Title: Applying the pulsed ion chamber methodology to full range reactor power measurements /
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Title: Applying the pulsed ion chamber methodology to full range reactor power measurements /
Physical Description: x, 101 leaves : ill. ; 28 cm.
Language: English
Creator: Kaiser, Bruce John, 1950-
Publication Date: 1977
Copyright Date: 1977
 Subjects
Subject: Fast reactors   ( lcsh )
Nuclear Engineering Sciences thesis Ph. D   ( lcsh )
Dissertations, Academic -- Nuclear Engineering Sciences -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaf 99.
Statement of Responsibility: by Bruce J. Kaiser.
General Note: Typescript.
General Note: Vita.
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Bibliographic ID: UF00099391
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 - 000187959
oclc - 03418177
notis - AAV4563

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APPLYING 3'HE PiUSED 10N CH2AEk METHODOi..[O1

TO FULL RANGE REACTOR I .. ;EASURFMENTS














BRUCE J. 'A3,SER


















4 ODSSERTATION PRESE.NTEDi T H TH: .PTLATF COUNCIL OF THE
UNIVErIS TY OF FiCRIDA
IN PAiT AL FULLFILLi'NT OF THE F, TP,- Q'INTS OR THE
DEGREE OF DOD.702 OF PFI 05CPHY


UlERl '; Y OF rLAU..l
197













A CNOWLMEDGLM?.TS


The author is especially indebLed to his committee chairman Dr.

William Ellis, whose input, guidance, and encouragement in this long

endeavor proved invaluable. Thanks is also extended the other members of

his committee, Dr. E. E. Carroll, Dr. N. J. Diaz. Dr. G. R. Dalton,

Dr. W. Mauderli a.nd Dr. C. K. Day for their interest anid support.

Much of the work to be described herein was performed at the H3nford

Engineering and Development Labcratory. The author is deeply indebted to

Dr. Ciiff Day and the Instrument Technology group at Westingho:use Haniford

whose avid su,-ort made the work possible.

Ackniowledgement is expressed for the financial SUopori: received from

a U!ive:.ity of Florida teaching assi:stiatship i;,d a NorthwesL College

and University Association for Science fellowship.

Final' words fail to express the (harks which is extended to tne

author's wife, Michelo. Her patience:, love, crd financial support proved

to be the difference b(-rween success and failure.













ABLE OF CONTENTS

Page

AC O L GEMEN S . . . . . . . . . . ii

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

LIST OF FIGURES . . . . . . .

ABSTRACT . . . . . . . . . . . ix

CHAPTER 1. INTRODUCTION . . . . . . .

CHAPTER ii. PULSED IONIZATION CHAMBER OPtRATIONAL THEORY ..

CHAPTER III. PIC POWER REACTOR MEASIJUREMNT SYSTEM . ... 27
PIC Eiectronic System . . . . . . . . .. 29
Detector Selection ....... . ........... 4

CHAPTER IV. EXPERIMENTAL PROCEDURES, RESULTS ANP METHrODS
OF DATA PROCESSING . . . . . . .... 43
initial System Setup ... . .......... ... 43
Experim;entali Measurements and Resuts ... . .. .... 44
Gasmma; C:r'rpernstion ....... . .... . 44
P'C Cnam.rer Temperaturc Response .... . . . . 5.
Source of Errors . . . . . . . .. 79

CiAPTER V. CONCLUSIONS . . . . . . . .... . 81

APPENDIX . . . . . . . . . . . . 83

REFERENCES . . ...... .. .. .. . 97

BIOGRAPii CAL SKETCH ....... . . . . ... . 9.













LIST I F TABLES


Tahib e Page

4-1 Gar;nvi Conopensatior Dato 53

4-2 Neofl Data 7'!

4-3 Aroon Dati 11













LIST OF FIGURES


Figure Page

1-1 Typical environmental profile for neutron sensors in
c PiR at full power ana at shutdown. 3

1-2 typical ranges and detectors used :n ex-core systems to
,cover the source, intermediate and power ranges. 5

1-3 Typical ranges and detectors used in in-core systems to
cover the source, intermediate and power ranges. 6

2-1 Results of PIC system with 1 atmosphere 3He chamber. 12

2-2 Charge density within a 1 atmosr;here ar-non filled
miniature missionn chamber. S = 107 ion pairs/sec, 3000K. 17

2-3 Charge density within 1 atmospnere argon filled minia-
ture fission chamber. S = 1013 ion pairs/sec, 3000K. 18

2-4 Pulse height versus source rate. 1 atimosphe-i: argon-filled
iriniature fission chamber at 3000K. 19

2-5 Pulse height versus source rate. 1 atlmosphere noon-filled
miniature fission chamber at 300K. 20

2--6 Gamma Compensation as a function of" gamma field strength. 23

2-7 Mean ievel ionization current as a function of reactor power
(neutron flux) and gas temperature for 1 atmosphere 4He-
filled fission chamber. 24

2-S Pulsed ionization chamber signal voltage as a function of
reactor poter (neutron flux) and gas temperature for a
1 atmosphere 'He-filled fission chamber. 25

3-i Biock diagram of full range single sensor reactor poi;er
measurement system. 28

3-2 Block diagram of the prototypic digits computer base PIC
reactor power control system. 31







_F., .,ES _o,, .d)

Figure Page

3-3 Photographs depicting the PIC system. (A) depicts the
entire digital computer hW d N'C s.'stct.l. (8) shows
somr. of the internal circuit layout of the hi:h volt-
age pulser and raw data acqiiis/ition systems. 32

3-4 The PIC so'id state high voltage pulser (HVP). 33

3-5 PIC equivalent circuiT wit! pulsing sequence. 34

3-6 The PIC raw data acquisition system. 38

3-7 RSN-34A-Mi fission chaM!er used in UiiiK; research. 42

4-; Wlestinghouse Hanford 230 kCi 1"Co irradiation facility. 45

4-2 Exposure rate versus vertical position for port 6 of
the 60Co facility. 46

4-3 Steady state current versus exposure rate. 1 atrmusphere
Ar-5% N,_-filled RSN-34.-il fission ch3:rbers. 48

4-4 PIC voltage signal versus exposure rate. 1 atmosphere
Ar-5% N2-filled RSN-34-M1 fission chambers. 49

4-5 PIC voltage signal versus steady state current. 1
atmosphere Ar-5% N2-filled RSN-34--MI fission chambers. 50

4-6 Gamma Compensation as a function of exposure rate. 54

4-7 Cross sectional view of the oven built to accommodate a
matched pair of RSN-34-M1 chambers. Maxii.um temperature
55GC. 56

4-8 PIC signal versus steady state ioniza tici current for 2
atmosphere Me-filled gamma sensitive (4) and neutron-gamma
sensitive (l) chambers at the temperature 250C. 57

4-9 PIC signal versus steady state ionization current for 2
ait.msphere tie-filled gamma sensitive (4) and neutron-gammna
sensitive (M) chambers at the temperature 71"C. 58

4-10 PIC signal vrsus si:eady state ionization current for 2
atmosphere Ne-filled gamma sensitive (i) and neutron-gamma
sensitive (La) chambers at the temperature i29C. 59







FIGU eS_(Curt d)

Fiygues Page

4-1i PIC signal versus steady state ionizatinn current for 2
tmr.osphere Ne-filIed gamma sensitive ( a) and n-eutron-gamma
sensitive (Q) chambers at the temperature 179C. 60

4-12 PIC signal versus steady state ionizatisn curreilt for 2
atmosphere Ne-filled gamma sensitive i+) ard neutrn-gemima
sensitive (0) chambers at thP temperature 217C. 61

4-13 PIC signal versus steady state ionization currea.t for 2
atmosphere Ne-filled garmmn sensitive (+) and neutron-gamma
4-15 sensitive (n) chambers at the temperature 2820C. 62

4-!1 FIC signal versus steady state ionizatiori current, for 2
atmosphere Ne-filled gamma sensitive (+) and neutron-gamma
sensitive (2) chambers at the temperature 320C. 63

4-15 PIC signal versus steady state ionization current for 2
atm csphere Ne-filled gamma sensitive (+) and neutron-gamima
sensitive (ri) chambers at the temperature 380C. 64

4-16 PIC signal versus steady state ionization current for 2
atmosphere Ne-filled gamma sensitive ()4 and !eutron-gamma
sensitive (E) chambers at the temperature 432"C. 65

4-17 PIC signal versus steady state ionization current for I
atmosphere Ar-5% N2-filled neutron-gammna sensitive (+) and
gamma sensiLive (2) chambers at the temperature 250C. 66

4-i8 PIC signal versus steady state ionization current for 1
atmosphere Ar-5% N2-filled neutron-gamma sensitive (+) and
gaama sensitive (.I) chambers at the temperatures 91 C. 67

4-19 PIC signal versus steady state ionization current for 1
atmosphere Ar-5% N2-fi ied neutror-gamma sensitive (+) and
qammln sensitive (Q) chambers at the temperature 152'C. 68

4-20 PIr signal versus steady state ionization current for I
alimosphere Ar--5% N2-filled neutron.-gamma sensi ti e (+) and
gam;a sensitive (n) chambers at the temperature 19')"C. 69

4-21 PIC signal versus steady state ionizatiorn current for 1
atmosphere Ar-5% N2?-fil!ed neutron-gamma sensitive (+) and
gamma sensitive (0) chambers at the temperature 2600C. 70








FIURU'IS (Cont'd)

Figures Pa"g

4-22 PIC signal versus steady state ion ztion c rresnt for 1
atmosphere Ar-5% N;-Filled neutron-gamma sensitive (+) and
gamma sensitive (l) chamniers at the tcimperaturc 2970C. 71

4-2 2iC signal versus steady state ionizatio:, current for 1
atmosphere Ar-5% N2-filled neutron-gamma sensitive (+) aid
gamma sensitive (m) chambers at the temperature 377"C. 72

4-24 PIC signal versus temperature For 2 atmosphere Ne-filled
neutron-gaw'ma sensitive (x) and gamma sensitive (+) cham-
bers at position 3.. 78

4-25 PIC signal versus temperature for 1 atmosphere Ar-'b%
N2-filled ,eutron-gammra sensitive (x) and gamma sensi-
tive (+) chambers at position 3. 79


Vi i













Abstract of Uissertation Presented t'; the Graduate Council of the Univer-
sity of Florida in Partial Fulfillment of the Kequirements for the Degree
of Doctor of Philcsophy

APPLYING TIH PULSiD ION CHA lPER tiETHUOOLOGY
TO FULL RANG! REACTOR POWER ,IEASUREMENTS

By

3rucp J. Kalter

June, 1977

Chairman: Dr. William H. Ellis
Major departmentt : Nuclear Enginer'ing Scic;nce

A computer based/controlled PIC solid state electronic system ir

presented ii its entirety. its operaLion is described and evaluated both

as a plasma diagnostic instrument and a basic reactor power measurement

system. The system, in conjuncLion within two sets of matched ionizaT.iii

chambers (one with a 93% enriched 235U coating the other without), is

evaluated in terms of response in radiation fields of 10i tc 3 x i R/.hr

at temperatures ranging frori 250 to 475C. Two different sets of chain

bears ere used, one containing Ar-5/%NF, the other Ne. Gamma compensation

to within -5 5% proved_ fi'caible, at a gi' vn tempe-raLture from, 10"' to 3

x 10 6 R/n.

