fundamental mode.
Gozani's treatment is a significant improvement over Sjostrand's
method. Gozani proposed the extraction of the fundamental mode of
prompt neutron decay from the impulse response curve and the extrapola
tion of this curve to zero time. The reactivity in dollars can be found
by integrating under this curve; the method is independent of the pres
ence of higher prompt spatial modes.
The Garelis-Russell technique, similar to Gozani's extrapolated

67
area-ratio method, is of practical value because of its intrinsic
elimination of the effect of prompt higher harmonics. This method,
which was used in the present work, was postulated originally for a
repetitively pulsed (with a delta function source in time), bare,
monoenergetic reactor but has proven to be of broader application.
Garelis and Russellpostulate, that for the conditions specified above:
1/R 1/R
.fNp exp( (k|3/£,) t)dt = £Npdt + Nj/R
where
Np = prompt contribution to the neutron density'
= delayed contribution to the neutron density
R = pulsing rate
The following conditions should be satisfied for the correct ap
plication of the method.
a) R>>X, where X is the decay constant of the shortest lived
precursor group.
b) R a, where a is the prompt fundamental decay constant.
c) The system must be pulsed a sufficient number of times so that
exp (magn/R) << exp (-agn/R) where m + 1 is the total number of pulses
and the agn are the roots of the inhour equation.
d) The prompt root dominates the decay.
The Garelis-RusseUtreatment permits the determination of p ($)
when all the above conditions are satisfied, by the relation:
($) =
k e/£
- 1
An absolute value of p is obtained by the use of a calculated effective
delayed neutron fraction. Garelis has discussed the use of the method
in reflected systems; the technique seems to be of practical value in

68
these systems [15].
Becker and Quisenberry were able to compute a correction [16] for
the observed spatial dependence of the reactivity in two-region systems
by recognizing the differences in the spatial distributions of prompt
andjdelayed neutrons. Their excellent comparative study of the above
techniques emphasized the need for their recommended spatial correction
unless the neutron detector is properly positioned to minimize this
correction.
The study of Garlid and Bierman [17] correctly points out that in
very large systems "an asymptotic spatial distribution cannot be estab
lished before the pulse has decayed away, since the asymptotic mode is
one that is uniform everywhere in space." They proceed to apply a
combination of first flight, age, and time-dependent diffusion theory
to the study of pulsed measurements in large aqueous media; their con
clusion is that their measured apparent decay constant is a good ap
proximation to the asymptotic value and that pulsed measurements in very
large multiplying systems may also give good results.
Inverse Multiplication Measurements
The safe approach to the design value of k^^ <^99 was undertaken
with the conventional 1/M measurements until k ~0.95 and then by both
eff
the 1/M and the pulsing technique.
To establish detector positions free from geometrical effects
(source-detector-water level), six different locations were used until
a water level of 60 cm (k ~ .98) was reached and four locations afterwards
Two of the detector locations, the closest to the neutron source, failed
to describe the multiplication of the system. Shown in Fig. 15 are the

GRID POSITION
WEIRS
FIG. 15 DETECTOR POSITIONING SCHEME

70
locations employed for these measurements and for the absolute
determination by pulsing. Two 1 cu, centrally located Pu-Be sources
were used for these measurements.
The measurements were performed in the following sequence:
a) Unmultiplied counts vs. water level were obtained from a water
level of 20 cm to 91.4 cm above the bottom of the active fuel in steps
of 5 cm.
b) The fuel was loaded in the assembly in the presence of two
centrally located Pu-Be sources, with proper monitoring.
c) Multiplied counts vs. water level were obtained from a water
level of 20 cm in 5 cm steps until an effective multiplication factor
<_.99 was reached. This procedure follows the criteria established for
Initial Loading of the assembly, Part 2, Chapter III of this work; the
5 cm steps were more conservative increments than those specified for
the Initial Loading of the assembly.
The results of these measurements are shown in Figs. 16 (A, B).
All the curves were well behaved in the sense that none "nose-dived."
Position 2 and 4 failed to properly describe the multiplication of the
assemblies because of their nearness to the source. Position 1 seems
to overestimate the multiplication, mainly because the unmultiplied
count rate was extremely low at this position thus an apparently high
ratio of multiplied/unmultiplied counts was obtained. A detector more
sensitive to high energy neutrons was used in locations 1 and 6.
It should be noted that when the inverse multiplication is plotted
2
vs. 1/H the predictions become quite linear much earlier than when
2
plotted versus H. Better predictions are therefore made with the 1/H
curves but the approach can become less conservative by underestimating

Inverse Multiplication
Moderator Level (cm)
FIG. 16A INVERSE MULTIPLICATION vs. MODERATOR LEVEL

Inverse Multiplication
Moderator Level (cm)
FIG. 16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT

73
the multiplication.
Shown in Table III are the values estimated for k for the four
eff
locations that seemed to represent the system best. Position 3 gives
a lower limit and Position 1 an upper bound. No attempt was made to
establish the error associated with measured k but it is believed
eff
that the 0.99 value obtained at the last water level is within +.005
of the true value.
Absolute Determination of kef£
After an estimated value of k >.95 was obtained from the 1/M
eft
measurements, an independent determination of k was required by the
operating license at every new increment in the moderator level (as
determined by the criteria established in Part 1, Chapter 3). The
technique chosen for this determination was the Garelis-Russell method
of measuring k3/& and a simultaneous determination of the prompt funda
mental decay constant.
Different detector locations were used to determine the influence
of the source and of higher order harmonics contamination. Strong
"spatial effects" were observed in both a and k3/£. This phenomena will
be discussed in detail in Part 2, Chapter V because of its importance.
A seemingly true fundamental decay constant and "spaced-converged"
kS/i were obtained at large distances from the source and were used to
determine the reactivity of the system.
A Fortran IV, IBM 360 computer program named UNIPUL was coded to
perform a unified analysis of the pulsed neutron data (see Appendix B).
The program calculates the decay constant using Peierl's statistical
analysis [18] and k8/£ using the Garelis-Russellapproach after the data

74
TABLE III
SUMMARY OF 1/M AND PULSED MEASUREMENTS
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
INVERSE MULTIPLICATION PULSED EXP PREDICTED
Moderator3 keff k0ffb keff
Height (cm) Pos. 1 Pos. 3 Pos. 5 Pos. 6
20
.415
.481
.425
.581
.7675
25
.744
.629
.705
.771
.8287
30
.867 .
.737
.824
.865
.871
35
.914
.794
.881
.900
.9022
40
.944
.84
.908
.927
.925
45
.9612
.873
.934
.946
.9419
50
.973
.895
.950
.961
.948+.01
.955
55
.98
.918
.962
.969
.965+.007
.9655
60
.985
.936
.973
.971
.972+.006
.974
65
.9891
.95
.980
.979
.9796+.005
.980
70
.9925
.96
.9853
.986
.9855+.004
.986
75
.9949
.971
.989
.990
.990+.003
.9906
80
.9944
85
.9976
91.4
1.00117
Above
bottom of ,
active fuel
Averaged from 3 <
detector positions

75
has been resolution time corrected and background subtracted. A "pure"
delayed neutron background is statistically calculated and used to
determine k$/£. The data can be normalized to a reference detector
position for the analysis of the pulse propagation measurements in the
time and in the frequency domain. A Fourier analysis of the pulse can
also be performed if required.
Shown in Fig. 17 (A, B) are the experimentally determined a, kg/i,
and k as a function of moderator height obtained by averaging results
from three chosen detector locations in the "asymptotic" region. The
results are summarized, together with the 1/M measurements and theoreti
cally calculated values in Table III. The excellent agreement between
the experimental and theoretical results should be considered somewhat
fortuitous. The calculations were done following the method outlined
in Appendix A. Some later calculations [19] done by the Phillips
Petroleum Co.,showed more disagreement, especially at low water levels.
The last calculations tried to account for the fact that there is a
fissionable reflector above each experimental moderator height. This
fact was disregarded in the calculational results shown in this work.
The agreement at the 75 cm water level is good for all calculational
methods.
Conclusions
The University of Florida SPERT Assembly has been operated for
several months with very few operational problems. The system has
proven to be extremely reliable and the instrumentation has performed
adequately. The calibration of the system has established that mean
ingful values for the reactivity can be obtained when applying the

(sec
Moderator Level (cm)
FIG. 17A DECAY CONSTANT vs. MODERATOR LEVEL

kg/£ (sec
FIG. 17B kg/i, AND k vs. MODERATOR LEVEL

78
Garelis-RusseHtechnique to a reflected slab assembly when proper care
is taken. Agreement between calculated and experimentally determined
values of the reactivity is termed excellent but since only one case
has been studied judgement on the overall applicability of the technique
to this type of reactor configurations should be reserved until the
other assemblies to be studied in the UFSA facility are duty analyzed.
It should be pointed out that multiple detector positions are necessary
to establish when an asymptotic decay constant is obtained, and that the
value of k£/Jl is affected by the input pulse width. As mentioned previ
ously, a more detailed analysis of the pulsed neutron reactivity meas
urements is conducted later in this thesis.

PART 2
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY

CHAPTER I
INTRODUCTION
Statement of the Problem
The dynamic behavior of large reactor cores is recognized as one
of the areas of reactor analysis in which practical, reliable calcula-
tional methods are needed. Although a significant amount of theoretical
work has been done in this area, the experimentation has been restricted
to the fundamental work done by Miley and co-workers at the University
of Illinois [20, 21, 22] and the dispersion law studies in a heavy
water-moderated, natural uranium assembly performed at the University
of Florida [23]. The work at Illinois was hampered by the very broad
input pulse obtained at the thermal column of the TRIGA reactor, by
the neutronic size of the assembly and by the low value of the effective
multiplication (ke^ j^.92). The work at Florida, using comparatively
narrow pulses from a neutron generator (and thermalizing tank), was
also restricted by the neutronic size of the system and by the k
No clean determination of "complete" spatial effects in multiplicative
media has been reported.
The Reactor Safety Division of the United States Atomic Energy
Commission established the Large Core Dynamics Experimental Program,
as proposed by the Atomic Energy Division of the Phillips Petroleum
Company, to study the behavior of large reactor cores. The objective
80

81
is the experimental verification of present space-time kinetics
models and to guide the development of new calculational techniques.
Phase I of the Large Core Dynamics Experimental Program is being
conducted at the University of Florida SPERT Assembly, under Subcon
tracts C281 and C635 with the Phillips Petroleum Co. This part of the
program will provide the most fundamental neutron physics type of in
formation as the redistribution characteristics of the neutron flux in
a close-to-critical assembly are studied in the absence of inherent
feedback effects. The adequacy of basic parts of the analytical models
can be tested accurately by concentrating on the neutron physics
problem.
In this work, the propagation of a narrow, non-asymptotic neutron
burst is studied in the time and in the frequency domain. The experi
mental results are compared with results obtained from the two-group,
space-time dependent, one-dimensional diffusion theory calculational
scheme known as the WIGLE program [24]. A stringent test of the model
is provided by a combined analysis in the time and frequency domain.
Clean, unambiguous experimental information will be shown demonstrating
the presence of spatial effects in large cores.
Description of the Study
Pulse propagation phenomena in a large-in-one-space dimension side
reflected core were studied by introducing a fast neutron burst through
one face of the assembly. A Cockcroft-Walton (TNC) type generator was
employed to produce square neutron pulses of selected widths using the
(d,t) neutron reaction.
The assembly which was studied is described in detail in Part 1

82
of this work. The subcritical assembly consists of a square array of
4.8% enriched UC^ SPERT F-l fuel elements moderated by light water and
with essentially an infinite light water reflector on the sides. The
core is 243 cm long, 16.35 cm wide, has an effective height of 76 cm
with 30.5 cm wide side reflectors. The effective multiplication con
stant of the assembly has been determined to be 0.990+.003.
A fast, reliable set of electronic instrumentation was developed
and used to record the very high, time-varying count rate as a function
of position in the core of the assembly. A technique was developed to
subtract the contribution of epicadmium neutrons from the recorded
time profile of the neutron flux.
The study of the pulse propagation phenomena was conducted in a
two-fold manner: in the time and in the frequency domain. The study
in the time domain consisted of several sections, focusing the attention
on basic aspects of the space and time dependence of propagating dis
turbances. The following aspects were investigated:
a) The propagation of 0.5 and 1.0 msec wide input pulse intro
duced at one end of the assembly. This investigation constituted the
main part of the research; it involved a detailed comparison of the
experimental results with the predictions of the WIGLE calculational
scheme. The sensitivity of the one-dimensional model to small varia
tions in the transverse leakage was also investigated.
b) Static flux traverses were conducted to determine the steady-
state neutron distribution in the asymptotic region. Dynamic flux
traverses were performed to determine whether any propagation occurs in
the transverse direction.
c) The effect that the input pulse width has on the propagation

83
phenomena was studied.
The space-time data was also analyzed in the frequency domain by
numerically obtaining the amplitude and phase of the zeroth Fourier
moment of the pulse. The experimentally determined dispersion law of
the system is compared to that predicted by the WIGLE scheme. The
results of the WIGLE calculations performed for the analysis in the
time domain were Fourier analyzed so that a one-to-one comparison could
be performed.
Space dependent effects on reactivity measurements were studied
by analyzing the pulsed data using the Garelis-Russellmodel.
Nomenclature- Used in the Description of Pulse
Propagation Phenomena
A series of directly measurable or inferred parameters are used
to describe the pulse propagation phenomena, in the time and in the
frequency domain. The most important of these parameters are defined
below. The pulse shapes and the conventional full-width-at-half-
maximum also form part of the analysis.
Delay Time
The delay time, t^, is defined as the time displacement of the
peak of the pulse from a reference position to the position under con
sideration. In this work all delay times are referred to zero time;
this corresponds physically to the initiation of the pulse at the
neutron generator.
Propagation Time
The propagation time of a narrow pulse in the assembly is defined
as the delay time between two extreme positions in the assembly.

84
Asymptotic Velocity of Propagation
The asymptotic velocity of propagation, v is defined as the
inverse of the slope of the delay time vs. distance curve in the
asymptotic region.
The Asymptotic Dynamic Inverse Relaxation Length
The asymptotic dynamic inverse relaxation length, k^, is defined
as the inverse of the distance required for the amplitude of the pulses
to attenuate by a factor e.
The Damping Coefficient of the Neutron Wave
The damping coefficient of the neutron wave, a, is a measure of
the exponential attenuation of the amplitude of the wave for a given
frequency. The damping coefficient is determined from the amplitudes
of the zeroth Fourier moment by numerical transformation for each
frequency of interest.
The Phase-Shift per Unit Length
The phase-shift per unit length of path, £, is determined from
the phase angles of the zeroth Fourier moment by numerical transforma
tion for each frequency of interest.
The damping coefficient and the phase shift per unit length of
path are the real and the imaginary components of the complex inverse
relaxation length, p, respectively.
It should be noted that in this work pulse and wave propagation
from the "conventional" viewpoint, i.e., propagation of a residual
disturbance rather than the propagation of a pulse or wave front, is
being studied.

CHAPTER II
THEORETICAL NOTES
Introduction
The main concern of this work has been the experimental investiga
tion of space-time kinetics effects on a large core subjected to a
perturbation; the basic aspects of the neutron physics phenomena were
studied. The analysis of the experiment has been conducted in both
the time and the frequency domain. The theoretical model used for
comparison with experiment, in the time and the frequency domain, was
the two-group, space-time dependent diffusion equations numerically
solved by the WIGLE code [24]. A one-to-one comparison of theory and
experiment was performed in the time domain. For the corresponding
study in the frequency domain both the WIGLE and experimental time
profiles as a function of position were analyzed into its wave compo
nents by a numerical Fourier transformation; this method was suggested
by Moore [25] and confirmed by Booth [26]. In this work only the
zeroth Fourier moment is analyzed; the amplitude and phase angle of
the zeroth Fourier moment correspond to those measured by the conven
tional neutron wave experiment.
Review of the Literature
A considerable amount of theoretical effort has been devoted to
the space-time kinetics problem in nuclear reactors. The more important
85

86
methods presently in use are:
a) Direct solution of the multigroup, space-time diffusion
equations, referred to as the "exact" method. This method constitutes
a benchmark for the other techniques. The most prominent of these
calculational schemes are:
1) WIGLE, a two-group, one-dimensional space-time diffusion
theory computer program [24, 27, 28].
2) TWIGLE, a two-dimensional version of WIGLE [29].
3) FREAK, a fast reactor multigroup kinetics code [30].
4) A four-group, one-dimensional space-time diffusion theory
computer program [31] developed by the Phillips Petroleum Co.
b) Flux Synthesis methods, which used the idea that the flux
shapes which occur during a transient can be bracketed by a set of
shape functions [32, 33, 34].
c) Conventional Modal methods, exemplified by the Foderaro-
Garabedian technique [35] in which the flux is expanded in terms of
the eigenfunctions of the wave equation (Helmholtz modes).
d) The Quasistatic approach of Ott [36, 37], a more sophisticated
"factorizing" technique (the flux is factorized into an amplitude and
a shape function). Use is made of the fact that the time dependence
of the shape function is less important than the time dependence of
the amplitude function.
e) The Adiabatic approximation [38], a "factorizing" technique
in which, besides ignoring the time dependence of the shape function,
no distinction is made between the prompt and delayed neutron sources.
Other related studies, on a somewhat different context,were performed
by Kystra and Uhrig [39] and by Kavipurapu [40]. They studied the

87
space dependent reactor transfer function, within the framework of a
combination of time-dependent Fermi-Age and diffusion thories.
A parallel field of study has been the neutron wave technique
[41, 42, 43]. A major improvement in the neutron wave field was
achieved when Moore proved [25] that the pulsed technique is equivalent
to the neutron wave method when the pulsed data is analyzed in the
Fourier transform plane. The work by Booth [26] confirmed this simpli
fying and time-saving approach to the powerful but time-consuming neu
tron wave measurements.
The study of multiplying media by neutron wave (or pulse) propaga
tion has not been developed as extensively as in non-multiplying media.
Brehm made a very elegant analysis of the problem, showing the excita
tion of slowing down modes whose relaxation lengths he was able to
compute [44]. Dunlap and Perez studied the dispersion law of a heavy
water-moderated, natural uranium assembly [45].
To date, no complete analysis of a pulse propagation experiment,
i.e., in the time and in the frequency domain is available in the
literature.
The WIGLE Calculational Scheme
The version of the WIGLE code used for the calculations performed
in this work is an IBM 360 version of the WIGLE-40 program described
by Radd [27]. The following description is extracted from Ref. 27.
WIGLE is a one-dimensional, two-energy-group, time-dependent dif
fusion program. It calculates the space-time behavior of the neutron
flux in a reactor during a transient. The calculation is restricted
to one-dimensional slab geometry with zero gradient or zero flux

88
boundary conditions. Up to six delayed neutron groups can be con
sidered in the calculations. The feedback subroutine may be used to
introduce arbitrary changes in the reactor parameters, either for
inherent feedback or for other time-dependent variations.
The basic equations solved by the WIGLE program are as follows:
D1 v*l Z1 h + X1 (vi:f *1 + vZf2 4>2) (1 Y1B)
1 1 3*1
+ E i + si = ^-ir
1=1 1
(1)
VD2 V2 E2<*>2 + x2 ^vEf1 ^1 + vZf2 ^ y2B^
1 i 92
+ S + Cl 6) C2iXi + S, = (2)
3C
Xi Cli + Y1 Bi vEfl *1
li
3t
3C
Xi C21 + Y2 Bi vEf2 ^2 = "3t
2i
(3a)
(i = 1, 2, ..., I)
(3b)
The number (I) of delayed neutron groups may be 0, 1, or 6. 6 can
be 1 or 0. When 5=1 and = y2> these equations are the conventional,
two-group, time-dependent diffusion equations. .
The time-dependent equations, and those equations necessary to
represent the inherent feedback effects if they are considered, are
reduced to finite (time) difference equations and numerically solved.
WIGLE can handle up to 60 regions, 251 mesh, points and 999 time steps.

