Group Title: Spectroscopy of fission fragment excited atmospheric pressure argon and xenon plasmas /
Title: Spectroscopy of fission fragment excited atmospheric pressure argon and xenon plasmas
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00097523/00001
 Material Information
Title: Spectroscopy of fission fragment excited atmospheric pressure argon and xenon plasmas
Physical Description: xvii, 294 leaves : ill. ; 28cm.
Language: English
Creator: Davie, Robert Nelson, 1945-
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subject: Atmospheric pressure   ( lcsh )
Argon   ( lcsh )
Xenon   ( lcsh )
Spectrum analysis   ( lcsh )
Nuclear Engineering Sciences thesis Ph. D   ( lcsh )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 284-292.
Additional Physical Form: Also available on World Wide Web
Statement of Responsibility: by Robert N. Davie, Jr.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00097523
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000167867
oclc - 02871113
notis - AAT4258

Downloads

This item has the following downloads:

PDF ( 11 MBs ) ( PDF )


Full Text










SPECTROSCOPY OF FISSION FRAGMENT EXCITED
ATMOSPHERIC PRESSURE ARGON AND XENON PLASMAS














By

ROBERT N. DAVIE, JR.


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


1975













ACKNOWLEDGMENTS


I would like to begin by expressing my sincere

thanks to the chairman of my supervisory committee, Dr.

R. T. Schneider, and the other members, Dr. H. D. Campbell,

Dr. E. E. Carroll, Dr. W. H. Ellis, Dr. M. J. Ohanian,

and Dr. T. L. Bailey. Their numerous efforts on my behalf

throughout my stay at the University of Florida are

appreciated.

Execution of the research described herein required

the support of nearly the entire Nuclear Engineering

Sciences Department at one time or another from its chair-

man, Dr. M. J. Ohanian, on down. In spite of the number,

I feel compelled to list the individual contributions.

Administrative support was provided by Joan Boley, Barbara

Davis, Lois Carroll, and Michey Kaselnak in funding. They

were always willing to help me out "right now" when neces-

sary. The reactor safety subcommittee was both patient

and helpful in formulating an experimental approach con-

sistent with safety guidelines. In particular Dr. Dalton,

from whom I also learned a great deal in the classroom,







was extremely helpful in solving the various safety prob-

lems. With respect to the actual experimental work, most

of the precision machining was done by Ralph Jones. Ernie

Whitman did most of the heli-arc welding and gas filling.

Joe Mueller must be credited with getting those big jobs

done such as building the optical bench, beam trap and

various shielding. The ideas of these three individuals

had significant impact on every facet of the system design.

The reactor staff under the direction of Dr. N. J. Diaz

and Les Constable consistently made every effort possible

to support this research. Henry Gogun and George Fogle

provided numerous ideas and support, particularly during the

initial setup and checkout of the system in the reactor.

The swing shift operation of the reactor by Ed Donner was

essential in getting that extra running time required to

meet schedules. Ken Fawcett of the electronics shop saw

plenty of action keeping the experimental equipment work-

ing. Willy Nelson supported this work through the timely

procurement of various supplies and unglorified manual

labor when I most needed it. An individual who always

seemed available to help and put in many hours at the

critical times was Dudley Carter; and he did almost any-

thing from heli-arc welding to system alignment. Don

Price, Harvey Norton, Gordon R~enshaw, and Richard McGinley

of Radiation Control were extremely helpful and always

willing to do things immediately. I am indebted to all the







above individuals for their assistance; each played an

important part.

Working with other students in the department was

a pleasurable and educational experience for me. My

closest association was with John Davis, for we used the

same equipment for our research and worked together build-

ing most of it on a day-to-day basis. I consider this

association my pleasure. Technical discussions with G. R.

Shipman and Bruce Schnitzler, particularly during the early

stages of my research, taught me a great deal. Other stu-

dents to whom I am indebted for one reason or another are

Jim Fuller, Bruce Kaiser, Eric Holtzclaw, Ken Sprague,

and Dave Sterritt.

Support of the United States Air Force is acknowl-

edged for paying my salary and providing me this unique

educational opportunity. My research expenses were

supported by NASA grant NGL-10-005-089.

Credit for the typing of this manuscript goes to

Nancy McDavid and for the drafting to Robert Naranjo.

Finally, I express my deepest gratitude to my wife,

Janet, and my two sons, Rob and Chris, for the sacrifices

they made so that I might be able to pursue this educa-

tional goal. Their continual encouragement and support

were also essential to its accomplishment.






















































n


TABLE OF CONTENTS


Page

ii

ix

xi

xiv


ACKNJOWLEDGM1ENTS .................

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

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

ABSTRACT. . . . . . . . . . *

CHAPTER

1 INTRODUCTION.. .. ..........
1.1 Interest in Fission Fragment Produced
Plasmas. . . . . .
1.2 Summary of Past Related Work ....
1.2.1 Fission Fragment Excitation
Experiments... ......
1.2.2 Analytical Studies of Spatial
Effects . . . .
1.2.3 Secondary Electron Energy
Distributions.... ....
1.2.4 Experimental Studies of Plasmas
Produced by Other Forms of High
Energy Ionizing Radiation ..
1.3 Specific Objectives of This Research.

2 THEORETICAL CONSIDERATIONS.........
2.1 Energy Loss of Fission Fragment in
Gases. . . . . . .
2.1.1 Primary Ionization and Excitatior


by Fission Fragments. ....
2.1.2 Delta Rays and Secondary Elec-
trons . . . . . .
2.1.3 Excited State Kinetics. ...
2.2 Fission Fragment Plasma Characteri-
zation . . .
2.2.1 The Corona Model...... .
2.2.2 Recombination Riegime......
2.2.3 Trapping and Optical Thickness.
2.2.4 Collisional Transfer of Excita-
tion. . . . .
2.2.5 Qualitative Summary Description
of the Plasmas.........







TABLE OF CONTENTS (continued)


CHAPTER

2 2.3 Energy Deposition Calculations and
(cont.) Spatial Effects...........
2.3.1 Energy Deposition Calculation.
2.3.2 Thermalized Electron Density
Calculation..... ....
2.3.3 Fragment and Electron Energy
Spectra. . . . .
2.4 Discussion of Experimentally M~easur-
able Parameters.. ........
2.4.1 Spatial Variations......
2.4.2 Emission Intensity as a Func-
tion of Reactor Power Level..
2.4.3 Pressure Effects.......
2.4.4 Electric Field Amplification.
2.4.5 Temperature Effects......

3 EXPERIMENTAL SYSTEM DESCRIPTION.
3.1 Design Considerations. ......
3.2 Overall System Concept........
3.3 MCFIG Details.. .........
3.3.1 Valve and Thermocouple Port.
3.3.2 Sapphire window.. .....
3.3.3 UO2 Source....... ..
3.4 Optical System.. .........
3.5 Instrumentation System........
3.5.1 System Evolution.......
3.5.2 Spectral Sensitivity.....
3.5.3 Spectral Resolution......
3.6 Reactor Environment....... .
3.6.1 Neutron Flux. .......
3.6.2 MCFIG Temperature.. ....
3.7 Test Procedures........ ..
3.7.1 Gas Filling.........


Page


Spatial Calibration and MCFIG
Loading. . . . . .
Initial Reactor Startup...
Data Acquisition......
Posttest Procedure.....


3.7.2

3.7.3
3.7.4
3.7.5


4 DATA ANALYSIS METHODS.. ........
4.1 Spectral Line Identification Tech-
niques. . . . . . . .
4.2 System Absolute Calibration.....
4.2.1 Relative Calibration Details.
4.2.2 Monochromator and Photomulti-
plier Absolute Calibration .
4.2.3 Relative Calibration Scaling.
4.2.4 Optical Collection Efficiency.
4.3 Calculation of Excited State Popula-
tions . . . . . .








TABLE OF CONTENTS (continued)


CHAPTER Page

5 ARGON RESULTS AND DISCUSSION . .. .. 133
5.1 Argon Spectra and Excited State
Populations .. .. .. .. .. 134
5.1.1 Arl. . ... .. .. .. 136
5.1.2 ArII,. .. .. .. ... 144
5.1.3 2250A Continuum. .. .. 162
5.1.4 Unidentified Lines .. .. 163
5.2 Observed Spatial Effects. .. .. 166
5.3 Emission Intensity Versus Reactor
Power ... .. .. .. .. 175
5.4 Temperature Effects .. .. .. 177
5.5 Reassessment of Walters' Data .. 178
5.5.1 Pressure Effects .. .. 178
5.5.2 Electric Field Amplifica-
tion .. .. .. .. .. 180
5.6 Discussion. .. .. .. .. .. 183

6 XENON RESULTS AND DISCUSSION .. .. 190
6.1 Xenon Spectra and Excited State
Populations .. .. .. .. .. 191
6.1.1. Xel... .. .. . ... 193
6.1.2 Xell . .. .. ... .. 197
6.1.3 Visible Continuun. .. .. 204
6.1.4 Unidentified Lines . ... 208
6.2 Observed Spatial Effects. .. .. 210
6.3 Emission Intensity Versus Reactor
Power . .. .. .. . 215
6.4 Temperature Effects .. .. .. 217
6.5 Discussion. . .... .. .. 220

7 CONCLUDING REMARKS .. .. .. 222
7.1 Summary of Significant Results and
Conclusions . .. ... .. .. 222
7.1.1 Ar Data Base . . . . 222
7.1.2 Xe Data Base .. .. .. 223
7.1.3 Model of Fission Fragment
Excited Plasmas. .. .. 223
7.1.4 Implications for Nuclear
Pumping. . ... .. .. 224
7.1.5 Spatial Effects. .. .. 226
7.2 Implications for Future Research. 226
7.2.1 Gamma Excitation of Gases. 227
7.2.2 Radiation Effects. .. .. 227
7.2.3 Source Geometry. . ... 228
7.2.4 Improvements of Experimental
Setup. ... . .. . 228








TABLE OF CONTENTS (continued)


APPENDICES Page

A SOME OBSERVATIONS ON THE LUMINESCENCE OF
ALPHA-Al203 (SYNTHETIC SAPPHIRE) IN A
REACTOR ENVIRONMENT,............ 230

B COMPLETE Ar SPECTRA. .. ... .. .. 243

C TABULAR SUMMARY OF WATERS' DATA FOR ARGON. 258

D COMPLETE Xe SPECTRA. .. ... .. .. 266

BIBLIOGRAPHY .. .. .. . . . . . . . 284

BIOGRAPHICAL SKETCH. .. .. . ... ... . 293


V1














LIST OF TABLES


Table Pase

1.1 Summary of Past Spectral Investigations of
Ar and Xe Excited by Ionizing Radiation .. 16

5.1 Arl Excited State Population Densities. .. 137

5.2 Comparison of Arl Relative Excited 2pn State
Populations with Those of Walters and with
Electron Excitation Cross Sections. .. .. 142

5.3 ArlI Excited State Population Densities .. 145

5.4 List of Observed and Inferred ArlI Laser
Transitions ... .. .. .. .. .. .. 151

5.5 Comparison of ArlI Relative Excited State
Populations with Those of Walters, those of
Rudko and Tang, and with Electron Excitation
Cross Sections. .. ... .. .. ... 154

5.6 Analysis of Observed ArlI Cascade Transi-
tions .. .. .... .. .. .. .. 160

5.7 List of Unidentified Lines in tfe Ar Spectrum 164

5.8 Tabulation of Selected Arl Spatial Measure-
ments ... .. . ... .. .. ... 168

5.9 Tabulation of Selected ArlI Spatial Measure-
ments .. .. .. ... ... .. .. 171

5.10 Relative Emission Intensity of Selected Por-
tions of the Ar Spectrum at Various Reactor
Power Levels. . .. .. .. .. .... 176