Tie cn.ar,ers' responses altered over .he t.e:peratire range used.

The PIC s ninal for neon at 3 x 106 R/hr and 25GC was 2.03V where at 432'C

it wYas 4.7V,. For the Ar 5% N 2 chambers u',der the sa re conditions

the signal iicrasud from .9W t to ?.74 volts. The Ar-N, cia;mb,'r talnperaljrev

resionsLe was expectr-d. The Ne teemperanure rso.r.;e .was constant :o !o














2820?( as predicted. However, at this tiemperatirc the signal btgan to

show a slow increasing trend which continued up to the maximum temperature

used, 475C. This requires more study.














CHAPTER I
INTRODUCTION


The need for dependable and accurate monitoring of neutoni flux

reactorr power) presents the nuclear ec:ineer with o~ie of hi s most diffi-

cult d;:s cn tasks. For safety reasons, commercial reactors of all types

require the flux to bp monitored ovor at l:1:.;t twe ve decades with *-r 0

accuracy. This range, even under optimum environmental conditions,

require; : a minim ,lil ofi two detcir opera tirna muMde Hiowver, in dll

cases, ?three Mses are used to insure over i- (recdunlancy) and thus the

isa3e opieratior of the reactor. In addition to the range rc,.:uirements,

the detectors ,ust operate coo.sistently and ascura.tey i'er Lhe miosL

adverse ehvi'-!nmrerial conditions. 'ihisi, ; ;62pending O( the situation,

iicl;de high tenoerat,,res, excc- si;e bac groundund radiation' lev.l.'. c)

high neutron flux levels, over extended periods of time kmonhtir'.

For the most parc, adequate monitoring systems exist for tihos

nuclear plants which are in use a the present time 't,,u'ever', the limits

of these current systems are exceeded when one attestt,; t.c -pply them to

the retids of the fast breeder reactor cr rthe r:ew geierrtio.' of large co'r

light water rea.cors. T!;ese no; plants reosiire fas,. f 'es',, -e ir-co-re

detecti ni sys t:o s Unf, rtulately, the in-cor ::nvi, ..:neni is extree il

both th: t ;e'ra ure a'nd flux d i,'.ns and as yvt, .o syst:r'i a f.nc-

tioned adequately under such conditions.

To del ineate the exart n ur.;i. of t-.e pr.i'bjl : acei O;e i:t liare-

fully t'amine thi reactor power: rsureo.;-', 5ysktr: pr:;'t 1 beino








utilized. Such an examirnat.iun c i i rf only suc st ;.- eire, and possible.

how, improvement can he micde in c urr:enti sy'. ems, but ic will also point

to the pressing need for a full rdncl';, hi lh femppi' e ture single sensor

system.

The first division between neutrorjn ensinq systems comes from

whether they utilize in-core or ex- ore sensors. Examining Figure 1-1 we

see why such a division exists. There is a difference of a factor of 10

in temperature and a factor of 10V in galmuz and neutron fluxes between

the two regions. It is apparent that thes, systems designed for in-core

monitoring must be an extremely hearty breed. For this reason, only one

of the four major reactor types (PWR, HTGR, LMFBR, and BWR) has the

neutron flux "evel safety control monitors in-core. The BU'R, due to its

large volume and particular design characteristics (large cruciform

control rods and boiling water) requires in-core flux monitoring for

safety reasons. This requirement, coupled with the lack of dependable

in-core systems, together, comprise one of the most difficult problems

the BWR engineer faces today.

Figure 1-i also serves to define the upper limit operating specifi-

cations for both the in-core and ex-core environment. The lower limits

corresponddin to reactor shutdown are depicted in figure 1-1 as well.

The great range in reactor power makes the use of a single sensor and

circuit impossible with current technology. Thus a detector of any given

design is of use only over a specific part of the flux range and must be

compiimented with o-her sensor-circuit designs. Overlapping one or two

decades of each design sacrifices part of their useful range but insures

smooth transfer of control ard safety f'unctons from one control circuit

to the next.










Thermal
'.- Insuii action
T her 111 I IIii'\\


. : '
I" Niuetro"n Sensor

i ). . .'\
I ~


14
Flux, nv
'I-
1010


106

650F!
Temperature
,800


10
Fluxs (nv)


10"
y-Field (IR/hr) I


emperia ture


!140
(F)


'I










~-7



---- --
t






__. _. __


Figure I-1, Typical environmental prof-ile To neutron sensors in a PWR
at full powder and at shutdown


Ppra Potier
at Power


Parameters
at Shutdownr








Three ranges are used to divide netcron: flux levels found in reactors

from startup to -fui power; the source:, intermediate, and full or operat-

Sing power range. Figures 1-2 and 1-3 slhi' the limi s cf these ranges,

along with the typical neutron detectors used in common ex-core and BWR

in-core control systems.

It is apparent from figure 1-3 that the so r ce range monitoring

system must -tilize sensitive detection methods. Proportional and Fission

counting systems offer the greatest sensitivity with maximum gamma dis-

crimination. Three neutron sensitive materials a'-e commonly used in the
10 3 10
proportional counters; OBF3 gas, 3He gas and I as a lining. Each has

its advantages and disadvantages. 1BF3 offers high sensitivity but the

necessary high polarizing voltages cause rapid degradation of the gas in

high flux environments The 3He gas proportional counter offers greater

sensitivity and stability than the IOBF3, but has a smaller Q value,

which makes the gamma sensitivity proportionately greater. The '"' lined

chamber is loss sensitive than the 0BF3 but more stable in high inten-

sity fields. Fission chambers have their electrodes coated with uranium

highly enriched in 235U.

In both in-core and ex-core systems, the minimum allowable count

rate for safety reasons is 1 to 10 counts per second. [hus the detec-

tor's sensitivity in each case must be adjusted to insure that the shut-

down reactor ineutron Flux results in a count rate of greater than 1 count

per second. Due to the resolution limitations of such counting systems,

their fastest possible response is on ths order of 106 counts per second.

lo the point, a -tate of the art mission counter can accurately indicate

neutron flux levels over six decades w;hill immersed i a gammtda fiu;; as

high a; 10 R/hr. Although counting syst;es hive their problems, no







i-3
10 3i i J0 i
",12
10 J0
| X -o4 ~ 12r
e10 4- 102 I *L 100




10 1 7 J1

6 0 1100

2 -



5 4 -o-8
S 4310 i01
S- 4 "10

,0 1054

-10 10 5
T10104 J o

u.l
S 2 0-5


10 -10


i 00O'


2- i I



C
-i lO


Propori on or Con'rinsated Ion
Fission Counte'' on Chamber Chamber


Figure 1-2. Typical range, and detectors used in ex-core systems to
cover the sowice, intermediate and pov.er ranges.









10

I4 125
"104 -'102 100

.' 1,013 013 0




S10_ 10 0" 10

+10 0 -2 10
10 0 0 .[10

c
> 1010 0 0
7 C" ."2 f s


J G10-4 I -.0s
S I ., -
'710 -i0 -!04
to




C C




i-a
ei



Fission F ssi on F lssion-lor
Counter Chai e r Chamber



Figure 1-3. Typical ranges arid detectors used in in-core systems to
cover the source, intermediatI and power ranges.








other system! yet developed oCF.-rs the re-quired sensitivity in conjunction

with the necessary gamma d'i `-imiatier, th..t they Ya. Countirng systems,

when stretched to their limits. cover only half of the tvelve decade

range.

ihe intermediate range instrumenrtticn covers most of the remaining

six decades, overlapping two to four decades of the source range and part

or all of the power range. Ihe sensors used to span this range are ion-

ization chambers of various designs with boron or fissile electrode coat-

ings. When simple fssion (or boron) chambers are used, the associated

signal processing circuitry is designed so that tie resulting system's

output is some measure of the mean square voltage meann of the squares of

the deviation from the mean), abbreviated MSV. Since Poisson statistics

govern the pulses from a nuclear radiatich sensor, a measure of the mean

square voltage is a direct Measurie of the mean conr.ting rate. This

method nas just recently been developed and offers at least three impor-

tant advantages over the conventional compensated ionization chambers:2

increased gamma discrimination (100 times nore than the CIC), improved

operation when chambers and cables are exposed to elevated temperatures,

and more efficient use of sensors.

Compensated ion chambers (CIC, are the sensors commonly used to

cover the intermediate range. Such chambers provide signals which have

the gamna induced component reduced by a factor of 20 to 100 times over

that of a conventional ionization chamber. The methodology employed to

achieve this is simple. The CIC is constructed with two separate sersi-

tiv volumes; one, having the confiingi eicctrode surfaces coated with

necutron sensitive nimaterial, is sensitive tl bjLth gammas and neutrons, and

the other, having no such coating-,n, is s2nsiti\e lo onlly gammas. The








sensitivity of the two volumes is adjusted so that they are equally

responsive to gafrmas, Thus- when the radiation induced ionization from

both volumes is collected and subtracted, the resultant signal is, in

theory, that induced solely by the neutroon interactionrs. Such a procedure

is necessary because, while the prompt gamma flux is proportional to the

noecron flux, the gamma flux due to radioactive decay is not. Thus, all

gaimma response must be negated as much as possible. This, however, is

true only for the intermediate range. At high power levels, when the

neutron field is much more intense than the backg';rourd gamma field, no

compensation is necessary. Because of this fact, conventional ionization

chambers are used as the control monitors from 1 to 100% of reactor

power.