89
Neutron Wave Analysis
The neutron wave technique has proven to be a very powerful method
of determining the deficiences a model has in predicting propagation
phenomena or in establishing the "quality" of the results from a corre
sponding experiment.
The study of the space-time data in the frequency domain "looks"
at the overall behavior of the asymptotic spatial region of the assem
bly with parameters that include information on all spatial points for
each frequency of interest. The comparison of the predicted and meas
ured real and imaginary components of the complex inverse relaxation
length, 5, is therefore a more comprehensive evaluation of the discrep
ancies than the point-wise comparison in the time domain. The analysis
in the 6^ plane is an especially stringent test of the model and the
experimental data.
In this work, the comparisons in the frequency domain were made
by numerically determining the zeroth Fourier moment of the data meas
ured in the time domain. This method was suggested by Moore.^
Moore expressed Fourier moments of the space-time data as
. n -2-rrift .
i|>n(r, f) = / dt t e ij>(r, t)
(A)
where iKr, t) is the neutron pulse at space point r as a function of
time, t, and f is the frequency in cycles per second.
The fundamental space and energy mode propagating through the
medium is given by:
1. The author acknowledges Dr. M. N. Moore for several enlightening
discussions on the subject of neutron waves propagation.

90
^0(r, f) = A1(J (f) Q23 (r2, r3, B^)
exp {[-o^Cf, B) + i (f, b£)]z}
where:
A1q specifies the source condition.
2
Q23 (r2> r3> B ) specifies the transverse space dependence.
and are respectively the real and imaginary components of
the complex inverse relaxation length.
The Fourier transform (r, f) of the unit impulse response
(r, t) is the transfer function of the system. Therefore the ampli
tude and phase curves obtained from a numerical Fourier transformation
of the pulse propagation data corresponds to those measured directly
by the wave experiment.
It should be mentioned that, although most common nomenclature
refers to the pulse propagation phenomena and/or the neutron wave
propagation as "thermal" neutron propagation because of the "close-to-
thermal" source employed and the characteristics of the media studied,
there is no such "pure" phenomena in a multiplying medium. The dis
turbance propagates whether it started as a "fast" or "thermal" pulse
and quickly losses memory of its origin (specially in water moderated
media). The only difference between inserting a thermal or a fast
burst of neutrons lies in the spatial distribution.of source neutrons.
The thermal source will appear essentially localized at the point of
insertion while the fast source neutrons will penetrate deep into the
assembly.

CHAPTER III
DESCRIPTION OF THE MEASUREMENTS
Introduction
In most pulse propagation and/or neutron wave measurements the
experimental technique employed to obtain the thermal neutron pulse
shape is the so-called cadmium difference method. In this technique
the contribution of the epicadmium source neutrons is subtracted by
making measurements with and without a cadmium shutter between the
source and the system. No attempt is usually made to subtract the
epicadmium neutron contribution due to fissions if the medium being
studied is multiplicative.
But, most neutron detectors interact with epicadmium neutrons with
varying degrees of efficiency; therefore to isolate the thermal neutron
pulse shapes a different experimental technique was used in this work.
Thus, it was possible to make a one-to-one comparison of the experi
mentally obtained thermal neutron pulse shapes with the corresponding
results from the analytical scheme.
The subcritical configuration and electronic instrumentation used
has been detailed in Part 1, Chapter IV. Unless specified, the meas
urements were made at a moderator height of 75 cm, corresponding to a
keff = 0.99+.003.
The system was operated under continuous water flow conditions.
No heating of the water was observed by either the energy transferred
91

92
by the pump or the low operating average power level of the system
( 0.13 watt). The large volume of circulating water aided in main
taining the temperature constant. In one 14-hour period of operation
the temperature change was about 1C.
The Epicadmium Subtraction Method
The use of a thermalizing tank and the cadmium difference method
is widespread for pulse propagation measurements. In the particular
case of the UFSA assembly this technique is not pertinent, since the
primary reason for the measurement was to test the analytical model
under stringent, viz. non-asymptotic, conditions; furthermore, with
the WIGLE model it is possible to account for the spatial and energy
dependence of the fast source rather well within a two-energy group,
slab geometry scheme. Therefore, no thermalizing tank was used and no
cadmium plate was inserted between the source and the assembly.
3
The He detectors used for the measurements respond to epicadmium
neutrons, although with decreasing efficiency of detection as the
neutron energy increases. Therefore, to obtain a true basis of compar
ison between the model and experiment, the contribution of the
epicadmium neutrons was subtracted from the time profile recorded by
the detector.
The thermal and epicadmium neutron time profiles measured in the
assembly do not differ significantly in shape in the asymptotic region
but show significant differences in the time scale, the relative atten
uation and the shapes near the source. Although the detectors used
are about ten times more efficient for detecting thermal neutrons, the
epicadmium flux is much larger than the thermal flux throughout the
system and, in particular, close to the source. Therefore, the

93
following technique was used in most of the measurements:
a) Measurements were taken with the bare movable detector
at each designated position and a normalization factor
obtained from the fixed detector.
b) Measurements were taken with the same movable detector
covered with a 0.018 in thick cadmium sleeve (the Cd cut
off energy for this thickness is -.53 ev) at the same posi
tions and a normalization factor obtained from the fixed
detector.
c) The time profile from each measurement was resolution time
corrected, background subtracted and normalized with
reference to the fixed detector (refer to Part 1, Chapter IV).
d) A point by point subtraction of the epicadmium time profile
from the total time profile yielded the thermal neutron flux
pulse shape at each spatial point.
It should be mentioned that, to be rigorous, a correction should
be applied to the epicadmium flux at each space point to take into
account the perturbation of the thermal flux introduced by the cadmium
sleeve; this was not attempted in this study. It should not be signif
icant in the highly absorbing medium being considered here.
As a corollary, it was expected that the epicadmium flux time
profile could be compared with the theoretically predicted fast flux.
The main problem encountered with this comparison lies in the fact that
the energy-dependent efficiency of the detector affects the character
istics of the pulse. The efficiency of detection for the thermal group
(0-.5 ev) is fairly constant and the comparison with the calculated
thermal flux is on solid grounds; the same argument is not valid

94
however for the fast group. Although the results for the epicadmium
flux obtained in these measurements will be presented, they should be
looked on with the reservation that the energy-dependent neutron
counting statistics invalidate the one-to-one comparison with calcu-
lational results. The epicadmium flux was obtained primarily for the
necessary correction of the time profiles. The analysis of the thermal
neutron group is duly emphasized.
Shown in Fig. 18 is a typical plot of the total and epicadmium
time profiles recorded in the experiment and the thermal pulse shape
obtained by subtraction. The magnitude of the correction is space-
dependent, since no constant thermal/fast ratio (as detected by the
counter) was observed. The correction varied from 3-10% of the total
flux values.
The Geometrical Arrangement
Shown in Fig. 19 is a plan view of the source-subcritical assembly
arrangement used throughout this work. The detector positions used for
the measurements are clearly indicated. The numbers shown correspond
to the positions of fuel pins with respect to the end of the assembly
facing the neutron generator. There were 7 grid-holes between detector
positions, giving a distance of 12.72 cm between data points. Through
out the rest of this report the positions of the data points will be
referred to as PXX, where XX is the grid-hole number at which the data
was recorded, i.e., P41 refers to position number 41 starting from the
front face of the assembly. A total of 134 rows of fuel pins were in
the assembly. Data was taken at nineteen spatial points for the main
part of the research. The target assembly of the neutron generator

FLUX IRELATIVE UNITS)
FIG* 18 THE TOTALtEPICADMIUM AND THERMAL FLUX 117-44 CM FROM THE SOURCE

Dimensions in cm
PIG. 19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL ARRANGEMENT
- PLAN VIEW -

97
penetrated 10 cm into the core. The purpose of this arrangement was
to increase the solid angle subtended by the target in the assembly to
augment the number of neutrons going into the system and to reduce the
number of unscattered fast neutrons dispersing into the room and
creating a shielding problem.
Synopsis of the Measurements
Flux .Traverses
A series of flux traverses were done on the assembly to determine
the flux shapes across the width and the height of the assembly. The
traverses were done dynamically and statically.
Static traverses were performed with Indium foils at a distance of
66.6 cm from the neutron source. Measurements were done on the width
and height of the assembly with the neutron generator in the continuous
mode for a period of 6 hours to achieve the saturation activity of the
foils. The foils were 5 mil thick, 7/16" in diameter, and 99.97+%
Indium.
Dynamic traverses were performed across the width of the core at 41,
54, 130 cm from the neutron source with the generator in the pulsing
mode to determine whether any propagation occurs in the tranverse
3
direction. The long He detectors were used for the measurements,
which employed pulse widths of 0.5 and 1.0 msec as input.
Clean Core Pulse Propagation Measurements
A whole series of measurements using narrow, square, fast bursts
of neutrons as a disturbance were carried out to determine the most
important characteristics of the pulse propagation phenomena. Most
of the measurements utilized the entire length of the assembly. Certain

98
aspects of pulse propagation phenomena were studied using a few or a
single detector location in the clean core; these measurements will be
discussed separately from the main part of the research as complementary
experiments. .
Pulse propagation measurements across the entire length of the
core were conducted with input pulse widths of 0.5 and 1.0 msec. The
time profile of the thermal neutron flux was obtained by the cadmium
subtraction method at nineteen locations in the core. The first
detector position was 3 cm from the neutron target and measurements
were taken every 12.72 cm thereafter. The data thus obtained was then
analyzed in the time domain.
With the exception of the measurements at the last four detector
locations, 2^ or 2^ counts were accumulated in the peak channel of
the analyzer and two measurements conducted at each position. The full
1024 available channels of the analyzer were used. The channel width
was 20 microsec with an intrinsic 10 microsec storage dead time giving
an effective time between channels of 30 microsec. Running times
varied from 3 minutes close to the source to two hours at the position
farthest from the source.
Propagation of a Narrow Pulse
To test the analytical model under more severe conditions, a
narrow, 100 microsec wide input pulse was introduced into the assembly
and the pulse profile recorded at a few detector locations. The exper
iment is identical to the one described above except that fewer detec
tor locations were employed.
Propagation of a Wide Pulse
To illustrate the propagation characteristics of a pulse violating

99
the Johnson criterion [25] a wide, 10 msec square pulse was introduced
into the assembly. Three selected positions were used for these meas
urements.
Pulse Propagation vs. Pulse Width
During the experimentation described above, the observation was
made that narrow input pulses will yield the same pulse shape in the
asymptotic region, with the peaks displaced in time. To gain an
insight into this predicted occurrence, measurements were taken at one
detector location (P83) with input pulse widths of 0.1, 0.5, 1.0, 2.0,
3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 and 10.0 msec.
Effect of Room Return at Peripheral Detector Positions
The effect of neutrons reflected from the concrete walls on the
measurements was investigated by recording pulse shapes at peripheral
detector positions. The measurements were done with and without a
shield of borated paraffin in the region in which the detector was
located.

CHAPTER IV
EXPERIMENTAL AND THEORETICAL RESULTS
IN THE TIME DOMAIN
The Analytical Model
The analytical results were obtained using an IBM 360 version of
the WIGLE code^ supplied by the Phillips Petroleum Company, and made
operative on the IBM 360-50 at the University of Florida. Certain modi
fications were made to WIGLE to obtain punched card output of the time
profile at selected spatial points. In this manner, the pulse shapes
at the detector positions corresponding to the experimental measurements
were readily available for direct comparison with experiment.
The WIGLE scheme, being a one-dimensional model, requires that the
transverse leakage be taken into account by the proper adjustment of
the parameters. The two-group nuclear parameters for WIGLE were obtained
by the procedure outlined in Appendix A. The eigenvalue, three-di
mensional flux shapes and the bucklings were obtained from the CORA [46]
computer program. The core width was set at 16.35 cm, the reflector
width at 30.5 cm and the reactor height at 76 cm. The experimental
measurements were made with 75 cm of water above the bottom of the ac
tive fuel but there was a small water reflector at the bottom; thus the
1. The author is indebted to Mrs. M. E. Radd, Nuclear Safety Research
Branch, Phillips Petroleum Company, for her valuable cooperation in
familiarizing the author in the use of the WIGLE code.
100

101
"effective" core height is very close to 76 cm. The transverse leakage
was taken into account in the WIGLE scheme by changing the absorption
2
cross section of the fast and the thermal group with the proper D^B^
obtained from the above calculations.
The aluminum port in which the target section of the accelerator
is located created a large void in the source section of the core.
Shown in Fig. 20 is a plan and front view of this arrangement. To mock-
up the physical situation as closely as possible the input to the WIGLE
code consisted of parameters for two different types of regions: one
for the normal core and one for the region depicted in Fig. 20. The
parameters calculated for the UFSA core were then volume-weighted
together with two group parameters for aluminum and light water as a
first approximation to the parameters in the source region (Region 1 in
the calculations).
In Fig. 21 the type of material, number of mesh points and the
mesh spacing used in the calculations is shown. Table IV shows the
value of the parameters for Region 1 and for Regions 2, 3, 4, 5 respec
tively. Before the final runs were made the importance of the mesh
spacing was investigated by running two identical cases with 166 and 99
mesh points respectively. No difference was found between results of
these two cases.
The choice of time increments was more critical. When time steps
of 5 ysec were used in the vicinity of the time where the value of the
4
fast source was changed from 10 to 0 severe oscillations developed at
the first space point. To avoid this problem, time steps of 0.2 to 0.5
ysec were employed in this time region and the magnitude of the source
was reduced in two steps; first to one-half the original value and then-

102
16.35
i r
i i
i i
K?.5-h
i i
-^pss
in
co
r\
-1
vJ
m
m
co
i
\o
FIG. 20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE

REGION NO.
1
2
3
A
5
6
MATERIAL NO.
2
1
1
1
1
1
NO. OF MESH POINTS
12
9
A
7
6A
1
MESH SIZE (cm)
.9916
1.0
1.179
1.8166
3.17905
2.777
MESH POINT NO.
DETECTOR POSITION
13
25
32
36
AO
AA
A8
52
56
60
6A
68
72
76
80
8A
88
92
96
NO.
6
13
20
27
3A
A1
A8
55
62
69
76
83
90
97
10 A
111
118
125
132
FIG. 21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE WIGLE CALCULATIONAL
SCHEME

104
TABLE IV
INPUT PARAMETERS FOR THE WIGLE
CALCULATIONAL SCHEME
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
CORE
Region Regions
1
2,3,4,5,6
ALUMINUM
WATER
D^(cm) 1
.5211
1.06379
1.9338
1.1370
EaiCcnf1)
.055588
.054350
.000228
.000589
Ir^(cm
.02116
.025224
.000159
.0483
vEfl(cm-1)
.003247
.007337
.00
.00
D2(cm-^)
.2895
.20809
3.6078
.14938
Ia2(cm-1)
.4234
.12217
.01048
.019242
vlfzicm-^)
.10027
.22662
.00
.00
[l/v^3(cm ^sec)
5647E-7
3324E-7
[l/v2](cm "'sec)
.3324E-7
.3324E-5
Note: Thermal group
: 0-0.53
ev

Fast group:
0.53 ev
- 10.0 MeV
V

105
to zero with 2-5 ysec (10 time steps) between the two steps. It was
also observed that a long time after the input pulse was cut-off oscil
lations developed at spatial points close to the source when time
imcrements larger than 50 ysec were used.
The time increments used for the 0.5 and 1.0 msec input pulse
problems are shown in Table V. Stable operation of the code was ob
tained with these time steps. Running times were of the order of 20
minutes in the UF IBM 360-50.
The main problem in establishing a fair comparison between the
calculational and experimental results lies in an adequate physical
description of the spatial distribution of the external fast source.
For example, when calculations were done with a spatially localized,
1 cm wide source placed at the physical location of the neutron target
(Fig. 20) the calculated pulse shapes were found to agree reasonably
well with experiment but the peaks of the pulses were delayed by 50 to
500 microsec with respect to the experimental values. Furthermore the
calculations predicted a much sharper attenuation of the peak of the
pulse near the source, although predicting an asymptotic relaxation
length in agreement with experimental results. Therefore, a careful
study was undertaken to obtain the "best" description of the spatial
distribution of the source.
The best approximation to the source that could logically be
assumed based on physical grounds was that of a spatial distribution
I Z
given by a first-flight kernel of the form e r where £r is the removal
cross-section for source neutrons. The distribution used is shown in
Fig. 22. The choice of a plane source kernel is reasonable especially
at points a few cm removed from the source due to the physical

TABLE V
TIME STEPS USED FOR THE WIGLE CALCULATIONS
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
Input Pulse Width = 0.5 msec
Time Step
(Microsec)
2
4
1
5
1
2
5
10
25
50
To Time
Step No.
40
140
160
170
205
235
315
415
655
795
Time Step
(Microsec)
To Time
Step No.
Input Pulse Width = 1.0 msec
3
5
1
.5
1
2
5
10
25
50
30
210
220
230
265
295
375
475
695
834
106

Relative Amplitude
FIG. 22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED INTO THE WIGLE SCHEME
107

108
configuration of the source and the assembly. The planar nature of the
source was confirmed experimentally by obtaining pulse propagation data
across the width of the core close to and far from the source.
The removal cross-section for the uncollided source neutrons in
region 1 was chosen to be the removal cross-section of neutrons from
the fast group in that region as obtained from the two-group scheme
(ref. Table IV). For regions 2,3,4 and 5 the corresponding removal
cross-section was taken to be the removal cross-section of neutrons
from the fast group in the four-group scheme.
It should be noted that the results are not sensitive to the value
of the removal cross-section in region 1. The above choice of the
\
removal cross-section for the remainder of the assembly is consistent
with the overall calculational scheme used and with the value deter
mined empirically for 14 Mev neutrons in light water.
This choice of a first-flight source gave calculational results
in surprinsingly good agreement with experiment, particularly for the
delay times and the spatial attenuation. The predicted pulse shapes
are somewhat narrower than the pulse shapes obtained from experiment.
No significant differences between the results of the localized sources
case mentioned above and a point kernel source distribution were ob
served. The point kernel source distribution underpredicts the pene
tration of the first collision fast neutrons into the assembly.
At this point a few comments on the energy distribution of the
source neutrons are pertinent. A pure tritium target bombarded with a
beam of monoenergetic deuteron ions will produce essentially mono-
energetic neutrons, since the relationship between the energy of the
ions, the neutron energy and the angle of emission is unique. However,