5.11 Walters' Excited State Populations Mlultiplied
by Total Transition Probability and Divided
by the Excitation Cross Section .. ... 179

6.1 Xel Excited State Population Densities. .. 194

6.2 Xell Excited State Population Densities .. 198







LIST OF TABLES (continued)


Table Page

6.3 List of Observed and Inferred Xell Laser
Transitions .. .. .. ... .. .. 200

6.4 Analysis of Observed Xell Cascade Transi-
tions .. .. .. . .. . . . . 203

6.5 List of Unidentified Lines in the Xe Spec-
trum. .. .. .. .. ... . . . 209

6.6 Tabulation of Selected Xe Spatial Measure-
ments .. ... .. .. .. . . . 213

6.7 Xe Emission Intensity as a Function of Power. 216

6.8 Summary of the Behavior of Observed Portions
or the Xe Spectrum After Reactor Startup. . 219












LIST OF FIGURES


Figr Page

1.1 Effect of the Energy Dependence of the
Excitation Cross Section. .. . .... 10

1.2 Delta Ray Energy Spectrum Induced by Alpha
Particles at the Centerline of a 2.5-cm-thick
Helium Slab for Various Gas Pressures . .. 11

1.3 Electron Energy Distribution in Fission Frag-
ment Excited He and Ar as a Function of
Pressure. .. . .. ... .. .. ... 13

21A2 and Ar2 Potential Energy Curves Showing
Also Arl Levels and Important Transitions
After .. .. ... ... .. .. .. 32

2.2 Geometry for Energy Deposition Calculations
and Spatial Effects Evaluation. . .. ... 43

2.3 Volumetric Energy Deposition Rate as a Function
of Distance x from Source Where y =z = 0,
S= 2x1012n/cm2-sec, and t = 3pm. .. .. 50

2.4 Volumetric Energy Deposition Rate as a Function
of Distance z from Center of 90urc9 where
y = 0 and x = ro/2, 4 = 2x101 n/cm -sec, and
t = 3Um .. .. .. .. .. .. .. .. .. 51

2.5 Electron Density as a Function of Dis1 nce x
from Source Where y = z = 0, O = 2x10 Ln/cm2-
sec, t = 3um. .. .. .. .. ... .. 54

2.6 Electron Density as a Function of Distance z
from Center ofo~ureS Where y = 0 and x=
r /2, = 2x10 n/cm -sec, and t =3pm. ... 55

2.7 Geometry for Calculation of Fission Fragment
Path Length Distribution Function .. .. 60

2.8 r f(r) as a Function of x/ro for n=1. . .. 63

2.9 rof(r) as a Function of x/r, for n=2. . .. 64








LIST OF FIGURES (continued)


Figure Page

2.10 Eoh(E) as a Function of x/ro for n=2. . .. 66

2.11 Average Relative Fragment Energy as a Func-
tion of x/ro . . . . . . . . 67

3.1 Overall Layout for MCFIG Gas Irradiation
Studies ... .. .. .. .. ... . .. 74

3.2 Test Tube End Cap Details and Gas Handling
System. .. ... .. ... .. .. .. 75

3.3 Multipurpose Capsule for the Irradiation of
Gases ... .. .... . ... .. 78

3.4 Energy Distribution of Fission Fragments from
a 2.53-Micron-Thick, 93% Enriched UO2
Coating . . . . . . . . 81

3.5 Coating Effectiveness as a Function of
Thickness .. .. . ... .... . .. 83

3.6 Optical Setup for MCFIG Gas Irradiation
Studies .. .. .. .. .. ... .. .. 85

3.7 End on View of MCFIG Showing Spatial Sampling
Region. .. .. .... .. .. .. .. 86

3.8 Instrumentation System for MCFIG Gas Irradi-
ation Studies .. .. .. .. ... .. 89

3.9 Relative spectral Sensitivity of M~onochromator
and Photomultiplier Compared to That for the
Entire Instrumentation Systems Used in the
Argon and Xenon Studies ... .. .. .. 93

3.10 Neutron Flux Distribution in the UFTR Hori-
zontal Thruport . ..... .. .. .. 95

3.11 MCFIG Temperature as a Function of Time After
Reaching Full Power .. .. .. .. .. 97

4.1 Schematic Showing Procedures to Effect an
Absolute System Calibration .. ... .. 107

4.2 Optical Setup Used for Relative Calibration 110






LIST OF FIGURES (continued)


Figure rage

4.3 Optical Setup for the Absolute Calibration of
the M~onochromator, PMI Tube, and Associated
Instrumentation .. .. .. .. ... .. 116

4.4 Slit Image at Source and Lens Closest to
Source. ... .. .. .. .. .. . ... 122

4.5 Geometrical Layout for Calculation of dey
Showing the Four Regions for Which day is Non-
zero. . .. .. .... .. ... .. 124

4.6 Collection Efficiency for Region I. . ... 125

4.7 Collection Efficiency for Region III. .. 127

4.8 Collection Efficiency for Region IV .. .. 128

5.1 Arl Level Diagram Showing the 2p, Levels and
Transitions Seen in This Study. . .. ... 140

5.2 ArlI Level Diagram Showing Lines Observed in
This Study. .. .. ... ... .. .. 150

5.3 Comparison of Emissions Around 3093A from this
Study and from Walters' Data. .. .. .. 167

5.4 Scaled Ratio of the Intensity of the 4545A
ArlI Line to That for the 696i5A Arl Line as a
Function of Distance from the Source. . .. 174

5.5 Flow Diagram showing Important Processes in
Fission Fragment Excited Ar .. .. .. .. 184

6.1 Xe Visible Continuum as Observed Close to and
Far from the Source .. . ..... .. 205

6.2 True Intensity of Xe Visible Continuum 1.7mm
from the Source ... .. ... . .. .. 206

6.3 Variation of the Intensity of the 82801 Xel
Line and Continuum at 3300a as a Function of
Distance from the Source. . .. .. ... 211

6.4 Ratio of 3300A Continuous to 8280A Line
Emission as a Function of Distance from the
Source. .. .. ... ... .. ... 212

6.5 Intensity of Continuum at 3300A as a Function
of Reactor Power. . ... ... .. .. 218


X111







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

SPECTROSCOPY OF FISSION FRAGMENT EXCITED
ATMOSPHERIC PRESSURE ARGON AND XENON PLASMAS

By

Robert N. Davie, Jr.

December, 1975

Chairman: Dr. Richard T. Schneider
Cochairman: Dr. Hugh D. Campbell
Major Department: Nuclear Engineering Sciences

Results of a spectroscopic investigation of atmos-

pheric pressure Ar and Xe excited by fission fragments are

reported. Spectra were taken at various distances from a

planar fission fragment source, and a combined analytical

and experimental absolute system calibration permitted

estimation of excited state densities. The study was

undertaken as part of an effort to develop new nuclear

pumped laser systems, for which Ar and Xe are candidates.

A cylindrical gas containing chamber with a rec-

tangular shaped planar 3 pm 93%s enriched U02 fission frag-

ment source mounted off center and parallel to the chamber

axis was irradiated in the horizontal throughport of the

University of Florida Training Reactor and subjected to a

neutron flux of 1.6xl012n/cm sec. The optical emissions

were monitored using a model 218 McPherson 0.3m scanning

monochromator and EMI 9558QB (S-20) photomultiplier.







The spectral range sampled was 2000 to 8400A, being

limited by radiation damage to optical components in the UV

and by the photomultiplier in the IR.

The most prominent spectral lines observed were

from low lying atomic levels, 2p2 in Ar and 2p5 in Xe.

Of significantly lower intensity are numerous ion lines

which included 10 ArlI and 4 Xell known laser transitions.

Other transitions could be inferred from the data. Sig-

nificant cascading into several upper levels was observed.

A continuous emission was found in Ar around 2250A and in

Xe around 2500A which extended at lower intensity to longer

wavelengths. All emissions were found to vary linearly

with reactor power, and ArlI emissions were slightly

enhanced relative to Arl close to the source. The spatial

variation in the case of Xe was more complex.

The data are analyzed and compared with available

information for other modes of excitation. The unpub-

lished data of W~alters for fission fragment excitation of Ar

from 25 to 760 torr (with and without electric field ampli-

fication) were revaluated and tabulated. The spatial

variation of volumetric energy deposition rates, electron

densities, and fission fragment energy spectra are analy-

tically treated for the source geometry used in the

experiment.






Ionic lines are presumed to result from direct

electron excitation from the atomic ground state and cas-

cading. The ArlI relative populations appear consistent

with the coronal approximation and differ substantially

from those typical in electrically pumped Ar ion lasers.

Potential population inversions are approximately a factor

of 104 below the estimated threshold for lasing; however,

lasing should be possible at higher fluxes for both gases.

Atomic emissions apparently result from dissociative recom-

bination of the molecular ion with collisional redistribu-

tion of the energy among the atomic levels. While several

atomic laser transitions were seen or inferred, they do not

appear particularly promising for nuclear pumping. The

Ar continuous emission was attributed to molecular recom-

bination of excited atoms with ground state atoms. This

process in Ar and associative ionization in both cases are

considered responsible for depopulating the higher atomic

levels not seen in this study. The observed Ar spatial

variation is attributed to hardening of the electron energy

spectrum near the source. Speculations are made as to the

origin of the Xe continuum and the observed Xe spatial

variation. The spectra in this study compare favorably

with those for excitation by other ionizing radiations,

suggesting excitation is due to secondary electrons and

may be relatively independent of the primary ionizing

particle type.







An appendix reports simultaneous optical trans-

mission and luminescence measurements made during a reactor

irradiation of a-Al203 (synthetic sapphire) Transmission

decreased monotonically with irradiation time, being most

degraded in the UV. The luminescence peak centered at

4100A also decreased monotonically. The emission around

3300A initially increased and appeared to saturate, remain-

ing constant thereafter.


XVll













CHAPTER 1


INTRODUCTION


The scientific community has had a sustaining inter-

est in the interaction of fission fragments with matter

ever since the discovery of nuclear fission in 1939. Most

of the early work in the field was empirical due to the

inherent difficulties in treating the problem theoreti-

cally. Today, although fission fragment interactions are

qualitatively better understood, a general theoretical

solution to the problem does not exist, and we continue to

rely on empirical relationships. Fission fragment inter-

actions are one facet of the more general problem of ion-

izing radiation interactions; however, they constitute the

most difficult and least understood aspect of the problem.

Details on the fission process and fragment properties

are presented elsewhere [1]. From an interaction standpoint

fission fragments are distinguished from other charged

particles by their higher mass (~97 for light fragments and

-138 for heavy fragments) and higher initial charge (~+20 e

and +22 e, respectively). The fragments are born with

energies of ~95 and ~67 MeV [21.









The slowing down or interaction of fission fragments

with matter may be qualitatively described over two energy

regions. For high energies the fission fragment is highly

charged and loses energy primarily by inelastic collisions

with orbital electrons of the target atoms; these produce

ionization and excitation of the target medium. Delta rays

produced in ionization reactions (and later generation

secondary electrons) can cause additional ionization and

excitation. As the fragment slows down below velocities

on the order of its electron orbital velocities, it gradu-

ally approaches a neutral state by capturing electrons. In

this region losses by elastic collisions with the target

nucleus become increasingly important and eventually

dominate. Ionization and excitation then occur primarily

from secondary interactions of the recoiling target. In

summary, the fission fragment bombardment results in ioniza-

tion, excitation and heating of the medium, the ultimate

distribution of which is highly complicated, particularly

at higher pressures, because of the numerous secondary

interactions and processes which follow the initial frag-

ment interaction. The research described herein is directed

at enhancing our understanding of the excitation produced

in high pressure (760 torr) gases by fission fragment inter-

actions, with specific emphasis on Ar and Xe.