The use of a gamma-compensated detector extends the reactor control

range, compared to that of an uncompensated chamber, by approximately two

decades. The reason this extension is so small lies in the fact that

with fixed voltages compensation is exact at only one given reactor

power iejel. This point has also given rise to the recent practice of

operating with fixed voltages anl designing :safety systems that avoid

total control dependence on iiore than twc decades of compensation.

The upper limit of any ionization chamber's operation is fixed by

either recombination affects, wnirih cause nonlinea.r resounses, or by the

inability to apply sufficient co!lectioi: voltage to the electrodes. The

flux level at which either of these occur dependss on the overall design

of the sensur. Leakage current through the insulators, due to the applied

voltage, becomes the limiter for measuring low ,nutron Flux levels. In

addition to insulation leakage, the lower limit of the ionization chamber








operation mea be affected by bw. kigr'undn cui'ret caused by the activation

of chamber materials, neutrcio svsitive material reaction product activity,

or background alpha current for mission chambers.

it was ,mentioned at the beginning that present monitoring systems

are adequate, and they are, but just barely so. Points which are diffi-

cult to get across in a summary of this kind are the ccmple-,ity, failure

rate, and field engineering problems that these systems present. The in-

core BWR system is a case in point. low is one to calibrate, normalize,

and keep in operating condition the hundreds of detectors present in the

core of an operating reactor? The need for a distinct system to cover

each of the three flux ranges makes things just that much more difficult.

it is apparent that a single sensor, full range reactor power measure-

ment system, which could cover the entire flux range without beino stretched

to its limit, would vastly improve the situation. Such a system should

function in the source range as a counter, with inherent gamma compensa-

tion through pulse height discrimination, anc should smouthiy switch to

the intermediate range measurements with substantial overlap to insure a

linear transition. At intermediate flux levels, the system should be

capable of both gamma compenseciin and miniiizaticn -uf leakage current

contributions to the signal, especially at the elevated temperatures

encountered in the in-core eniiroinient. Build up of neutron sensitive

material reaction products should not adversely affect the system. For

power measurements, the range of operation should not be restricted by

recombination effects. To be of use, such a system, must provide a linear

(or o) output over the entire power range under al expected environ-

menta' condiLions. The Pulsed Ionization Chamber (PIC) technique, which








is to be the topic r'f h;is dissertation research report, and which was

developed and investigated by Ellis and his students at the University of

Florida, appears to have most, i:f not a'll, of the above mentioned

characteristics.

The promise of the PIC rrethodoluny for meeting the real needs and

future requirements, alluded to above, I. considered to constitute more

than adequate justification for undertaking a research program for further

developing the PIC system towards practical nuclear power reactor applica-

tions. Therefore, to better impiiment the concepts and demonstrate the

desired operational characteristics, the development of a much more

sophisticated and practical solid state PIC pulsed high voltage and

control system would need to be undertaken.

Thus, the main goal in initiating the research described in the sub-

sequent chapters of this dissertation was to develop and evaluate a

single sensor compensated PIC system, capable of full range in-core

reactor power measurements. In order to establish an initial base on

which to develop this research topic- a review of the PIC system's basic

operational characteristics and previous research results therewith is

presented in the following chapter.













CHAPTER IT
PULSED IONIZATION CHAMBER OPERATIONAL THEORY


[he Pulsed ionization Chamber (PIC) mode, which was originally

developed for plasma diagnostic purposes, is a new mode of operating gas

filled ionization chambers. In its initial stages, the PIC mode was

applied to the measuring of ionization densities and recombination para-

meters in gas filled chambers exposed to neutron radiation. ihe logical

deduction made at that time was that if the PIC output was known as a

function of the neutron flux, then such output could be used to measure

unknown fluxes. This was proven to some extent as reported by Markwell4

who demonstrated the basic PIC performance over eight decades of reactor

power, figure 2-1.

The PIC methodology involves the periodic application of a single

polarity voltage collection potential across the electrodes of an ioniza-

tion chamber Sufficient time is allcwed between nigh voltage pulses for

the ionization density in the gas fill; d gap, batwoen the chamber elec-

trodes, to approach its asymototic steady state limil.. The application

of -he collection voltage result s in the co'a election of first the electrons

and subsequently the ions of the equilibrium ionization density, n. The

Fact tt t tlhe electrons ai'e collected approximately a thousand times

faster than the ions makes it feasible to use the collection of only one

of these charged particle types in measuring the steady state ionization

density. Which of these is used depeJds almost entirely on the chamber










10 -
Ion Chamber

f-f



/ C u.,. c =2500pf.
F /s

/ / 1
/ / /'




I- / -I







!Coiecion !otage -100v
I. t 400v
Signal Gate at 15 mic'osec.

.001 .01 1 1 10 !0 1000 10000
REACTOR PCOIR (,,atts)


Figure 2-1. Results of PIC system with 1 atm, 3He chamber.








design, and the fill gas composition anr pressure. For the research

reported here, the ions were the 'species used in order that some of the

problems associated with electron kinetics5 could be avoided. The theory

derived and presented in the fonio;ing para.3raphs will revolve around ion

collection rather than electron collecticn used in earlier works.

There are two factors basic to the feasibility and usefulness of the

PIC system for the field of r'adijc.tion re.:isu;'ment. The first of these is

that the ionization riensity in a chamber, ,whsn it is exposed to ionizing

radiation, rows rapidly (10 to 100 milliseconds) to an asymptotic limit

dependent on the source intensity. The second factor is that it must be

possible to theoretically relate the measured voltage signal, due to the

collection of ions, to the asymptotic iOn-lonation density, and thus the

source intensity.

The description of the positive ion and electron densities growth to

their asymtotic value lies ii the following gas kinetics equations;


t V. (D7n_) a, n_ 2 nn 4- S, (2-1)





where: n = positive ion density (cm ),

n = negative ion density (cm-3,

c = first order electron loss coefficient,

a2 = second order loss coefficient,

S = ionization source rate (ion-pairs/second),

and De = effective diffusion coefficient which is functionally

dependent or the radial position of n in cylindrical

geometry because of the vair ncs of n in tila direction.








it s hnould be noted that these 'oiu.pled eouations, when used, generally

constitute a iaonlinear pair of equations within no possible analytical

so lu.i.on. However. for the densities ci interest in this stuGy, the

equations may be mrd-kedly simplified. The two ior density regions of

interest are those controlled by the free dif,%si.r ,eegime and the ambi-

po ar-volume recombination regime.

.econ! order loss mechanisms can be neglected at ion densities where

free diffusion dominates and the asymtot;r form of (.quation 2-2 reduces

to;


D+~ 2n + S = 0 (23)



When this equation is applied to cylindrical geometry and is subject to

the boundary conditions,


n+a() = n(b) = 0,



where a and b are the outside boundary of the inside electrode and the

inside boundary of the outer electrode, respectively, the exact solution





,(r) = b [(2-a2) nr In (b/a)r + a'lnb b1na]. (2-4)


At ion densities greater than iiO8 cm'3 ambipolar diffusion is con-

trolling the mechanism for spatial dist-ibution of charged particles and

volu';m combinationn becomes the major loss vrechinism. Because of ambi-

poier diffusion, r.h ion-electron diffusiuc-ai losses become approximately








equal, thus validating the appr.;imat ion n, = n_ at such densities. This

approximation leads to,

D 22
Da '2n ,22 + + 0, (2-5)

which is the decoupled ion density equation for n>-10. This equation,

when written in cylindrical coordinates, is the Eraden differential equa-

tion which can he solved using only ilumerical methods.i

The PIC voltage signal amplitude v(tc), at the time t when all of

the ions are collected, for a large RC cathode circuit time constant

(large with respect to t ), and for coaxial detector electrode geometry,

is analytically and experimentally related to the steady state ionization

density, n+, in the chamber gas by,


v(c 2e r n(r)dr, (2-6)



where; 1 = length of the chamber,

C = cathode circuit capacitance,

e = the unit of electron charge.



The final link in relating the measured vol Lace peak signal v(t )

to the neutron and gamma flux, is provided by the equations;


EoN
S (2-7)
n w


and


S qly,








where; E- the average energy deposited in the gas per neutron
interaction,

w = the nmern eneriry required to create an electron-ion pair,

a average neutron iineracticn cress section,

i; = atom density of the neutron sensitive material,
= the flux density in the vicinity of the detector,

g = gas ionization efficiency which is for a given
radiation field and chamber design

I gamma source intensity.

The ion source rate, S, is directly relatable to the relatively easily

measured experimental valve Iss' the steady state ionization current.

I is measured by applying a constant collection potential to chamber

electrodes and measuring the current between those electrodes which

result from the ionizing radiation.

In particular,



S ss (2-9)
eU '


where, e = the unit of electronic charge,

i = the sensitive volume of the chamber.