109
the (d,t) reaction rapidly becomes contaminated with the (d,d) reaction
due to the accumulation of the deuteron beam on target. After ~ 600
microamp-hr per unit area of accumulated beam on target the original
neutron yield from the (d,t) reaction has dropped to half of its
original value while (d,d) neutrons account for 1% of the neutron
beam. After ~ 2000 microamp-hr per unit area of accumulated bean on
target, the number of (d,d) neutrons has increased to 2%; this .repre
sents a detectable contamination, and may have some effect on the
removal cross-section of source neutrons. In the present case, how
ever, due to the coarse energy mesh used in the calculation scheme the
effect is not considered to be important.
Typical results obtained with the WIGLE code are shown in Fig. 23
(A, B, C) for a 0.5 msec input pulse. The general characteristics of
the pulse propagation phenomena are clearly displayed. The calculated
spatial distribution of the neutrons as a function of time is shown for
times of 1,2,3,5,7 and 9 msec in Fig. 24 (A, B). The spatial dispersion
increases with time while the pulse attenuates severely in time and
space.
The WIGLE results are discussed simultaneously with the results of
the clean core measurements.
Flux Traverses
Static and dynamic flux traverses were obtained in the clean core
to establish the following:
a) The asymptotic steady-state flux shapes in the transverse
direction.
b) The planar propagation of the neutron pulse. This is extremely

FLUX (RELATIVE UNITS)
FIG. 23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
110

FLUX (RELATIVE UNITS)
FIG. 23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
111

rLUX (RELATIVE UNITS)
FIG. 23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
112

113
FIG. 24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE

114
FIG. 24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE
13
12
11
10
9
8
7
6
5
4
3
2
1
0

115
important since the one-dimensional WIGLE calculations cannot account
for transverse propagation of a disturbance.
Static Flux Traverses
Shown in Figs.25 and 26 are the mapped steady-state fluxes across
the height and the width of the core respectively, at a distance of
66.6 cm from the neutron source. This location was chosen because'the
delay time and attenuation of the pulses showed it to be at the begin
ning of the "asymptotic region", viz. the region in which both the
velocity of propagation and the relaxation length have reached their
asymptotic values. Both flux maps were done with Indium foils and
appropriate corrections were applied to account for self-shielding and
interference (shadowing) effects between foils.
The fluxes calculated from four-group diffusion theory using the
AIM-6 code are displayed together with the experimental data. A cosine
fit was made on the vertical flux and is shown as a solid line in
Fig. 25; the fit obtained was excellent. The analysis of the results
in this direction gives an extrapolation distance between 5 and 7 cm.
The results were not as consistent across the width of the core.
A sophisticated aluminum foil holder was built to permit the location
of the foils between two rows of fuel; the foils were inserted in slots
parallel to the axis of the assembly. Due to the mechanical difficulty
of positioning the foils in the assembly, the physical impossibility of
having them perfectly horizontal and the arduous, significant correction
due to the short distance between foils, only one irradiation was per
formed. When all this is taken into account the results look reason
able. It was found that the bowing of the fuel rods affected these
measurements significantly. This was determined by positioning the

Flux (Relative Units)
FIG. 25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX
116

Flux (Relative Units)
R1 Clean Core
66.6 cm from the source
In Foil Activation
FIG. 26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX
117

118
long detector in one position and rotating the fuel elements that
surround it. The narrow core (6.5 in wide) is obviously very suscep
tible to this effect and to the exact centering of the neutron source
whose location could not be determined to better than 0.5 cm accuracy.
Dynamic Flux'Traverses
Dynamic flux traverses across the width of the core and reflector
were carried out at distances of 41, 54, and 130 cm from the source.
As mentioned above, these measurements are important since the theoret
ical model is one-dimensional and planar propagation is conceptually
desirable.
Shown in Table VI are the "peaking times" obtained for several
positions across the width of the core and side reflectors. The exper
iment was performed with both 0.5 and 1.0 msec input pulses. Only the
results for the 0.5 msec input pulse are shown. The results for the
1 msec case display the same behavior. All the peaks occurred well
within the experimental accuracy. Comparison of pulse shapes at dif
ferent positions across the core and reflector revealed no differences
in the basic shapes. Near the outer wall of the reflector a secondary
pulse, which peaked at a time corresponding to the input pulse width,
was observed. It was confirmed experimentally that this was due to
neutron reflections from the walls of the facility room.
From the pulse propagation measurements, reactivity data was also
obtained. These results are analyzed in Part 2, Chapter VI.
Clean Cor Pulse Propagation Measurements
The main portion of the research propagation measurements in the
clean, cold, side-reflected assembly. These most detailed experiments

119
TABLE VI
DELAY TIMES MEASURED ACROSS THE WIDTH OF THE CORE
- 0.5 MSEC INPUT PULSE -
UFSA R1 core
0.5 M/W ratio
16.35 cm wide reflected core
Delay Times (msec)
Position Distance to Distance to the source
No Core Center (cm) 53.9 cm 130.2 cm
A
7.27
.860
2.42
B
5.45
.830
2.51
C
3.63
.830
2.48
D
1.82
.830
2.45
E.
0.0
.830
2.42
F-
3.63
.830
2.54
G
5.45
.830
2.42
H
7.27
.860
2.51
I
10.9
.860
2.42
RE1
12.5
.890
2.45
RE2
14.3
.920
2.48
RE3
16.1
.950

RE4
17.9
.920
2.57
RE5
28.9
.920

RE6
31.8

2.45
RE7
34.3
.890


120
were conducted to investigate the propagation, throughout the core, of
0.5 and 1.0 msec input pulses. As mentioned in the previous section,
particular aspects of the propagation phenomena investigated are dealt
with separately.
The experimental technique used has already been described.
Briefly, the time profile of the normalized thermal neutron flux is
obtained at selected positions by the integral count method of normal
ization and the epicadmium subtraction technique. Nineteen detector
positions were used for these measurements. For each pulse width two
runs were made at each position, except at the far end of the core where
data acquisition times became significantly longer. Most of the ex
perimental errors assigned to the data were obtained by analyzing the
results of these two measurements.
Following the nomenclature developed by Doshi and Miley [20] at
the University of Illinois, the delay times t^, the dynamic inverse
relaxation length k^, the asymptotic velocity of propagation v the
full-width at half-maximum (FWHM) of the propagating pulse and the
pulse shapes will be analyzed to describe the propagation character
istics of a neutron burst in the very close to critical assembly. The
experimental results are presented together with the calculated values.
It should be noted that practically all the figures showing the
pulse shapes were plotted using a Calcomp plotter which is part of the
IBM 1800 Computer facility in the Nuclear Engineering Sciences Depart
ment at the University of Florida. The data is plotted in a continuous
manner and the points are superimposed later for convenience.' Typi
cally the experimental pulse shapes were plotted from 333 time steps;
the corresponding calculational results have 231-245 time steps.

121
Shown in Fig. 27 (A, B, C) are a set of the experimentally
determined thermal neutron time profiles for the 0.5 msec input pulse
case. A representative set of the experimentally determined spatial
distribution of neutrons in the assembly for increasing times after
the source pulse is shown in Fig. 28 (A, B). The space and time de
pendent redistribution of the thermal flux as the disturbance propa
gates through the assembly is clearly displayed.
Tables VII and VIII show the experimentally determined and theo
retically calculated delay times with reference to zero time (this
time corresponds to the time at which the neutron generator initiates
the burst and the multichannel analyzer starts its sweep), the FWHM
and the counts at the peak of the pulse normalized to position 83
which is located in the asymptotic region. In Figs. 29 through 32 the
delay times and the spatial attenuation for both pulse widths is
shown.
Very good agreement is obtained between the theoretical and
experimental results, throughout the length of the assembly, including
the region near the source and the region farthest removed from the
source where end effects are significant. This apparent agreement is
encouraging and vouches for the calculational scheme and source descrip
tion used.
The Propagation Time and the Asymptotic Velocity of Propagation
The propagation time, which is defined as the total delay time
between peaks at the two extreme positions of the assembly, is 3.65 +
0.1 msec.
The asymptotic velocity of propagation is defined as the inverse
of the slope of the curve of the delay time vs. distance in the

FLUX (RELATIVE UNITS)
NORMALIZED TD
THERM-5- 20
PULSE WIDTH = 0-5 MSECS
TIME CM;
E)
FIG. 27A EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
122

FLUX (RELATIVE UNITE)
FIG. 273 EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE TJFSA R1 CORE
123

FLUX (RELATIVE UNITS)
1-0 +
0-3
0-B +
0-7
0-B
J3
0-4
0-3-
0-2
0-1-
NORMALIZED ID
THERM--5- 76
PULSE WIDTH = 0-5 MSECS
P104
Â¥ * 9 W
9 _* ft
? a .a*
9 ft ft -ft9
ft0-^a0
9e_
0,i0c-c5
>iS o '.-'P ' Jk
-o0.t.Vn^
e W vLT ','^->
wLvJ
0
-L
4
7
S
10
TIME (MSEC)
FIG. 27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
124

125
e
!=>
0)
>
te
t-H
Pi
X
d
iH
tn
Position Number
FIG. 28A EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE

Flux (Relative Units)
126
UFSA R1 Clean Core
12.716 cm between points
Position Number
FIG. 28B EXPERIMENTALLY DETERMINED SPATIAL DISTRIBUTION OF
THE NEUTRONS AT DIFFERENT TIMES AFTER THE PULSE

TABLE VII
CLEAN CORE PULSE PROPAGATION STUDIES
EXPERIMENTAL AND THEORETICAL RESULTS
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ration
16.35 cm wide reflected core
POSITION
DISTANCE TO
PEAK
AT (msec)
FWHM
(msec)
PEAK
COUNTS3
NO
SOURCE (cm)
Theory
Exp
Theory
Exp
Theory
Expb
6
3
0.500
0.50+.01
0.542
0.540+.03
81.22
94.8+6
13
15.71
0.501
050+.01
0.615
0.540+.03
72.68
81.9+5
20
28.43
0.504
0.52+.01
0.779
0.779+.03
48.13
49.9+.8
27
41.15
0.635
0.63+.01
1.098
1.080+.03
27.35
32.7+1.6
34
53.86
0.840
0.82+.03
1.398
1.470+.06
16.37
16.5+.4
41
66.58
1.060
1.04+.03
1.766
1.800+.06
10.27
10.6+.5
48
79.30
1.300
1.28+.03
2.055
2.13+.06
6.65
6.4+.3
55
92.01
1.560
1.50+.04
2.355
2.52+.09
4.42
4.39+.11
62
104.73
1.840
1.82+.04
2.655
2.82+.09
3.00
2.97+.10
69
117.44
2.125
2.11+.04
2.925
3.11+.09
2.055
2.03+.06
76
130.16
2.400
2.40+.05
3.195
3.42+.09
1.427
1.53+.07
83
142.88
2.700
2.65+.06
3.465
3.72+.09
1.000
1.00+.005
90
155.60
3.000
2.96+.06
3.735
3.90+.12
0.7056
0.7062+.03
97
168.31
3.300
3.29+.06
3.900
4.17+.12
0.5000
0.5065+.02
104
181.03
3.570
3.50+.06
4.050
4.38+.12
0.3534
0.362+.007
111
193.74
3.810
3.85+.08
4.125
4.44+.12
0.2460
0.2512+.005
118
206.46
4.000
4.00+.08
4.200
4.47+.12
0.1630
0.1764+.004
125
219.17
4.150
4.18+.08
4.200
4.47+.15
0.0957
0.1161+.0035
132
231.88
4.210
4.21+.09
4.200
4.53+.15
0.0367
0.0437+.003
a Normalized to Position 83
b Errors assigned from the deviation from the mean of two measurements except for the last 5 space
points. This error is usually larger than the counting statistics error. The error of the last 5
points was calculated from counting statistics.
127

TABLE VIII
CLEAN CORE PULSE PROPAGATION STUDIES
EXPERIMENTAL AND THEORETICAL RESULTS
- 1.0 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ration
16.35 cm wide reflected core
POSITION
DISTANCE TO
PEAK
AT (msec)
FWHM
(msec)
PEAK
COUNTS3
NO
SOURCE (cm)
Theory
Exp
Theory
Exp
Theory
6
3
1.000
0.97+.03
1.020
0.930+.06
48.25
56.5+1.5
13
15.71
1.000
1.00+.03
1.065
0.960+.06
47.62
56.7+1.7
20
28.43
1.00
1.03+.03
1.140
1.080+.06
36.52
37.9+.9
27
41.15
1.046
1.04+.03
1.365
1.290+.06 .
23.60
29.6+1.6
34
53.86
1.215
1.19+.03
1.620
1.62+.06
14.99
14.9+.2
41
66.58
1.410
1.33+.03
1.875
1.92+.06
9.720
10.1+.3
48
79.30
1.630
1.65+.06
2.175
2.19+.06
6.431
6.43+.05
55
92.01
1.880
1.81+.06
2.468
2.49+.09
4.332
4.32+.04
62
104.73
2.150
2.10+.06
2.760
2.82+.09
2.955
3.11+.04
69
117.44
2.420
2.41+.06
3.030
3.12+.09
2.041
2.15+.05
76
130.16
2.725
2.71+.06
3.315
3.45+.09
1.423
1.41+.02
83
142.88
3.025
3.01+.06
3.585
3.69+.09
1.000
1.00+.03
90
155.60
3.275
3.30+.06
3.750
3.96+.09
0.7070
0.663+.01
97
168.31
3.575
3.58+.06
3.945
4.29+.09
0.5019
0.489+.009
104
181.03
3.850
3.85+.06
4.110
4.44+.12
0.3553
0.356+.007
111
193.74
4.075
4.10+.08
4.185
4.59+.12
0.2471
0.254+.003
118
206.46
4.275
4.30+.08
4.200
4.56+.12
0.1640
0.184+.003
125
219.17
4.425
4.475+.09
4.275
4.53+.12
0.0962
0.121+.0025
132
231.88
4.500
4.600+.12
4.275
4.56+.15
0.0369
0.0585+.00012
a Normalized to Position 83
k Errors assigned from the deviation from the mean of two measurements except for the last 5 space
points. This error is usually larger than the counting statistics error. The error of the last 5
points was calculated from counting statistics.
128

Delay Time (msec)
129

FIG. 29 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 0.5 MSEC INPUT PULSE -

Delay Time (msec)
130
ft
ft
FIG. 30 CALCULATED AND EXPERIMENTAL DELAY TIMES
- 1.0 MSEC INPUT PULSE -

Flux (Relative Units)
131
FIG. 31 AMPLITUDE ATTENUATION OF THE THERMAL NEUTRON FLUX
- 0.5 MSEC INPUT PULSE -

Flux (Relative Units)
132
FIG. 32 AMPLITUDE ATTENUATION OF THE THERMAL NEUTRON FLUX
- 1.0 MSEC INPUT PULSE -

133
"asymptotic region of the assembly. In this region a linear rela
tionship between delay times and distance from the source exists.
The asymptotic velocity of propagation for the clean UFSA core is
given in Table IX.
TABLE IX
ASYMPTOTIC PROPAGATION VELOCITY v
P
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm reflected core
Input Pulse
Width (msec)
Theory
vp (m/sec)
Experiment
0.5
456
448+9
1.0
456
452+7
It should be mentioned that the asymptotic velocity of propaga
tion is independent of the assumed distribution of the source. When
a localized source in space was introduced into the WIGLE scheme the
results yielded the same asymptotic velocity as the calculations with
a spatially distributed source. This is to be expected since v^ is a
characteristic of the system and has been defined in a region removed
from source effects.
The Dynamic Inverse Relaxation Length
. The dynamic inverse relaxation length, k^, is defined as the
inverse of the distance required for the amplitude of the pulses to
attenuate by a factor e. is determined by the relationship between
the logarithm of the magnitude of the peak of the propagating pulses
and distance in the "asymptotic" region where this relationship is
linear.

134
The attenuation of the amplitude of the peaks for the UFSA assem
bly were shown in Figs. 31 and 32; the normalized peak values were
tabulated in Tables VII and VIII. Again excellent agreement was ob
tained between theory and experiment, not only in the asymptotic region
but throughout most of the assembly. The first two data points (P6 and
P13) are considerably larger in magnitude than the values predicted by
WIGLE. This is probably caused by an undercorrection for the epicadmium
flux detected at these positions and by not accounting for the signifi
cant neutron streaming in the large void created by the aluminum port
in which the target is located. Position 27 is probably the only "bad"
data point and no explanation has been found for its behavior since
four consecutive runs were made at that position and all four showed
identical behavior. The WIGLE results reflect the influence of end
effects more markedly than experiment. It should be noted that reflec
tions from the concrete walls in the assembly room are significant at
peripheral detector positions.
TABLE X
DYNAMIC INVERSE RELAXATION LENGTH <.
d
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm wide reflected core
Input Pulse
Width (msec)
Theory
Experiment
0.5
.03025
.0297+.0012
1.0
.03025
.0301+.0010

135
The Full Width at Half-Maximm (FWHM)
The FWHM is defined as the time-width of the pulse at half the
peak amplitude. The FWHM is one of the parameters conventionally used
to compare pulse shapes and is therefore included in this study.
An analysis of the experimental and calculated values of the FWHM
tabulated in Tables VII and VIII showed the following.
a) Close to the source, theory predicts slightly larger FWHM
values than experiment, the difference decreasing with distance from
the source. As discussed above the discrepancy near the source is due
to difficulties in adequately describing the void region behind the
source.
b) Between P27 and P34 the FWHM are practically identical.
c) Past P34 the experimentally determined FWHM becomes increasing
ly larger than the WIGLE prediction. The maximum difference is about
350 microsec which corresponds to ~ 8% of the experimental value.
The agreement is still considered to be very good.
The Flux Shapes
A detailed comparison of the theoretical and experimental flux
shapes obtained for the UFSA assembly was also made.
Plots of the time profiles of the thermal flux at each detector
position are included in Appendix C for the 0.5 and the 1.0 msec wide
source pulses. The peaks are normalized to unity.
The following information is supplied in each figure:
a) Identifying Run Number
b) Location of the Experimental Peak in Time
This parameter is determined directly by a computer routine which is
part of the plotter program. The routine simply finds the time channel

136
in which the largest number of counts was recorded and in many in
stances is not the best value for the location of the peak. The values
quoted in Tables VII and VIII represent refined values obtained by
inspection of the experimental data.
c) The Input Pulse Width
d) The Experimental and Theoretical FWHM
e) The Location with Respect to the Source is given in the
figure title.
A comparison between the theoretical and experimental pulse shapes
reveals the following:
a) Shapes agree very closely in the spatial region dominated by
the neutron source.. Small discrepancies start to show up near P41.
b) Past P41 the theoretical pulses become consistently narrower
than the experimental one. As discussed above, the other main charac
teristics describing the propagation of the pulses are well matched.
Discussion of the Clean Core Results
The fact that good agreement was found between the theoretical and
experimental results deserves some elabotation since the agreement may
seem fortuitous.
The calculational scheme used to obtain the WIGLE input parameters
is well established. The parameters are therefore considered to be as
reliable as the present state of the art permits. The main uncertainty
as far as the calculational model is concerned is in the allocation of
a transverse buckling.
To investigate the sensitivity of the two-group, one-dimensional
model to changes in the transverse buckling (incorporated into the
WIGLE scheme as a change in the absorption cross-section) a series of

137
calculations were performed in which the height of the assembly was
varied from 70 to 85 cm. The respective core heights with their
corresponding vertical bucklings, k ^ (calculated using AIM-6) and
"absorption" cross-sections used in the WIGLE code are listed in Table
XI.
The results of the calculations showed a marked sensitivity to
changes in the transverse buckling. The delay times and the peak
counts vs. distance to the source are shown in Fig. 33 and 34 respec
tively. The experimental results for 76 cm are also shown. The data
for the attenuation curves was normalized to the attenuation at P83
of the 76 cm WIGLE calculations. Pulse shapes for the different heights
are shown together with the experimental results at 76 cm in Fig. 35
(A, B, C) for three representative positions in the assembly.
Some additional experimental measurements were also made at a
given position for different core heights to supplement the calcula-
tional predictions. It should be pointed out that these measurements
are of a preliminary nature, made over a short period of time simply
to obtain confirmation of the theoretical trends. The results of these
measurements are shown in Fig. 36.
It is not surprising that the results for the core showed as much
sensitivity to changes in the transverse buckling since the width and
height of the core are rather small in comparison to the length of the
assembly. It is to be noted that the changes in the "absorption"
cross-section due to changes in the transverse buckling are rather
small and are reflected in the third significant figure in the fast
group cross-section and the fourth significant figure in the thermal
group cross-section. This emphasizes the importance of an accurate