1.1 Interest in Fission Fragment Produced Plasmas

Research efforts in this field are currently moti-

vated by three major applications. The first, and primary

motivation for this study, is the development of a direct

nuclear (fission fragment) pumped laser. Such a system

potentially offers operational advantages over conventional

electrically pumped systems. The concept and review of

past work are presented elsewhere [3-6]. Only recently has

the feasibility of nuclear pumping been clearly established

by the nearly simultaneous demonstration of nuclear pumping

by University of Florida researchers using a He-Xe mixture

[6-7] and by Sandia Corporation workers using CO [81.

Since these initial successes, nuclear pumping has also

been achieved using a Ne-N2 gas mixture at the University

of Illinois [91. Other nuclear pumping efforts are planned

and some are perhaps underway at this time. So far, how-

ever, nuclear pumping has been demonstrated only at longer

wavelengths and by using high flux pulsed reactors, even

though some of the observed transitions should also operate

in a CW mode. The immediate challenge now is to build a

laser system which will operate in a CW mode. Since CW

flux levels and corresponding input power densities to the

gas will be orders of magnitude lower than for pulse sys-

tems, this task will be difficult. In addition it is

desirable to develop nuclear pumped laser systems which

operate at shorter wavelengths in the visible and in the UV









where higher inversions are required to overcome threshold.

Because of the cost and difficulty involved in performing

nuclear pumping experiments, other simpler methods (e.g.,

spectroscopy) to evaluate possible population inversions

and better understand the fission fragment generated

plasma are essential.

The second motivation for fission fragment generated

plasma research is the development of a plasma core reactor

system [7]. Such a plasma core or "nuclear light bulb" re-

actor, employing presumably some gas mixture containing UF6'

has some attractive features. Removal of the energy from

the reacting volume in the form of optical radiation (per-

haps even coherent) represents direct conversion of nuclear

energy to light, and fission products could be retained on

one side of an optically transparent barrier. Clearly an

understanding of the radiative processes within such a

plasma is an essential input to any system design.

The third area motivating fission fragment generated

plasma research is the field of applied radiation chemistry.

The relatively high energies of fission fragments and their

availability in nuclear reactors make them attractive to

promote chemical reactions. Such a concept has been of

interest for some years and has been reviewed relatively

recently [10].








1.2 Summary of Past Related Work


Although there exist a great many data on fission

fragment stopping powers and ranges in gases, because of

the complex nature of fission fragment interactions and

experimental difficulties, excitation of gases by fission

fragments has not been studied much until relatively re-

cently, and most work has by necessity been experimental.

The excitation data acquired for other charged particles,

however, are of course useful in any study of fission frag-

ments, particularly since it is generally accepted that

most excitation from ionizing radiation is produced by

secondary electrons. In fact the similarity of VUV spectra

excited by 250 KeV electrons and 4 MeV protons has been

clearly shown [ll].

The most applicable analytical work have been efforts

undertaken to characterize the secondary electron energy dis-

tribution. Past studies generally have given the most at-

tention to He, with considerably less effort applied to the

heavier noble gases owing to their complexity. However,

from an engineering standpoint the heavier ones are more

interesting.



1.2.1 Fission Fragment Excitation Experiments


Past experiments to study fission fragment excita-

tion in gases have used two types of fission fragment sources.








The first type uses fragments from the spontaneous fission

of 25Cf which, while convenient, generally suffer the dis-

advantage of low light output and may also not realisti-

cally represent the kinetic effects seen in a plasma of

larger volume excited by a large number of fragments (e.g.,

recombination may proceed by a different mechanism). Some

early experiments conducted by Axtmann and Sears [12] of

this type investigated excitation in N2 at pressures from

28 to 266 torr. They used a PM tube to examine the excita-

tion of the second positive group of the molecular N2 spec-

trum by fission fragments and alphas and found they exhibited

nearly the same efficiency for excitation. They concluded

excitation must proceed by way of secondary electrons. In

1970 Pagano [131 studied several gases (e.g., CF4, AR,

N2) and mixtures as scintillators for fission fragment
kinetic energy spectrometry. He studied integrated light

output as a function of pressure. Also in 1970, Calo [14]

published results of luminosity as a function of pressure

for 25Cf fission fragments in N2, CO2, and CO. None of

the above work with Cf provided any real spectral resolu-

tion. Ongoing 25Cf experiments by Shipman [15] are de-

signed to address this latter problem and may thus demon-

strate the feasibility of acquiring spectral data on

plasmas generated by 25Cf fission fragments.

The second type of experiments used 235 fissions

and a reactor as a neutron source. In 1966 Morse,








Harteck, and Dondes [16] conducted in pile studies using
235
U glass fibers placed in a vessel containing 1 to 3

atmospheres of He, N2, or Ar. The vessel was irradiated

at flux levels of 1012n/cm2-sec. They used a quartz rod

to get the light out of the reactor into the spectrograph

and took photographic data which showed some line structure

and numerous impurities.

The next series of in pile fission fragment experi-

ments were performed by Walters and Schneider [17-18] at

the University of Florida in 1972. Fission fragment exci-

tation of He, Ar, and CF4 was studied spectroscopically

from 25 to 760 torr with and without electric field ampli-

fication. These experiments, although somewhat plagued by

impurities, established the feasibility and desirability

of conducting spectroscopy of in pile irradiated gases.

The pressure data measured by Walters for Ar and CF4 must

be interpreted with care for two reasons. First, his opti-

cal system had a collection efficiency which was a function

of location in his source region. Since at higher pres-

sures this source region was larger than the fragment

range, the collection efficiency is very important and

could easily have caused his observed pressure variations

about 100 torr (the relative spectra he presents for differ-

ent pressures are still completely valid). The second reason

for careful interpretation of pressure data is that close

to the fission fragment source, the fragments (and









secondary electrons) will have a different energy distri-

bution than far from the source, and also the volumetric

energy deposition rate will vary,affecting secondary

reactions. This in turn would be expected to affect

excitation and produce a so-called "spatial variation" of

the excitation depending on the distance from the source

that the optical system is set up to sample at a given

pressure. Resolution of some of these uncertainties in

Walters' data was an important factor in the decision to

initiate the research described herein.



1.2.2 Analytical Studies of Spatial Effects

Theiss and Miley in 1969 [19] and 1971 [20] spe-

cifically consider the problem of predicting the spatial

distribution of primary excitation as well as ionization

source rates in a medium being irradiated by a slab source

of charged particles. The approach is to calculate the

spatial dependence of the energy spectrum of charged par-

ticle currents in the media and use cross section informa-

tion to calculate the primary ionization or excitation

rates. Their work was motivated by the restriction imposed

in preceding studies of spatial variation of ionization

which did not take into account the energy dependence of

the charged particle current in such a way they could make

use of energy dependent cross sections. Miley and Theiss

obtained cross sections for ionization and excitation by









using available data to normalize Bethe-Born cross sec-

tions. The effects of secondary electrons were taken

into account by a pseudo cross section (i.e., all secondary

effects were presumed to occur at the delta ray birth

place). They present data for the excitation of helium

by alpha particles in 1969 and by fission fragments in

1971. Although their data would change if excitation by

recoiling neutrals and delta rays were included, they

clearly show (see Figure 1.1) the importance of the energy

dependence of the cross sections for He. This type of

effect in heavier noble gases is a subject of the present

experimental effort. Experimentally, however, one has the

effects of delta rays and secondaries realistically in-

cluded along with plasma kinetics effects.

In 1972 Guyot, Miley and Verdeyen [21] calculated

the space dependent (in terms of data at a fixed point from

the source but at different gas pressures) delta ray energy

spectrum produced by alpha particles and lithium ions in

helium at various pressures. Their approach was to calcu-

late a spatially dependent energy flux of charged particles

at a point using the previously discussed method of Theiss

and Miley [20] and then employ Gryzenski classical cross

sections (the Born approximation is not expected to give

accurate results because of the low ion velocities). Some

of their resulting calculations appear in Figure 1.2 and


















O



O
O -10.30


tow 0.25
Oz

0- 0.20-
t' -n'S and n'D States \
Z~-(left scale )\
S0.15 .
--- n'P States ( right
W scale )\
0w 0. 10


0.0 5


O 02 0.4 0.6 0.8
REDUCED COORDINATE, Z


Figure 1.1: Effect of the Energy Dependence of the
Excitation Cross Section










CURVE


1000


L CO IO 200
eV








la 200 400 600 800 1000
ENERGY (eV )





Figure 1.2: Delta Ray Energy Spectrum Induced by Alpha
Particles at the Centerline of a 2.5-cm-thick
Helium Slab for Various Gas Pressures [21]









show that the secondary electron energy spectrum will vary

spatially. Unfortunately such calculations for fission

fragments and heavier gases have not been made.



1.2.3 Secondary Electron Energy Distributions


Since most of the observed excitation in fission

fragment generated plasmas has been attributed to the popu-

lation of secondary electrons, several efforts have been

undertaken to characterize their energy distribution. The

only experimental data available were reported by Walters

and Schneider for argon and helium as a function of pres-

sure in 1973 [22]. This is shown in Figure 1.3.

The remaining analytical efforts worked the problem

in terms of a given delta ray source energy. In 1972 Lo and

Miley [23] reported calculations of the electron flux spec-

tra as a function of initial delta ray energy for He, Ne,

Ar, Kr, and Xe. One could then in principle represent

the equilibrium electron spectrum from a real distributed

source by a superposition of results for various delta

ray energies, which for the case of alpha particles has

been calculated [21] and agrees well with Walters' data for

fission fragment excitation of He. Walters' results for

fission fragments indicated an elevated population at high

energies relative to Lo's calculations for alpha particles.























,II lill
I3 l I O' I 101 102 103
ELECTRON ENERGY (eV)


la2 p


ARGON


.64


284 torr
450 torr


760 tort
600 torr


ELECTRON ENERGY (eV)


Electron Energy Distribution in Fission Fragment Excited
He and Ar as a Function of Pressure [22 ]


Figure 1.3:








Wang and Miley reported in 1973 [24] more extensive

results from a Monte Carlo simulation of radiation induced

plasma. They calculated the electron spectra resulting

from a monoenergetic volume source of electrons in helium,

including effects of an electric field. Their model

included ionization, leakage, recombination, elastic

scattering and inelastic scattering. Monte Carlo can

simulate the physical processes involved as well as they

are known; and in the present case this is the major limi-

tation of the method, especially at high pressures where

secondary effects are poorly understood.

Thus the basic analytical techniques to study

electron energy distributions in fission fragment generated

plasmas have been developed and applied to excitation of

helium by alpha particles. What remains to be done is

to apply these techniques to fission fragment excitation,

a formidable problem, particularly in view of the fact

we do not yet qualitatively understand the problem in

most cases of practical interest. The results to date

do, however, provide us insight into the problem.