Equations 2-4 through 2-9 tnus provide a direct, relatively simple rela-

tionship between the PIC output signal v(tc) and the ionizing radiation

field strengths, and, as such, serve as the theoretical basis for this

entire endeavor. With the aid of the author, detailed numerical calcula-

tions were performed by Herravi for a miniature fission chamber filled

with neon and argon. Some of the results, are presented in figures 2-2

through 2-5. The curves in figures 2-2 and 2-3 represent the radial























5-

E
01
rr
.0.0

C)
a












"-c
r 0






tCD


4 -.-,












-1 C
L I t4L




a m c o
c o m a a *c o








> .-..-. C
1Q' l- 0o- p





S C
".C Cr






C-
















iq^isueaj 110 OAn~sOud paiZ[L(Lh 0N



















S:

















L) 0
ww














C)4CD
0-



CC
C it
'4 CC 0
41

C;I I *
/ a7
i'

STi
oU 0




~a a
.^ 0 0) ^
| 1 ) 3 4)
ii- orC
.4- Lii Co.-
1 C)"
s~~d r I- ',
1-C '*-




C)- -



t II (12(1
\ re "~
oon











o o' a to .
CISM3 C)1 3
AIIN3 NCI rI1iuduf'VWGoI

















L.-

.0




















'i
01













L.)
C .
-- r- "










,'-.





on





E 0

D I-







v c

jt- 2

L1J (J









\ o nC
(snflA, f l 1



II

\~i 0 t










- 7- a 7


(SIT j tH 0H ->SY

















































'Ir




































''1








N
CC)* -~ C)C)C


(S~i iOA) IHSI3th ]Si~dc


;4'



C-)


r'- ")















co .C



Ic





C

























01
o r
-.







CC
C-




























S2
M5



1--1
AZ- Z


















-0.
In








4-c
C
c\;

$-
::

en)



u-








charge distribution in an aroon filled !h~mber for low and high ioniza-

tion source rates, respectively. The se', r flattening of the distribu-

tion of n at the higher source rate is due to volume recombination.

Figures 2-4 and 2-5 depict the theoretically determined v(t ) versus S

for argon and neon gas filled miniature fission chambers. In both cases

the response is at first linearly controlled by free diffusional losses.

At approximately 106 ion pair/sec, amifipolar diffusion becomes the con-

trolling factor and there is a lateral shift in the linear response due

to the more rapid ambipolar diffusional loss mechanism. Above 108 iun

pairs/sec volume recombination becomes the controllingg loss mechanism and

the response becomes second order. These results were, to some extent,

experimentally validated by Markwell.' Figure 2-1 shows measurements

taken in the University of Florida Training Reactor (UFTR) with a PIC

system. Over seven decades of reactor flux were measured. Both first

and second order gas kinetic response region are observed, as was predicted.

A milliwatt was the minimum measurable reactor power, due to the noise

and time jitter of that PIC system. The upper limit of 10 Kw was then

the maximum output of the UFTR, Note that care must be taken in directly

relating the experimental and numerical data shown, since the former

deals with the collection of electrons and the later with the collection

of ions.

The effective replication of the characteristics of the sets of data,

resulting from either gamma or neutron caused ionization, indicates the

basic dependence of the PIC operation on The ionized 5as kinetics, regard-

less of which radiation induced the iunization. Thus, although a neutron

sensi-tive chamber results in a; signal which is comprised of both neutron








and gamma induced ionizatio,, by matching .his oetectur with one that is

sensitive to qammas only, compensation i.s possible, at least at a given

temperature, as was shown by Coo:er.7 Some of his experimental results

are shown in figure 2-6.

Conventional in-core ionization chambers suffer greatly from high
4
temperature induced leakage current effects as shown in figure 2-7.

The departure from linearity of the ionization current, as a function of

reactor power at low flux levels, results from temperature enhanced

leakage current. The PIC method's ability to greatly reduce such current

effects was shown by Ellis and Imani and reported in Markwell's thesis.4

Figure 2-8 shows their results. The change in signal output for increased

temperatures was shown to be due to the change of the recombination

coefficient with temperature. However, such a change would complicate

the application of the PIC methodology to reactor' power measurements.

Fortunately, however, Sanders8 results indicate that this drawback could

possibly be averted in chambers using neon as a fill gas, since neon's

recombination coefficient was reported to be independent of temperature

over the range of 70F (25C) to 572'F (300C).

Even though the previously developed PIC systems were adequate for

the proof-of-principle application described above, they fell far short

of being prototypic of a practical reactor power measurement system. The

bases for such a practical design was set Forth by Ellis.9 The principle

technique of his system involved direct analog signal processing in com-

bination with direct logic system gating resulting II live time feedback

range and operation! mode control. The major advantage oF this approach,

in terms of reactor safety and control, would be its fast response time

characteristics. However, it would suffer from the inherent disadvantage









:-


V ~I K- >

ci~ / 7/i /1

/,i
~///

to 8 6 4 2 0 2 4 6 8 10
DES) lA- lC r: FCM UL 0 I' f TOTA
igure ?-6. Gamma comoensatio~n as a function c-F gamma field strength.








7 0 9
10 10NT i09


...- NEUTRON TLUX (I-i/c, se-c)
4 NEUTRON FL'iX (,iicm~sec;


110-5 IIVI // Z

/


I 0- -0 50 0C













Collection Voltage -100%f
S5500C -"--- / ./1


















1 100 1 000 0000
RECTOR PO a--L /








Figure 2-7. Mean lave! ionization current as a function of reactor power
(neutron ux) d g temp re f 1 atm. e-filled

f issin chambers
1 ]0 100 1i000 I0000

REACTOR POURER (waLts)

Figure 2-7. Mean level -onzatif.n current e.s a function of reactor power
(neutron fiux) and gas temperature fcr 1 atm. 4He-filled
fission chamber.







*,o6 1Or7 Ts '" i


0102 2
L 0 4 1; '10

L NEUTRON FLUX (n/cm-sec)





/^/
-10 /
~: J / / '-
550



S-K 7
3O0C C = 600 pF
"1
-7 73




1 Atm Fission Chamber (4He)
Collection Voltage lo0v

1 10 10 1C0 10000
REACTOR POWRt (wats)
Figure 2-8. Pulsed ionization chamber :!gn&l' voltage as a function of reac-
tor power (neutron flux) and gas temperature for a atm. eHe-
filled fission chamber.








of voltage level instabilities and' drifi: characteristics of analog systems

and the inflexibility iihich is associated" with hard-wired signal process-

ing r :nd control systems.

State-of-the-art digi tal data processing and control systems are

capable of speeds more than adequate for reactor application with the PIC

system. Use of such a system would result in both greater system stability

and adaptive flexibility. However, such a high speed computer for develop-

ing a prototypic system might incur an unnecessary expense, since the

performance capabilities of a high speed digital computer PIC reactor

control system could be adequately demonstrated through the use of a more

readily available digital computer having less stringent response and

processing characteristics. Thus, for this reason, a more moderately

priced, but adequate unit was sought. The HP9821, having the desired

characteristics, was adapted as a component of the prototypic digital

computer based PIC power reactor control system (PUCPIC) which was de-

signed and built for this dissertation.

In the following chapter the general design and operatior:na charac-

teristics of the PDCPIC are presented in detail. This is Followed in

Chapter IV by a presentation of the experimental techniques used to

evaluate: the system in terms of gamma comiensaticn and detector tempera-

ture response; two important operational chhdractri'-tics which needed

further study. The results of these tests art: then ea duated. Finally,

in Chapter V, the author's conclusions are put forward and the areas

requiring additional research are state.














CHAPTER III
PIG POWER REACTOR MEASUREMENr SYSTEM


The potential benefit of the research, if not already clear, will be

clarified in the following general description of a PIC full range, in-

core, single sensor, reactor power iieasuremeont system.

Three operational modes are to be used to cover the expected power

range: count rate, compensated PIC, and gamma only PIC operation. Based

on available performance data, a decade or more overlap between these

modes for safety purposes should be easily attainable.

The count rate mode, as summarized earlier, is the best low flux

measuring, high gamma discrimination method available. Integration of it

into the PIC scheme requires only the coupling of the count rate system

to the detector cathode and applying a constant collection bias to that

electrode as depicted in figure 3-1. Such a cor.figuration would cover

the in-core flux range of 103 to 10 rneutrons/cm2/sec.

The CIC mode, as previously mentioned, has some serious drawbacks;

the PIC compensated mode, because of its irsensitivity to leakage current,

should offer a wider, more stable range of response. The in-core compen-

sated PIC system would cover a 6 decade range; 10 to iO13 neutrons/cm2/

sec. The operation of this mode could prove to be quite complex and will

be discussed later.

