A measurement of neutron temperature in a uranium rod-water moderated lattice

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Title:
A measurement of neutron temperature in a uranium rod-water moderated lattice
Series Title:
BNL ;
Physical Description:
9 p. : ill. ; 27 cm.
Language:
English
Creator:
Kouts, Herbert J. C
Brookhaven National Laboratory
U.S. Atomic Energy Commission
Publisher:
United States Atomic Energy Commission, Technical Information Service
Place of Publication:
Oak Ridge Tenn
Publication Date:

Subjects

Subjects / Keywords:
Neutron irradiation   ( lcsh )
Nuclear fuel rods   ( lcsh )
Uranium   ( lcsh )
Genre:
federal government publication   ( marcgt )
non-fiction   ( marcgt )

Notes

Statement of Responsibility:
by H. Kouts ... et al..
General Note:
Cover title.
General Note:
Originally published 1954.
General Note:
"August 16, 1954."
General Note:
"Subject category: Physics."
General Note:
"Brookhaven National Laboratory, Upton, New York."
General Note:
"Work performed under Contract No. AT(30-2)-Gen-16."--P. 2 of cover.
General Note:
"Date Declassified: October 27, 1955."--P. 2 of cover.

Record Information

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University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 004703658
oclc - 432301893
System ID:
AA00012184:00001


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Su ?oLASSIFIED


UNCLASSIFIED


BNL-1986

Subject Category: PHYSICS



UNITED STATES ATOMIC ENERGY COMMISSION



A MEASUREMENT OF NEUTRON
TEMPERATURE IN A URANIUM
ROD-WATER MODERATED LATTICE

By
H. Kouts
K. Downes
G. Price
R. Sher







August 16, 1954

Brookhaven National Laboratory
Upton, New York



Technical Information Service, Oak Ridge, Tennessee


L
7'~, .d t3: Z"r


















Work performed under Contract No. AT(30-2)-Gen-16.


Date Declassified: October 27, 1955.


This report has been reproduced directly from the best
available copy.

Issuance of this document does not constitute authority
for declassification of classified material of the same or
similar content and title by the same authors.

Printed in USA, Price 15 cents. Available from the
Office of Technical Services, Department of Commerce, Wash-
ington 25, D. C.


GPO 987852


This report was prepared as a scientific account of Govern-
ment-sponsored work and is made available without review or
examination by the Government. Neither the United States, nor
the Commission, nor any person acting on behalf of the Commis-
sion makes any warranty or representation, express or implied,
with respect to the accuracy, completeness, or usefulness of the
information contained in this report, or that the use of any infor-
mation, apparatus, method, or process disclosed in this report may
not infringe privately owned rights. The Commission assumes no
liability with respect to the use of, or for damages resulting with
respect to the use of any information, apparatus, method, or proc-
ess disclosed in this report.







A MEASUREMENT OF NEUTRON TEMPERATURE IN A URANIUM ROD-WATER MODERATED LATTICE

By H. Kouts, K. Downes, G. Price, and R. Sher





Abstract: The relative danger coefficients of boron and cadmium have been

measured p an assembly of 1.15% enriched uranium rods in ordinary water, at

a water to uranium volume ratio of 3. The experiment consisted in finding the

relative effects on neutron multiplication of measured amounts of boron and

cadmium in the water moderator. The ratio of the observed danger coefficients

is a measure of the ratio of the cross-sections of the two poisons, and since

the two have very different cross-section curves in the thermal range, a basis

for the estimation of a neutron temperature exists. The measurement resembles

somewhat one done by G. P. Gavin (KAPL 112).


Under the aswBmption that the thermal neutrons have a Maxwell distribution of

velocities, the measurement imnlies a characteristic temperature of .0262

.001 volts (304 160 O). The water temperature at the time of the measure-

ment was 297 OK.


rperinmental Methods: A lattice of 1.15% enriched uranium rods, .600" diameter,

as loaded in a light water moderator until a multiplication of about 500 was

reached. The method of loading, and the safety precautions were as described

in BNL Log No. C-7605 (Safety of Subcritical Loadings in T-526), except that

now the console and instrumentation have been greatly improved. For instance,

during the measurement described in this report the flux levels were monitored

by six separate detectors and channels of instrumentation, and the safety rod


-1-






-2-

we set to trip on any one of four flux level monitors. In addition, a manual

rod trip and a manual water dump were available,


After this predetermined stopping point had been reached, the source was re-

noved, and the count rate from multiplication of spontaneous fission neutrons

was measured. A measured amount of boric acid solution was added to the water

moderator, after the equivalent volume of rure water was removed, and the count

rate was again measured. A measured amount of cadmium sulphate solution was

then added (again after removal of the same volume of moderator), and the count

rate was measured a third time.


Three counters were used to measure the flux levels at each stage. One was a

small BF3 counter at the center of a triangular lattice cell; the second was

a mall enriched uranium fission chamber at the center of a triangular lattice

cell, and the third was a fission chamber located inside a fuel rod. Three de-

tectors were used in order that independent checks on the results might be had;

they also increased the statistical accuracy, in that the determination of

relative flux level would be based on adding up the count rates from all counters.


While the flux level measurementa were made, the water temperature was monitored

by means of & chromel-alamel thermocouple.