1.2.4 Experimental Studies of Plasmas Produced
by Other Forms of High Energy Ionizing Radiation


Experimental work has been done on alpha particle,

proton and electron (primarily high energy electron beam)

excitation of high pressure noble gases. Unfortunately

most work has been qualitative in that complete spectral

intensity information is not published in a form suitable

for comparison with other data. Low light levels in the ex-

periments have been an incessant problem limiting the spec-

tral details subject to study. Also data over the visible

spectral range have not been of much concern lately owing

to the great interest in the VUV, stimulated by laser

research. A brief summary of past studies of Ar and Xe at

high pressures and over our range of spectral sensitivity

is listed in Table 1.1. Included are the fission fragment

experiments mentioned in a previous section. Not included

are the numerous experiments concerned with gases or

gas mixtures other than Ar and Xe and numerous studies

solely concerned with the VUV. It is interesting that a

complete optical emission spectrum giving relative line

intensities and excited state populations has not been

published to date in the open literature.

The experimental work using particles produced from

the nuclear decay of various sources generally involves

small volumetric energy deposition rates and plasmas of








TABLE 1.1: SUMMARY OF PAST SPECTRAL INVESTIGATIONS OF Ar AND Xo EXCITED BY IONIZING RADIATION

Pressure
Excitation Gases Range Spectra)
Researchers Mechanism Studied (Torr) Range (A) Comments

W.R. Bennett (25] 5.1 MeV Alpha He, Ne, Ar, 350 2400-5500 Ar: Detected only 2 lines
(1962) particles Kr-, Xe (PM Tube) (3083 & 3093)
239 Xe: State rich spectral out-
Su' put obtained but report
only very general fea-
tures of it.


T.D. Strickler and 5.3 Alpha Ar including 50-2000 1000-5400 Observed only a broad con-
E.T. Arakawa [26] particles mixtures (PM Tube) tinuum centered at 2250A
(1964) 210 and 3093A line
o P


V.W. Hanle, 50 KeV Ne, Ar, KCr, 5-500 Unspecified Present photographic spectra
E. Kugler and Electron Xe but estimated without relative intensity
A. Schmillen [27] Beam Pulse to be 2600- information. Studied time
(1964) 7500 (photo- dependence of segments of
graphic and spectrum using a PM tube and
PM tube with interference filters.
filters)


R. Hlenck and 5.3 MeV Alpha He, Ne, Ar, 350-4560 2000-5000 Observed only continuum cen-
A. Coche [23] particles Kr, Xe (PM Tube) tered around 2250-2575A and
(1965) (210, N2 emissions









Pressure
Excitation Gases Range Spectral
Researchers Mechanism Studied (Torr) Range (A) Comments

S. Dondes, 5.3 MeV Alpha He, Ne, Ar, 780 2400-12000 Present photographic spectra
P. Harteck, and particles Kr, Xe and (photographic) without any line identifi-
C. Kunz [29] 210p N2 mixtures cation or quantitative inten-
(1966) o sity information. Studied
electric field effects.
Ar: Red Arl lines and noted
continuum from 2600-2900A
when cell cooled
Xe: A number of lines and
continuum from 2600-5000A;


F. Morse, P. Har- Fission He, Ar, and 760-2280 2400-12000 Observed photographically only
teckt and S. Fragments N2 mixtures (photographic) 6965A Arl line and mostly N2
Dondes [16] (Reactor) impurity emissions
(1966)


R. Henck and 5.3 MeV Alpha Ar 400-7600 2000-5000 Observed onlyocontinuum cen-
R. Voltz (30] particles (PM Tube) tered at 2250A and N2
(1968)p 21 emissions


G.S. Hurst and 4 MeV protons Ar 50-1400 1000-2300 Include study of continuum at
T.E. Bortner [31] (PM Tube) 2100A
(1969)


Table 1.1 (continued)











Pressure
Excitation Gases Range Spectral
Researchers Mechanism Studied (Torr) Range (A) Comments

G.G. Dolgov-Saveley, 600 KeV He, Ne, Ar 5-760 Unspecified Present intensity versus
V.A. K~nyazev, V.V. Electron (PM Tube) pressure for 7635, 9685,
Kuznetsov [32] Beam Pulse 7503, 8264, 8115, 8015A~
(1969) Arl lines


S. Arai and 500 KeV Ne, Ar, Kr, 200-1180 3500-1600 Measured time dependence of
R.F. Firestone [33] Electron Xe (PM Tube) emission and absorption
(1969) Beam Pulse


P.E. Theiss and 5.3. MeV Alpha He, Ne, Ar 1-760 3300-8500 Observed 6965, 7503, 7724,
GH. Miley [34-37} particles and various (PM Tube) 7635B, Arl lines. Studied
(1971-1975) (210p mixtures pressure and electric field
o effects


R.A. Walters [17] Fission He, Ar-, CF4 25-760 2000-8300 Presents complete spectra.
(1973) Fragments (PM Tube) Studied pressure and electric
(Reactor) field effects


G.A. Carlson [38] 250-300 KeV He, Ar, 02 0.1-10 3500-6300 Present photographic spectra
Electron N air (photographic without line identification
Beam Pulse and image or intensity information.
converter) Studied time and pressure
dependence of emissions.


Table 1.1 (continued)









commensurately low electron densities. The applicability

of the resulting spectral data to more highly ionized

plasmas is not established owing to the secondary kinetic

processes involved. Electron beam and in pile fission

fragment excited plasmas typically have involved electron

densities on the order of 1010-1011/cc. These facts must

be kept in mind when comparing different kinds of excita-

tion data.



1.3 Specific Objectives of This Research


This research project was a part of the University

of Florida fissioning plasma and nuclear pumped laser

program. During the course of this research, the effort

was guided by a number of objectives, not all of which

were clear initially.

The major initial objective was to assess the

importance of the aforementioned spatial variation, par-

ticularly with respect to nuclear pumped laser design and

our basic understanding of fission fragment generated

plasmas. This, of course, implied development of a method

for acquiring in pile spectral data consistent with the

most recent University of Florida training reactor (UFTR)

safety philosophies.








Ar was selected as the initial gas to study be-

cause it would directly yield a checkpoint to confirm

the validity of Walters' [17] measurements, and further

is itself a potential candidate for nuclear pumping. In

fact, nuclear pumping of Ar has been attempted [5, 171 but

with inconclusive results. A fill pressure of 760 torr

was selected partially because the range of a fission frag-

ment in 760 torr Ar is about 1.3 cm, which enables taking

data over the entire fragment path. While other pressures

in this range could have been used, it was desired to

maximize impurity effects for comparison with Walters'

results. 760 torr was the highest pressure Walters used, so

it was selected. The selection of Ar under these condi-

tions also supported the planned work of Davis [39] on

Ar-N2 mixtures.
The next gas studied was 760 torr Xe which, because

of its high stopping power and known laser potential, is of

definite interest in nuclear pumped laser research. Xe

data would further serve as a baseline for future mixture

studies involving this gas.

Initially it was desired to quantify somehow the

amount of light emitted from these fission fragment gen-

erated Ar and Xe plasmas. It later became apparent that

an absolute system calibration was possible enabling cal-

culation of approximate excited state densities. The poten-

tial rewards from such information motivated a combined ana-

lytical and experimental effort to effect this calibration.












CHAPTER 2


THEORETICAL CONSIDERATIONS


This chapter has two objectives. First, an attempt

is made to present a basic theoretical description of the

fission fragment produced plasmas investigated in this

study. This is done by describing the basic processes

thought to be important in the plasma, and indicating the

current status of our knowledge with respect to Ar and Xe.

Second, a theoretical or analytical description of the

actual experiment is presented in terms of energy deposi-

tion calculations, spatial effects calculations (e.g.,

fission fragment spectra) and a discussion of experimen-

tally measurable parameters. The correlation of these

theoretical aspects and experimental results will be pre-

sented in the last three chapters.



2.1 Energy Loss of Fission Fragment
in Gases


Prior to directing our attention to an analysis of

the specific details of this experiment, a brief discussion

of fission fragment energy loss in gases will be presented.

Most of the early analytical work on fission fragment









interactions with gases had as its primary goal the estab-

lishment of reliable stopping power relations. A good

review of both theoretical and experimental work on the

passage of heavy ions through matter was conducted by

Northcliffe in 1963 [40] and more recently by Miley 141].

Our interest, however, goes beyond this in that we would

like to know the ultimate fate of the energy lost by fis-

sion fragments, and even more specifically how much of the

energy results in excitation of the gas, or radiation.



2.1.1 Primary Ionization and Excitation
by Fission Fragments


Qualitatively slowing down of fission fragments can

be described in the following way. At high energies

(E > 30 MeV) the highly charged fission fragments lose

energy primarily by inelastic collisions with electrons

of the stopping gas which directly produces ionization

and excitation of the target gas. Because of their rela-

tively large mass a fragment path is not expected to sig-

nificantly deviate from a straight line in this region.

However, while slowing down, a fission fragment has a

finite probability of capturing or losing an electron dur-

ing one of these collisions. When the fragment reaches a

velocity lower than the orbital velocity of the first

electron, the capture probability becomes very large

relative to that for loss. As the fragment continues to slow









down, electrons are captured until the fragment becomes a

neutral atom. At the lower energies (E > 30 MeV) the frag-

ment may lose energy by elastic collisions with the screened

nuclear field of the atom, and at sufficiently low energies

Buis process is the dominant loss mechanism [14]. In this

region the fission fragment direction may be changed appre-

ciably. Although some electronic interaction may take place

through the quasi-adiabatic interpenetration of the electron

clouds of the fragment and target atom, most of the energy

lost by the fragment at lower energies will appear initially

as kinetic energy of the recoiling gas atoms [42]. Thus,

primary fission fragment ionization and excitation of the

gas is expected to be most significant at higher energies or

during the first part of the fragment path.



2.1.2 Delta Rays and Secondary Electrons


High energy delta rays are electrons inelastically

scattered during the electronic interaction of fission frag-

ments and the target gas. They can have energies up to the

KeV range. For electron energies exceeding the ioni-

zation potential, the ionization cross sections are much

greater than those for excitation. Thus delta rays

can result in numerous additional or secondary electrons.

It is these secondary electrons that are the most im-

portant source of the excitation produced by fission frag-

ments. This means information on gas excitation









by virtually all forms of high energy ionizing radiation is

useful in interpreting and understanding fission fragment

excitation and other forms of high energy ionizing radiation.

Furthermore, as previously mentioned, their energy distribu-

tion function is highly important in determining the excita-

tion that is observed. This quantity would be expected to

vary according to the target gas, gas pressure, incident

radiation and numerous secondary effects. Delta ray (and

resulting secondary electron) excitation effects may be

considered to take place at the delta ray birth point, since

even the range of a 10 KeV electron in 760 torr Ar is only

about 0.1 cm.

The relative ionization yield of a charged particle

is usually expressed by w, which is defined as the energy

of the charged particle divided by the number of ion pairs

produced. This parameter, in principle embodying a number

of complex physical processes, has been found very useful in

practice and will be employed in later sections to calculate

electron source rates. Following the analysis of Platzman

[43], the energy balance for the energy loss of a high energy

particle, T, may be written


T = N.E. + N, E, + N. E 2.1


where N. ions at an average energy expenditure of E., N

excited atoms at an average energy expenditure of E_ and








N. subexcitation electrons having an average kinetic energy

Share produced in the slowing down process. The expression

for w can then be written simply as:



w T E. + N. E + E 2.2



Note that will be eventually dissipated as heat to the

gas. Platzman goes further and points out that for the

noble gases N./N, = 2.5 which is equal to the correspond-

ing cross sections averaged over the degradation spectrum

of particle energies. Clearly most of the initial particle

energy produces ionization. For alpha and beta particles

w has been found approximately constant for a given gas.