Above approximately '09 nrutr.ns/cm2/sec, the field strength from

the prompt fission gaammas begins to exceed that resulting from radioactive






























r2:i


K21%


CL




3 )2? '1-
c O. O? n-





< T- <.. I

0_ 1 *Y


Hi_i
~~~1 F i



'tF]1 i._

I-~-._.i ilN


+ i


I








decay of the fission product inventory. Thus, above 1011 neutr.ns/cinm

sec, the output of the gamma-only section of the compensated chamber can

be used to determine the power level of a r-actor, Depending on the

overall detector design, fluxes as high as 10'7 could be measured using

this technique. Thus, a single sensor system utilizing the modes des-

cribed, with the proper sensor, would indicate reactor power over the

full expected range of operation, encompassing a possible neutron flux

range of 10 to 17 neutrons/cm /sec.

To design and assemble such a system from the basis which existed

at the initiation of this program would not only have been difficult but

also impractical. While verification of so-me of the basic PIC responses

were performed, the entire range and depth of its response had not been

proven as a whole. For instance, neither full range gamma compensation

nor the chamber's response to temperature variations of greater than

approximately 280C had beer, examined fully.

For this reason the prototypic system described below was designed

not only for demonstrating the operational characteristics of the PIC

instrumentation, but also to callow the ganmma coomnpoeation capability to

be better evaluated and the temperature characteristics measurements

to be extended and reverified. The assembling .of such a prototypic

system not only indicates the feasibility of cost uc ing the entire

reactor grade system, but aiso offers a vehicle for examining, in depth,

all the PIC methodology characteristics.


PIC Electronic S stem

The PIC electronic system is composed of 5 basic units; the high

voltage pulsrr (HVP), the raw data acquisition system (RDA), a computer








controlled PIC to steady state r'ode switc:hig system, the computer inter-

face modules and finally the HP9821 computer system. A system block

diagram is given in figure 3-2. Photographs of it assembled are shown in

Fiqure 3-3. With the exception of two analog to digital converters, a

picoa!T'eAter, certain power supplies,, and the HP9821 system, the electronics

were designed and built by the experimenter. Because of the newness of

the desIgn approach taken and the resulting improvement over all previous

PIC electronics, its design and operation are carefully outlined below.

The solid sl.te high voltage piaiser is depicted in figure 3-4. There

were te;o ba ic design goals for this. unit. The first was to apply a 35C

volt psot.t;l across a detector-cable system totaling approximately 500

pf capwacitce in approximately 500 usec., The second goal was to return

the cathode, .hi..h was essentially grounded in order to meet the first

requiremeiit, to a high impedance state ,' tiiin 100 rnec after fill v-:!tage

appli ations so that little of tie collected charge wauld be lost. These

tco C.als ,.'-er to be accomplished using sclic state electronics. Timen

.jitteUing components previously used 3'4'6'7 such as mercury wetted

reldys ,'eo to be avoided at dll cost,

Figure 3-5 gives a simp! ifie c description of ihe i.sic pulser opera-

tion. A close study of it makes following the circuit description below

easier.

The integrated circuit (IC) used throughout the entire system is

an SN74121, monostable muriivibrator. This 14 pin IC is triggered by a

+-5 to OV transition input at pins 3 "nd/or 4. Pins I and 6 provide the

resulting negative going (i5 to OV) and ;:n:sitive Q:i:ny (0 to 5V) output

pulses, respectively. The p "ise .' :iiths aro! ccrrl ile'd y th;e capacitive












CHAMBERS


;, -- --
isI


A I B


SIGH VOLTAGE D RAW DATA ACQUISITION
PULSER SYSTEM



F2 F C1 B1

I__ I
MODE AND CHANNEL COMPUTER
SWITCHING INTERFACE
___ __. F--_ ... .. -
F 2 c--

HI:PS71 1DGITAL COMPUTER

L .
LEGEND
A HIGH VOLTAGE PULSE OR HIGH VOLTAGE
B and C v(tc) or Iss (ANALOG)
Bj and C v(t,) or Iss (BCD)
B2 and C2 v(tc) or Iss (ASCII)
0 DATA ACQUISITION TRIGGER SIGNAL
E and El DATA READY SIGNAL
F, Fi, F2, and F, MODE AND CHANNEL SWITCHING SIGNALS


Figure 3-2. Block diagram of the prototypic digital computer based PIC
reactor power cornicI system.









N f




I3 I

I ~-r~ F- *'a


A. COMPLETE DIGITAL COMPLITER CASED PIC SYSfTEM.


I- ,






I
\I I



I I


i- -
t : , . . .- , ;1





B. SO:AE OF TIIE 1TE4iNAL CIRCUITRY OF THE iHVP AND RDA.

F'igure 3-3. i'htc, raphs depiciring the PIC system.


11 r-^.

-'--


1
; -


I~~
6 Ij

.


'r
:s;sr;;?k4~a~i;;-r~;i-T;r
-~ --- r~*--



















'V1 Ir~


-- -- i I


--~------1`------~` ----rr-------- ,-

: f'! -~-- I
I/ ; 'c~`~

"''
~L1~


----'ilJ
-~---,-----~-


1__
ii
:-5
`1/
: ii
Lj! L
,,

i;l



---1


c.-
3-

L


..TI

-1.1
m
c,
v,

'r
F
O



fL

C.r
5:
I--


6-
I
C':

ii'
E-

C:
'r-
rl.







PIC EQU'vAL.EM CIPRCU


v(t)





300V
"OOV


EVENT
(1) S, CLOSES
(2) S2 CLOSES
(3) S, OPENS
(4) SiGNAL PEAK DUE TO ION COLLECTION IS MEASURED
(5) S; OPENS
(6) IONIZATION DENSITY BUILDS UP TO ITS EQUILIBRIUM
VALUE
(7) S, CLOSED BEGINNING A NEW CYCLE


TIME ELAPSED
0
0
.1 to .8 psec
1 to 150 usec
1 to 100 msec
"90 msec


OPERATION PULSING SEQUENCE


I

;II A



1 .--Ir^ 3 :----1


TIME


TIME


v(t) ,

Fi e -- ''r-------u TICNSni I h

ire 35 IC ulet it ith psn sequ


Figure 3-5. PIC -quiva'lent cirt.uilt with pulsing sequmce.


n








loao across pins 10 and 11 and resistive load between pin 9 and 15 volt

supply. Note that since both outputs 1 an 6 appear simultaneously,

,tilizing the positive rather tha t lhe ne activee ouLput to trigger the

next 74121 t inputs 3 and/or 4, results 'r it being triggered at the

end of the input pul se. Thus its output is cdlayed Ly the width of the

input puise. Trnis fact ;as often u:.se ir the desig'; of the system now

described.

The pulsing-sa'mpling rate of the e;-,tie cmpiter based PIC system is

controlled, wi'thiii limits, by the SNh55 i: ti;ig IC. The falling edge of

its positive output is used .o trigger IC-;:, an S;74121 icnostable multi-

vibrator. (Note al; the remaining designate' ICs are SN74121.) IC-2

provides the necessary variable time delay between the application of HV

and triggering of the cathod'e impedance :i:-'c~it.y. i'h trailing edge of

the positive output pulse of IC-2, whose width is controlled by P-2,

serves to trigger IC-3, The positive output of IC-3 is then fed irito che

driving transistors Q--1, which inverts the pulse aind drives the high

voltage transistors Q-2 through Q-5, rapidly t their ios impedance state,

thus applying voltage to the outer shoil of the chamber.

The leading edge of tih negative output of IC-2 triggers IC-4. Note

that this occurs sIometime before the hihg voltiage is applied. IC-4

provides the necessa''y variable time of occurrence required so that the

pulse which forces the cathode switching transistor into a high impedance

state may be ositioied to occur immediately after the chamber has been

charged tc its full potential. he trailii g edge of the positive output

pulse of IC-4, whose width is controlled by P-4, serves ta trigger IC-5.

The positive ;output of IC-5 is then fed irino the driving transistors Q-6


~_








and 7. These i vert the puls a nd drive oihe two ,witchinig transistors Q-

8 a:id 9, forcing them into a hi;h impeerkise &,20CMt) state.

On examining the circuit ciosel. rie t.Jtes -hat the power supply

for Q-1 and the IC's I, 2, and 3, is floctirSc abou 3501. The reason for

this lies in the way the high voltage transistors Q-2 through 5 are used.

In Particular, note that to get (-2 -nto a non-conductinq state the base

must be at a higher potential than the mniitierc, urhich is at 350 volts.

To achieve this using a 5 volt pulsino system, one has simply to float

that pul sing sytem about 350 volts. Thus a voltage of 352 cr 347 volts

car be placed on the base of Q-5 forcing it oFF or an, respectively.

The critical parts to this un;t are the high voltage and the catnode

impedance switching transistors. The ones used in Roth cases are state-

of-the-art and were selected only after an extensive search. The cath-

ode impedance switching transistors had to have the capability of con-

ducting a large current (, .5 amp) at lotw voltage for a short period of

time (a 500 nsec) and yet return to a high impedance state in ', 100 nsec.

Although this is out of specification for almost all transistors due a

basic design problem, the 2N2857 performed perfectly under these condi-

tions. The high voltage transistors had .o meet the same basic require-

ment as those just listed, except, in addition, they hao to be able to

isolate 350 volts. The 2N3743, although not :s fast as desired, performed

quite well. The HVP could drive a 360 p F capacitive vcihwiber-ccble load

to 350 volts in 800 nsec and switch from low to high impedance in 50 nsec.

The Raw Cara Acquisition system (ERA) had two basic tasks; measure

the PIC output voltage v(tc) and the steady state current is for the two

chambers and present the results to the computer interface in binary

coded decimal (BCD) format. The main compone',ts of the RDA system depicted








in figure 3-6 are; 2 0!I! track and holds (7-H), two analog to digital (A-

D) converters, a 4i9 Keithly pic ammeter. two 31. operational amplifiers

(op amps), and four 302 op ai ps. The logic of this system is given

beiow.

The v(t ) signal cominil From Cte cat'hodc of the chamber, when the

system is in the PIC node, is Led into a 302 op amp with a gain of one.

The signal is then attenuated by a factor of 2 in giin, by using a resis-

tor network, and fed into the positi', differential input of a 318 op

amp. The signal is reduced oy .1 factr.) of .wo because o i the fact that

the 318 op amp is much more stable when operated at a gEin of approxi-

mately 2. The use of the 318 op amp allows one to apply a zeroing d-c

shift to the input as well as to adjust rthe gain so that the entire PIC

system has a gain of one. The signal from the 312 op amp then serves as

the input of the OEI 5892 track and hold (T-H). The T-H takes a 400 nsec

sample at a given time after the collection voltage is api'lied to the

chambers. The time at which the sample is taken is set by the experimen-

ter by adjusting P-6 of IC-6. Note that IC-G is tripped by the negative

going pulse of IC-5 and thus for given poL settings, nas a definite time

relationship with respect to the time of application for the collection

potential. IC-7 serves as the T-H sample pulse wl1th controller.

The output of the T-H is then fed into the first analog to digital

converter (A-D1) which presents the data to the compuLter interface in the

required BCG format.