Analysis: The reciprocal of the observed count rate is, for loadings sufficiently

near critical, linear in keff:

1 ff 1 the operator, as done her, ll


If a anall amnunt of poison is added to the moderator, as uwas done here, ke will
off






-3 -

change because of the effect on f. For sufficiently small increments, the change

in keff is proportional to the macroscopic cross-section of the poison in the

moderator:

SkoffO Zpoison

and we suppose this relation to hold for the poison concentrations used in this

measuremat. We let the subscripts 0, 1, 2 refer respectively to situations

where the moderator ws pure water, where it contained boron, and where it con-

tained boron and cadmiu. Farther, we let the changes in keyf produced by the

addition of the boron and the cadmium be respectively -$and -A Then

Il-( -ko = 1 -1 -
1MC1-k k





1 2 1 -k2 =1 k1

h1 e. 1



R2 R1 od

with the same constants of proportionality in both relations.

Therefore

1 1
R2 7cd
1 1 7
R1 Ro


Again, the macroscopic cross-sections are proportional to the mole fractions M

times the microscopic cross-sections, with Avogodro's number the constant of






-4-


proportionality. Thus

R2 R1 d cd

I I MB 1B
W, R

The cross-sections to be used in this expression are averages over the energy
distribution of the themal neutrons in the lattice. If we assume the flwc to

have a Maxwell energy distribution

% (E) dE = 1 EK
(kT)2 dE

then the averages are so

o = dE $ (E) ao (E) = eldB E1/2e-

o = dE (E) () = C2 dE 1/2 .-ET
S(E- E)2 (+ /4
The boron cross-section we take as 1/v, with cl = 11P.6. This corresponds to

the latest cross-section value of 750 barns at .025 e.v. The cadmium cross-

section is by recent data* characterized by BE = 0.176 e.v.,r = 0.115 e.v., and

a cross-section of 7700 barns at the peak of the resonance. Accordingly, e2 is

assumed to be 10.680.

The boron cross-eection can be integrated immediately, to give

oB 105 barns

Integration of the expression for the cadmium cross-eection is more involved.

It us accomplished in two ways by numerical integration for several values of

kT, and by an analytic approximation. This latter method involves transforming
the integral to


* J. Harvey, Private canmnnication.






5-

cd = 0 .2 O-2AT da
Q (U2 E,)2 +*2

than (using Paarseval's theorem on the convolution of two Fourier transforms)

into the form o

a = e2 dt F (eS2) u 2
-d 2 (U. 0g)2 +


The symbol "P" means here "Fourier transform of". This latter form can again be

transformed to lead to error functions of complex argument. These in turn lead

to expressions of the form
a a

e 2sin b v d 2 cos b vd v

0 o

These integrals can be evaluated by means of an approximation valid over the

entire range of the argument to better than one part in 105:

,2 -, d -n2
e 11t +2 Z2e cosh 2n
\(I n = 1)
Finally, all integrals involve only tabulated functions trigonometricc, hyper-

bolic, and error functions of real argument).


The calculation is only sketched, because of its length. The two independent

evaluations of oed (nuerical and analytic) agree to better than 1%.


The curves of ao, ocd, and ced are given as figures 1, 2, and 3.


Prior to the poisoning of the moderator, a curve of the spontaneous fission

multiplication was run as a function of rod loading. From this the critical


* See H. E. Salser, Mathenatical Tables and other aids to computation, pp. 67-70
(1951).






-6 -

mass was determined. This permitted rough estimation of the change in kef

caused by the poison. We found that adding the boron changed kef by about

3.6 x 10 ; the effect of adding cadmium uws to reduce keff again by about

2.8 x 10 3. These changes are certainly small enough to permit assuming linear-

ity between keff and Z poison"


Results: The observed count rates are given in table I. By the methods of the

preceding section, we calculate for the three cases:

BF3 counter: .780 .035

Fission chamber a
in moderator: .840 .053

Fission chamber 754 09
in fuel rod: = .754 + .049
Counters summed: .790 .022

The mole fractions used were respectively .09332 of cadmium and .5587 of boron.

Thus

.09332 "cd
.9332 cEd-= .790 a .022
.5587 an

%ed = 4.73 .17
OR

From figure 3 we get, then,

kT = .0262 .0014 ev

= 304 a* 160

The water temperature during the measurement us 2970 K. Thus the neutron

temperature was 70 160 above the moderator temperature.


The probable error cited is based solely on statistical considerations. There is

a possible additional source of error, from incorrect cross-sections. e estimate

that this uncertainty could increase the error by at most .OWV6 electron volts,

or 7 K.













BORON CROSS-SECTION AVERAGED OVER A MAXWELL
DISTRIBUTION WITH CHARACTERISTIC ENERGY kT
(ASSUMING o = 750 BARNS AT .025e.v.)




700



650-



S600
m


550



500
.025 .030 .035
kT (ev.)


Fig. I


















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x
-1




cr.
w


z
r. Lw




w

cr-



zo
0







O0
cn z
0a
II
p z


SNUV9


-8-


U)
z


O 4D >
0 (0 LO
o *

w-
O





3:


1






-9-





UNIVERSITY OF FLORIDA


3 1262 08229 990 9




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