A reasonably recent and detailed review of such w values

for various gases is published elsewhere [44]. w values

for fission fragments, however, show a complex variation

with energy and gas type and in particular are higher (ly;

approximately 7%) than values for alpha particles giving

rise to a so-called "ionization defect." This is pur-

portedly the result of the fragment having a variable

charge as it slows and the importance of energy loss by

elastic collisions [45]. However, as pointed out by

Orvis, some of this defect may be due to columnar recombi-

nation affecting the experimental data [461. Since the

w correction is small and columnar recombination effects









will be corrected for in the recombination coefficient, the

correction will not be made here and w values for alpha

particles will be used.



2.1.3 Excited State Kinetics


The expected excited state sources and losses may be

briefly summarized in the following steady state balance

equation for a given state:


[excitation from recombi- + [primary excitation by fis-
nation events] sion fragments)


+ [secondary excitation + [secondary excitation by
by electrons] recoiling gas atoms]


+ (cascading from higher + [collisional transfer of
energy states] excitation to the state]


= radiativee decay from + [collisional transfer out
the state] of the state]


While the above balance can be easily stated it clearly

represents a most difficult physical problem at high

pressures such as in this study.

While primary excitation by fission fragments and

secondary excitation by recoiling gas atoms can be neglected

as noted above, to even get an estimate of secondary exci-

tation by electrons requires knowledge of their energy

distribution function, excited state densities, etc.

Regarding collisional transfer of excitation, it can only








be qualitatively assessed. Cascading from higher energy

states can be estimated only where knowledge of the higher

state populations is available, When there are no radi-

ation trapping effects, the radiative decay is straight-

forward to evaluate. Population of excited states through

recombination events will be discussed in further detail

in a later section on recombination.



2.2 Fission Fragment Plasma Characterization


The purpose of this section will be to roughly

characterize the fission fragment plasmas examined experi-

mentally in this study. The plasmas are typified by rela-

tively low thermalized electron densities which are in the

range of 1011/cc as will be demonstrated in a later sec-

tion and is also consistent with measurements by Walters

[22]. The distinction between epithermal and thermal

electrons is important because the density of the former

will be a linear function of power input to the plasma

(inversely proportional to the w value) while the latter

will be proportional to the square root of the power

because of recombination.



2.2.1 The Corona Model


At these low electron densities the plasmas in

this study are far from local thermodynamic equilibrium








(LTE). The primary (electron induced)excitation and

ionization in the plasma is described by the corona model.

In effect this model assumes that only electron colli-

sions with ground state atoms are important (i.e.,

recombination is ignored for the moment) (47]. Thus the

distribution of ion and excited states is determined

primarily by cross sections. For excited atomic states

one can simply equate the electron excitation and radi-

ative (or collisional) decay rates which yields


n K(p)
=~p 2.3




where n(p) and n(o) are the excited and ground state

atom densities, ne is the electron density, A(p) is the

total (including collisional losses) transition proba-

bility from the pth state and K(p) is an effective (in-

cluding electron energy distribution effects) electron

excitation cross section from the ground state. Colli-

sional sources to the pth state have been neglected, and

it is the collisional sources and losses that prevent the

practical application of the model at high pressures. A

similar relation can be written for ionic states. The

electron ionization rate (including production of excited

ionic species) is set equal to the ion loss rate by








collision and also radiation for excited ions. Recombi-

nation is not considered a loss because all ions are

first converted to the molecular ion which undergoes

dissociative recombination as will be described in the

next section. This balance enables us to write



nz(p) ne K'(p)
2.4
nZ-1 A' (p)



where nz (p) and nz-1 are the densities of the pth ionic

and atomic ground states, and K'(p) and A'(p) are the

appropriate effective cross sections and transition

probability (including collisional effects) for the

ionic states.



2.2.2 Recombination Regime


A recent (1974) in-depth review of the historical

development of recombination to which the reader may wish

to refer has recently been published by Bates [48]. It

includes an excellent list of references on all facets of

the problem. In addition Bardsley and Biondi [49] in 1970

published a detailed review of dissociative recombination

from which much of the discussion to follow is extracted.

A significant effort has been expended in recent years to









determine the recombination coefficients for the noble

gases, and at the pressures and electron densities en-

countered in this study the controlling species are the
+ +
molecular ions, Ar2 and Xe2 Recombination thus proceeds

by way of the following dissociative recombination process

(equations and discussions below will be specifically

written for the case of Ar, but the situation is completely

analogous for Xe):


+ *
Ar2 + e Ar2 (unstable) 2.5


where + and indicate ionized and excited states respec-

tively. The unstable Ar2 immediately dissociates into two

Ar atoms, one of which will be excited as indicated below:


*
Ar2 (unstable) -t Ar + Ar + K.E. 2.6


This process is known to give rise to atomic transitions

observed in afterglows. It has been studied in most

detail for Ne afterglows [50-51] and to a lesser extent

for Ar [51]. The approach in these studies was to measure

the Doppler broadening of the afterglow. lines caused by

the recoil motion of the excited dissociation product.

Most afterglow line shapes were found broader than for the

corresponding discharge lines, indicating that the 2pn








(Paschen notation will be used for Arl and Nel levels)

excited levels of Ar and Ne are produced by dissociative

recombination. Unfortunately only for Ne are the after-

glow line intensities specified. The above process is

illustrated using potential curves in Figure 2.1. Mention

only will be made of one additional such study which in-

vestigated Kr afterglows [52] but which was inconclusive in

establishing the dissociative recombination origin of the

Kr afterglow lines. Analogous processes are, however,

expected to occur in both Kr and Xe.

The radiative processes which follow dissociative

recombination lead to production of 1sn levels. These

levels then collisionally give rise to the Ar2 dimer,

the de-excitation of which is the basis of the recently

developed VUV Ar (53] and Xe [54] lasers. The potential

curves for this process are also shown in Figure 2.1

The relative contribution of dissociative recombina-

tion to the spectral lines (from the 2p, states) observed in

a steady state charged particle excitation situation is

difficult to experimentally assess. Hanle, Kugler, and

Schmillen [27] have studied the time dependence of portions

of the spectra (using filters) of noble gases excited by a

pulsed electron beam. The afterglow they found could be

broken into a fast (representing higher energy electron

effects) and a slow (representing an afterglow situation)

decaying component. Ar and Xe at 100 and 200 torr

















~

e
3


rri

c,
rl
a

id


x

k
ar
d
w

ct
nJ
rl
c,
c
a,
L,
o
e,



























G











Figure 2.1:


A9r +Ar


Arl


Ar +Ar


2pn-1sn
Afterglow
Transitions


1s2

1ss


Transition


Internuclear Separation


Ar2 and Ar2 Potential Energy Curves Showing
Also Arl Levels and Important Transitions
After [51]








respectively were reported in detail. In Ar the ratio of

the amplitude of the slowly decaying component to the am-

plitude of the emission during the pulse over the region
O O
7000-7200A (includes 7067 and 7147A Arl lines) was deter-

mined to be 10%. They conclude the afterglow emissions

arise from either radiative recombination or electron

excitation from metastable levels. In view of the more

recent work on afterglows as already discussed, the former

cause seems correct. In Xe the ratio for various spectral

regions reaches as high as 95%. The large number of lines

(Xel and II) in each spectral region make the data more

difficult to interpret than in the Ar case. They do con-

clude, however, that the lines from Xe primarily result

from dissociative recombination. More definitive informa-

tion at higher pressures has not been published.

The bulk of the measurements of dissociative recombi-

nation coefficients have been made at low electron tempera-

tures and also under conditions where the ion, electron

and gas temperatures are approximately equal. The cause

has been the convenience of working with afterglows. The

recombination coefficient is known to be a function of

electron temperature, Te, and for the case of Ar has been

found proportional to Te6 {55]. Xe hsntbe tde

in this respect, but the temperature variation is probably

not greatly different from the theoretical Te. variation.









Experiments with Ne, Ar and N2 lend support to this assump-

tion [49]. More rigorous model results are available [56]

but are not warranted for use here. The Te dependence

implies that one would expect to find the recombination

coefficient for a gas excited by ionizing radiation to be

dependent upon the electron (including of course all secon-

daries) energy distribution which may not be so simple to

characterize by a single Te value. Given a fixed radiation

source incident upon a gas, this effect would be expected

to manifest itself as a pressure dependence of the recombina-

tion coefficient.

When investigating recombination in plasma created

by highly ionizing radiation, columnar recombination effects

must be considered. when a charged particle slows down and

creates ions and electrons along its path, a certain period

chtime exists (until the particles diffuse significantly

away from the particle path) when the electron and ion

densities will be quite large near the path. During this

time, near the particle track recombination rates will be

much higher than in the bulk of the ionized medium because

of these higher local densities. If one measures the re-

combination coefficient for recombination over the entire

volume based upon the average electron density, it will be

higher than for a uniformly ionized medium such as that

produced by gamma rays. This problem most recently has








been treated theoretically by Orvis [46] and Wilhelm [57].

Experimentally Ellis and Imani [58] investigated the effect

by comparing the observed volume recombination coefficients

for gamma and fission fragment generated plasmas. Coeffi-

cients for fission fragment plasmas were higher by a factor

of 3 to 4. The enhancement due to columnar recombination

effects agreed with that predicted by Wilhelm's theory to

within 4%. For this reason Wilhelm's theory will be used

here to estimate a recombination coefficient for the plasma

in this study.

Following the approach of Ellis and Imani [58] the

recombination coefficient for fission fragment ionization,

a ,can be written as follows in terms of the coefficient

for gamma ionization, a ,


af = a o 2.7
4aDa rn 1+" No



where No is the initial ionization density expressed in ion

pairs per unit length and Da is the ambipolar diffusion

coefficient. A maximum No for Ar and Xe is 1.8x106 and

7.3x106 ion pairs per cm (as calculated in the section on

energy deposition). Da may be calculated from the following

expression [59]








2kT -4 T
D 9 2D p=4.8xl0 9 2.8


where k is the Boltzmanslconstant (8.62xl0-5 eV/oK), P is

the pressure in torr, T is the ion temperature in OK, e is

the electronic charge, and p and p0 are the ion mobility and
+ +
reduced mobility in our case for Ar2 and Xe2 Reasonable
+ 2
values for 90 appear to be 1.9 for Ar2 160-611 and 0.79
2 +
cm /N sec for Xe2 (62]. Corresponding values for Da at

a temperature 4000K (the actual temperature measured for the

Xe case) are .192 and .080 cm2/sec. For Ar at higher

pressures aX has recently been measured by Kaiser 163] and
-6 3
for 760 torr is 3.0xl0 cm /sec. The reason for the

higher a value at high pressure is not known. This result

compares well with those from an investigation of a in the

noble gases from 5-150 torr excited by a beam of 600 KeV

electrons [64]. In this latter study at 150 torr a(Ar) =
-6 -6 3
5.Cul10 and cr(Xe) =1xl0 cm /sec and their variation with

pressure is asymptotic, suggesting these are also good values

at 760 torr. Thus 3.0x10- and lxl0- cm /sec will be used

here for Ar and Xe respectively. For Ar and Xe af is
-6 -6 3
calculated to be 5.7x10 and 3.4xl0 cm /sec respectively.

These values which will later be used to calculate the

electron densities show that columnar recombination is im-

portant in the present situation. That the effect is not

several orders of magnitude, however, is suggestive that









substantial recombination does not occur at extremely high

local electron densities. Most recombination will still

proceed by way of the molecular ions.

There are two sources of Ar2 in the plasma, 3-

body conversion of Ar+ ions by the reaction


+ 1 +
Ar + Ar + Ar -> Ar2 + e + Ar 2.9



and associative ionization by the reaction



Ar + Ar 2> Ar2 + e" 2.10



where k1 and k2 are the appropriate rate coefficients.