Once both data channels have been read in the PIC mode, the computer

then switches the mode relays so that a ccn'stant d-c collection potential

is applied to the chambers and the cathode of each chamber is, in its











time, fed into the 419 piceiaiter-. PThe oi lput of the ammeter is fed

into A-01 which is read hy the computer. Th' computer examines the

readini tot determine whether the amm'eter is the he right scale. If it is

not, the computer raises or lovers the amnmeter rangc by one decade and

reexamines the resulting 41i output. This is drine until the meter reading

indicates the an:meLer has the right range setting. This data are then

stored .nd the computer switches to tne second char.nel and repeats the

above sequei:ce to obtain a correct currentt reading. Thus data are is recorded

in both PIC and steady state modes autom-atically. Once this is done the

chambers are exposed to a different intensity rad;atior field by moving

the chambers closer or farther from the source. .nd the computer is then

given a command to repeat t.he above sequence.

The channel and mode switching system (CIS) is composed of transis-

tors reed relays, and diodes. it is an intcg-iil ja-t of both the HVP and

RDS system and, as such, is included in their schen'atics. Switching from,

PIC to steady state mode is accomplished wv.hen the computer, through the

interface, provides a positive 3 volt output whirh is applied to the base

of Q-10 and Q-ll or Q-12. This results in relays R1 and 2 or 3 closing.

Note R2 is closed when the current from channel i is baing measured and R3

is closed for measurement of the current from channel 2. Note also that,

when the current is being meas;ured ir each ci-rnnr-l the PIC mode cathode

circuitry is disconnected. The coaxial switch serves to route data to A-

D1 as described below.

R-6 is closed in the PIC mode for nleasurment of v(t) from chamber

1. The v(tc) sigrna from chamber 2 is routed through A-,2 when the system

is in the PIC mode, R-5 is closed as w-F, ;,s R-1 and R-2 when measuring








the I from chamber 1. R-4 is closed ss w;' 1l as R-1 and R-3 when measuring
ss
I from chamber 2.

The timing sequence for one data recording cycle in the PIC mode begins

when the cathode impedance circuitry is tripped to its high state by IC-

4. The positive going pulse of IC-4 is fed into JC-8. The negative

output of IC-8 is then inverted by 0-21 and theni fed to IC--9 and IC-10. The

pulse width of IC-8 is set such that it is slightly greater in w-idth then

that of those used in the T-Hi triggering circuitry from IC-6 and 7. This

is to ensure that the A--D converter's are commanded to read their inputs

only after the T-H has the data sample rea~y for them. IC-9 and IC-10

provide the pulses necessary to activate tne A-D's. Since the A-D con-

verters require 250 msec to sample, the output pulses of IC-9 and IC--C1

are set accordingly. IC-11, which is triggered by IC-iO at the end of

its pulse, indicates to the computer, through the interface, that the

data is ready to be read. The IC-11 pulse width is set so as to allow

the HP9821 250 msec to record the data fro;i both A-0 converters.

When the system is in the steady state i.mode, only A-D1 is resd by

the computer, as described earlier. The codes used by the computer to

control the system and output Ihe resulting do aa are given in the Appendix.

The system operated flawlessly over the 3 months of evaluation. No

major deficiencies were found. The systems response remained both linear

and free of gain drift with the calibrating accuracy of _2%.

Detector Selection

The fundamental part of any nuclear radiation measuring system is

the detector. The capability of a syst.ei, even with the most sophisticated

electronics, is ultimately determined by the sensor. the only detector








proven capable of approaclhing the limits ;aet forth in the beginning of

this chapter; is the 5U fission chamber, it gives the maximum possible

gamma discrimination, with relatively icw nurnnup andi has been proven to

operate under the most adverse conditioni, all of whichh are necessary

characteristics for the PiC application. For these reasons two matched

pairs of RSN-34A-Ml fission chambers were obtained. A scale diagram is

shown in Figure 3--7. Of each pair, one had a coating of 93% 23U. Thus

one chamber of each set ,as sensitive to both neutrons and gammas, while

the other was sensitive only to gammas. As a consequence they formed a

gamma compensating pair. One set wds filed a: the manufacturing facility

with 1 atmosphere (STP) of a high purity Ar-b%N2 gas mixture. The other

set was ordered with fill tubes attached. They were pumped down to 2 x

10-8 torr at 300C, cooled, and then filed to 2 atmospheres with research

grade high purity neon. The argon-nitrogen gas mixture was used because

of its proven characteristics in conventional fission chamber operation.

Neon on the other hand, was reported to have a volume recombination

coefficient that was independent of temperature; a desired gas charac-

teristic of the PIC reactor power measurement system.

These chambers, along with the previously described PIC system,

were then evaluated. Chapter IV describes the experimental procedures

used to accomplish this, as well as the results obtained.


































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CHAPTER IV
EXPERIMENTAL PPCCFDURcLS, KPESI 13 AND
METHODS OF DATA PROCFSSING

Initial St.strni Selup


The limiting factor of the samping rate of the system described in

the previous chapter was the analog to digital conversion speed of com-

ponents used. One complete da ta reading requi -ed 250 msec. Because of

this limit the system's pulse rate was s.et at l.55/sec.

The high voltage pulse width was set at 15 msec, which was more

than sufficient to sweep the chambers free of the ions which constituted

the steady state charge density. The colection time for the No ions

in the RSN-34A-M1 chamber, with a 200 volt collection potential applied,

was 100 isec. For the Ar-N2 chambers, with a 300V collection potential

applied, the ion collection time was found to be 150 usec. A time of

630 msec was allowed for the ionization in the chamber to reach its

equilibrium value. This was found to be :nore than sufficient, since the

ionization density reaches its steady state value in less than 100 msec.

The maximum possible collection potentials were used in each case

to ensure rapid collection of the ions. The neon filled chambers had

200 volts applied, because, above 235 volts, their response was observed

to suffer from breakdown. The Ar-N2 filled chambers were operated at

350 volts, because as stated earlier, that was the upper limit of the

HVP.

Tie system was run continuously for tto months, with linearity, gain

and zero drift being monitored periodically during that time. The linearity








and gain were checked over the full voltage and current range of interest

by injecting known signals. C;er the entire period of operation the sys-

tem's response remained both linear and at 3 constant gain within a +2%

accuracy. On ihe other hand, zero drift in the Pfr mode was found to be

a strong function of the ambient temperatures of the HVP. The impedance

switching transistors Q-8 and Q-9 were identified as the cause. Their

temperature coefficient was approximately 10 mV/'C. For the measurements

taken, baseline drift was carefully monitored to ensure False readings

were not obtained.


Experimental 'Measuremenrit & Results

Gamma Comuensation

After carefully ascertaining the system's linearity and verifying

its calibration, measurements of exposure rate versus L(tc) were begun.

The radiation source utilized was the Wes;inghouse Hanford 230 kCi 60Co

irradiation facility, which is depicted in fiTurc 4-1. A plot of the

radiation intensity versus ve-tical position: for the port used is shown

in figure 4-2. The data points wero Obtained usir.g an RSG--A gamma

ionization chamber. The curve represents a sevenTh order polynominal

fit of the data;

log(R/hr) = 6.226 1 .4033y .19392 025.624,
t4 -656
2.2067x1- x + 1.682x10-4 3.3963A10x-6

+ 4.0521x10O 7,

where is the digital position : of the hanibers in the irradiation port.

x ranges from! I to 22. Note this curve fit ecuaticr, was used in the PIC

System Data Recording Code given in the Appendix.

The first system response to be examined was its ability to gamma

compensate. To do this the matched pair of Ar'-i2 chcamers were utilized.



















, -4

-Y I


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'I

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Figure 4-1. lWestingho use Hanford 230 kCi 60Co irradiation facility.


'4 K.


------ .----- -------~


































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They were placed side by side in a cyl'inc.rdal styrotoam !iold and lowered

in 6 inch increments down into the rd;;ti;, port, while the computer

system recorded v(tc) and T s of both r ahimbers ar. each point. The code

used to control the system is giver in the Appendix under the title PIC

System Data Recording Code. Note this code was used to take all Lhe

v(t ), R/hr, and Iss data reported in this chapter. Typical plots of the

v(t c ss, and R/hr data taken are shewn in figures 4-3, 4-4, and 4-5.

It is immediately apparent from figures 4-3 and 4-4 that the chamber with

the 23U deposited on its walls was 3 times more sensitive to gamma

radiation. This fact shows that the coipositicn of the wal material has

a strong effect on the gamma sensitivity of a giver; chamber. The non-

linearity observed in the low-end response of the neutron sensitive

chamber was due to ionization produced by the 234U alpha activity in the

uranium coating en its inner walls.

In the plot of v(t ) versus Iss it can be seen that the curves for

the two chambers lie virtually on top of each other. it shall be remembered

that S, the ionization source strength is linearly related to Is1, i.e.,


S ss
eU


where e and U denote, the unit of electronic charge in caulnmbs and

sensitive volume of the chamber, respectively.

Thus ficiure 4-5 shows that., at a given ion production rate S, regard-

less of wnicn chamber is used, the resulting measured v(tc) is the same.

This proves that the chambers and electronics fcr each channel are closely

matched, a very basic requirement for gamma compensation. Note, however,





f


to *a t %





... ......3.Q ,i; -..*.r . ..': r ..






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as stated earlier, for a given exposure rote, the ionization rates in

both chambers are not equal. du crc the rflc'fct ot the uranium wall coat-

ing in the neutron sensitive chamber.

Exam;ining figure 4-4, one can see tht presence of the linear and