138
TABLE XI
CHANGES IN THE NUCLEAR PARAMETERS
DUE TO CHANGES IN THE TRANSVERSE BUCKLING
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
WIGLE X-Section
(cm )
Reactor
Height (cm)
Estimated
k ,,
eff
Vertical
Buckling
(cm-2)
S
70.0
.986
20.14
E-04
.054671
.12223
72.5
.988
18.78
E-04
.054526
.122207
76
.990
17.08
E-04
.054345
.12217
77.5
.992
16.43
E-04
.054277
.122158
80.0
.995
15.42
E-04
.054169
.122137
85.0
.998
13.66
E-04
.053981
.122096

Delay Times (msec)
139
FIG. 33 DELAY TIMES OF THE THERMAL FLUX CALCULATED BY THE
WIGLE CALCULA!IONAL SCHEME FOR DIFFERENT CORE HEIGHTS

Flux (Relative Units)
140
FIG. 34 AMPLITUDE ATTENUATION OF THE THERMAL FLUX CALCULATED BY
THE WICLE CALCULATIONAL SCHEME FOR DIFFERENT CORE HEIGHTS

FLUX (RELATIVE UNITS)
FIG. 35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING

FLUX (RELATIVE UNITS)
FIG. 35B THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING
142

FLUX (RELATIVE UNITS)
FIG. 35C THE SENSITIVITY OF THE ONE-DIMENSICNAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING
143

FLUX (RELATIVE UNITE)
FIG. 36 EXPERIMENTAL PULSE SHAPES AS A FUNCTION OF CORE HEIGHT

145
evaluation of the nuclear parameters.
The asymptotic propagation velocity and dynamic inverse relaxation
length as a.function of core height ar shown in Table XII. As ex
pected, the velocity of propagation and the attenuation decrease as
criticality is approached.
The above analysis puts the good agreement between experiment and
theory on a firmer footing. When the observed phenomenon is very sen
sitive to small variations in system characteristics the probability
that fortuitous agreement may be obtained between theory and experi
ment diminishes with the degree of sensitivity.
Comments on the Fast Group Results
The following comments are pertinent regarding the fast group
results as calculated by the two-group WIGLE model:
1. The curve of delay times vs. distance remains flatter than
the corresponding curve for the thermal group near the source region;
it then bends rapidly to yield the same asymptotic velocity of propaga
tion as that of the thermal group.
2. The fast group flux peaks between positions P6 and P13; this
has been confirmed experimentally. In contrast the thermal group flux
peaks at P6. The asymptotic inverse relaxation length of the fast
group is, as expected, identical to the one determined for the thermal
group.
3. The fast group pulse profiles are slightly wider than those
for the thermal group.
The time profiles from the cadmium-covered detector measurements,
which were used to determine the thermal group pulse profiles by the
epicadmium subtraction method were compared with the calculated fast

146
TABLE XII
THE CALCULATED ASYMPTOTIC VELOCITY OF PROPAGATION AND
DYNAMIC INVERSE RELAXATION LENGTH VS. CORE HEIGHT
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Core
0.5 M/W Ratio
16.35 cm wide reflected core
Core
Kd
V
Height
(cm)
Q
(cm X)
P
(msec )
70
0.03565
571
72.5
0.03233
506
76
0.03027
456
77.5
0.02772
435
80
0.02515
397
85
0.02047
321

147
group pulse shapes. Several typical examples are shown in Appendix
D. The following features were observed:
1. The calculated pulse shapes are delayed in time in comparison
to the measured shapes throughout most of the length of the assembly.
2. The measured and calculated attenuation of the peaks is in
poor agreement.
3. The measured and calculated pulse shapes are practically
identical.
The validity of the comparison between theory and experiment in
this instance is not clear, however. The main question is whether the
experimental measurement corresponds to the fast group used in the
calculations, since the sensitivity of the detector rapidly diminishes
with increasing neutron energies. Therefore the conclusions based on
the above comparison must be taken with some reservation, until a more
detailed study can be conducted.
Propagation of a Narrow Pulse
A series of measurements were made in the clean core utilizing a
100 microsec wide input pulse. Only 4 positions along the longitudinal
axis were studied. The purpose of these measurements was to obtain a
qualitative idea of how well the WIGLE scheme can predict the space-
time kinetic behavior of a system perturbed by a very narrow pulse.
From the experimental viewpoint the narrow input pulse resulted in
much poorer count rates, thus requiring longer data acquisition times.
Listed below are the calculated and measured FWHM and delay times
for these measurements; the pulse shapes at the different positions
are included in Appendix E.

148
TABLE XIII
DELAY TIMES AND FWHM FOR A NARROW INPUT PULSE
DISTANCE TO
SOURCE (cm)
PEAK AT
Theory
(msec)
Exp
FWHM
Theory
(msec)
ExP
53.9
0.60
0.580
1.35
1.62
79.3
1.08
1.06
2.06
2.28
130.2
2.27
2.26
3.20
3.51
142.9
2.50
2.53
3.47
3.75
Significant discrepancies between theoretical and experimental
pulse shapes were noted in the region where source effects are still
noticeable; in contrast, excellent agreement was found in this region
for the 0.5 and 1.0 msec input pulse cases. Deep in the asymptotic
region the measured pulse shapes are identical to those determined for
the 0.5 and 1.0 msec input pulses.
The results are somewhat inconclusive, however, since near the
source the measured pulse shapes appeared wider than the corresponding
shapes for the 0.5 and 1.0 msec input pulsed, although they occur
earlier in time. Unfortunately, the assembly was dismantled before
these comparisons were completed. The observed discrepancies deserve
further experimental study.
It should also be noted that noticeable oscillations were observed
in the WIGLE results in the spatial region close to the source.
Propagation of Wide Pulse
A series of measurements were also made in the clean core with a
10 msec wide input pulse. This pulse is much wider than the

149
characteristic propagation time (^3.7 msec) across the assembly of a
narrow (0.5 msec) pulse. It should be recalled that the Johnson
criterion [47]postulates that to be able to observe spatially dependent
effects, the HWHM of the input pulse should be smaller than the charac
teristic propagation time across the assembly. For example, the experi
ments of Miley and co-workers at the University of Illinois [20, 21, 22]
showed that for an initially asymptotic very wide input pulse no shape
changes were observed as the pulse "propagated" across the assembly.
The pulse shapes resulting from these measurements at three posi
tions in the assembly are shown in Appendix F. The delay times, the
FWHM and area under the pulses, normalized to unity at the first posi
tion, are given below in Table XIV.
TABLE XIV
DELAY TIMES AND FWHM FOR A WIDE INPUT PULSE
DISTANCE TO
SOURCE (cm)
PEAK AT
(msec)
FWHM
(msec)
AREA UNDER
THE CURVE
41.2
10.07
10.1
1.0
79.3
10.17
10.7
1.15
142.9
10.22
10.5
0.92
From these results it seems that, although the delay times between
the recorded peaks are quite small a certain "rearrangement" of the
initially non-asymptotic pulse takes place. Close to the source the
pulse is practically square, at a distance of 79 cm it has widened some
what and at large distances from the source the pulse seems to be trying
to achieve the normal "dumbbell" shape. Johnson's criterion appears to

150
be too restrictive, since some spatial redistribution of the input
pulse does occur, although the effect is certainly much less pronounced
than in the case of a narrow pulse. In the case of the Illinois exper
iments the input pulse was ^30 msec wide and already had an asymptotic
shape, with the characteristic propagation time being of the order of
a few msec.
In the next section the propagation of pulses as a function of the
input pulse width will be studied qualitatively. These measurements
were made to complement the above results.
Pulse Shape vs. Input Pulse Width
The analysis of the measurements with input pulse widths of 0.1,
0.5 and 1.0 msec revealed that these propagating pulses achieved
identical shapes, within the experimental accuracy, at distances larger
than 130 cm from the source. This fact was believed to hold for input
pulses much narrower than the characteristic propagation time in the
assembly. A series of pulse shapes were measured as a function of
input pulse width at a distance of 142.9 cm from the source; these
measurements should provide information on the qualitative behavior of
propagating pulses arising from widely differing input pulse widths.
The results of these measurements are shown in Appendix G; the
peak times and the FWHM for each input pulse recorded at P83 are given
in Table XV.
As previously observed, the peaks are increasingly displaced in
time as the input pulse widens. This behavior has been well predicted
by the two-group, space-time dependent diffusion theory model. It
appears that for the 2 msec wide input pulse deviations from the

151
TABLE XV
PULSE SHAPES VS. INPUT PULSE WIDTH
UFSA Rl Core
0.5 H/W Ratio
16.35 cm wide reflected
core
INPUT PULSE
PEAK AT
FWHM
WIDTH (msec)
(msec)
(msec!
.1
2.53
3.75
.5
2.65
3.69
1.0
3.04
3.69
2.0
3.79
4.20
3.0
4.39
4.68
4.0
4.72
5.28
5.0
6.02
5.95
6.0
6.97
6.70
7.0
7.67
7.40
8.0
8.62
8.30
9.0
9.67
9.20
10.0
10.22
10.5

152
"characteristic asymptotic" pulse shape already exists. Characteristic
"dumbbell" shapes are observed however until the HWHM ^ propagation time.
For wider input pulses, the "propagating" pulses are unable to achieve
the smooth shape observed for narrower pulses. Still, a certain
spatial "re-arrangement" of the shape occurs, as was discussed above
for the 10 msec input pulse.

Effect of Room Return at Peripheral Detector Positions
At positions farthest removed from the source, it was observed
that a secondary peak was occurring at times corresponding to the input
pulse width. This was also observed at peripheral positions in the
reflector tanks. To prove that neutrons reflected from the concrete
walls were the cause of this secondary peak, measurements were made at
the outer edge of the reflector tanks with the neutron detector
shielded by borated paraffin placed outside the reflector tank and with
the detector unshielded.
The results of these measurements are shown in Fig. 37A. A
pronounced peak at M).5 msec was found when the detector was not
shielded from the walls and practically disappeared when about 6" of
borated paraffin was placed between the reflector tank and the concrete
wall. The input pulse width was 0.5 msec. Shown in Fig. 37B is the
result of subtracting the "shielded" pulse from the "unshielded" one.
A sharp 0.5 msec pulse is obtained. The "early" peaks are therefore
blamed on fast neutrons reflected from the walls.
The penetration of these neutrons into the reflectors was analyzed
by positioning a detector at increasing distances from the outer reflec
tor tank wall. It was found that the effect was negligible at a

flux (relative: units)
1-0 +
0-0
0-0
0-7-
0-G
0-5
0-4
0-3
V

UNSHIELDED
ft
*
ft
*
ft
ft
f
ft

ft

I \
/****'*?>> A A**
fit'* y?
\a^ f
* y
&
4
a-
§r
SHIELDED
r
%
*h
? rw
i n:
r
&
5.
2f.\
0-1
i
i
a
if /
f/
-UJ
*H\ft
/
VA
Vni1
n\
NORMALIZED TO
R1REFREF7G
pulse: width = 0-5 msecs
EXP- FWHM = 3-570 MSECS
V**4<

10
0
J.
4
G
7
B
3
TIME (MSEC)
FIG- 37A EFFECT OF ROOM RETURN AT PERIPHERAL DETECTOR POSITIONS
153

:~LUX (RELATIVE UNITS)
R1REFREF7G
PEAK AT 0-4S0 MSECS
PULSE WIDTH = 05 MSECS
EXP" FWHV1 = 0-570 MSECS
UNSHIELDED SHIELDED
M
Ui
-C~
4

3 4 5 S 7
a
8
CJ
10
TIME (MSEC)
FIG- 37B EFFECT DF ROOM RETURN AT PERIPHERAL DETECTOR POSITIONS

155
distance of 5 cm from the outer wall. At the far end of the assembly
the reflected pulse "propagated" into the assembly, attenuating and
dispersing with distance to the end wall. This pulse quickly dissi
pated into the.assembly with no significant effect on the measurements

Chapter v
EXPERIMENTAL AND THEORETICAL
RESULTS IN THE FREQUENCY DOMAIN
Introduction
The results of the pulse propagation measurements and of the space
time-dependent WIGLE calculations were analyzed in the sensitive Fourier
transform plane. This neutron wave type analysis probes into the defi-
ciences of the model and/or the experimental data that the analysis in
the time domain might fail to reveal. In this study the analysis is
performed with the sole intention of testing the model and not to ex
tract parameters.
The WIGLE predicted time profiles of the propagating disturbance as
a function of space and the pulse propagation data were Fourier analyzed
in an identical manner; the amplitude and phase angle of the zeroth
Fourier moment thus obtained were least-squares fitted (log amplitude vs.
z and phase angle vs. z for each frequency of interest) yielding the
damping coefficient, a, and the phase shift per unit length, £. The
predicted and measured dispersive characteristics of the system are then
2
compared in the p and p plane.
The neutron wave analysis was applied to both the 0.5 and 1.0 msec
input pulse space-time measurements and calculations.
156

157
Method of Analysis
The following method of analysis was applied to the calculated
and measured results of the UFSA R1 clean core space-time studies:
1. A conventional zeroth moment Fourier transformation was
performed on the experimental data. The numerical integration employed
Simpson's rule of integration. Equal time steps (30 microsec) were
used throughout this analysis. The number of data points varied from
500 to 800, depending on where a stable neutron background was reached,
as determined by an statistical analysis performed in the UNIPUL pro
gram. A computer code, MORE, was coded for this purpose.^"
2. A conventional zeroth moment Fourier transformation was
performed on the space-time results obtained from the WIGLE calcula
tions. It should be recalled that the WIGLE calculation employs a
series of time increments in different time intervals. To conform to
this scheme Simpson's rule of integration with different time incre
ments was used for each time interval. Trapezoidal integration was
used to bridge the gap between the different time intervals. A computer
program, MORWIG, was coded for this purpose.
3. The amplitudes and phases of the zeroth Fourier moment as a
function of frequency, obtained from the MORE and MORWIG numerical
transformation, were least-squares fitted to obtain the damping coef
ficient and the phase shift per unit length for the frequencies of
interest.
In this manner, the theoretical and experimental results in the
1. The MORE and MORWIG programs were coded by Dr. M. J. Ohanian,
University of Florida.

158
time domain were transformed to the frequency domain, with identical
numerical and fitting procedures, setting a firm basis for a one-to-
one comparison.
The following interesting numerical problems are worthy of note:
a) To determine to what extent the numerical transformation is
affected by the accuracy of the operations of the IBM 360 computer,
sample problems were run in single precision (4 byte words) and double
precision (8 byte words) using the MORWIG program. No differences were
found in the results up to the sixth significant figure, but the double
precision computations consumed almost twice the amount of time as
the single precision ones.
b) Initially, the results of every third WIGLE time calculation
was punched on cards for the comparison in the time domain and for the
input to the Fourier transformation code. Less than 250 time points,
with time increments of up to 150 microsec, were available for each space
point. The numerical transformation performed on these results was
somewhat unsatisfactory since not all the amplitude and phase curves
2
were smooth and in the p plane the scattering of points was significant.
The WIGLE calculations were then performed again, with smaller time in
crements, carried farther in time and every time step punched for input
to the MORWIG program. A total of 997 and 998 points respectively were
now available for the Fourier transformation for the 0.5 and 1.0 msec
input pulse cases. The largest time increment was 32 microsec. The
calculation was carried to about 19.2 msec after the initiation of the
pulse. A significant improvement was noted in the results of the numer
ical transformation. The results were smooth throughout up to ~ 800
cps, where a certain amount of scattering was observed.

159
Comparison of the Theoretical and the Measured
Results of the Neutron Wave Analysis
To determine the effect that the input pulse width could have on
the results of the wave analysis, the study was performed for both the
0.5 and 1.0 msec input pulse cases. These experimental and theoretical
results in the time domain were presented in Part 2, Chapter IV of this
work.
Shown in Figs. 38 through 41 are the amplitude and phase of the ex
perimental data obtained by numerical Fourier transformation, for both
the 0.5 and the 1.0 msec input pulses. The results for the 0.5 msec
case are consistently "smoother" than those for the 1.0 msec case. In
the 0.5 msec case the results "blow-up" past 1000 cps while the 1 msec
case seems to be good only to 800 cps. The behavior of the amplitude and
phase is as expected. The data was still good in a frequency region were
most wave type measurements in multiplying media reported to date had
already broken down. For example the experiments of Dunlap were only
good to ~ 250 cps [23]. Undoubtedly, the frequency content of the nar
row, fast burst is superior to the smeared pulse that is normally ob
tained if a thermalizing tank is used. The wave analysis on the WIGLE
space-time results showed an identical behavior throughout the fre
quency range.
The real and the imaginary components of the complex inverse
relaxation length are shown for both theory and experiment in Tables
XVI and XVII, for the 0.5 and the 1.0 msec input pulses respectively.
A graphical comparison of these results is shown in Figs. 42 and 43.
The following comments are pertinent:
a) A distinct but not significant difference is found between the
results of the 0.5 and the 1.0 msec cases in both theory and experiment.