Typical values for kl at 3000K are 2.5x10-3 [65] and
-31 -6 -1
3.6xl0 cm sec (66] for Ar and Xe respectively. The

corresponding lifetimes for the atomic ions from this

process are 5.5 and 3.8 ns at 760 torr which are clearly

shorter than the lifetune of the atomic ion to recombination

(on the order of microseconds for our plasma). Recombination

must proceed by way of the molecular ion as previously

assumed.

Associative ionization has also been studied in Ar and

Xe 167]. The thresholds for the process were found to be

14,71 and 11.16 eV for Ar and Xe, respectively. For the

various Ar levels studied the ratios of de-exciting to








diatomic-ion-formation collisions ranged from 2.5 to .13.

Values for Tk2 for various higher excited levels (the

product of the effective radiative lifetime and diatomic-

ion-formation rate constant) ranged from 3.6xl0-1 to
-16 3
1.28xl0 cm .At 760 torr and 3000K the ratios of the

radiative to collisional lifetime may be calculated from

these values and are found to be in the range 96-3440.

Radiation arising from levels above the threshold for

associative ionization is not likely to be observed. Hanle

et al. [27] invoked the process of associative ionization

to explain why in their electron beam excitation studies

the violet Arl lines were so weak compared to the red Arl

lines. While this is probably valid for levels above the

14.71 eV threshold, it is unlikely the 3p, levels would be

affected since all but one of the levels is below this

threshold. Detailed rk2 data for Xe are not available, but

it is probably a safe assumption to say that radiation from

Xel levels above 11.16 eV is unlikely.



2.2.3 Trapping and Optical Thickness


At the high pressures employed in this study trap-

ping of resonance radiation will enhance the branching rates

for decay to lower excited states by preventing escape of radi-

ation emanating from ground state transitions. The effective

lifetime of the trapped states will show a corresponding









increase [68]. In the case of Ar and Xe this means that

the Is2 and Is4 levels will have substantially longer life-

times and higher steady state populations. This makes

these levels along with the Is3 and 185 metastable states

potentially available for excitation by electrons to higher

levels. For a metastable state this is written:



Ar +e Ar + e 2.11



Except for the above consideration the plasmas in this

study may be considered optically transparent owing to the

relatively low excited state densities expected,



2.2.4 Collisional Transfer of Excitation


Although a number of collisional processes are pos-

sible in a plasma, because in our case the plasma is weakly

ionized and excited, only collisions with neutrals need to

be considered. Two such reactions (2.9 and 2.10) have already

been discussed. Of interest in this section are collisions

of the type


At *
Ar + Ar = Ar + Ar + KE 2.12



between close-lying excited states (designated by ** and *).









Such collisions occur with a reasonable cross section for

excited states lying closer than several kT of the gas

apart. In the present case kT 2 .05 ev. The cross sections

would be negligible for states having separations of more

than a few tenths of an eV [25). The above reaction will

have a tendency to cause populations to build up for states

separated from the next lower state by a substantial energy

difference. While the above reaction is almost certainly

of importance in the high pressure plasmas studied, a quanti-

tative assessment of the effects are beyond our present

capability because of their complexity.



2.2.5 Qualitative Summary Description of the Plasmas


An attempt will now be made to put the above indi-

vidual pieces of the picture together in a qualitative way.

The fission fragments produce an electron population to

which all the plasma effects may be attributed. The elec-

tron population will be roughly Mlaxwellian at low energies

(with a temperature close to that of the gas) and have a

high energy component corresponding to the electron slowing

down spectrum. The higher energy electrons produce ionization

(and excited ions) and excitation from the ground state

according to the corona model. Superimposed on the dis-

tribution of ions and excited states as determined by the

corona model are the following effects:









1) 2pn excited state ppulation from dissociative
recombination of A2to which all Ar+ is rapidly
converted.

2) 2p excited state population by low energy
electron excitation of the 1sn long lived states.

3) higher (>14.710 eV) excited state losses by
associative ionization.

4) a redistribution of close-lying states from
collisional excitation transfer.

Xe is purely analogous to the Ar case, although the relative

importance of the various effects may be appreciably differ-

ent.



2.3 Energy Deposition Calculations and Spatial Effects


Previous fission fragment excitation experiments

have used cylindrical fission fragment sources in order to

enhance the volumetric energy deposition. In this study of

paramount importance was the desire to obtain spectra at

different distances from the fissioning source, reflecting

excitation by different average fragment energies and

different volumetric energy deposition rates (and resulting

electron densities). Specifically it was desired to assess

the importance of the fission fragment energy spectrum in

determining the excitation character. As most excitation

is attributed to secondary electrons, this can also be

interpreted as an examination of delta ray energy spectrum

effects. Each of these aspects of the problem will now be

examined analytically.









2.3.1 Energy Deposition Calculation


The geometry for the problem is depicted in Figure

2.2. Essentially we have a finite rectangular plane source

and desire to calculate the volumetric energy deposition at

every point P(x,y,z) in our observation region (i.e., where

the monochromator will be sampling during the spatial

measurements). For a given P(x,y,z) any point on the source

less than one fission fragment range away can contribute to

the dE/dV for that point. The problem is clearly two di-

mensional owing to the lack of symmetry. More specifically

this can be stated as follows:



dE~xy z IdE
gyxV~ z = d-(x'ylz;x ',y)dxsdys 2.13



where As is the area of the source and dE/dV is the volu-

metric energy deposition rate at P(x,y,z) per unit source

area from a point (sx'ys) on the source.

The approach taken here to evaluate 2.13 is to divide

up the source into small incremental areas and for each

point P(x,y,z) sum the calculated contribution to dE/dV

from fragments produced in each incremental area of the

source (in effect a numerical integration). If the origin

of the coordinate system is taken at the center of the










P(x,y,z)


(0,$54 y (x,y,0)

x (x,0,0)


1/2
r = [x2 + x-ys 2 + (z-zs 2]

cosO = where 0 is the angle r makes with the yz plane

n = vector normal to the source plane









Figure 2.2: Geometry for Energy Deposition Calculations
and Spatial Effects Evaluation








rectangular source, dE/dv (x,y,z) need only be evaluated

for positive y and z since by symmetry



dE dE
-(x,y,z) (x, +y, +z) 2.14
dV dV


The following factors must be taken into account in

evaluating dE/dV(x,y,z; xs'Ysn:

(1) Since fission fragments are not emitted iso-

tropically from the source, the angular distribution func-

tion, p(R), is important. p(R) is the probability per unit

solid angle that a fragment is emitted at an angle, 6, from

the normal to the source. p(n) will be independent of 6,

and it is further tacitly assumed here that the average

fragment energy is independent of 6.

(2) dE/dr is a function of range (or fragment energy)

along the fragment path.

(3) The effective length, ar, over which the fragment

deposits energy in an imaginary (and arbitrary) incremental

volume, AV or Axayaz, with the point P(x,y,z) at its center

depends on 6.(Note: This imaginary volume element is only

a tool to better visualize what is happening.)

(4) The effective fragment source rate per unit area

of source, SA, must be related to the source volumetric

fission rate and include the effect of self-absorption.









The energy, dE, deposited in aV by an incremental

area, AAs, of the source at (sx' s) can be written


dE
dE(x,y,z; xs ys) = SA aAA p(R)aR dr r21


where AG is the solid angle subtended by the imaginary

incremental volume.

Based upon an experimental effort investigating the

angular and energy dependence of fission fragments emitted

from UO2 coatings, P(R) is proportional to cos6 [691. The

separation of energy and angular dependence was shown to be

justified for thick coatings, which is true in the present

case (i.e., the 3-micron coating is about one fission frag-

ment range thick). Thus P(R) can be written as a normalized

probability distribution function simply as



p(n) cos 2.16


where the normalization is such that



nJ p(n) dG = 1 2.17



The effective length, Or, can be expressed as a

function only of ax, if we make ay and az large enough

with respect to ax. Specifically, we want to insure









that Ar only intersects the sides of our imaginary volume

at the two planes defining Ax. This is allowed because

AV is completely arbitrary. Thus based on geometrical

considerations one can write



Ar = Ax2.18
cos6


The nR subtended by AV can simply be written in

terms of steradians as



AD= gn 2.19




Upon direct substitution into the expression for

dE and dividing by aV yields the following expression for

the volumetric energy deposition rate at the point P(x,y,z)

due to an incremental area of source, AAs, located at

(sx' s '


cos6 dE
dE
dV(x.y~z; xs' s) = SAAAs r2 dr 2.20


Incidentally, equation 2.13 reduces to a particu-

larly simple form on the source surface (i.e., when x=0):



dE dEl dE
dV{,y,z) =Sgl = 2SZ 2.21
x=0 r=0








The factor of 2 in 2.21 arises because in the increment

ax next to the source, the average track length, ar,

through the region defined by ax is



r = I2 fr2 p(iZ) sin~d~d6 2.22
0 0



27F 7/2
= J Ax os6sin~d~d6 = 2nx
0 0 cos6 CvS


Thus we can write from conservation of energy that



dE dE dE
ax = ar =2 --ax 2.23
dx dr dr


In order to effect a calculation from this point

using either 2.13 or 2.21 one must select an expression for

the specific energy loss of the fission fragments. Owing

to the complexity of the problem a purely theoretical

approach is generally considered impractical and the

following simpler semi-empirical power law [41] for

charged particle slowing is employed


E r
Eo 1 2.24


where Eo and ro are the initial fragment energy and total

range respectively and n is an exponent based on an empiri-

cal fit to experimental data. This expression does have a








theoretical basis (when n=2) but is limited in its appli-

cability to fission fragment slowing because of the im-

portance of nuclear elastic collisions at low fragment

energies. The expression's simplicity and past success

(when n is an empirically derived number) justify its use

here. From this expression we can derive


n-1
dE nE IIr



where the negative sign signifies an energy loss. The

experimental range energy data of Fulmer [70] for light and

heavy fission fragments in Ar at 760 torr wr~e fitted to

determine the best average value of n. It was found to be

1.38. By interpolation of the data reported by Kahn, H~ar-

man and Forgue [71] for a 3-micron UO2 source thickness the

relative fragment escape energy, R, was found to be .56.

Using 83 MleV for the average fission fragment initial (upon

fissioning) energy, the escaping fragment will have an

average energy of 46.5 MeV. Again using Fulmer's data [70],

a corresponding average fission fragment range, r was

found to be 1.32 cm. For Xe, lack of experimental data

necessitated selecting n=1.38 on the basis Xe and Ar

would not be expected to have radically different slowing

down mechanisms for fission fragments. The average range,

ro, for Xe was found to be .40 cm based on that for Ar and








the assumption that the range is inversely proportional to

gas density [4l].

Calculation of the effective fragment source rate,

SA, or average number of fragments per second per unit area
is straightforward. It is simply written as


SA = NE~t 2.26

where N = number of density of 23U in the source (2.07x

1022/cc for 93% enriched UO2]
235
a = average U fission cross section (330 b for

a neutron temperature of 2600C)

S= reactor thermal flux in UFTR (2xl012n/cm2-sec)

t = source thickness (3xl0-4 cm)
9 2 -1
SA is thus calculated to be 4.1xl0 cm sec .Also
using 2.21 and 2.26 the volumetric energy deposition rates

on the source surface (the maximum value anywhere in the
volme is4.x117an 1.3xl018 eV/cc-sec for Ar and Xe

respectively. Assuming w values of 26.3 and 21.9 eV [44]

the corresponding average initial ionization densities

(calculated by dividing dE/dr by w) along the fragment

tracks will be, using 2.25, 1.8x106 and7.x6iopar/m

The volumetric energy deposition rates were numeri-

cally calculated using the procedures indicated above at

various points in the volume. Figures 2.3 and 2.4 illustrate

























C
U
Q,
V)
I
U
U


.2 .3 .4 .5 .6 .7 .8 .9 .LO 1.1 1.2

x ( cm .)