second order response regions of v(tc) versus R/hr as predicted by the

theory given earlier. However. the presence of transition regions and

their characteristics should be noted. In the fission chamber curve,

this region extends from approximately 104 to at least b x 106 R/hr. The

gamma chamber appears to have a much iore drFinud transition region; from

10 to 106 R/hr. These effects are observed in figure 4-5 as well. The

broad exposure range covered by tne transit ion region, coupled with the

fact that this region of response does rot coincide between chambers,

makes gammia compensation diffici(i'it. he gamma chamber signal cannot be

simply multiplied by a constant and subtracted from the fission chamber

to give full compensation over the full range of exposure rates, because,

as seen, due to the increased ganmma sensitivity of tha fission chamber,

the two chamber responses are not linearly related. Thus, to accomplish

gamma compensation, using the chamber selected, maore than simple differ-

entia! gain controlled inputs, as were used by Cooper and suggested by

Ellis, were required. To compensate using nonlinear electronics would

have been complicated. On the other hand, compensating through cori.puter

methods appeared relatively simple and straight forward.

Computer based compensation was accomplished as follows. The chaei-

ber responses shown in figure 4-4 were curve Fitted Lt eighth order poly-

noninals, using .',"-, .. Pclynominals. 4 A description of the code is

contained ir, the AppPndix. The resulting equations warn;








S- 5.161 + 1.49865' .C05y3 .4586y4 (4-1)

+ .2038y5 .36i' + .08162y7 .00980y8

x 5.6355 + 1.532!z + 1500z2 .32413 + .0488424 (4-2)

+ .4138z5 .2519z + .05276:: + .002576z/,

where; x = log R/hr,

y = log vf(tc),

z = log v (tc),

vf(tc) = the PIC voltage signal from the fission chamber,

v (t ) = the PIC voltage signal from the gamma chamber.

A code was then written for the HP9821 which caused it to record the v(tc)

signals from the chambers, at given exposure rates, compute the measured

R/hr from equation 4-1 or 4-2 for the corresponding chamber, subtract the

results, compute the compensation error and finally output all results.

The code is listed in the Appendix under the title of Compensation Code.

Table 4-1 contains a set of typical results of this application.

The sixth column in the table plotted in figure 4-6 indicates the com-

pensation results. The first six values are as iarge as they are for two

reasons. The first is that the curve fit did not fit the low data points

well and, second, the system's 'elctronic stability was +2mV, which, as one

can see, has a large effect on the cnmputed P/hr values at the low ex-

posure rates. The remainder of the values in tnat column, nevertheless,

indicate that, at least For fixed temperature:, reasonable compensation

can be obtained. The fluxuations that do exist are due to curve fitting,

chamber positioning, and the cr.ecision of the measu-ring system. The last

of these was measured at 41%. The other two were difficult to accurately

determine, hut combined, are on the order of +5%.








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% DEVIATION FROM TOTAl CCO'ENSATION
Figure 4-6. Gamma compensation as a fun'.t-'r of exposure rate.








PiC Chamber Teisierature Respoi_.-

Once Cganma compensation was pi even feasible, using the computer

based method, v(t ) for both chamber sets was examined as a function of

temperature at various exposure rates. This was accomplished by con-

structing the 3.8 inch diameter, doiubie tubed oven shown in figure 4-7.

The Ar-N2 chambers were inserted into the oven and connected to the long

RG62-U leads from the PIC 1VP by 2-foot lengths of high temperature

mineral (Si02) insulated cables. However, when the Ne-filled chamber

measurements were taken, air coax w'.,as used in place of the mineral cables

because they suffered from voltage breakdown at 4000C. The oven was

capable of reaching temperatures up to 550C when used in conjunction

with a 120 volt variac.

The cylindrical oven-chamber assembly was placed in the same port as

was used for the gairma compensation experiment. Tie data were then taken

for both the Ar-N2 and Ne chamber pairs. The most pertinent of this is

displayed in figures 4-8 through 4-23.

Some basic chamber response characteristics are immediately apparent.

The most obvious being the rise in leakage current as the temperature is

increased. Tntis fact accounts for the drastic change in the slope of the

beginning data points as the temperature is increased. Note that the Is

values became next to useless as the temp-erature was increased, because

the leakage current far exceeds the current caused by the radiation. On

the other hand v(tc), even at the highest temperatures, maintains its

basic functional response to the exposure rate. (Note, in figures 4-7

through 4-22 the tabulated values from top to bottomi co.'respond to ver-

tical port p-sitions 14, 13, 12, 11.5, 11, 10.5, 10, 9.5, 9, 8.5, 8, 7.5,

7, 6.5, 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.5, ;nd 1.5, ir: that order.)
















pl iE WALL

b- A T a' CONNtCTING CATTLE











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EMIENETS
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Figurc 4-7. C~rocs sectiajn?' vf,?vj of D,,i~~~~'jt D LCrCcnod'a-te a
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To glean information from th; data ,.-,e easily, the leakage current

was subtracted froa-m al current values and the rat.i of :5 /v(t ) was

computed for all d'ta points. Tables 4-2 and 4-3 contain the results

for the Ar-N2 and Ne chambers, respectively. The blank spaces indicate

the result obtained was msean.inless. Figures 4-24 and 4-25 present the

tabl.;ated Iss/v(tc) ratio at position 3 as a function of temperature for

Ne and Ar-N, data, respectively.

The reason for calculating the ratio was to smooth out fluctuations

in the data caused by vertical and rotational positioning differences

between data sets. Since IS is constant for a given exposure rate,

over the temperature range of interest, v(tc) accounts fur the variation

in the ratio I s/v(tc). If v(t ) gets larger in the second order region,

this indicates that the volume recombination coefficient is decreasing.

Note, as well, that as v(tc) nets larger iss/v(t ) gets smaller.

With these facts in mind examine the Ne data in Table 4-2 and

Figure 4-24. In particular choose a position where (t c) is in the

second order region, for instance, position 3. Ihe ratio of I /v(tc)

changes considerably over the temperature range of interest. At 25C

the ratio for the gamma chamber is 4.36 x 106 while &t 477C it is 1.32

x 106. The same temperature range for the fission chamber gives a

ratio range of 4.94 x 106 to 1. 7 x 10 -. Note that the relative

changes are approximately equal for both climbers. As one will see this

is not true for the Ar-N2 chambers. This indicates the a2 decreases

with increasing temperature For Ne; a fact which appears to contradict

Sandars7 results. Sanders fund u2 constant for Ne from 250C to 3000C.

Examining the data given in the lower part of Table 4-2 (positions 1.5,

2.5, 3, 3.5) more closely, one noteA that the ratic is virtually constant
























I i






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up to 2820C. At 282C it takes a sudden drop and continues down over

the rest of the temperature range. Ti-hus rathrr then contradicting

Sanders data, it validates his conclusi;:n to some extent tnat a2 for Ne

is essentially constant from 25' to approximi;ltely 300C. Note also

that a atmosphere chamber was used in Sanders experiment while the

ones used here contained Z atmospl:e;es of Ne.

The gradual decrease in the ratio at a g;ven temperature in; due to

the transition between weak linear diffusional losses and stronger

volume recombinational losses as the steady state ion density increases.

Table 4-3 contains the Ar-N2 data. For the highest exposure rates,

where volume recuombination predominates, tle i /v(tc) ratio changes by a

factor of 10 for the gamma chamber and by a factor of 5 For the fission

chamber. There is no theoretical explanation for this if both chambers

were prepared in the same manner and filled with the same gas. A possi-

ble explanation is that these chambers were not thoroughly baked and

pumped before filling. The fission chamber, having its walls coated with

pure uranium, maintained a purer gas mixture as the temperature was

raised because the gas impurities in the walls were trapped hy the coat-

ing. The cgamma chamber, however, having no such protection, had wall

trapped gas impurities mixed in with the Ar-N, ill gas. Such impurities

would, in general, enhance the temperature de;eiid2ncc of -12' an effect

which is apparent in the data.

Little was said of the transition and first order data regions for

two reasons. The first being, it is a well known fact that diffusion,

which controls losses in the first order reegio, is both temperature and

pressure dependent in rather cormlex ways. Thus a simple explanation

of the results does not exist and it would be inappropriate to go into it








in this paper, since it is not needed and many excellent works on diffusion

have been published. The second reason is that for practical reactor

operation gamma compensation is not necessary until an exposure rate of

greater than 105 R/hr is experienced. As one call see in figure 4-4,

above i05 R/hr second order effects predominate.

Sources of Errors

The main source of error in this experiment was detector position-

ing. A +-5% error in positioning produced as much as a +15% error in the

measured signal. The reason for the magnification was the rapid vari-

ation of flux with position. in the temperature measurements the posi-

tional error became even more aggravated due to the oven. The oven was

allowed some rotational freedom as it was moved vertically. Thus, the

chambers were rotated in the horizontal plane with respect to the source.

This effect was minimized when the styrofoan mold was used, but when the

oven was used,appreciable (+5%) exposure rate fluctuations were experi-

enced at the chambers due to self shielding. This variation accounts, in

part, for the apparent staggered look of the data tabulated in Table

4-2 and 4-3. Only trends are meaningful in this data and point by point

comparison should be avoided.

Another source of error in measuring v(tc) was the drift in the base

line caused by the temperature dependence of the impedance switching

transistors (10 mV/'C). This error was al.os, impossible to accurately

determine. However, the base line was monitored before and after each

set. of measurements, if it was Found to have drifted more than + 10 mV