Amplitude (Relative Units)
160
FIG. 38 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE -

Amplitude (Relative Units)
FIG. 39 AMPLITUDE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE -

9
8
7
6
5
4
3
2
1
O
162
R1 Core
12.716 cm between points
48 62 76 90
Position Number
104 118 132
. 40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE -

9
8
7
6
5
4
3
2
1
O
163
Position Number
. 41 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 1.0 MSEC INPUT PULSE -

164
TABLE XVI
THE REAL AND THE
IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION
LENGTH
- 0.5 MSEC INPUT PULSE -
FREQUENCY
a (cm
'1)
5
(rad/cm)
(cps)
Theory
Exp
Theory
Exp
0
.02286
.02248
10
.02290
.02254
.001557
.001558
20
.02305
.02270
.003095
.003098
30
.02328
.02296
.004595
.004600
40
.02359
.02331
.006046
.006054
50
.02396
.02373
.007435
.007451
60
.02438
.02423
.008765
.008780
70
.02483
.02476
.01004
.01006
80
.02532
.02536
.01128
.01124
100
.02640
.02663
.01358
.01349
120
.02755
.02797
.01563
.01541
140
.02866
.02937
.01753
.01714
160
.02986
.03081
.01932
.01868
180
.03101
.03223
.02092
.02026
200
.03215
.03359
.02244
.02148
220
.03330
.03495
.02391
.02278
240
.03442
.03627
.02521
.02396
260
.03545
.03757
.02650
.02508
280
.03658
.03878
.02775
.02619
300
.03766
.04002
.02883
.02726
350
.04028
.04285
.03153
.02979
400
.04272
.04576
.03401
.03213
450
.04505
.04813
.03627
.03434
500
.04724
.05018
.03841
.03661
550
.04941
.05272
.04037
.03803
600
.05146
.05475
.04224
.04060
650
.05344
.05754
.04391
.04138
700
.05534
.05934
.04550
.04234
750
.05727
.06095
.04695
.04118
800
.05910
.06237
.04829
.04425
900
.06276
.06852
.05091
.05150
1000
.06636
.07404
.0530
.05650

165
TABLE XVII
THE REAL AND THE IMAGINARY COMPONENTS OF
THE COMPLEX INVERSE RELAXATION LENGTH
- 1.0 MSEC INPUT PULSE -
FREQUENCY a (cm"1) ? (rad/cm)
(cps)
Theory
Exp
Theory
. Exp
0
.02444
.02346
,
10
.02330
.02324
.001500
.001499
20
.02343
.02344
.002987
.002980
30
.02365
.02361
.004438
.004427
40
.02394
.02393
.005963
.005951
50
.02429
.02437
.007338
.007319
60
.02469
.02484
.008655
.008623
70
.02512
.02535
.009920
.009864
80
.02558
.02597
.01115
.01104
100
.02665
.02724
.01343
.01320
120
.02775
.02861
.01559
.01516
140
.02883
.03004
.01739
.01688
160
.02995
.03148
.01918
.01846
180
.03111
.03292
.02081
.01995
200
.03220
.03438
.02230
.02129
200
.03330
.03577
.02380
.02257
240
.03444
.03714
.02515
.02377
260
.03547
.03834
.02640
.02493
280
.03650
.03959
.02770
.02605
300
.03764
.04068
.02883
.02712
350
.04013
.04288
.03160
.02925
400
.04246
.04465
.03409
.03138
450
.04496
.04896
.03634
.03362
500
.04708
.05121
.03840
.03568
550
.04920
.05420
.04031
.03771
600
.05122
.05625
.04200
.03814
650
.05329
.05813
.04363
.03881
700
.05528
.06113
.04501
.04008
750
.05746
.06276
.04638
.04389
800
.06000
.06396
.04777
.04848
900
.06530
.06692
.05230
.05410

a
o
os
C\
FIG. 42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED DAMPING
COEFFICIENT a

5 (rad/cm)
P
Frequency
FIG. 43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED PHASE SHIFT PER
UNIT LENGTH £
167

168
The predicted and measured values are in excellent agreement up to 200
cps; theory follows closely the measured difference between the 0.5 and
the 1.0 msec cases. The differences in the damping coefficient at zero
frequency are somewhat puzzling. A steady-state measurement of the
inverse relaxation length yielded a value of 0.0221 cm \ in excellent
agreement with the experimental 0.5 msec case and ~ 5.% lower than the
1.0 msec case.
b) The theoretical and experimental tx's and £'s start to diverge
"significantly" past 200 cps. The deviation is larger for the 1.0 msec
input case. The deviation is ~ 6% at 400 cps for a and 5 (0.5 msec
case), and about 8% at 800 cps. Still both the theoretical and experi
mental results were smooth functions of frequency throughout the range;
both collapse dramatically at ~ 1000 cps.
c) An analysis of the least-squares fitting performed on both the
predicted and the measured values reveals that a "poor" fit is obtained
at 0 cps.. The fit gets increasingly better with frequency up to 400
cps were fluctuations are observed in the values. The criteria used to
select the value of a and £ quoted were that of spatial convergence, i.e.,
the chopping technique was employed to determine a spatially converged
value. This was not always encountered, especially past 500 cps in both
theory and experiment. A judgement was made to select an appropriate
value in each case where convergence was not obtained. This made the
theoretical and experimental results look worse at high frequencies
because they had different trends and the same criteria had to be used
for both.
The system p dispersion law is shown in Fig. 44. The agreement can
be termed good, considering the percentage differences and other previ
ously reported results [23]. A smooth trend is followed until theory

5 (rad/cm)
169
FIG. 44 THE UFSA R1 CORE p DISPERSION LAW

170
and experiment approach 1000 cps.
The differences observed reflect those noticed when the comparison
in the time domain was conducted. The fact that the WIGLE pulses are
consistently narrower than the experimental ones is reflected in the
smaller damping coefficients at large frequencies.
The differences showed up much more markedly in the ultrasensitive
2 2 2 2
p plane. Since a < a and E > 5 the real part of p =(a -£ )
^ th exp th exp r
seems to indicate a discrepancy that is not as large as it appears.
2
Shown in Fig. 45 is the real part of p for both theory and exper
iment as a function of frequency. Although they start to diverge sig
nificantly at f = 100 cps, it should be remarked that any small dif-
2
ferences in a and £ are magnified out of proportion in the p plane.
2
In contrast, the imaginary part of p =(2a0 appears to signify perfect
agreement in the results, since the deviations in a and £ cancel each
other (see Fig. 46).
2
The p dispersion law of the UFSA R1 clean core is shown in Fig.
47. This is a most sensitive index. Any small error in the data or
2
failure of the model will immediately appear "blown-up" in p Although
2
the theory and experiment diverge in the p plane, after 100 cps, both
behave smoothly; the differences should be considered within the con
text of the over all analysis. Certainly it can be said that the WIGLE
results do not follow the experimental results throughout the frequency
range but that is to expected; the actual discrepancies observed in the
2
time domain and the numerical uncertainties propagate into the p plane
so significantly that perfect agreement seems to be unreachable with
the present models and knowledge of parameters.
The steady-state inverse relaxation length =.023 (and the corresponding
ctf_o) is significantly smaller than the dynamic inverse relaxation =.030.

19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
Exp
O

s=
20
FIG. 45
Frequency
COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED (cx2-£2)
171

Frequency
FIG. 46 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED 2 a K
172

173
looo
>
FIG. 47- THE UFSA R1 CORE p2 DISPERSION LAW

CHAPTER VI
SPATIAL DEPENDENCE OF PULSED-NEUTRON
REACTIVITY MEASUREMENTS
Introduction
A resume of pulsed-neutron reactivity measurements was presented
in Part 2, Chapter V of this work. During the nuclear calibration of
the UFSA assembly certain "spatial" effects were observed in the deter
mination of the reactivity of the long assembly. In this chapter these
effects are investigated.
The pulse propagation measurements performed in the UFSA R1 clean
core were analyzed using the Garelis-RusseUtechnique [8] to determine
the ratio kB/,; the "fundamental" decay constant was obtained by ap
plying Peierls statistical analysis to the tail of the pulse and the
effective delayed neutron fraction was calculated and assumed constant
with respect to reactivity. A strong "spatial" dependence of the
measurements conducted along the center line of the core was observed.
An asymptotic spatial distribution was obtained long times after the
pulse; at these times only the positions farthest from the neutron
source had not reached background level. The Garelis-Russell technique
was found to be very sensitive to the finite width of the input pulse.
A computer program, UNIPUL, was coded and used to perform the
Garelis-RusseU type analysis on the impulse response curves determined
as a function of position in the UFSA R1 core. The same program
174

175
yielded the decay constants at different times after the pulse and
computed a value of p ($), as well as absolute p and k^^ using a
calculated fc>ef£ for each decay constant.
The Decay Constant
A series of decay constants were obtained by analyzing the tail
of the pulse at increasing times from the peak. The convergence of the
decay constant in time was sought, before background is reached, and
the value that gave the least deviation according to Peierls statis
tical analysis was considered to give the decay constant at that posi
tion.
The decay constants determined close to the source decreased
monotonically as the fitting was performed farther away in time from
the peak. Once the "asymptotic" source region, as defined in the pulse
propagation measurements, was reached, an apparent decay constant was
found at each position. This decay constant is observed to converge
or to vary very slowly with respect to time and decreased in magnitude
as the distance to the source increased. At large distances from the
source a fundamental decay constant is observed, seemingly when an
asymptotic distribution of the neutrons is established in the assembly,
more than 9 msec after the burst.
An analysis of the time-space behavior of the neutron flux (ref. .
Fig. 28) reveals that, indeed, more than 9 msec are required for the
assembly to achieve an asymptotic neutron distribution. Therefore,
only at large distances from the source can a true fundamental decay
constant be measured; prior to P83 (142.9 cm) background is reached
before a uniform spatial distribution is established.

176
Shown in. Fig. 48 are the experimentally determined decay constants
as a function of position in the assembly, for a 0.5 and 1.0 msec input
pulse. As distance to the source increased, more "waiting" time was
available to extract the decay constant. The values found past P83 are
believed to represent the fundamental decay constant of the assembly.
It should be noted that the instantaneous decay constant at dif
ferent times after the pulse was calculated for all the detector posi
tions in the assembly, using the WIGLE code. The results agree closely
with those measured experimentally at different times after the peak.
The two-group, space-time dependent model describes well the observed
phenomena.
The Ratio k8/5,
The Garelis-RusseUtechnique was applied to the two-medium system
referred to as the UFSA R1 core. The measured kg/5, values, determined
as a function of distance from the source, showed a "spatial" depend
ence. This was somewhat surprising since the detector was supposedly
located to minimize the Becker-Quisenberry correction [16] and a more
uniform value of kg/5, was expected. Although the model lacks a good
energy representation of the system being studied such a strong spatial
variation in kg/5, was not expected.
Shown in Fig. 49 are the measured kg/5, values for input pulses of
0.5 and 1.0 msec. A prominent feature is the noticeable difference
between the results obtained with the two different, finite width
input pulses. Attention was focused on the sensitivity of the Garelis-
RusselLmodel to the finite input pulse widths use in the experiments.
As mentioned previously, the model utilizes a delta function input

Decay Constant (sec
FIG. 48 DECAY CONSTANT VS. AXIAL POSITION
177

210
200
190
180
170
160
150
O 0.5 msec input pulse width
O 1.0 msec input pulse width x)
'O
c/
/
/
/
X '
p
p"
if
/
/
9'
M M O* C?.. ' 1
__ .Q o
o o
-Q-
UFSA Ri Clean Core
12.72 cm between data points
? i ill I l
6 20 34 48
I I i 1 t ! I I I
62 76 90 104 118 132
Position Number
49 vs. AXIAL POSITION
178

179
pulse.
Tabulated in Table XVIII are values of kg/5 determined using the
Garelis-Russell technique on pulses arising from widely differing input
pulses; the measurements were made at one position far from the neutron
source. The effect of the finite pulse width on kg/5, is significant.
An analysis of the results shown in Fig. 49 points to the fact that at
very large distances from the source a value of kg/5- close to the one
that would be obtained from a delta function input pulse is obtained.
Some comments on observed facts about the Garelis-RusseU tech
nique are pertinent. A dominant factor in the determination of kg/5, is
the delayed neutron background, which is strongly dependent on the
repetition rate of the neutron generator (which should be determined
very accurately). Meaningful values of kg/5, are obtained far from the
source for not too wide input pulses. A correction on the determined
kg/5, values to account for the finite width of the input pulses was
developed by G. A. Mortensen, Nuclear Safety Division, Phillips
Petroleum Co. [48] after the experimental observation of the phenomena.
The suggested method was applied to several of the cases under consid
eration but an overcorrection seems to result; the "corrected" values
keep changing drastically at long distances from the source where the
influence of the input pulse is negligible. Further work in this cor
rection should improve the results.
The Measured Reactivity and kef£ Values
The reactivity in dollars is obtained, following the Garelis-
Russell method, by the expression
P($) -
a
kg/5,
- 1

180
TABLE XVIII
THE DECAY CONSTANT AND kg/A VALUES
MEASURED AS A FUNCTION OF INPUT PULSE WIDTH
- 0.5 MSEC INPUT PULSE WIDTH -
UFSA R1 Clean Core
0.5 M/W Ration
16.35 cm wide reflected core
PULSE
WIDTH
(msec)
a
(sec
k8/£
(sec
0.1
511+10
213+4
0.5
488+11
202+5
1.0
501+6
193+5
2.0
503+8
183+7
3.0
51.0+4
172+9
4.0
523+16
169+9
5.0
494+6
144+10
6.0
504+5
136+10
7.0
505+5
126+9
8.0
522+17
118+11
9.0
524+13
111+8
10.0
496+16
108+9

181
Using a calculated value of = 0.0079 for this assembly configura
tion, the absolute value of the reactivity p, is obtained. The cor
responding value of k^, is then found by the relation
k =
eff 1 + p
Shown in Fig. 50 are the measured absolute reactivity and ke££ as a
function of position in the lattice. It is obvious from what has been
said above regarding the behavior of a and kg/£, that a meaningful
value for either k ,, or p cannot be obtained in this case until 143
cm separate the source and detector. The assigned value of k^^ was
0.990+.003. This value compares very favorably with a value of
0.990+.0025 found by inverse multiplication measurements and a calcu
lated value of 0.9906. Although the agreement obtained could be some
what fortuitous, it can be said that a representative value of the
reactivity was found. It seems that, if proper care is taken, the
pulsed reactivity measurements will yield good results in large multi
plying media.
Region-wise Dependence of the Reactivity Measurements
Becker and Quisenberry, as well as Waltar and Ruby [49] have
pointed out the spatial dependence of pulsed source reactivity measure
ments in two-media systems. Differences in the measured reactivity can
be present whether the detector is located in the core or in the reflec
tor.
A series of pulsed source traverses were conducted across the UFSA
R1 clean core and reflectors, at three different distances from the
source. No differences were found for this core in the reactivity
measured in the core or in the reflector. Shown in Table XIX is a

Reactivity (-$)
FIG. 50 REACTIVITY (-$) AND k .. VS. AXIAL POSITION
eff
Effective Multiplication Factor

183
TABLE XIX
REGION-WISE DEPENDENCE OF THE REACTIVITY MEASUREMENTS
Measurement across the core width
UFSA R1 Clean Core
0.5 M/W Ratio
16.35 cm wide reflected core
POSITION
NO
DISTANCE TO
CORE CENTER
(cm)
a
, -Is
vsec )
k B/i
(sec
P
k
eff
A
7.27
508
205
.01169
.9884
B
5.45
504
2C7
.01132
.9888
C
3.63
497
208
.01102
.9891
D
1.82
505
207
.01137
.9887
E
0.0
517
203
.01227
.9878
F
3.63
504
209
.01119
.9889
G
5.45
510
206
.01168
.9884
H
7.27
503
207
.01124
.9889
I
10.9
512
203
.01205
.9881
RE2
14.3
501
205
.01147
.9887
RE4
17.9
490
199
.01154
.9886
RE6
31.8
474
187
.01214
.9886

184
list of the decay constants, kg/£, p and ke^ measured across the core
and side reflector at a distance of 130.2 cm from the source.
The core-reflector configuration investigated is too narrow to
observe any transverse propagation of the pulse; consequently no dif
ference in the value of the reactivity was measured across the system.
The value of a and of kg/£ obtained near the outer edge of the reflector
was low compared to the other values but somehow compensated each other
to maintain p approximately constant.

CHAPTER VII
CONCLUSIONS
The space-time kinetics behavior of a large-in-one-space dimension,
side-reflected, highly multiplicative (k^^ ~ 0.99) subcritical assembly
has been studied by the use of the pulse propagation technique. The
experimental results were used to test the predictions of the one
dimensional two-group, space-time diffusion theory calculational scheme
(WIGLE). The analysis of both the theoretically predicted and experi
mentally measured results was performed in the time as well as the fre
quency domain.
The comparison of theory and experiment in the time domain shows
good agreement. WIGLE accurately predicted the delay times and the
attenuation of the peak of the pulse when a first flight kernel was used
to describe the spatial distribution of the fast source. At large dis
tances from the source the time profiles predicted by WIGLE are con
sistently narrower than the measured pulse shapes. The sensitivity of
the one-dimensional model to small changes in the transverse buckling
was studied; WIGLE (and experiment) showed a large sensitivity to these
changes. These results point to the necessity of obtaining the best pos
sible estimate of the nuclear parameters to be used in space-time ki
netics calculations.
The comparison of theory and experiment in the sensitive frequency
domain confirms the good agreement found in the time domain. The
185

186
comparison of the WIGLE results and the pulse propagation data were put
on the same basis by performing identical Fourier transformations and
fitting procedures on both. The predicted and measured real part of
2 2 2
p =(a -£ ) diverge past 100 cps. This is almost a "natural" occurrence
2
in the ultrasensitive p plane in which the opposing discrepancies of
2 2
a and £ are blown out of proportion. The agreement in the p disper
sion law of the system is good and within the experimental accuracy and
capabilities of the model.
It is believed that WIGLE did predict accurately the dynamic
behavior of the narrow, long core studied. It is also believed that the
sensitivity of the one-dimensional calculational scheme to small changes
in the transverse buckling should be born in mind when feedback effects
and/or two-dimensional effects are to be considered.
The followings topics deserve future investigation:
1. The sensitivity of the dynamic behavior of the system to small
changes in the transverse buckling. This can be accomplished by a
detailed pulse propagation study at two core heights or at two core
widths.
2. Impose a more severe test of the model by conducting measure
ments with a narrower input pulse.
3. Further interpretation of reactivity measurements in large
systems is needed. A correction for the influence that the input pulse
width has on the determination of kg/S, by the Garelis-Rus sell method is
necessary. The extrapolated area-ratio method should provide a basis
for comparison.
4. A comparison should be made between the calculational results
of two-group diffusion solved directly in the frequency domain and those
obtained by numerical transformation of the WIGLE results.

APPENDIX A
CALCULATIONAL PROCEDURES USED IN THE
DETERMINATION OF THE NUCLEAR PARAMETERS
AND THE k VALUES
eff

188
Determination of the Four Group Parameters
A four-group diffusion approach was used to calculate the effective
multiplication factor of the six UFSA configurations to be studied as
Phase I of the large core dynamics experimental program. The calcula
tion of the parameters was performed by the Nuclear Safety Research
Branch of the Phillips Petroleum Company [31].
The four energy groups were divided as follows:
Group 1 8.21 X 105 107 EV
Group 2 5.53 X 103 8.21 X 105 EV
Group 3 0.532 5.53 X 103 EV
Group 4 0 0.532 EV.
To obtain the four-group constants, the following sequence of cal
culations was performed for each of the six cases mentioned.
1. Fast group (groups 1-3) constants were calculated by the PHROG
[50] computer program. These calculations include resonance integral
and Dancoff correction calculations as provided by the RAVEN [51] cal-
culational scheme.
2. Thermal constants were calculated by the TOTEM [52] computer
program.
The constants used for the core object of this work are given
below. It should be mentioned that the procedure described was also
employed to determine the two-group parameters used for the WIGLE
calculations.

189
UFSA R1 CORE PARAMETERS
0.5 M/W ratio
16.35 cm wide reflected core
Group
1
2
3
4
D
1.6079
0.94239
0.61401
0.20809
^a
0.0035411
0.0023701
0.23109
0.20809
Zr
0.090927
0.096727
0.084015
_
vlf
0.0068929
0.0012609
0.015301
0.22662
1/v
5.25 Ox 10-10
2.637 x 10"9
1.843 x 10~7
3.324 x 10"6
_3
Void Coefficient of Reactivity: 3.14 x 10 Ak/% void
Temperature Coefficient of Reactivity: 1.03 x 10 ^ Ak/C
Determination of k
eff
Using the constants tabulated above, eigenvalue calculations were
performed with the AIM-6 computer code [53].
' AIM-6 is a multigroup, multiregion, one-dimensional diffusion
theory code that has been widely used for criticality calculations.
The code will handle as many as 18 energy groups, 101 space points
and 20 regions. Basically, the code solves the equation
- D^Vir) + 4 4(r) = x^ir) + ^ E j+i j(r)
i J-q s
1 < i < NOG < 18. NOG = number of groups
The symbols follow conventional notation and
X* = the integral of the fission spectrum over the lethargy range
represented by group i.

190
N0G ( Ef)i<¡>i(r)
s(r) = z L-
i=l X
where X is the eigenvalue. The code then sets and solves a set of
finite difference equations.

APPENDIX B
DESCRIPTION OF THE COMPUTER PROGRAMS
UNIPUL
MORE
MORWIG
ALXILS
MULTIPLOT

192
General
A set of computer programs was coded for the data processing and
the analysis of the results of the pulsed measurements.^ The programs
were written for the IBM 360-50 computer, with the exception of
MULTIPLOT which was coded for the IBM 1800 computer.
UNIPUL
The FORTRAN IV, IBM 360 computer program UNIPUL is used for a
unified processing of the data obtained from conventional pulsing or
pulse propagation measurements. A complete description of the program
and the input requirements are available in Ref. 54.
The main operations of UNIPUL are:
1. Resolution time correction of the data, using a non-paralyzing
counting correction.
2. Statistical determination of the neutron background. If the
system under study is multiplicative, the delayed neutron background
is calculated and stored in COMMON for the calculation of k8/JL.
3. Determination of the fundamental decay constant using Peierl's
statistical method [18]. The decay constants can be calculated at dif
ferent waiting times from the peak of the pulse to determine the time
convergence. The a's are stored in COMMON for the reactivity determina
tion.
4. The background is subtracted from the data. A test is made to
find if any channel has a negative number of counts. If a few channels
have negative counts, their value is set to zero. The number of
1. The cooperation of Dr. M. J. Ohanian in the coding of these
programs is gratefully acknowledged.

193
channels is now reduced to an odd number of points terminating where
the background has been determined to start.
5. Determination of the ratio kf3/£ following the Garelis-Russel
method. Simpson's integration is used for the pulse and the Regula-
Falsi iterative method is used to find the root.
6. The data is normalized according to a selected normalization
scheme (see Part I, Chapter IV). The normalized data can be punched
in cards for further analysis.
7. If a neutron wave type analysis is desired, a numerical
Fourier transformation is performed and the amplitude and phase of the
pulse for each frequency selected is printed and punched for further
processing.
UNIPUL was used to process the pulse data punched in cards from
original perforated paper tape (at the IBM 1800 computer of the
Department of Nuclear Engineering Sciences, University of Florida);
the paper tape is the output of the multichannel analyzer used in the
experimentation.
MORE
The FORTRAN IV, IBM 360 computer program MORE performs a conven
tional numerical Fourier transformation of the pulse neutron data
(zeroth moment only) for the analysis of the experiment in the fre
quency domain. The transformation used equal time steps, a maximum
of 1023 time points and Simpson's integration scheme. An odd number
of points are required by the program. Thermal neutron data can be
entered directly as input or the total and epicadmium neutron flux
are required to obtain the thermal flux by subtraction.

194
MORE punches in cards the amplitude and phase of the zeroth
Fourier moment of the pulse for input to the ALXILS program. A com
plete description of the program and input requirements can be found
in Ref. 55.
MORWIG
The MORWIG program is a version of the MORE code written to
perform a numerical Fourier transformation on a pulse with unequal
time steps. It is intended specifically for the neutron wave type
analysis of the space-time data calculated by the WIGLE scheme. See
Ref. 56 for a complete description.
ALXILS
The FORTRAN IV, IBM 360 program ALXILS performs a least-squares
fit of the amplitudes and phases obtained from the Fourier transforma
tion performed by either the MORE of the MORWIG program. A linear
least-squares scheme is- used. The values of ALPHA are obtained by fit
ting the log amplitude vs. distance for each frequency. The values of
XI are obtained by a linear fit of the phase angle vs. distance. The
channel chopping technique is used to determine the convergence of a
and £ in space. The weighting of the points can be set to (1/observed
value) or to equal weights. Statistical quantities determining the
"goodness of the fit" are calculated for each fit. A complete descrip
tion can be found in Reg. 57.
MULTIPLOT
The FORTRAN IV, IBM 1800 computer program MULTIPLOT used the out
put of the UNIPUL and/or the WIGLE codes to plot the time profiles of

195
the pulses. A CALCOMP plotter is used in connection with the 1800
computer for the actual plotting of the pulse. The program is capable
of normalizing to the peak counts of a reference pulse for the super
position of related time profiles.

APPENDIX C
UFSA Rl-CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT NINETEEN CORE POSITIONS
FOR INPUT PULSES OF 0.5 AND 1.0 MSEC

FLUX (RELATIVE UNITS)
FIG- Cl
TIME PROFILE OF THERMAL NEUTRON FLUX 3-0 CM FROM THE SOURCE

flux (relative units)
TIME PROFILE OF THERMAL NEUTRON FLUX 15*71 EM FROM THE SOURE'E
FIG- C2

(RELATIVE UNITS)
ID
-J
THERM--3- SO
PEAK AT 0-320 M,SEEDS
PULSE WIDTH = 0-3 MSECS
THECRY FWHVt = 0-773 MSEECS
EIXP FWHM = 0-773 MSECS
0-3
B 7
VO
VO
10
TIME (MSEi;)
C3
TIME PRCF'ILE DF THERMAL NEUTRON FLUX SB 43 EM FROM THE SOURCE

UX (RELATIVE: UNITS)
FIG C4 TIME PROFILE OF THERMAL NEUTRON FLUX 4115 EM FROM THE SOURCE

FLUX (RELATIVE UNITS)
1-0
0*9
0-9
0-7
I
,*2 .
* '
\
THERM--5- 34 '
PEAK AT 0-950 MSE.'CS
PULSE WIDTH = 0-55 MSECS
THECRY FWHM = 1-3559 MSECS
....... EXP- FWHM = 1-470 MSECS
0-G
I
S
s
0-55
0-4
0*3
03
0-1
0 1
*
%
9
%
hO
O
{1
V
******
***.
-i-
-L.
*"****..*
....[
10
3
4 5
TIME (MSECD
9
FIG- C5
TIME PRDFILE GF THERMAL NEUTRGN FLUX
53 BS GM FRDM THE SOURCE

FLUX (RELATIVE UNITE)
TIME (MSEC)
TIME FRCFILE CF THERMAL NEUTRON FLUX
FI CL- C6
B6-5S CM FROM THE SDJRCE
mu)

FLUX (RELATIVE: UNITS)
FIG* C7
TIME PROFILE DF THERMAL NEUTRGN FLUX
73*30 CM FROM THE SGURCE

UX (RELATIVE UNITS)
FIG- C8
TIME PROFILE GF THERMAL NEUTRGN FLUX
35"01 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
X
FIG* C9 time PROFILE CF THERMAL NEUTRON FLUX 104-73 CM FROM THE SOURCE

FLUX (RELATIVE UNITE)
FIG- CIO TIME PROFILE OF THERMAL NEUTRON FLUX 117-44 CM FROM THE SOURCE

FLUX (RELATIVE UNITED
f
FIG- Cll time PROFILE OF THERMAL NEUTRON FLUX 130-16 CM FROM THE SDURCE
207

P'LX (RELATIVE UNITS)
FIG*. C12 TIME PROFILE OF THERMAL NEUTRON FLUX 145-BB CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG* C13 TIME PROFILE DF THERMAL NEUTRDN FLUX 155-53 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG C14 TIME PROFILE OF THERMAL NEUTRON FLUX IBS-31 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG- C15 TIME PROFILE OF THERMAL NEUTRON FLUX 181-03 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG- C16 TIME PROFILE OF THERMAL NEUTRON FLUX 133-74 CM FROM THE SOURCE
212

FLUX (RELATIVE UNITS)
FIG- C17 TIME PROFILE OF THERMAL NEUTRON FLUX PCS-46 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG- C18 TIME PROFILE OF THERMAL NEUTRON FLUX 219-17 CM FROM THE SOURCE
214

FLUX (RELATIVE UNITS)
FIG* C19 TIME PROFILE OF THERMAL NEUTRON FLUX 031-QQ CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG- C20 TIME PROFILE OF THERMAL NEUTRON FLUX
3-0 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG* C21 TIME PROFILE GF THERMAL NEUTRON FLUX
15-71 CM FROM THE SCURCE

FLUX (RELATIVE UNITS)
FIG- C22 TIME PROFILE OF THERMAL NEUTRON FLUX
2B-43 CM FROM THE SOURCE
218

FLUX (RELATIVE UNITS)
FIG* C23 TIME PROFILE OF THERMAL NEUTRON FLUX 41*15 CM FROM THE SOURCE
219

FLUX (RELATIVE UNITS)
FIG- C24 TIME PROFILE OF THERMAL NEUTRON FLUX 53-8G CM FROM THE SOURCE
220

FLUX (RELATIVE UNITS)
FIG- C25 TIME PROFILE OF THERMAL NEUTRON FLUX
EG-58 CM FROM THE SOURCE
221

FLUX (RELATIVE UNITS)
FID- C26 TIME PROFILE OF THERMAL NEUTRON FLUX 73-30 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG* C27 TIME PROFILE OF THERMAL NEUTRON FLUX 32-01 CM FROM THE SOURCE
223

FLUX (RELATIVE UNITS)
FIG- C28 TIME PROFILE OF THERMAL NEUTRON FLUX 104-73 CM FROM THE SOURCE
224

FLUX (RELATIVE UNITS)
FIG- C29 TIME PROFILE OF THERMAL NEUTRON FLUX 117-44 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FID* C30 time PROFILE OF THERMAL NEUTRON FLUX ISO*IB CM FROM THE SOURCE
226

FLUX (RELATIVE UNITS)
FIG C31 TIME PROFILE OF THERMAL NEUTRON FLUX 142-09 CM FROM THE SOURCE
227

FLUX (RELATIVE UNITS)
FIG C32 TIME PROFILE OF THERMAL NEUTRON FLUX 155-53 CM FROM THE SOURCE
228

FLUX (RELATIVE UNITS)
FIG C33 TIME PROFILE OF THERMAL NEUTRON FLUX IBB*31 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG- C34 TIME PROFILE OF THERMAL NEUTRON FLUX 181-03 CM FROM THE SOURCE
230

FLUX (RELATIVE UNITS)
FIG- C35 TIME PROFILE OF THERMAL NEUTRON FLUX 193-74 CM FROM THE SOURCE
231

FLUX (RELATIVE UNITS)
FIG* C36 TIME PROFILE OF THERMAL NEUTRON FLUX E0G-4S CM FROM THE SOURCE
232

FLUX (RELATIVE UNITS)
FIG* C37 TIME PROFILE OF THERMAL NEUTRON FLUX 219*17 CM FROM THE SOURCE
233

FLUX (RELATIVE UNITS)
FIG- C38 TIME PROFILE OF THERMAL NEUTRON FLUX E31-8B CM FROM THE SOURCE
234

APPENDIX D
UFSA R1 CLEAN CORE
TIME PROFILES OF FAST NEUTRON FLUX
AT SEVERAL CORE POSITIONS
FOR INPUT PULSES OF 0.5 AND 1.0 MSEC

FLUX (RELATIVE. UNITS)
FIG D1
TIME PROFILE OF FAST NEUTRON FLUX 1571 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
1-0
0*9
0-E3
0-7
0-G
0 *5
0-4
0-3
ft
I
0-
0-1
T
0
3
3 4
=F
5
RIFS 30-1
PEAK AT 0-430 MSECS
pulse: width = o-s msecs
THEORY FWHM = 0-747 MSEC
EXP- FWHM = 0-750 MSEC
to
OJ
0
9
f
10
TIME (MSEIO
FIG- D2
TIME PROFILE OF FAST NEUTRON FLUX 38-43 CM FROM THE SOURCE
UVJ1

FLUX (RELATIVE UNITS)
FIG- D3
TIME PROFILE OF FAST NEUTRON FLUX 53-BG EM FROM THE SOURCE
238

FLUX (RELATIVE UNITS)
1-0
0*3
0-E3
0*7
0-S
0*5
0-4
0*3
0-3
0-1
RIFS 41-1
PEAK AT 0-340 MSECS
PULSE WIDTH =0-5 MSECS
THEGRY FWHM = 1-7BS MSECS
EXP- FWHM = 1*710 MSECS
to
u>
MO
10
TIME (MSE:C)
TIME PROFILE OF FAST NEUTRDN FLUX 66-5B CM FRDM THE SOURCE
FIG- D4

FLUX (RELATIVE UNITS)
FIG- D5
TIME PROFILE OF FAST NEUTRON FLUX 79-30 CM FROM THE SOURCE
240

FLUX (RELATIVE UNITS)
FIG- D6
TIME PROFILE OF FAST NEUTRON FLUX 133-7-4 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG* D7
TIME PROFILE OF FAST NEUTRON FLUX 15-71 CM FROM THE SOURCE
in in

FLUX (RELATIVE UNITS)
FIG* D8
TIME PROFILE OF FAST NEUTRON FLUX 41*15 EM FROM THE SOURCE
243

FLUX (RELATIVE UNITS)
TIME (MSEC)
TIME PROFILE OF FAST NEUTRON FLUX 53-SB CM FROM THE SOURCE
FIG* D9
(JILO

FLUX (RELATIVE UNITS)
FIG- DIO TIME PROFILE OF FAST NEUTRON FLUX EG-58 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG* Dll TIME PROFILE OF FAST NEUTRON FLUX IBB*31 O'M FROM THE SOURCE
246

FLUX (RELATIVE UNITS)
FIG- D12 TIME PRDFILE OF FAST NEUTRON FLUX 101-03 CM FROM THE SOURCE

APPENDIX E
UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT FOUR POSITIONS IN THE CORE
FOR A 0.1 MSEC INPUT PULSE

FLUX (RELATIVE UNITS)
TIME (MSEC)
FIG* El
TIME PROFILE OF THERMAL NEUTRON FLUX
53*BS CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
FIG' E2
TIME PRDFILE OF THERMAL NEUTRON FLUX
73-30 CM FROM THE SOURCE

FLUX (RELATIVE UNITS)
TIME PROFILE OF THERMAL NEUTRON FLUX 130IS CM FROM THE SOURCE
FID- E3

FLUX (RELATIVE UNITS
TIME (MSEC)
FIG- E4 TIME PROFILE' OF THERMAL NEUTRON FLUX 142-8E3 CM FROM THE SOURCE
252

APPENDIX F
UFSA R1 CLEAN CORE
TIME PROFILES OF THERMAL NEUTRON FLUX
AT THREE POSITIONS IN THE CORE
FOR A WIDE (10 MSEC) INPUT PULSE

FLUX (RELATIVE UNITS)
1-0
FIG* FI PROPAGATION OF A PULSE WIDER THAN THE SYSTEM PROPAGATION TIME
- EXPERIMENTAL -
254

APPENDIX G
UFSA R1 CLEAN CORE
SHAPE OF THE PROPAGATING PULSE
AS A FUNCTION OF INPUT PULSE WIDTH
Pulse Width (msec) = 0.1,0.5,1.0,2.0,3.0,
4.0,5.0,6.0,7.0,8.0,
9.0,10.0

FLUX (RELATIVE UNITS)
FIG. G1 SHAPE OF THE PROPAGATING PULSE AS A FUNCTION OF PULSE WIDTH
- EXPERIMENTAL -
256

FLUX (RELATIVE UNITS)
FIG* G2 SHAPE DF THE PROPAGATING PULSE AS A FUNCTION OF PULSE WIDTH
- EXPERIMENTAL -
257

LIST OF REFERENCES
1. S. O. Johnson and R. W. Garner, private communication (1966).
2. R. E. Uhrig, £t al, "Design and Summary Hazards Report of the
University of Florida Accelerator Pulsed Subcritical Assembly"
(1964).
3. M. J. Ohanian, N. J. Diaz and R. B. Perez, "Design and Hazards
Report of the University of Florida SPERT Assembly" (1967).
4. M. J. Ohanian and N. J. Diaz, "Reply to Request for Additional
Information in Connection with Review of Application for SNM
License"(Ref. No. D.M.L.:RLL 70-1068) (1967).
5. M. J. Ohanian and N. J. Diaz, "Addendum to the Design and Hazards
Report of the University of Florida SPERT Assembly," communication
to USAEC Materials Licensing Division (1968).
6. L. B. Myers, "UFSA Safety Instrument and Control Systems Report,"
Internal Report, Dept, of Nuclear Engineering Sciences, University
of Florida (1968).
7. S. 0. Johnson and R. W. Garner, private communication (1967).
8. E. Garelis and J. L. Russell, Jr., "Theory of Pulsed Neutron
Source Measurements," Nuc. Sci. Eng., 16, 263 (1963).
9. R. L. Coates and N. R. Horton, "RSAC A Radiological Safety
Analysis Computer Program," IDO-17151 (1966).
10. R. J. Wagner, "IREKING Program for the Numerical Solution of the
Reactor Kinetics Equations," IDO-17114 (1966).
11. S. R. Bierman, K. L. Garlid and J. R. Clark, "Resolving Time of a
Pulsed-Neutron Source Data-Acquisition System," Nuc. Applic., 2
(1964).
12. B. E. Simmons and J. S. King, "A Pulsed Neutron Technique for
Reactivity Determination," Nc. Sci. Eng., _3, 595 (1958).
13. N. G. Sjostrand, "Measurements on a Subcritical Reactor Using a
Pulsed Neutron Source," Arkiv Fysik, 11, 233 (1956).
14. T. Gozani, "A Modified Procedure for the Evaluation of Pulsed Source
Experiments in Subcritical Reactors," Nukleonik, 4, 348 (1962).
258

259
15. E. Garelis, "A Calculation of the Prompt Decay Constant for a
Reflected Assembly," Trans. Amer. Nuc. Soc., 10, 2, 594 (1967).
16. M. Becker and K. Quisenberry, "Spatial Dependence of Pulsed
Neutron Reactivity Measurements," AEC Symposium Series No. 7
(1966)
17. K. L. Garlid and S. R. Bierman, "Applications of Pulsed Neutron
Measurements in Very Large Systems," Nuc. Applic., 2_, (1966).
18. R. Peierl, Proceedings of the Royal Society (London), A 149, 467
(1935).
19. M. E. Radd, private communication (1968).
20. P. K. Doshi and G. H. Miley, "Reactor Neutron Pulse Propagation in
Multiplying Media," Trans. Amer. Nuc. Soc., 11, 191 (1968).
21. P. K. Doshi, "Reactor Neutron Pulse Propagation Through Multiplying
Media," Unpublished Ph.D. Dissertation, University of Illinois
(1968).
22. H. A. H. Hasson, "Experimental and Theoretical Studies of Space-
Time Nuclear Reactor Kinetics," Unpublished Ph.D. Dissertation,
University of Illinois (1968).
23. J. H. Dunlap, "Neutron.Wave Propagation in a Heavy Water, Natural
Uranium, Subcritical Assembly," Unpublished Ph.D. Dissertation,
University of Florida (1967).
24. W. R. Cadwell, A. F. Henry and A. J. Vigilotti, "WIGLEA Program
for the Solution of the Two-Group Space-Time Diffusion Equations
in Slab Geometry," WAPD-TM-416 (1964).
25. M. N. Moore, "The Dispersion of Thermal-Neutron Pulses in Neutronic
Systems," Nuc. Sci. Eng., 25, 422 (1966).
26. R. S. Booth, "A Theoretical and Experimental Study of Neutron Wave
Propagation in Moderating Media," Unpublished Ph.D. Dissertation,
University of Florida (1965).
27. M. E. Radd,"WIGLE-40, A Two-Group, Time Dependent Diffusion Theory
Program for the IBM-7040 Computer," IDO-17125 (1965).
28. A. F. Henry and A. V. Vota, "WIGL 2, A Program for the Solution of the
One-Dimensional, Two-Group, Space-Time Diffusion Equations Accounting
for Temperature, Xenon, and Control Feedback," WAPD-TM-532 (1965).
29. J. B. Yasinsky, M. Natelson and L. A. Hageman, "TWIGL A Program
to Solve the Two-Dimensional, Two-Group, Space-Time Neutron Dif
fusion Equations with Temperature Feedback," WAPD-TM-743 (1968).