Volumetric Energy Deposition Rate as a Function of Distance x from Source
Where y = 2 = 0, 4 = 2xl012n/cm2-sec, and t = 3pm


Figure 2.3:


































Z (cm)

Volumetric Energy Deposition Rate as a Function of Distance z from
Centg of source (Toward Edge) Where y = 0 and x = ro/2, 4 =
2xl0 ~n/cm -sec, and t = 3pm


Figure 2.4:








the distribution in the x and z directions. Effectively

dE/dV(x,y,z) is independent of y except within one fragment

range of the end of the source. Also because the height of

the monochromotor slit is roughly equal to the source width,

the z variation in actual measurements will be small (i.e.,

in Figure 2.4 only z values less than .8 are sampled).

The x variation is the controlling factor in the volumetric

energy deposition rates sampled.



2.3.2 Thermalized Electron Density Calculation


Since diffusion losses to our recombination dominated

plasma may be neglected the steady state balance equation

for electrons may be written


dn 2
dt 0 =S -a fne 2.27


where S is the electron source rate and ne is the electron

density. Solving for ne and expressing S in terms of the

volumetric energy deposition rate yields

1 1

n = -- = |' r 2.28
e f a a w~ dVd


This expression was evaluated at various points in the

plasma volume. The value taken for af was the average of

the columnar recombination coefficient over the fragment








range (i.e., the average of the maximum and minimum a().

To work the problem more rigorously would require treating

each fragment for columnar recombination since fragments

reaching a given point have different energies and thus No

values. The values used were 4,4xl06 for Ar and 22l-

for Xe. The variation of ne with distance from the source

is depicted in Figure 2.5. The variation of ne as a function

of z can be seen from Figure 2.6. Note that the effect in

both cases is to reduce the apparent variation in terms of

a percent of the maximum n .
It is interesting to note that the maximum value of

ne does not necessarily occur where dE/dV is largest,

since arf will in actuality depend upon what parts of the

individual fragment paths are contributing to the calculated

dE/dy. They could have significant impact on the design

of fission fragment excited systems at high pressures

(where No is high) where maximizing ne is important.


2.3.3 Fragment and Electron Energy Spectra


Every point in our volume has been characterized by

a particular dE/dV and n, value. In addition, the fission

fragments and secondary electrons will have a particular

energy distribution characteristic of the point. The sig-

nificance of the secondary electron spectra has already been

discussed. Of most importance here will be the high



















I Ar










101(


O .2 .3 .4 .5 .6 .7 .8 .9 1.0 LI I.2
x ( cm.)
Figure 2.5: Electron Density as a Function of Distance x from Source Where y = z = 0,
O = 2x1012n/cm2-see, t = 3pm

































. 2 3


. 6 7 8 9 I.0


Z ( cr.)


Figure 2.6:


Electron Density as a Function of Distance z from Center of Source
(Toward Edge) Where y = 0 and x = r /2,4 = 2xl012n/cm2-sec,
and t = 3pm









energy part of the electron spectrum (i.e., that from the

slowing down of delta rays), since the Maxwellian part of

the spectrum should be relatively unaffected by the ini-

tial delta ray energy spectrum. It was this sort of energy

dependence which produced (through the energy dependence

of the cross sections) the spatial variations analytically

observed for primary alpha particle processes by Theiss

and Miley [19-20].

Calculation of the energy of fission fragments

losing energy at a particular point is relatively straight-

forward. The energy spectra of electrons ejected in the

resulting ion-atom collisions, however,have not been

studied for collisions between high energy ions having a

mass typical of fission fragments and lighter atoms such

as Ar and Xe. A review of available data was made by

Ogurtsov in 1972 [72). He presents some data for Ar -Ar

collisions, and data for Xe -Xe collisions are also avail-

able [73]. These data would be applicable to a study of the

ionization produced toward the end of the fragment path where

ionization is produced by recoil gas atoms from nuclear elas-

tic collisions between the fragment and gas atom. Unfortun-

ately, it does not help solve the most important problem of

primary interactions. This discussion is merely intended to

point out that at the present time sufficient data do not

exist to determine with any degree of confidence the delta








ray spectra arising from fission fragment interactions.

Ogurtsov 1721 points out that modeling of collisions be-

tween heavy atomic particles does appear promising, so

solution of the problem may not be far off. Qualitatively

we do know that delta rays will range from the eV to the

KeV range. The distribution will always favor the lower

energies, but for higher fragment energies the spectrum

will be hardened considerably.

Since based upon the above discussion, one can only

make qualitative observations based upon the fission frag-

ment energy, this will be investigated in more detail.

Instead of looking at an energy spectra we will look at the

spectrum in terms of r/ro which directly yields a fragment

energy spectrum based upon a range energy relation such as

2.25, the semi-empirical power law. The problem can then

be worked in general terms and apply to any stopping

medium. Also to avoid specifying the exponent, n, in 1.21

the problem will be worked for n=1 and n=2 which bounds any

practical problem one might expect to encounter. The

objective of the remainder of the section will be to develop

insight into the problem sufficient to enable interpreta-

tion of the experimental data. We wish only to know

roughly how much the fragment energy spectrum varies as

sampled different distances from the source.








At any given point, P, in our volume a distance x

from the source, no fragment can reach P without having

gone at least a distance x and no more than a distance

r the fragment range. Of interest is what the distribu-

tion is for r/ro for the fragments which are losing energy

at the point P. Furthermore it is desirable that the dis-

tribution function be weighted by dE/dr since we are in-

terested in what the r/ro (-or energy) distribution for the

fragments which deposit most of the energy at P, not those

that just barely reach P. Also one must consider angular

distribution of the emitted fragments, p(n), which is

taken as before to be proportional to cos6. The assumption

is now made for simplicity that the source is an infinite

plane. This assumption is considered justified for two

reasons. First, experimentally we only sample the region

directly in front of the source, so the calculated results

(i.e., ^/r ) will be worst case. Specifically P will actu-

ally be closer to x than what we calculate because for a

finite source, the maximum distance from which a fragment

may arrive at P can only be less than ro. Secondly, only

results for small x/ro values will be affected since as x

approaches r only a small area of the source nearest P
will contribute to the result. This effect is further

amplified by weighting the distribution by dE/dr and








Assuming an infinite source, the only part of the

source from which a fission fragment can reach x is a

circle defined by a line which is a distance ro from x.

The geometry of the problem is depicted in Figure 2.7.

In this figure ro is the radius of the circle of the source

from which fragments can reach P and r' is the distance

from the center of the circle to the source coint a dis-

tance r from P. The unnormalized distribution function,

f(r'), which represents the relative number of fragments

which reach P from a radius r' on the source weighted by

cos6 and dE/dr can be written by inspection as


cos6 d
f~r') =-2 drr 29



We are interested in f~r) which requires the following

relation between dr' and dr':



dr' _d 2 2 j=r 2
dr dr r'J


The expression for f(r) is now found from the relation



f(r)dr = f(r')dr' 2.31



to be simply


cos6 dE x dE
f~r) --23
r dr 2 I23




























SIDE VIEW OF SOURCE


FRONT VIEW OF SOURCE


Figure 2.7: Geometry for Calculation of Fission Fragment Path Length Distribution Function









Dropping the x since it is not a function of r yields



f ( r ) 1 d d 2 3 3



Now using 2.25 with n=1 and 2 for dE/dr and retaining only

the r dependence produces the following relations where it

is understood that x < r < ro

for n=1:

f(r) 2 2.34



for n=2:


1 1
f(r) =2.35
2 rr
r o


These can be conveniently normalized by dividing the above

expressions by their integral from x to ro
for n=1:

2 -1
f~r) = -2 -'-1 2.36



-for n=2:



[2 ---1
f 1r -- I -1i 2.37
f~) r r i ~ r x11 xn









It is convenient to rewrite these relations in the follow-

ing form for computations where the range of validity is

b < a < 1 for n=1:



rof-(r) =al 2.38



for n=2:



rof(r) = alabl1 2.39



where


r r
O O
a = -and b-
r x



The function r f(r) for n=1 and 2 is plotted in Figures

2.8 and 2.9. The curves for n=1.38 would fall somewhere

in between those shown.

The purpose in presenting these plots is to show

(by examining the spectrum of path lengths traveled)

roughly the energy spectrum resolution that was achieved

in this experiment. It is quite good for small x because

of the cos6 term (discriminates against longer r values)

and good for large x (i.e., as x approaches r ) because

all fragments reaching x must have gone a distance between

x and r For x values inbetween these extremes the





E r


~= .875


1.0
o7 fo1


6-70

4X -


2- -






O .1 2 3 .4 .5 .6 .7
r/rTo or )

Figure 2.8: rof(r) as a Function of x/ro for n=1


.8 .9


































Figure 2.9: rof(r) as a Function of x/ro for n=2









resolution is not as good. The important point here is

that it is possible to sample the beginning and end of the

fragment paths.

Incidentally, the above expressions can be trans-

formed into distribution functions in terms of the fission

fragment energy, h(E),

For n=1:


r f(r)
h) OE-- ; Eoh(E) = rof Ir) 2.40


For n=2:


r f~r) r f(r)
h(E) _o ;E h(E) _o g 2.41
2JE o 2 o
o E

For the case where n=1 Figure 2.8 already directly shows

the energy spectrum with the plot running from high to low

energies. The case for n=2 is shown in Figure 2.10. The

plots of E h(E) in effect illustrate the same things as

those for r f(r). One can further calculate an average

energy /EO as a function of x/ro in the following way

r2
E 1 Ef(r)dr 2.42
o ox

This information is plotted in Figure 2.11 for n=1 and 2

and results from straightforward application of the above

equation.











= .05


4~ -

3 -









O .1 .2 .3 4 .5 ,6 .7 .8 .9 1.0
E/E. c
Figure 2.10: Eoh(E) as a Function of x/ro for n=2





















0


.5


.9 LO0


O .1 .2 .3 .4 .5


X /Ro

Average Relative Fragment Energy as a Function of x/ro


Figure 2.11:









2.4 Discussion of Experimentally Measurable Parameters


The purpose of this section will be to briefly relate

the theory already presented to the parameters we can experi-

mentally measure. Included also are short discussions on

pressure dependence and electric field amplification as

these were investigated in previous studies which have

obvious impact on the interpretation of the data acquired

in this study.



2.4.1 Spatial Variations


Sampling spectra at different distances from the

source effectively samples different volumetric energy

deposition rates, electron densities, fission fragment

energy spectra, delta ray energy spectra, secondary elec-

tron energy spectra (particularly at intermediate and high

energies), and columinar recombination effects (ionization

per unit path length will be higher for fragments near the

source). Interpretation of any spatial variations must

rely upon assessing the importance of these several vari-

ables either by measuring some other plasma parameter or

analysis.









2.4.2 Emission Intensity as a Function
of Reactor Power Level


The volumetric energy deposition rate and square of

the thermalized electron density are proportional to reac-

tor power. Linearity with reactor power would be expected

for recombination processes (i.e., dissociative recombina-

tion) and excited atomic and ionic lines if high energy

electrons (before they are sufficiently thermalized to

undergo recombination) directly excite them from the ground

state. Essentially what this says is that the number of

high energy electrons slowing down is proportional to

power. For excitation from an excited state (e.g., meta-

stable) whose population is linear with power, the upper

excited state populations would be expected to be non-

linear unless these levels were in LTE with the lower

excited state.