the set of data was discarded and the measuie;ient repeated.

As stated in the first pat of the chapter the electronics remained

both linear and accurate to within -,2%, ovpr the 3 months the system

was used.







In measuring v(t ) a source of error other than instrument error was

present. I s, which contributes to v(tc) oIly minutely at low exposure

rates, at the high exposure rates could begin to signrificantiy contribute

to the v(tc) measured. Ideally v(tc, should be constituted of only the

steady state ion density collected. The equation which describes the Iss

current contribution is,


vss(t) = IsR ( exp(-t/RC)),

where RC is the circuit time constant. For t << RC his reduces to


vss(t) = IssR.

Note that vs(t) can be reduced by reducing R, just as long as t << RC.

Also, to avoid affecting v(tc) adversely Re. must remain significantly

greater than tc. In this experiment R was 20 Mn, C was 400 pf and tc was

100 ;sec. Thus RC was 8 msec, a factor of 8000 greater than t At the

high exposure rates vss(100 isec) constituted approximately 5% of the

measured v(t.). This could have been reduced by a factor of approximately

20 by reducing R to 1 Mt. Such a reduction wuuld have had a minimal

effect on the true value v(t ).

Anciher possible source of error incu-red during the neon chamber

temperature measurements involved the 2 foot air coax used to connect the

chamber to the RG62U cables coming froii the HVP. Sincc approximately a

two inch section of the air coax was partially heated during the experi-

ment the chance in the characteristic of t air coax with temperature

could possibly have had a meas'jrable effect on the parentt response of

the noon chamber. However, it is felt that due to the gas kinetic charac-

teristics of air and the relatively small volume involved, the air coax

temperature effect on the measured sir.al was negiigih)!e.














CHAPTER V
CON:CLUSIONS


To verify the Pulsed Ion Chamber app icbi !ity to the measuring of

the full range of reactor power- three basic s-eps were required. A

computer based, solid state, dual chamber PIC system had to be designed

and built. Gamma compensation for the expected mixed order (linear

and/or second order) response region had to se clearly verified. The PIC

mode chamber response had to be proven to bO independent of temperature

over a range of 25 to 500C.

The design and building of the computer based PIC system took con-

siderable time and effort, but the end result was success. It met all

the design requirements and more. Its versatility simply as a plasma

diagnostic too! is apparent. One has full control over all pulsing-

samiplinu sequences, as one can see in figure 3-3 all the timing sequence

potentiometers are on the front panel. The system is free from the time

jitter and position orientation problems which plagued the most advanced

mercury weite reed pulsers previously used. The impsdance switching

circuit ha: a response time on the order of )i nsec, die to the use of

the most advanced g'gi.iertz switching transistors. This in itself is an

improvement of a factor of 5 over the previous systems. Thus the system

is a significant advancement of the PIC state of the art.

Verifying the feasibility of gamma compensation ,as accomplished

relatively easily using the PiC computer based system. Compensation, at








a given temperature for the e';;osure rates ihera comlpeinsrtion would be

required, can be obtained to wii.in -22% ot the total gamma signal.

The PIC :mode chamber response was proven to be temperature dependent

over the range of 25 to 500'C For Ne as wel0 as the Ar-N2 fill gas

mixture. Hiowevr, as stated earlier, the NI response was constant up to

,282C. this constant range could he extended by reducing the pressure

of the Ne fill gas. The 300C temperatLure range is the operating range

of current light water reactors. Thus this [FIC system offers all the

required characteristics and more for an in-core wide rang" neutron

measuring system for present light va,,ter reactors,

A fiil gas whose PIC response is independent of temperature over

the 24EC to 500C range must he found before the sys-em could recalis-

tically be applied to power mrasurpnencs in the nmew iwre advanced HTGR

and LTEfBR reactors. Seeing that this is apparenT'ly the only remaining

sti:ur, lircg clock to the use of the PIC system for wio;. ra.nje reactor

pnwer measurements in these reactors a concentrated effort to find a

suitable gas should be launched.

In conclusion, since new findings and aavancemne;it ot the state-of-

the-art, both of which have been accomsilished here, are t nhe essence of

research, this was indeed a successful end-av i .













APPEN~!) i

HP 9821 Codes


The following HP9821 program were used to control the PIC system,

read and record data, perform ,:ata ann'lysis, aid finally output the data

in plot form.

PIC System Data Recordcing Cjode

This code records the Is, v(tc) and R/hr data used in this thesis.

0: PRT "THIS PROGRAM"

1: PRT "RECORDS S.S."

2: PRT CURRENT VS. PIC"

3. PRT "VOLTAGE SIGNAL"

4: PRT 'DATA AND STORES"

5: PRT "IT IN FILE"

6: PRT "GIVEN."

7: SPC 3

8: ENT "iTS NO. C.-MGDE I", R!2

9: ENT "'WTR NO. C-MODE 2", R13

10: ENT "VOLf. FULL ,AI.E", U7

11: EIT "VOLTS ZERO SCALE", R6

12: ENT "I FULL SCALE?", RIU

13: ENT "I ZERO SCALE?", R9

14: 21 -> RIG; 0 R17








In the above statements the expected value I limits of v(t ) and I

a:-e input as well as the range control n.;lumbers for the Keithley 119 pico-

amp; statements 8 and 9,

15- WTB 1, 192

16: CiM "?VS": FMT *; RED 13, A

17: 1- X

18: RED 3, Y, Z

19: X t 1 X; IF x < 200; JMP -1

20: CMD "?V5"; FMT *; RIED 13, B

21: B-A - C; IF C > 100; INT (C/l00) 60 + (C--NT (C/100) 100) C

22: C 1E6/200 R5; FLT 5; PRT "FERIOD IN 10-6 SECONDS ---", R5

Statement 15 contains the command w''hh switches the system into the

PIC mode. The remainder of this section measures the period of the

system utilizing the HP clock which is addressed in statements 16 and 20.

23: ENT "POSITION ?", X

24: "2"; WTC 1, R12; R3 -- X

25: 6.226376 + .403346 X .193881x 1 4 Y

26: Y + 1.168232E 4X + 5 3.396338E 6X + 6 + 4.052068E 8X + I -+ Y

27: 10 Y R (R16 + 4)

ThFe vertical port position is entered by .he exp.:rimenter and the

R/hr is computed from the seventh order curve fi i desci;-bed in Chapter

IV.

Statement ?4 switches the system inito t,;c steady state rode in order

to measure Iss for channel 1( i,,:)

28; "3"; GSB "DELAY"

29: RED 3, X, Y

30: I; Y < 200; IF R12 < 170; R12 + 1 i;-12: GET "2"








IF Y > 3000; IF R12 > 160; ki2 -- R!2 GTO "2"

GSB "DEI.AY"

RED 3, X, Z

IF ABS (Z-Y) > 60; GTO "3'

0 C


RED 3, X, Y

2 + Z; C + 1 -* C; IF C < 8; IMP 1

Z/10 7 Z

Z* .0033333 10 + (158 R12) RR16

IF R12 = 165; RR16 .1E-7 RR16; GTO "4"

IF R12 = 166; RR16 .05E 8 RR16; GTO

IF R12 = !67; RR16 1E9 X

IF R12 = 167; .03948 + .8529X + 7968E 6

3 Y; Y 1E 9 RR16


* X + 2 4.202E 4 X t


This section measures Iss1 10 times and then computes and stores

average.

'4"; WTB 1 R13

GSB 'DELAY"

RED 3, X, Y

IF Y < 200; IF R13 106, 313 + 1 + R13; 3JT "4'

IF Y > 3000; IF P13 > 96; R13 i -1 Ri3; l" "4"

GSB "DELAY:

RED 3, X, Z

IF ABS (Y z) > 60; GTO "K"

0 C

RED 3, X,

Z + Y Z; C + 1 C; IF C 1 8; JiP 1








z/10 Z

Z .003333 10 ', (94 R;3) F R ( +ii + 2)

R (R16 + 2) X

IF R13 = 10!; x .1E-7 R (R6- + 2); CO) "B"

i! R1. = 102; X -.05E-8 -- R ('16 4 2); GTO "B"

IF R13 103:, GTO "B"

X 1E9 X; .03948 + .8529X + 7968E-C X t 2 4.202E.-4 X + 3 Y

Y 1E-9 R (R16 + 2)

This section measures and store;: the iss value for channel 2.

"B"; WTB i, 192

0 C; 0 X; 0 Z, 0 R1 6; 0 R19

35 + X; GSB "DELAY"

RED 3, Y, X; RED 5, Y, Z

X RI18 R18; 4- R19 -> R1I; C + 1 C; IF C < 9; JMP -1

R18/10000 R (R16 + 1); R19/1000 R (R16 + 3)

FLT 4; PRT R (R16 + 4), R (R16 +1), R, R6, R (R16 + 3), R (R16 +2);

R16 + 6 R16; SPC 1

v(tc) for channels 1 and 2 are measured and stored in this section.

10 values of each are measured and then averaged together.

ENT 'MORE? YES 1 NO + 0", Y

ENT "POSITION?", R3

IF Y 0; GTO "2"

ENT "NEW SET? Y 1 NO + 0", Y

IF Y > O; Ri6 + RR17; R17 + 1 R17; GTO "2"

R1i6 -+ RR17

ENT "TAPE?", A," FILI?"', A

RCF A, R (R16 1)

GTO "END'


No te

70:

71:

72:

73:

74:

75:

76:

77:

78:








This section asks if more dt.ta are to ') taken. If so, the cycle is

repate.d. If not the data are stored on tape in the specified tile.

79: "DELAY"

80: C.ML) "?V5"; FMT *; RED 13, A

81: "0"; CMD "?V5"; RED 13, 3

82: Fl- X # 35; 10 + X

83: F B-A <_ X; GTO "0"

84: RET

85: ':END"; END

This is a subroutine addressed after switching from channel to

channel or mode to mode. It delays the data recording fcr 10 to 35 sec

to allow the system to stabilize.

Curve Fittig LBy Chebyshev Polynnminals

This program10 fits a least-squares curve to a set of given data

points (x!, yl), (x2, y2),.., (x yn,) where the x lie in an interval

(a, b) and are equally spaced. The user specifies a degree m ar,d the

program outputs the coefficients a., a,,..., am of a polynomial P(x) = a0

+ alx +...+a xm passing near or through each input point.

The program determines ihe a, by considering P(x) as a linear combin-

ation of Chebyshev pnlynomials Ti(x), P(x) = c,0T(x) + clT.(x) +...+

c T (x) and applying the least-squares criterion to the expression


n 2
S = yl P(x) to give a system of simultaneous equations -= 0,
i::i

j = 0, I,..., m from which the c can be determined. Calculation of the

ci is facilitated by using the orthogonality properties of the Chebyshev








polynomials aid evaluating "(x) at special points


c o s. ( 1) ,
x. =- 2-E +)---- within the interval (-I, 1) to force off-diagonal ele-



ments to be zero in this system of equations. Corresponding values yi

are needed in the system of equations in orde,- to be able to solve for

the c The program obtains these by apdpying a linear transformation to

the xi to bring the xi within the interval (-1, 1) and then using these

transformed values and applying the Lagrange interpolation formula to the

xi to obtain the yi. The system of equations is then easily solved for

the c.. The program then applies a linear transformation to x to change

the expression P(x) = c00l(-) + clT1(X) +...+ CmTm(x) to the forin P(x) =

a0 + a1x +...+amxm' over the original interval (a, b).

0: TBL 4; ENT "DEGREE?", 7 + 1 -+ R, "Xl ?", r X. "DELTA X?", R9;

CFG 13; TBL 2

i: PRT "DEGREE"; SPC 1; PRT Z; SPC 2; PRT "X", "Y"; SPC 1; 12 + RO Z

2: ENT "Y?", RZ; IF FLG 13 = 0; PRT x, RZ; SPC 1; X + R9 + X; Z + 1

Z R1; JMP 0

3: SPC i; PRT "COEFFICIENTS"; SPC 1

4: (((Mi--12 -+ R7) + R (1 A) R2) +- G 3) + R6 R4

5: COS ((-/2) (2A-1)/R6) R (R6-A + R2); J!MP (A -+ i A) > R6

6: R7 1 A; 2/A + B; -1 RRi; R1 C

7: RC + 8 R (C + 1); JMP (C -- 1 -> C) = R2 -1

8:

9:

10: 0 -> A; I -+ 5




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