260
30. M. A. Perks, "FREAK A Fast Reactor Multigroup Kinetics Program,"
ANL-7050 (1965).
31. R. W. Garner, private communication (1968).
32. S. Kaplan, 0. J. Marlower and J. Bewick, "Application of
Synthesis Techniques to Problems Involving Time Dependance,"
Nuc. Sci. Eng., 18, 163 (1964).
33. J. B. Yasinsky and A. F. Henry, "Some Numerical Experiments
Concerning Space-Time Reactor Kinetics Behavior, Nuc. Sci. Eng.,
22, 171 (1965).
34. W. M. Stacey, Jr., "A Variational Multichannel Space-Time
Synthesis Method for Nonseparable Reactor Transients," Nuc. Sci.
Eng., 34, 45 (1968).
35. A.Foderaro and H. L. Garabedian, "Two Group Reactor Kinetics,"
Nuc. Sci. Eng., 14, 22 (1962).
36. K. 0. Ott, "Quasistatic Treatment of Spatial Phenomena in Reactor
Dynamics," Nuc. Sci. Eng., 26, 559 (1966).
37. K. 0. Ott and D. A. Meneley, "Accuracy of the Quasistatic Treat
ment of Spatial Reactor Kinetics," Proceedings of the Brookhaven
Conference on Industrial Needs and Academic Research in Reactor
Kinetics, BNL 50117 (T-497) (1968).
38. A. F. Henry, "The Application of Reactor Kinetics to the Analysis
of Experiments," Nuc. Sci. Eng., _3, 52 (1958).
39. C. D. Kylstra and R. E. Uhrig, "Spatially Dependent Transfer
Function of Nuclear Systems," Nuc. Sci. Eng., 22, 191 (1965).
40. S. R. Kavipurapu, "Energy and Spatially Dependent Impulse Response
and Transfer Function of Nuclear Systems, Unpublished Ph.D.
Dissertation, University of Florida (1964).
41. A. M. Weinberg and H.. C. Schweinler, "Theory of Oscillating
Absorber in a Chain Reactor," Physical Review, 74, 851 (1948).
42. R. B. Perez and R. E. Uhrig, "Propagation of Neutron Waves in
Moderating Media," NuC. Sci. Eng., 17, 90 (1963).
43. M. N. Moore, "The Determination of Reactor Dispersion Laws from
Modulated Neutron Experiments," Nuc. Sci. Eng., 21, 565 (1965).
44. R. L. Brehm, "Analysis of Neutron Wave Experiments," Proceedings
of the Symposium on Neutron Noise, Waves, and Pulse Propagation,
AEC Symposium Series No. 9 (1967).

261
45. J. H. Dunlap and R. B. Perez, "Dispersion Law for a Subcritical
Assembly," Proceedings of the Symposium on Neutron Noise, Waves,
and Pulse Propagation, AEC Symposium Series No. 9 (1967).
46. CORA, an improved version of the IMP computer program. IMP is
described in IDO-17199.
47. S. 0. Johnson, SPERT PROJECT Quarterly Progress Report, Philips
Petroleum Co., IDO-17123, 43 (1966).
48. G. Mortensen, private communication (1968).
49. A. E. Waltar and L. Ruby, "Interpretation of Pulsed-Source Experi
ments in a Reflected Reactor," Internal Report, Department of
Nuclear Engineering, University of California (1964).
50. PHROG is a Phillips-Hanford revision of GAM-1 (G. D. Joanou and
J. S. Dudek, GAM-1, GA-1850 (1961).
51. F. J. Wheeler, "RAVEN, A Computer Package for Evaluating Resolved
and Unresolved Resonance Absorption Including Pin Shadowing,"
IDO-17212 (1964).
52. TOTEM links the TOPIC and TEMPEST codes for calculating thermal
constants (G. E. Putnam, TOPIC, IDO-16968 (1964), and R. H. Shudde
and J. Dyer, TEMPEST II, TID-18284 (1961)).
53. H. P. Flatt and D. C. Bailer, "AIM-6, A Multigroup, One-Dimensional
Diffusion Equation Code (1961).
54. N. J. Diaz and M. J. Ohanian, "UNIPUL, A Unified Data Processing
Program for Pulsed Measurements," Internal Report, University of
Florida (1969).
55. M. J. Ohanian, "MORE, A Conventional Fourier Transform Program for
Pulsed Measurements," Internal Report, University of Florida (1969).
56. M. J. Ohanian, "MORWIG, A Conventional Fourier Transform Program
with Variable Time Increments," Internal Report, University of
Florida (1969).
57. N. J. Diaz, "ALXILS, A Linear Least-Squares Program for the Fitting
of Alpha and Xi," Internal Report, University of Florida (1969).

BIOGRAPHICAL SKETCH
Nils J. Diaz was born in Moron, Cuba on April 7, 1938. He was
graduated in June, 1955 from LaSalle High School in Havana, Cuba. In
July, I960, he obtained the degree of Professional Mechanical Engine
ering from the University of Villanova, Havana, Cuba, with honors* He
worked as a plant design engineer from January, 1960 to April, 1961
and also as instructor of Machine and Plant Design at the University of
Villanova for two semesters after his graduation. He arrived in the
United States in October, 1961 and worked as a machine designer until
September, 1962. He then entered the Graduate School of the University
of Florida and received a Master of Science in Engineering in June, 1964.
He held a graduate assistantship and a Fellowship from the Organization
of American States until December, 1965. From January, 1966 to date he
held a Junior Faculty appointment, as an Engineering Assistant, in the
Nuclear Engineering Sciences Department of the University of Florida,
while working toward the degree of Doctor of Philosophy.
Nils J. Diaz is married to the former Zena G. Gonzalez and is the
father of three children, Nils, Ariadne, and Aliene. He is a member of
the American Nuclear Society and the Society of the SIGMA XI.
262

This dissertation was prepared under the direction of the chairman
of the candidate's supervisory committee and has been approved by all
members of that committee. It was submitted to the Dean of the College
of Engineering and to the Graduate Council, and was approved as partial
fulfillment of the requirements for the degree of Doctor of Philosophy.
March 1969
Dean, Graduate School
Supervisory Committee:
Chairman

Page 2 of 2
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AUTHOR: Diaz,Nils
TITLE: Space-time reactor kinetics studies with the University of Florida SPERT
Assembly, (record number: 955726)
PUBLICATION DATE: 1969
i. K\vW A. as copyright holder for the aforementioned
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Please print, sign and return to:
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5/28/2008



FLUX (RELATIVE: UNITS)
FIG* C7
TIME PROFILE DF THERMAL NEUTRGN FLUX
73*30 CM FROM THE SGURCE


259
15. E. Garelis, "A Calculation of the Prompt Decay Constant for a
Reflected Assembly," Trans. Amer. Nuc. Soc., 10, 2, 594 (1967).
16. M. Becker and K. Quisenberry, "Spatial Dependence of Pulsed
Neutron Reactivity Measurements," AEC Symposium Series No. 7
(1966)
17. K. L. Garlid and S. R. Bierman, "Applications of Pulsed Neutron
Measurements in Very Large Systems," Nuc. Applic., 2_, (1966).
18. R. Peierl, Proceedings of the Royal Society (London), A 149, 467
(1935).
19. M. E. Radd, private communication (1968).
20. P. K. Doshi and G. H. Miley, "Reactor Neutron Pulse Propagation in
Multiplying Media," Trans. Amer. Nuc. Soc., 11, 191 (1968).
21. P. K. Doshi, "Reactor Neutron Pulse Propagation Through Multiplying
Media," Unpublished Ph.D. Dissertation, University of Illinois
(1968).
22. H. A. H. Hasson, "Experimental and Theoretical Studies of Space-
Time Nuclear Reactor Kinetics," Unpublished Ph.D. Dissertation,
University of Illinois (1968).
23. J. H. Dunlap, "Neutron.Wave Propagation in a Heavy Water, Natural
Uranium, Subcritical Assembly," Unpublished Ph.D. Dissertation,
University of Florida (1967).
24. W. R. Cadwell, A. F. Henry and A. J. Vigilotti, "WIGLEA Program
for the Solution of the Two-Group Space-Time Diffusion Equations
in Slab Geometry," WAPD-TM-416 (1964).
25. M. N. Moore, "The Dispersion of Thermal-Neutron Pulses in Neutronic
Systems," Nuc. Sci. Eng., 25, 422 (1966).
26. R. S. Booth, "A Theoretical and Experimental Study of Neutron Wave
Propagation in Moderating Media," Unpublished Ph.D. Dissertation,
University of Florida (1965).
27. M. E. Radd,"WIGLE-40, A Two-Group, Time Dependent Diffusion Theory
Program for the IBM-7040 Computer," IDO-17125 (1965).
28. A. F. Henry and A. V. Vota, "WIGL 2, A Program for the Solution of the
One-Dimensional, Two-Group, Space-Time Diffusion Equations Accounting
for Temperature, Xenon, and Control Feedback," WAPD-TM-532 (1965).
29. J. B. Yasinsky, M. Natelson and L. A. Hageman, "TWIGL A Program
to Solve the Two-Dimensional, Two-Group, Space-Time Neutron Dif
fusion Equations with Temperature Feedback," WAPD-TM-743 (1968).


a
o
os
C\
FIG. 42 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED DAMPING
COEFFICIENT a


168
The predicted and measured values are in excellent agreement up to 200
cps; theory follows closely the measured difference between the 0.5 and
the 1.0 msec cases. The differences in the damping coefficient at zero
frequency are somewhat puzzling. A steady-state measurement of the
inverse relaxation length yielded a value of 0.0221 cm \ in excellent
agreement with the experimental 0.5 msec case and ~ 5.% lower than the
1.0 msec case.
b) The theoretical and experimental tx's and £'s start to diverge
"significantly" past 200 cps. The deviation is larger for the 1.0 msec
input case. The deviation is ~ 6% at 400 cps for a and 5 (0.5 msec
case), and about 8% at 800 cps. Still both the theoretical and experi
mental results were smooth functions of frequency throughout the range;
both collapse dramatically at ~ 1000 cps.
c) An analysis of the least-squares fitting performed on both the
predicted and the measured values reveals that a "poor" fit is obtained
at 0 cps.. The fit gets increasingly better with frequency up to 400
cps were fluctuations are observed in the values. The criteria used to
select the value of a and £ quoted were that of spatial convergence, i.e.,
the chopping technique was employed to determine a spatially converged
value. This was not always encountered, especially past 500 cps in both
theory and experiment. A judgement was made to select an appropriate
value in each case where convergence was not obtained. This made the
theoretical and experimental results look worse at high frequencies
because they had different trends and the same criteria had to be used
for both.
The system p dispersion law is shown in Fig. 44. The agreement can
be termed good, considering the percentage differences and other previ
ously reported results [23]. A smooth trend is followed until theory


150
be too restrictive, since some spatial redistribution of the input
pulse does occur, although the effect is certainly much less pronounced
than in the case of a narrow pulse. In the case of the Illinois exper
iments the input pulse was ^30 msec wide and already had an asymptotic
shape, with the characteristic propagation time being of the order of
a few msec.
In the next section the propagation of pulses as a function of the
input pulse width will be studied qualitatively. These measurements
were made to complement the above results.
Pulse Shape vs. Input Pulse Width
The analysis of the measurements with input pulse widths of 0.1,
0.5 and 1.0 msec revealed that these propagating pulses achieved
identical shapes, within the experimental accuracy, at distances larger
than 130 cm from the source. This fact was believed to hold for input
pulses much narrower than the characteristic propagation time in the
assembly. A series of pulse shapes were measured as a function of
input pulse width at a distance of 142.9 cm from the source; these
measurements should provide information on the qualitative behavior of
propagating pulses arising from widely differing input pulse widths.
The results of these measurements are shown in Appendix G; the
peak times and the FWHM for each input pulse recorded at P83 are given
in Table XV.
As previously observed, the peaks are increasingly displaced in
time as the input pulse widens. This behavior has been well predicted
by the two-group, space-time dependent diffusion theory model. It
appears that for the 2 msec wide input pulse deviations from the


FLUX (RELATIVE UNITE)
FIG- CIO TIME PROFILE OF THERMAL NEUTRON FLUX 117-44 CM FROM THE SOURCE


121
Shown in Fig. 27 (A, B, C) are a set of the experimentally
determined thermal neutron time profiles for the 0.5 msec input pulse
case. A representative set of the experimentally determined spatial
distribution of neutrons in the assembly for increasing times after
the source pulse is shown in Fig. 28 (A, B). The space and time de
pendent redistribution of the thermal flux as the disturbance propa
gates through the assembly is clearly displayed.
Tables VII and VIII show the experimentally determined and theo
retically calculated delay times with reference to zero time (this
time corresponds to the time at which the neutron generator initiates
the burst and the multichannel analyzer starts its sweep), the FWHM
and the counts at the peak of the pulse normalized to position 83
which is located in the asymptotic region. In Figs. 29 through 32 the
delay times and the spatial attenuation for both pulse widths is
shown.
Very good agreement is obtained between the theoretical and
experimental results, throughout the length of the assembly, including
the region near the source and the region farthest removed from the
source where end effects are significant. This apparent agreement is
encouraging and vouches for the calculational scheme and source descrip
tion used.
The Propagation Time and the Asymptotic Velocity of Propagation
The propagation time, which is defined as the total delay time
between peaks at the two extreme positions of the assembly, is 3.65 +
0.1 msec.
The asymptotic velocity of propagation is defined as the inverse
of the slope of the curve of the delay time vs. distance in the


FLUX (RELATIVE UNITS)
1-0 +
0-3
0-B +
0-7
0-B
J3
0-4
0-3-
0-2
0-1-
NORMALIZED ID
THERM--5- 76
PULSE WIDTH = 0-5 MSECS
P104
Â¥ * 9 W
9 _* ft
? a .a*
9 ft ft -ft9
ft0-^a0
9e_
0,i0c-c5
>iS o '.-'P ' Jk
-o0.t.Vn^
e W vLT ','^->
wLvJ
0
-L
4
7
S
10
TIME (MSEC)
FIG. 27C EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS IN THE UFSA R1 CORE
124


93
following technique was used in most of the measurements:
a) Measurements were taken with the bare movable detector
at each designated position and a normalization factor
obtained from the fixed detector.
b) Measurements were taken with the same movable detector
covered with a 0.018 in thick cadmium sleeve (the Cd cut
off energy for this thickness is -.53 ev) at the same posi
tions and a normalization factor obtained from the fixed
detector.
c) The time profile from each measurement was resolution time
corrected, background subtracted and normalized with
reference to the fixed detector (refer to Part 1, Chapter IV).
d) A point by point subtraction of the epicadmium time profile
from the total time profile yielded the thermal neutron flux
pulse shape at each spatial point.
It should be mentioned that, to be rigorous, a correction should
be applied to the epicadmium flux at each space point to take into
account the perturbation of the thermal flux introduced by the cadmium
sleeve; this was not attempted in this study. It should not be signif
icant in the highly absorbing medium being considered here.
As a corollary, it was expected that the epicadmium flux time
profile could be compared with the theoretically predicted fast flux.
The main problem encountered with this comparison lies in the fact that
the energy-dependent efficiency of the detector affects the character
istics of the pulse. The efficiency of detection for the thermal group
(0-.5 ev) is fairly constant and the comparison with the calculated
thermal flux is on solid grounds; the same argument is not valid


LIST OF REFERENCES
1. S. O. Johnson and R. W. Garner, private communication (1966).
2. R. E. Uhrig, £t al, "Design and Summary Hazards Report of the
University of Florida Accelerator Pulsed Subcritical Assembly"
(1964).
3. M. J. Ohanian, N. J. Diaz and R. B. Perez, "Design and Hazards
Report of the University of Florida SPERT Assembly" (1967).
4. M. J. Ohanian and N. J. Diaz, "Reply to Request for Additional
Information in Connection with Review of Application for SNM
License"(Ref. No. D.M.L.:RLL 70-1068) (1967).
5. M. J. Ohanian and N. J. Diaz, "Addendum to the Design and Hazards
Report of the University of Florida SPERT Assembly," communication
to USAEC Materials Licensing Division (1968).
6. L. B. Myers, "UFSA Safety Instrument and Control Systems Report,"
Internal Report, Dept, of Nuclear Engineering Sciences, University
of Florida (1968).
7. S. 0. Johnson and R. W. Garner, private communication (1967).
8. E. Garelis and J. L. Russell, Jr., "Theory of Pulsed Neutron
Source Measurements," Nuc. Sci. Eng., 16, 263 (1963).
9. R. L. Coates and N. R. Horton, "RSAC A Radiological Safety
Analysis Computer Program," IDO-17151 (1966).
10. R. J. Wagner, "IREKING Program for the Numerical Solution of the
Reactor Kinetics Equations," IDO-17114 (1966).
11. S. R. Bierman, K. L. Garlid and J. R. Clark, "Resolving Time of a
Pulsed-Neutron Source Data-Acquisition System," Nuc. Applic., 2
(1964).
12. B. E. Simmons and J. S. King, "A Pulsed Neutron Technique for
Reactivity Determination," Nc. Sci. Eng., _3, 595 (1958).
13. N. G. Sjostrand, "Measurements on a Subcritical Reactor Using a
Pulsed Neutron Source," Arkiv Fysik, 11, 233 (1956).
14. T. Gozani, "A Modified Procedure for the Evaluation of Pulsed Source
Experiments in Subcritical Reactors," Nukleonik, 4, 348 (1962).
258


LIST OF FIGURES (contd)
FIGURE Page
17A DECAY CONSTANT vs. MODERATOR LEVEL 76
17B kS/£ AND k vs. MODERATOR LEVEL 77
18 THE TOTAL, EPICADMIUM AND THERMAL FLUX 117.44 CM
FROM THE SOURCE 95
19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL
ARRANGEMENT PLAN VIEW 96
20 PLAN AND FRONT VIEW OF THE CORE REGION ENCLOSING THE
NEUTRON SOURCE 102
21 ONE-DIMENSIONAL ARRANGEMENT OF THE UFSA CORE USED IN THE
WIGLE CALCULATIONAL SCHEME 103
22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED
INTO THE WIGLE SCHEME 107
23A PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE 110
23B PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE Ill
23C PULSE SHAPES PREDICTED BY WIGLE AT DIFFERENT
POSITIONS IN THE UFSA R1 CORE 112
24A THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE 113
24B THE CALCULATED SPATIAL DISTRIBUTION OF THE THERMAL
FLUX AT DIFFERENT TIMES AFTER THE PULSE 114
25 THE ASYMPTOTIC STEADY-STATE VERTICAL FLUX 116
26 THE ASYMPTOTIC STEADY-STATE HORIZONTAL FLUX 117
21k EXPERIMENTAL PULSE SHAPES AT DIFFERENT POSITIONS
IN THE UFSA R1 CORE 122
xiv


(sec
Moderator Level (cm)
FIG. 17A DECAY CONSTANT vs. MODERATOR LEVEL


TABLE II (Continued)
B. NON-NUCLEAR
Measured Parameter
a. Reactor water temper
ature
Method of Measurement
Fenwall temperature switch in
inlet line
b. Reactor water level
c. Reactor door and per
sonnel
Barksdale pressure switch mounted
on weir"box"with sensing line
connected to core
Limit switches on doors and push
buttons inside reactor room
d. Reactor core width
Limit switches on reflector tanks
e. Reactor water level Barnstead pressure switch senses
level in weir box
f. Reflector tank water Float switches in reflector tanks
level (low)
g. Flow control valve Limit switch on valve
shut
h. Reactor flow Differential pressure cell and
pneumatic control
i. Reactor water level D/P cell and pneumatic system
Application
Scram reactor on low reactor
inlet water temp. (60F)
Scram reactor if water level in
core exceeds top of weir height
Scram system and shut down neutron
gun if reactor doors are opened
or interior switches are acti
vated
Prohibit filling reflector tanks
when distance between tanks
exceeds widest reflected core
width
Stops pump when water reaches 11cm
below weir apex
Indicates water is filling reflec
tor tanks
Requires closing valve before
starting pump
Control flow rate. Indicate and
record flow rate
Indicate and record water level


FLUX (RELATIVE UNITS)
FIG. 35A THE SENSITIVITY OF THE ONE-DIMENSIONAL, TWO GROUP, SPACE-TIME KINETICS SCHEME
TO CHANGES IN THE TRANSVERSE BUCKLING


FLUX (RELATIVE UNITS)
FIG* Dll TIME PROFILE OF FAST NEUTRON FLUX IBB*31 O'M FROM THE SOURCE
246


preferred over the BF^ variety at the University of Florida because of
the larger neutron absorption cross section and operational reliability.
3
He undergoes the following reaction
He^ + n H^ + p + 0.764 Mev.
The cross section for this reaction is 5327 + 10 barn at v = 2200
o
10 3
m/sec compared to 3840 +.11 barn for B He follows a 1/v law in the
3
energy range from 0 to 200 kev. The pulse heights yielded by a He
filled counter are proportional to the energy of the neutrons plus 764
kev. The reaction has been used for neutron spectroscopy from the 100
kev to 2 Mev energy range. Gamma discrimination can be easily accom
plished by the use of a biased integral discriminator.
The detectors were long and thin and each took the place of a fuel
element in the core. The active length of the counter is slightly less
than the active length of the fuel. Two one atmosphere (predominantly
thermal detection) and one ten atmosphere (more responsive to higher
energy neutrons) detectors were used in the experimental program. A
sketch of the physical characteristics of the counters is shown in
Fig. 10. The thin, long cylindrical shape enhances the time character-
3
istics of the counter. Although normally a 1 atmosphere He detector
operates with a bias voltage of 1000 volt, the minimum input pulse
voltage requirement of the pulse transformer was such that the operating
voltage of the counters had to be raised to 1200 volt. At this
voltage the slope of the counts vs. high voltage curve was about 8% per
100 volt; therefore very stable, low ripple high voltage supplies were
used to insure reproducibility of the detector response.


186
comparison of the WIGLE results and the pulse propagation data were put
on the same basis by performing identical Fourier transformations and
fitting procedures on both. The predicted and measured real part of
2 2 2
p =(a -£ ) diverge past 100 cps. This is almost a "natural" occurrence
2
in the ultrasensitive p plane in which the opposing discrepancies of
2 2
a and £ are blown out of proportion. The agreement in the p disper
sion law of the system is good and within the experimental accuracy and
capabilities of the model.
It is believed that WIGLE did predict accurately the dynamic
behavior of the narrow, long core studied. It is also believed that the
sensitivity of the one-dimensional calculational scheme to small changes
in the transverse buckling should be born in mind when feedback effects
and/or two-dimensional effects are to be considered.
The followings topics deserve future investigation:
1. The sensitivity of the dynamic behavior of the system to small
changes in the transverse buckling. This can be accomplished by a
detailed pulse propagation study at two core heights or at two core
widths.
2. Impose a more severe test of the model by conducting measure
ments with a narrower input pulse.
3. Further interpretation of reactivity measurements in large
systems is needed. A correction for the influence that the input pulse
width has on the determination of kg/S, by the Garelis-Rus sell method is
necessary. The extrapolated area-ratio method should provide a basis
for comparison.
4. A comparison should be made between the calculational results
of two-group diffusion solved directly in the frequency domain and those
obtained by numerical transformation of the WIGLE results.


Relative Amplitude
FIG. 22 SPATIAL DISTRIBUTION OF SOURCE NEUTRONS INCORPORATED INTO THE WIGLE SCHEME
107


170
and experiment approach 1000 cps.
The differences observed reflect those noticed when the comparison
in the time domain was conducted. The fact that the WIGLE pulses are
consistently narrower than the experimental ones is reflected in the
smaller damping coefficients at large frequencies.
The differences showed up much more markedly in the ultrasensitive
2 2 2 2
p plane. Since a < a and E > 5 the real part of p =(a -£ )
^ th exp th exp r
seems to indicate a discrepancy that is not as large as it appears.
2
Shown in Fig. 45 is the real part of p for both theory and exper
iment as a function of frequency. Although they start to diverge sig
nificantly at f = 100 cps, it should be remarked that any small dif-
2
ferences in a and £ are magnified out of proportion in the p plane.
2
In contrast, the imaginary part of p =(2a0 appears to signify perfect
agreement in the results, since the deviations in a and £ cancel each
other (see Fig. 46).
2
The p dispersion law of the UFSA R1 clean core is shown in Fig.
47. This is a most sensitive index. Any small error in the data or
2
failure of the model will immediately appear "blown-up" in p Although
2
the theory and experiment diverge in the p plane, after 100 cps, both
behave smoothly; the differences should be considered within the con
text of the over all analysis. Certainly it can be said that the WIGLE
results do not follow the experimental results throughout the frequency
range but that is to expected; the actual discrepancies observed in the
2
time domain and the numerical uncertainties propagate into the p plane
so significantly that perfect agreement seems to be unreachable with
the present models and knowledge of parameters.
The steady-state inverse relaxation length =.023 (and the corresponding
ctf_o) is significantly smaller than the dynamic inverse relaxation =.030.


long, 39 inches high, and of variable width. In this study, the core
was 6.5 inches wide and 30 inches high. The effective multiplication
constant of the assembly was determined to be 0.990jK003. The assembly
is equipped with nuclear instrumentation capable of automatic scram
action.
For the kinetics studies, a fast data acquisition system was
developed to handle accurately the very high, time-changing count rate
encountered in the measurements. It essentially consists of a trans
former-coupled pulse amplifier to produce a fast logic signal at the
input of a multichannel analyzer from the input signal originating in
3
a long, thin He counter. The instrumentation adequately handled count
rates up to 3 x 10^ counts/sec at the peak of the pulses. A high degree
of reproducibility and fidelity in following the pulse profiles was
obtained with this instrumentation.
The space-time kinetics studies were performed by analyzing the
propagation of a fast neutron burst introduced at one end of the assem
bly, in the absence of inherent feedback effects. The experimental
results are compared with the results obtained from the two-group,
space-time dependent, one-dimensional diffusion theory scheme known as
the WIGLE program. A stringent test of the model is provided by a
combined analysis in the time and the frequency domain.
Tiie WIGLE calculational scheme accurately predicts the delay times
and the attenuation of the pulses when a first-flight spatial distribu
tion is assumed for the fast source. At large distances from the source
WIGLE underpredicts (~ 8% in the FWHW) the spreading of the pulse. A
marked sensitivity to small changes in the transverse buckling was
'found for the model, as well as the experiment.
xx


Dimensions in cm
PIG. 19 UFSA SOURCE-SUBCRITICAL ASSEMBLY GEOMETRICAL ARRANGEMENT
- PLAN VIEW -


CHAPTER I
INTRODUCTION
Statement of the Problem
The dynamic behavior of large reactor cores is recognized as one
of the areas of reactor analysis in which practical, reliable calcula-
tional methods are needed. Although a significant amount of theoretical
work has been done in this area, the experimentation has been restricted
to the fundamental work done by Miley and co-workers at the University
of Illinois [20, 21, 22] and the dispersion law studies in a heavy
water-moderated, natural uranium assembly performed at the University
of Florida [23]. The work at Illinois was hampered by the very broad
input pulse obtained at the thermal column of the TRIGA reactor, by
the neutronic size of the assembly and by the low value of the effective
multiplication (ke^ j^.92). The work at Florida, using comparatively
narrow pulses from a neutron generator (and thermalizing tank), was
also restricted by the neutronic size of the system and by the k
No clean determination of "complete" spatial effects in multiplicative
media has been reported.
The Reactor Safety Division of the United States Atomic Energy
Commission established the Large Core Dynamics Experimental Program,
as proposed by the Atomic Energy Division of the Phillips Petroleum
Company, to study the behavior of large reactor cores. The objective
80


(RELATIVE UNITS)
ID
-J
THERM--3- SO
PEAK AT 0-320 M,SEEDS
PULSE WIDTH = 0-3 MSECS
THECRY FWHVt = 0-773 MSEECS
EIXP FWHM = 0-773 MSECS
0-3
B 7
VO
VO
10
TIME (MSEi;)
C3
TIME PRCF'ILE DF THERMAL NEUTRON FLUX SB 43 EM FROM THE SOURCE


9
8
7
6
5
4
3
2
1
O
162
R1 Core
12.716 cm between points
48 62 76 90
Position Number
104 118 132
. 40 PHASE OF ZEROTH FOURIER MOMENT vs. DISTANCE FOR
SEVERAL FREQUENCIES
- 0.5 MSEC INPUT PULSE -


51
FIG. 11 MOVABLE DETECTOR DATA ACQUISITION SYSTEM


19
FIG. 6 WEIR "BOX"


Inverse Multiplication
Moderator Level (cm)
FIG. 16B INVERSE MULTIPLICATION vs. SQUARED INVERSE HEIGHT


5 (rad/cm)
P
Frequency
FIG. 43 COMPARISON OF THE THEORETICALLY PREDICTED AND THE MEASURED PHASE SHIFT PER
UNIT LENGTH £
167


11
The end walls are permanently covered with Cadmium on the outside
surface while the side walls have movable Cadmium covers to define the
boundaries for the bare and reflected cases. To optimize the number of '
neutrons inserted into the assembly by the neutron generator, the accel
erator target penetrates about 4 inches into the core. A water-tight
port is provided for this purpose. The port can be removed and a blind
flange inserted in its place. Several fuel rods must be taken out, the
number depending on how deep the target goes into the assembly and on the.
lattice pitch.
The core section of the assembly consists of an interchangeable
fuel rod spacing system made of 3/4 x 1/2 x 1/8 inch channels, 5/8 x 1/4
inch bars and aluminum shims mounted on the base plate of the tank. The
bars have milled slots to accommodate the .25 inch end tip of the fuel
rod and to set the pitch along the core width. The shims are placed
between the channel bar units to set the pitch along the core length
(96 inches) (see Fig. 2). The top fuel rod spacing system consists of
an aluminum grating. The mesh is determined by the lattice pitch under
study. The grating is made of aluminum bars and spacers, as shown in
Fig. 3. Thus, fuel rod removal along the length of the core is pos
sible to locate the detector for the experimental measurements.
The one-half inch long rod tip is fully surrounded by aluminum,
with practically no reflecting characteristic, but there is a 7/8 inch
length of rod between the end of the active fuel and the tip which is
t
surrounded by water. This bottom reflector is unavoidable and will be
considered in the calculations.


9
is interlocked with the neutron generator and the subcritical assembly
scram system, as is the door on the only other entrance to the shielded
room from the fuel storage area. Across the front face of the assembly,
a screened wire cage with a lockable door controls access to the core.
While not in use in the assembly the fuel is stored in a room
adjacent to the facility, built entirely for this purpose.
A more complete description of the. facility and its characteristics
can be found in the Design and Hazards of the UFSA and its addenda
[3, 4, 5],
The system has been licensed under Atomic Energy Commission SPECIAL
NUCLEAR MATERIAL LICENSE SNM 1050, March 1968. The license allows for
the possesion of 5400 fuel rods with a total U235 inventory of 190 kgs.
Fuel Characteristics
The UFSA is fueled with Spert F-l type fuel elements provided by
the Phillips Petroleum Company.
The fuel characteristics are:
Fuel Composition: UO^ in pellet form
U235 enr:*-c^linent: 4.81 + .15%
Active Fuel Length: 36" + .062"
Active Fuel Diameter: .42" + .0005"
Fuel Tube Material: stainless steel
Fuel Tube Length: 41.625"
Fuel Tube o. d.: .4655" + .0025"


CHAPTER III
DESCRIPTION OF THE MEASUREMENTS
Introduction
In most pulse propagation and/or neutron wave measurements the
experimental technique employed to obtain the thermal neutron pulse
shape is the so-called cadmium difference method. In this technique
the contribution of the epicadmium source neutrons is subtracted by
making measurements with and without a cadmium shutter between the
source and the system. No attempt is usually made to subtract the
epicadmium neutron contribution due to fissions if the medium being
studied is multiplicative.
But, most neutron detectors interact with epicadmium neutrons with
varying degrees of efficiency; therefore to isolate the thermal neutron
pulse shapes a different experimental technique was used in this work.
Thus, it was possible to make a one-to-one comparison of the experi
mentally obtained thermal neutron pulse shapes with the corresponding
results from the analytical scheme.
The subcritical configuration and electronic instrumentation used
has been detailed in Part 1, Chapter IV. Unless specified, the meas
urements were made at a moderator height of 75 cm, corresponding to a
keff = 0.99+.003.
The system was operated under continuous water flow conditions.
No heating of the water was observed by either the energy transferred
91


Abstract of Dissertation Presented to the Graduate Council
in Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy
SPACE-TIME REACTOR KINETICS STUDIES WITH
THE UNIVERSITY OF FLORIDA SPERT ASSEMBLY
By
Nils J. Diaz
March 1969
Chairman: Dr. M. J. Ohanian
Major Department: Nuclear Engineering Sciences
A large-in-one-space dimension, side reflected, highly multiplica
tive (kgff ~ 0.99) subcritical assembly was designed and calibrated.
The sole purpose of the facility is the experimental investigation of
the dynamic behavior of large reactor cores and to provide a test for
space-time kinetics models presently in use. With this facility the
linear aspects of neutron physics phenomena can be investigated in the
absence of inherent feedback effects. This work was conducted under a
subcontract with the Nuclear Safety Research Branch, Atomic Energy
Division, Phillips Petroleum Company, under a prime contract with the
United States Atomic Energy Commission.
The University of Florida SPERT Assembly (UFSA) is a light-water
moderated subcritical facility fueled by 4.81% enriched UC^ pellets
encased in stainless steel tubes of 0.465 inch outside diameter (SPERT
F-l Fuel). The fuel arrays are contained in a rectangular tank, 8 feet
xix


20
perimeter of the weir "box" into the drain line effectively preventing
any further increase of the moderator level in the assembly.
The measurement of the water height in the core is accomplished by
fixing a reference mark on the slide block at the same level as the
bottom of the weir within the "box". An accurate scale is provided to
read off the distance between the bottom of the core and the apex of the
weirs. Continuous indication of the moderator level in the core is
provided on the console by means of a recorder calibrated between the
bottom of the active fuel and the maximum moderator height and by a
manometer, connected directly to the core, for precise measurement of
the water level. These two measuring systems insure reproducibility of
the moderator height for the experiments.
The water is pumped out of the storage tank by a constant speed
centrifugal pump which has a "no load" capacity of 20 gal/min. The
control valve is designed to restrict the flow to the maximum design
value of 12 gal/min. A deionization system is provided to keep the
water as pure as possible at all times. The pneumatic flow control
system consists of two differential pressure cells, transmitters, control
valve, and recorder-controller. The strip type chart recorder-con
troller records both flow rate and moderator level in the core. The
control valve is of the air-to-open type which will close in the case of
air supply loss, stopping the flow into the assembly. The flow diagram
for the air system is shown in Fig. 7. A pressure differential from the
pressure transmitters applied to the recorder-controller allows both
manual and automatic control' of the flow rate through the valve operated
by the controller.


137
calculations were performed in which the height of the assembly was
varied from 70 to 85 cm. The respective core heights with their
corresponding vertical bucklings, k ^ (calculated using AIM-6) and
"absorption" cross-sections used in the WIGLE code are listed in Table
XI.
The results of the calculations showed a marked sensitivity to
changes in the transverse buckling. The delay times and the peak
counts vs. distance to the source are shown in Fig. 33 and 34 respec
tively. The experimental results for 76 cm are also shown. The data
for the attenuation curves was normalized to the attenuation at P83
of the 76 cm WIGLE calculations. Pulse shapes for the different heights
are shown together with the experimental results at 76 cm in Fig. 35
(A, B, C) for three representative positions in the assembly.
Some additional experimental measurements were also made at a
given position for different core heights to supplement the calcula-
tional predictions. It should be pointed out that these measurements
are of a preliminary nature, made over a short period of time simply
to obtain confirmation of the theoretical trends. The results of these
measurements are shown in Fig. 36.
It is not surprising that the results for the core showed as much
sensitivity to changes in the transverse buckling since the width and
height of the core are rather small in comparison to the length of the
assembly. It is to be noted that the changes in the "absorption"
cross-section due to changes in the transverse buckling are rather
small and are reflected in the third significant figure in the fast
group cross-section and the fourth significant figure in the thermal
group cross-section. This emphasizes the importance of an accurate


FLUX (RELATIVE UNITED
f
FIG- Cll time PROFILE OF THERMAL NEUTRON FLUX 130-16 CM FROM THE SDURCE
207


NO
00
FIG. 8
UFSA SAFETY SYSTEM LOGIC FLOW DIAGRAM


under a prime contract with the United States Atomic Energy Commission.
The technical aid of the University of Florida Computing Center in the
development of the computer programs and their financial assistance is
gratefully acknowledged.
Special mention is due Messrs. S. 0. Johnson, R. W. Garner,
G. A. Mortensen and Mrs. M. E. Radd of the Nuclear Safety Research
Branch, Atomic Energy Division, Phillips Petroleum Company for their
continuous assistance and invaluable suggestions throughout the
research program.
To my sister, Miss Lydia Gonzalez, my sincere appreciation for.
typing an elegant manuscript from my unintelligible characters.
To the fellow students, who struggled with me to reach the un
reachable star, my space and time independent friendship.
iv


33
criterion.
d) Operating limits have been set to delineate the normal oper
ating ranges of the assembly.
e) Initial loading procedures have been established to determine
the safe operating multiplication factor of each configuration.
A series of administrative controls are necessarily applied to all
segments of the experimental program and strictly enforced.
Initial Loading
A series of calculations were done to determine which of the two
following schemes should be employed for the initial loading of UFSA:
I) Step loading of the fuel from the center out, accompanied by
step increases in water level with the usual inverse multiplication
determination.
II) Loading all the fuel into the dry tank and proceeding with a
careful evaluation of the multiplication as a function of water level.
Since the UFSA core is very loosely coupled as far as the lumped
reactivity parameter is concerned, the second method was selected due to
the fact that a better determination of the multiplication was possible
from a basic moderator height-zero loading inverse counts determination.
The slope of the kg^^ vs. water height curve has a slope substantially
smoother than the kg^^ vs. per cent fuel loading (full water height)
curve.
The moderator level control system in operation at the facility
provides a extremely reliable and safe mode of adjusting the water level
without safety compromises.
The following regulations were followed for the initial fuel