2.4.3 Pressure Effects


An increase in pressure will increase the recombi-

nation coefficient, columinar recombination, and colli-

sional effects (e.g., collisional de-excitation) as well

as reduce the volumetric energy deposition rate and elec-

tron densities. Experimentally in past studies these

latter two effects have been difficult to assess owing to

source geometry and stopping power effects.









2.4.4 Electric Field Amplification


The addition of an electric field is simple at

least in that it will only influence electrons and harden

their energy spectrum. This will in turn result in
-5
decreased dissociative recombination according to T

and increased excitation and ionization due to the in-

creased relative population of higher energy electrons.

The low energy part of the electron spectrum (the bulk of

the electron population) will be affected and the important

parameter is E/P.



2.4.5 Temperature Effects


In the reactor the irradiated gas will heat up by

approximately 1000C and emission intensities can be

monitored during heating. Heating will increase atomic

collisional rates and also raise the thermalized electron

temperature slightly.














CHAPTER 3


EXPERIMENTAL SYSTEM DESCRIPTION


3.1 Design Considerations


The system employed by Walters [17] to make his

spectral measurements proved quite effective and had the

advantage of simplicity. It also provided the capability

of changing the pressure of the irradiated gas while in

the reactor. This did, unfortunately, require a large

system with long pumping distances, thus limiting his ability

to control impurities. But by the time the present effort

was initiated, new local safety requirements existed which

negated use of Walters' basic design, so an entirely new

system had to be designed and built anyway. Walters' work

did, however, have significant impact on the entire system

to be described below.

A primary objective of the experiment was to provide

the capability to measure spectra at different distances

from the fissioning source. This required a plannar source

of fission fragments and an appropriate optical system to

sample a well-defined region at a desired distance from

the source. In addition it was desired to effect an absolute

calibration of the system, so a simple optical system,









ammenable to analysis, was important. Since in all past

studies the effects of impurities could not be eliminated,

it was desired to maximize gas purity. This suggested a

small gas volume in a capsule that could be carefully

evacuated and filled under controlled laboratory condi-

tions. The experimental system design also had to consider

the following factors normally encountered in these types

of studies: low expected light output, high noise level

from gamma radiation around the reactor, radiation damage

to in core components, possible system overheating from

the fission source, and current UFTR safety philosophies.

With respect to the last factor, of most importance is the

requirement that the experiment provide double containment

of fission products. This considerably limited design

alternatives and practically eliminated any gas handling

while the system was in the reactor.

The construction of a horizontal thruport (HTP)

in the reactor on a timely basis to support this research

proved of immense value. Besides the convenience of being

able to work at waist level, experiment loading and unload-

ing, radiation shielding, system calibration and optical

alignment were all greatly simplified. Had this work been

attempted in the UFTR center vertical port (CVP), the ex-

periment would have been significantly more complex and

time consuming, with some parts being impossible to carry

out.









3.2 Overall System Concept


The final result of the above design considerations

was the Multipurpose Capsule for Irradiation of Gases

(MCFIG) system shown in Figure 3.1. The MCFIG system

basically consists of a small capsule (the MCFIG) having

a sapphire window mounted in the end and containing a UO2

fission fragment source. The capsule is evacuated and

filled prior to insertion in the test tube assembly. The

test tube is an aluminum tube which extends through the

HTP and is sealed at each end by use of end caps which have

quartz windows for light transmission as shown in Figure 3.2.

Two lenses which are part of the optical system are also

mounted inside the test tube. After the MICFIG is loaded

inside the test tube from the west end of the UFTR and

the end cap replaced, the test tube is evacuated to a

pressure of approximately 10-2 torr using a pump located

at the west end and then isolated prior to reactor start-

up. The test tube provides secondary containment should

the MCFIG somehow leak, the test tube pressure being the

primary diagnostic tool to detect it. When a thermo-

couple was located on the MCFIG it was monitored by in-

strumentation at the west end of the UFTR.

Once the test tube was isolated the reactor was

brought up to power. The neutrons induced fissions in the

planar UO2 (aligned parallel to the monochromator slit)
















W <------ E


Shielding

Mirror


Fuel Boxes


Test Tube


Readout


Beam


Lens


Thermocouple


MCFIG


CI T1


Sapphire
Window
on MCFIG


Vacuum


Window
Inside
End Cap


Re ctor


Lead
Shielded
PM Tube


Lens /
Monochromator
Figure 3.1: Overall Layout for MCPIG Gas Irradiation Studies




CONFIGURATIONS
I) CHECK GAS SYSTEM INTEGRITY FOR
LEAKS: A AND 8 CLOSED, C OPEN.
2) EVAC UATE TEST TUBE: .A AND C
OPEN, B CLOSED.
3) ISOLATE TEST TUBE DURING REACTOR
OPERATION: B AND C CLOSED, A OPEN,
4) FLUSH SYSTEM WITH He: A AND B
OPEN, C CLOSED.


WINDOW OR
THERMOCOUPLE
FEEDTHROUGH
AS REQUIRED


HELIUM
BOTTLE
FOR
FLUSHING.




VACUUM GAGES


EAST END CAP -


TEST TUBE


LENS


WINDOW


L~PUMFP TO REACTOR STACK
VACUUM I. EXHAUST VIA APPROPRIATE
PUMP 17
I FILTERS
Figure 3.2: Test Tube End Cap Details and Gas Handling System








source which emitted fission fragments into the gas. As

the fragments flow in the gas the light emitted passes

through the MCFIG sapphire window and is collected by the

optical system consisting of three lenses and a rotatable

mirror (for looking different distances from the source).

The light is focused on the monochromator slit where the

spectrum is analyzed by measuring the output current of

the photomultiplier and displaying it on an X(-Y plotter.
Shielding or otherwise reducing the effects of re-

actor produced gamma radiation on the photomultiplier is a

perpetual problem in experiments around reactors. A total

system approach was taken here and may be of some future

interest as a significant level of effort was applied to

the problem. The approach consisted of the following

measures: (1) by shielding, minimizing the general radi-

ation level in critical areas; (2) positioning the photo-

multiplier as far as practical from the reactor and away

from hot spots; (3) shielding the photomultiplier itself;

and (4) using a low pass filter to discriminate out the

gamma noise. Only (1) will be discussed here, postponing

discussion of the other approaches until later sections.

With respect to area shielding, the west end of the

UFTR proved a minor problem since little personnel activity

takes place there. The only requirement was to reduce radiation

levels outside the UFTR building to within allowable









limits. Berated paraffin blocks, steel bricks, and a

large concrete block proved generally sufficient. At the

east end the shielding had to reduce levels in the working

areas (and the experimental instrumentation) to much lower

limits as well as provide a reasonably large aperture for

light to reach the monochromator. Several approaches

failed, so a beam trap w~as constructed and efforts made to

minimize placing material in the path of the beam emerging

from the HTP and entering the trap. This approach was

highly successful and also permitted easy access to the

mirror and its rotation assembly.



3.3 MCFIG Details


The M~CFIG is essentially a piece of stainless steel

tubing with a commercially available sapphire window welded

in one end, and a valve and thermocouple port in the other.

This is shown in Figure 3.3 with the exception of the

thermocouple port. A MiCFIG costs about $150 to produce and

can be reused several times depending on the degree of

activation. Stainless steel was used primarily because of

availability, machinability and cost; also it possesses

good vacuum characteristics. Its main disadvantages are

that it becomes highly activated when irradiated and has

a high reactivity worth. A special MCFIG shielded

transporter (MST) had to be constructed and procedures





















LIJ- -t~J~


Figure 3. 3: Multipurpose Capsule for the
Irradiation of Gases (MCFIG)


Li_____.625~









developed to overcome the activation problem. Reactivity

worth was not a problem in this experiment but should be

evaluated for any future work to insure the reactor can

achieve criticality with the system in place. The MCFIG

radial dimension was determined essentially by the HTP

dimensions. Two different lengths were used. The Ar data

hare taken with a short system which subjected the sapphire

to the high flux region. Luminescence and damage (see

Appendix A) to the sapphire resulted, consequently for Xe

measurements the MICFIG was constructed in a way to keep

the window out of the high flux region.



3.3.1 Valve and Thermocouple Port


The valve employed was a Nupro SS4H2 bellows type

valve which was specially modified so that it would fit

within the test tube inside dimension (1.709"). A valve

was used instead of a pinch off seal to facilitate handling,

particularly during recycle procedures when an irradiated

capsule had to be evacuated and refilled. The thermocouple

port was a small tube sealed on the inside of the MCFIG

which served as a receptacle for a thermocouple. The tube

was located just behind the UO2 source so as not to inter-

fere with the optical collection of light. The temperature

was measured only on the Xe filled MCFIG and found to reach

approximately 2500F, which is not significant from a MICFIG

structural standpoint.








3.3.2 Sapphire Window


The sapphire window was selected primarily because

sapphire is relatively resistant to radiation damage and

commercially available in a mount weldable to stainless

steel. Unfortunately the luminescence observed from this

material (see Appendix A) came as a surprise and necessi-

tated additional effort to quantify and understand the

luminescence and absorption effects. However, now that

these effects are well defined there have been additional

benefits such as use of the MlCFIG for UFg irradiation

studies in which quartz windows would be unacceptable.



3.3.3 UO2 Source


The fission fragment sources were 3-um thick 93%

enriched UO2 coatings on zircaloy plates which were ob-

tained courtesy of Los Alamos Scientific Laboratory. UO2

was selected as the coating material because of the

availability of information on it. The energy spectrum of

fission fragments as a function of coating thickness was

studied by Kahn, Harman, and Forgue [711 in 1965 and their

data for a 2.53 um coating appear in Figure 3.4. A 3-um

coating thickness was selected on the basis of their data

for average fragment escape energy, EAVG, and escape frac-

tion, PE, as a function of coating thickness. Specifically













































20 30 40 50 60 70 80 90 100 110 120


ENERGY ( MeV )


Figure 3.4:


Energy Distribution of Fission Fragments
from a 2.53-Micron-Thick, 93% Enriched CO2
Coating [71]









assuming a constant flux, the total energy of fragments

leaving the foil, ET, is proportional to EAVG' PE, and the

coating thickness, t.



ET = EAVG PEt 3.1



A plot of this relation for their data yields Figure 3.5

where ET has been normalized such that the maximum possible

energy input to the system is unity, thus representing a

coating effectiveness. The asymptotic behavior of the curve

is the direct result of the fact that fragments born more

than one fragment range in U02 from the coating surface do

not leave the coating. Clearly not much of an increase (only

12%) can be obtained by going to coatings beyond 3 um, and

thicker coatings would increase the heat generation in the

MCFIG and post irradiation fission product activity in

direct proportion to the thickness. The secondary electron

production from UO2 coatings (created as the fragment passes
through the coating) has also been studied by Anno [74].

He found an average of 300 electrons emitted from the coat-

ing surface per emitted fission fragment for a 3 pm coating

thickness. As their average energy ('20eV) is low their

effect is negligible relative to the energy of the fission

fragments (~46.5MeV).













I2 %


80 I

S70

> 60

so 5
LL
LL
OJ 40

z 30

O 20

10-


I2 3 4 5 6 7 8 9
UO2 COATING THICKNES (um )
Figure 3.5: Coating Effectiveness as a Function of Thickness




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs