I
MITNE-46
HEAVY WATER LATTICE
PROJECT ANNUAL REPORT
By
Irving Kaplan
D. D. Lanning
T.
J.
Thompson
September 30, 1963
Department of Nuclear Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts
I
LEGAL
NOTICE
This report was prepared as an account of Government sponsored work. Neither the United
States, nor the Commission, nor any person acting on behalf of the Commission:
A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use
of any information, apparatus, method, or process disclosed in this report may not infringe
privately owned rights; or
B. Assumes any liabilities with respect to the use of, or for damages resulting from the
use of any information, apparatus, method, or process disclosed in this report.
As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to, any information pursuant to his employment or contract
with the Commission, or his employment with such contractor.
This report has been reproduced
directly from the best
available copy.
Printed in USA. Price $2.50.
Available from the Clearing-
house for Federal Scientific and Technical Information, National Bureau of Standards, U. S. Department of Commerce,
Springfield, Va.
USAEC
DivisOn
o0Techica Infonoion
E
()so
, k
Ridge,
T-n-n
MITNE-46
PHYSICS
(TID-4500, 32nd. Ed.)
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF NUCLEAR ENGINEERING
Cambridge 39, Massachusetts
HEAVY WATER LATTICE PROJECT ANNUAL
REPORT
September 30, 1963
Contract AT(30-1)2344
U.S. Atomic Energy Commission
Editors:
Irving Kaplan
D. D. Lanning
T. J. Thompson
Contributors:
H. E. Bliss
F. M. Clikeman
W. H. D'Ardenne
J. W. Gosnell
J.. Harrington, III
I. Kaplan
H. Kim
D. D. L anning
B.
E.
A.
E.
R.
T.
G.
K. Malaviya
E. Pilat
E. Profio
Sefchovich
Simms
J. Thompson
L. Woodruff
TABLE OF CONTENTS
1. Introduction
1
2. Research Program
4
3. The Material Buckling
6
6
7
I. Lattice With 1.25-Inch Triangular Spacing
A. Axial Buckling of the 4-Foot Diameter Lattice
B. Radial Buckling of the 4-Foot Diameter Lattice
C. Radial Buckling of the 3-Foot Diameter Lattice
D. Axial Buckling of the 3-Foot Diameter Lattice
E. Material Buckling Values (Summary)
II. Lattice With 2.5-Inch Triangular Spacing
A. Axial Buckling of the 4-Foot Diameter Tank
B. Radial Buckling of the 4-Foot Diameter Tank
4.
Fast Fission Measurements and Related Studies
I. Theoretical Basis of the Measurements
A. 628
B.
C.
II.
625
Effect of Various Types of Foils on the
Fast Neutron Flux in the Test Rod
Experimental Procedures
A. 625 and 628
B. Fast Source Perturbation
III. Results
A.
B.
C.
9
10
12
12
12
13
13
15
15
15
16
17
18
18
22
26
628
625
Fast Source Perturbation
IV. Discussion of the Results
5. Studies of Epithermal Capture in U 2 3 8
Introduction
I. The U238 Cadmium Ratio and the Conversion Ratio
A. The U238 Cadmium Ratio
*
B. The Conversion Ratio, C
iii
26
29
32
37
41
41
41
41
45
TABLE OF CONTENTS (Concluded)
II. Microscopic Distribution of Intracell Activations
III.
6.
Studies of Techniques
Effect of Cadmium on Epicadmium Activity
53
B.
The Effect ot Foreign Material in the Fuel Rod
53
C.
The Effect of Counting Geometry
53
D.
Work Related to Effective Resonance Integrals
62
Intracellular Thermal Neutron Distributions
and Associated Problems
63
I.
63
Intracellular Thermal Neutron Distributions
A.
Experimental Methods
63
B.
Experimental Results
64
C.
Theoretical Methods:
11.
79
87
90
Introduction
90
I.
Measurement of Reactor Parameters
90
Buckling Measurements
91
Two-Region Lattices
95
Introduction
95
I.
95
Experiments
Single-Rod Measurements and Theory
98
Introduction
98
I.
98
II.
10.
Reactor Parameters
Research With Miniature Lattices
II.
9.
63
Introduction
D.
8.
53
A.
THERMOS and Cell Cylindricalization
7.
48
Theory
102
Experiments
Energy Spectra and Spatial Distribution of Fast Neutrons
in Uranium-Heavy Water Lattices
104
Control Rod and Pulsed Neutron Research
107
I.
II,
Stationary (Exponential) Experiments
107
Pulsed Neutron Experiments
115
iv
LIST OF FIGURES
Fig. 3.1
Fig. 4.1
4.2
4.3
4.4
4.5
4.6
4.7
"Best Value" of the Extrapolated Height H0 as a
Function of the Number of Points Used in Fitting
the Axial Activation Distribution
8
Axial and Radial Location of Detector Foil Packets
for Measurements of 628 and 625
19
Foil Arrangements for Cadmium Ratio and
Conversion Ratio Measurements
20
Equipment for Measuring Gamma Activity of
Depleted and Natural Uranium Foils
23
Axial and Radial Location of Detector Foil Packets
for Measurement of Fast Source Perturbation
24
Foil Packet Composition for Measurement of
Fast Source Perturbation
25
Foil Packet Compositions for Minimum Error
Determination of 628
27
Determination of the Function P(t) = 6 2 8 /F(t)
28
4.8a 628 as a Function of Radius,
Axial Location - 20", 2.50" Lattic.e
30a
4.8b 628 as a Function of Radius,
Axial Location - 20", 1.75" Lattice
30b
4.9
628 as a Function of Height,
Radial Location - 1.75", 1.75" Lattice
31
4.10 625 as a Function of Radius,
Axial Location - 20", 1.75" Lattice
33
4.11 6 25 as a Function of Height,
Radial Location - 1.75", 1.75" Lattice
34
4.12 Effect of Depleted Uranium Catcher Foils on
Depleted Uranium Fission Product Activity
35
4.13 Effect of Aluminum Sleeve Holders and Natural
Uranium Detector on Fission Product Activity
of Depleted Uranium Detector
36
4.14 628 versus Aluminum Catcher Foil Thickness
38
V
LIST OF FIGURES (Continued)
Fig. 4.15 Ratio of Fission Rate in U238 to Fission Rate in U235
628, for Uranium Rods, 1/4-Inch in Diameter
Fig. 5.1
5.2
39
Foil Arrangements for Cadmium Ratio and
Conversion Ratio Measurements
43
p 2 8 versus VM/V F
44
5.3a R 2 8 versus Radial Position in Lattice
46a
5.3b R 2 8 versus Axial Position
46b
5.4
Intracellular Copper Activity Distributions
49
5.5
Intracellular Gold Activity Distributions
50
5.6
Intracellular Depleted Uranium Activity Distributions
51
5.7
Intracellular Activity Distributions of CadmiumCovered Copper, Gold, and Depleted Uranium in
the 1.25-inch-pitch Lattice
52
Diagram of the Experimental Arrangement for
Microscopic Distributions to Study Effect of
Cadmium on Epicadmium Activity
54
Microscopic Np239 Activity of Cadmium-Covered
Depleted Uranium Foils, 1/ 16-Inch Diameter,
0.005-Inch Thick
55
5.10 Effect of Cadmium on Cadmium-Covered Foil Activity
56
5.11a Effect of Catcher Foils on Np239 Activity of
Depleted Uranium Foils
58a
5.11b Effect of Catcher Foils on Depleted Uranium
Np 2 3 9 Activity
58b
5.12 Effect of Aluminum Holder Foils on Depleted
Uranium Np 2 3 9 Activity
59
5.13 Relative Values of R 2 8
61
5.8
5.9
Fig. 6.1
6.2
The Holder for the Foils Irradiated in the Fuel Rod
Used in the Lattice with the 1.25-Inch Triangular
Spacing
65
The Holder for the Bare Foils Irradiated in the
Moderator Used in the Lattice with the 1.25-Inch
Spacing
66
vi
The Cadmium Box and a Section of the Holder Used
to Position the Box in the Moderator
67
6.4
The Three-Rod Cluster
68
6.5
Positions of the Foil Holders in the Experiments in
the Lattice with the 1.25-Inch Triangular Spacing
69
Directions of Intracellular Activity Traverses in
the Moderator
70
Gold Activity Distribution for Run A14; 2.5-MilThick, Gold Foils in a Lattice of 1/4-Inch Dianeter,
1.03% U 2 3 5 , Uranium Rods on a 1.25-Inch Triangular
Spacing
71
Gold Activity Distribution for Run A16; 4.3-Mil-Thick,
Gold Foils in a Lattice of 1/4-Inch Diameter, 1.03%
U 2 3 5 , Uranium Rods on a 1.25-Inch Triangular Spacing
72
Gold Activity Distribution for Run A13; 10-Mil-Thick,
Gold Foils in a Lattice oi 1/4-Inch Diameter, 1.03%
U2 3 5 , Uranium Rods on a 1.25-Inch Triangular Spacing
73
Fig. 6.3
6.6
6.7
6.8
6.9
6.10 Gold Activity Distribution for Run A4; 2.5-Mil-Thick,
Gold Foils in a Lattice of 1/4-Inch Diameter, 1.03%
U 2 3 5 , Uranium Rods on a 2.5-Inch Triangular Spacing
75
6.11 Gold Activity Distribution for Run A5; 4.3-Mil-Thick,
Gold Foils in a Lattice of 1/4-Inch Diameter, 1.03%
U 2 3 5 , Uranium Rods on a 2.5-Inch Triangular Spacing
76
6.12 Gold Activity Distribution for Run A9; 10-Mil-Thick,
Gold Foils in a Lattice of 1/4-Inch Diameter, 1.03%
U2 3 5 , Uranium Rods on a 2.5-Inch Triangular Spacing
77
6.13 Comparison of the Nelkin and Free Gas Energy
Exchanger Kernels for Heavy Water for Neutrons
Having an Initial Energy, E., of 8.4 kTM
78
6.14 Effective Activation Cross Sections for Metallic Gold
Foils (Note: E =0.548 cm-1, 2 =5.83 cm- 1 )
s
a
6.15 Gold Activity Distribution for Run A8; Dilute Gold
Foils in a Lattice of 1/4-Inch Diameter, 1.03% U2 3 5 ,
Uranium Rods on a 2.5-Inch Triangular Spacing
80
.81
6.16 Reflection of Neutrons from the Hexagonal and
Equivalent Cell Boundaries
82
6.17 Restrictive Paths for Neutrons in the Equivalent
Circular Cell
83
vii
LIST OF FIGURES (Concluded)
Fig. 6.18 Comparison of the One- and Two-Dimensional
THERM()S Calculations for the Lattice of 1/4-Inch
Diameter, 1.03% Enriched, Uranium Rods on a
1.25-Inch Triangular Spacing
86
Fig. 8.1
Cadmium Ratios in a Two-Region Lattice
97
Fig. 9.1
Single-Rod Experiment in MITR Lattice Facility
99
Fig. 11.1 Axial Flux Distribution in Tank of Pure Moderator
111
11.2 Measured Extrapolation Distance of Thermally
Black Cylinders as a Function of Radius
112
11.3 Fractional Change of Radial Buckling of a Pure
Moderator Tank, Produced by Cadmium Rods
of Different Radii
113
11.4 Radial Run With 2.60 cm O.D. Cadmium Rod
Placed Axially in Tank of Pure Moderator
114
11,5 Over-all Circuitry
116
11.6 Variation of Decay Constant With "Waiting Time"
118
11.7
120
Decay Constant vs. Buckling
viii
LIST OF TABLES
3.1
3.2
3.3
4.1
4.2
4.3
5.1
5.2
6.1
11.1
Radial Buckling of a Lattice With 0.25-Inch Diameter,
1.03% U 2 3 5 Metal Rods With a Triangular Spacing of
1.25 Inches
10
Material Buckling of the Lattice of 0.25-Inch Diameter,
1.03% U 2 3 5 , Uranium Rods in Heavy Water, With a
Triangular Spacing of 1.25 Inches
12
Material Buckling of the Lattice of 0.25-Inch Diameter,
1.03% U2 3 5 , Uranium Rods in Heavy Water, With a
Triangular Spacing of 2.5 Inches
14
Average Values of 628 Measured in the M.I.T. Lattice
Facility
29
Average Values of 625 Measured in the M.I.T. Lattice
Facility
32
Depleted Foil Correction Factors for Foil Configurations
Shown in Fig. 4.2
32
Values of the U 238 Cadmium Ratio in Lattices of
235
0.25-Inch-Diameter Uranium Rods Containing 1.03% U
45
Values of R28 Determined in Various Counting
Arrangements
60
Nuclear Parameters for the Lattices With 1.25-Inch and
2.5-Inch Spacings Obtained by Means of 1D and Modified
1D THERM(S Calculations
74
Measured Extrapolation Distances for Black Cylinders of
Different Radii
11.2 Experimental Results for Room Temperature (21*C)
Heavy Water
ix
110
121
ABSTRACT
An experimental and theoretical program on the physics of heavy
water-moderated, partially enriched lattices is being conducted at the
Massachusetts Institute of Technology. Experimental methods have
been adapted or developed for research on buckling, fast fission, resonance capture, and thermal capture. After being successfully tested
on lattices of one-inch-diameter, natural uranium rods in heavy water,
the methods have been applied to three lattices of 1/4-inch, 1.03%
enriched uranium rods, moderated by heavy water. Research programs
are also under way to take and correlate data from single-rod measurements, two-region lattice measurements, miniature lattice measurements, and pulsed neutron methods. In addition, a program is under
way to measure the effect of control rods in the lattice assembly.
x
1
1. INTRODUCTION
I. Kaplan, D. D. Lanning, and T. J. Thompson
This report is the third annual progress report of the Heavy
Water Lattice Project of the Massachusetts Institute of Technology.
The origin, early history, and main facilities of the project were described in the first progress report (NYO-9658, September 30, 1961).
The second progress report (NYO-10,208, MITNE-26, September 30,
1962) described the experimental methods adopted or developed, and
their application to three lattices of one-inch diameter, natural
uranium lattices in heavy water.
That report also included the initial
results obtained for a lattice of 0.25-inch diameter rods of uranium
containing 1.03% U 2
35
, clad in aluminum, in a triangular array with a
spacing of 1.25 inches.
The present report gives more extensive
results for this lattice and for another lattice of the same rods with a
spacing of 2.50 inches.
The following reports and papers on the work of the Lattice
Project have so far been published in addition to the progress reports
cited; further details of the work are contained in them.
1.
J. T. Madell, T. J. Thompson, A. E. Profio, and I. Kaplan,
Spatial Distribution of the Neutron Flux on the Surface of a
Graphite-Lined Cavity, NYO-9657 (MITNE-18), April, 1962.
2.
A. Weitzberg, I. Kaplan, and T. J. Thompson, Measurements
of Neutron Capture in U 2 3 8 in Lattices of Uranium Rods in
Heavy Water, NYO-9659 (MITNE-11), January 8, 1962.
3.
P. F. Palmedo, I. Kaplan, and T. J. Thompson, Measurements
of the Material Bucklings of Lattices of Natural Uranium Rods
in D 20, NYO-9660 (MITNE-13), January 20, 1962.
4.
J. R. Wolberg, T. J. Thompson, and I. Kaplan, A Study of the
Fast Fission Effect in Lattices of Uranium Rods in Heavy
Water, NYO-9661 (MITNE-15), February 21, 1962.
5.
J. Peak, I. Kaplan, and T. J. Thompson, Theory and Use of
Small Subcritical Assemblies for the Measurement of Reactor
Parameters, NYO-10,204 (MITNE-16), April 9, 1962.
6.
P. S. Brown, T. J. Thompson, I. Kaplan, and A. E. Profio,
Measurements of the Spatial and Energy Distribution of
Thermal Neutrons in Uranium, Heavy Water Lattices,
NYO-10,205 (MITNE-17), August 20, 1962.
2
7. J. T. Madell, T. J. Thompson, I. Kaplan, and A. E. Profio,
Calculation of the Flux Distribution in a Cavity Assembly,
Trans. Amer. Nuclear Soc. 5 (June, 1962), p. 85.
8.
A. Weitzberg, J. R. Wolberg, T. J. Thompson, A. E. Profio, and
I. Kaplan, Measurements of U2 3 8 Capture and Fast Fission in
Natural Uranium, Heavy Water Lattices, Trans. Amer. Nuclear
Soc. 5 (June, 1962), p. 86.
9.
P. S. Brown, P. F. Palmedo, T. J. Thompson, A. E. Profio, and
I. Kaplan, Measurements of Microscopic and Macroscopic Flux
Distributions in Natural Uranium, Heavy Water Lattices, Trans.
Amer. Nuclear Soc. 5 (June, 1962), p. 87.
10.
P. S. Brown, I. Kaplan, A. E. Profio, and T. J. Thompson,
Measurements of the Spatial and Spectral Distribution of
Thermal Neutrons in Natural Uranium Heavy Water Lattices,
Brookhaven Conference on Neutron Thermalization, April 30May 2, 1962.
11.
K. F. Hansen, Multigroup Diffusion Methods, NYO-10,206,
April, 1962.
12.
I. Kaplan, Measurements of Reactor Parameters in Subcritical
and Critical Assemblies: A Review. NYO-10,207 (MITNE-25),
August 15, 1962.
13.
I. Kaplan, D. D. Lanning, A. E. Profio, and T. J. Thompson,
M.I.T. Exponential Lattice Studies, NYO-10,209 (MITNE-35),
presented at the IAEA Symposium on Exponential and Critical
Experiments, Amsterdam, September 2-6, 1963.
14. J. R. Wolberg, T. J. Thompson, and I. Kaplan, Measurement of
the Ratio of Fissions in U28 to Fissions in U 2 3 5 Using 1.60Mev Gamma Rays of the Fission Product La 1 4 0 , NYO-10,210
(MITNE-36), presented at the IAEA Symposium on Exponential
and Critical Experiments, Amsterdam, September 2-6, 1963.
15.
H. Kim, Measurement of the Material Buckling of a Lattice of
Enriched Uranium Rods in Heavy Water, M.S. Thesis, M.I.T.,
June, 1963 (Thesis Supervisor: T. J. Thompson).
16.
J. Harrington, Measurement of the Material Buckling of a
Lattice of Slightly Enriched Uranium Rods in Heavy Water,
M.S. Thesis, M.I.T., July, 1963 (Thesis Supervisor:
T. J. Thompson).
17.
R. Simms, I. Kaplan, T. J. Thompson, and D. D. Lanning,
Analytical and Experimental Investigations of the Behavior of
Thermal Neutrons in Lattices of Uranium Metal Rods in Heavy
Water, NYO-10,211 (MITNE-33), October, 1963.
18.
B. K. Malaviya, T. J. Thompson, and I. Kaplan, Measurement
of the Linear Extrapolation Distance of Black Cylinders in
Exponential Experiments, Trans. Am. Nuclear Soc., 6,240
(1963).
3
The project staff, as of September, 1963, is as follows:
I. Kaplan, Professor of Nuclear Engineering
T. J. Thompson, Professor of Nuclear Engineering
D. D. Lanning, Assistant Professor of Nuclear Engineering
A. E. Profio, Assistant Professor of Nuclear Engineering
F. Clikeman, Assistant Professor of Nuclear Engineering
H. Bliss, AEC Fellow
W. D'Ardenne, Research Assistant
J. Gosnell, Research Associate (not charged to contract)
J. Harrington, AEC Fellow
B. K. Malaviya, DSR Staff
H. S. Olsen, Visiting Scholar
S. G. Oston, Research Assistant
E. E. Pilat, Research Assistant
E. Sefchovich, Teaching Assistant (not charged to contract)
R. Simms, Research Assistant
G. Woodruff, DSR Staff (not charged to contract)
J. H. Barch, Senior Technician
A. T. Supple, Jr., Technician
Miss B. Kelley, Technical Assistant
D. A. Gwinn, Research Assistant (part time)
4
2.
RESEARCH PROGRAM
The general objective of the M.I.T. Lattice Project is to carry
out experimental and theoretical investigations of the physics of subcritical lattices of partially enriched uranium rods in heavy water.
An initial study was made with natural uranium rods 1.0 inch in
diameter, in triangular lattices with spacings of 4.5, 5, and 5.75 inches,
respectively.
These lattices were used to test the accuracy of some
of the methods adopted or developed and to obtain some new information.
The general program includes the study of rods containing U
235
of concentrations between one and two per cent and having diameters
from 0.25 inch to 0.75 inch.
The ratio of volume of heavy water to
that of uranium is to be varied, with values in the range 10 to about
100.
The measurements made include those of the following quantities:
macroscopic radial and axial thermal neutron flux traverses (giving
the critical buckling); activation ratios related to the fast fission
effect;
quantities related to the capture of resonance neutrons, in-
cluding the ratio of U
238
average U
238
captures to U
235
fissions in the fuel rod, the
cadmium ratio in the fuel rod, and quantities related to
effective resonance integrals; intracellular thermal and epithermal
neutron density (or flux) distributions.
In addition to the normal uranium rods, the following uranium
rods are available:
0.25-inch diameter rods of 1.03% U
metal; 0.25-inch diameter rods of 1.14% U
inch diameter rods of 1.1% U
rods of 2% U
U
235
235
235
235
uranium
uranium metal; 0.4-
uranium oxide; 0.4-inch diameter
uranium oxide; 0.75-inch diameter rods of 0.95%
23523
uranium metal; and 0.378-inch diameter rods of 0.95% U 2 3 5
uranium metal.
In addition to the main subcritical (exponential) assembly, fed
by thermal neutrons from the thermal column of the MITR, a "miniature lattice" has been used to study some of the quantities mentioned
above.
Experiments are also under way on the distribution of neutrons
in and around a single rod (or a few rods) in moderator.
Studies have
also been started on the properties of "two-region" or "substituted"
5
lattices. The three different types of studies have the additional object
of providing information which may lead to simpler and more economical methods of studying lattice physics.
Studies are also under way with pulsed neutron sources, with the
object of supplementing steady-state lattice experiments. The emphasis so far has been on reactivity and control rod effects. The general
program has been extended to include experimental studies of the
neutron energy spectra in the lattices under investigation. This work
has been limited thus far to activation experiments with threshold
detectors, but it is hoped that it can be extended further to include
studies with a neutron spectrometer.
The experimental work has two objectives:
(1) to improve exist-
ing methods and develop new ones where possible, and (2) to apply the
methods to various lattices. A program of theoretical research is
carried on parallel to the experimental work. This program also has
two objectives: (1) to relate the experimental results to existing
theory, and (2) to extend the theory where possible.
Finally, the M.I.T. Lattice Project has a pedagogical purpose:
to train students at the Doctoral and Master's levels in Reactor
Physics and help satisfy the need for experienced research workers
in this branch of Nuclear Engineering.
6
3. THE MATERIAL BUCKLING
F. Clikeman, J. Harrington, III, and H. Kim
Values of the material buckling have been obtained, from measurements of radial and axial activation distributions, for two unreflected
lattices of 0.25-inch diameter uranium rods (clad in 0.028-inch thick
aluminum and containing 1.03 per cent U 235 ) in heavy water with a
D 2 0 concentration of 99.7 per cent. In one lattice, the rods had a
(triangular) spacing of 1.25 inches; in the second lattice, the spacing
was 2.5 inches. The measurements on the former lattice were made
first in the 4-foot diameter tank and then in a 3-foot diameter tank, to
see if the difference in tank size affected the values obtained for the
buckling.
The Lattice Facility and the general methods used for making
the measurements and for analyzing the results have been described
in earlier reports (3, 13) . Some changes have been made in the experimental methods because of the close spacing of the rods in the
lattices of partially enriched rods. These changes, which have to do
mainly with the support and positioning of the rods and the design of
foil holders, are described in detail in two Master's theses (15, 16).
The details of the irradiation and counting of the foils are also given
there.
I.
Lattice With 1.25-Inch Triangular Spacing
The measurements on the unreflected lattice with 1.25-inch
spacing were made and analyzed by Mr. J. Harrington (16) and later
re-analyzed by Professor F. Clikeman.
Measurements of relative neutron flux were made by activation
of gold foils 0.010 inch thick, either 1/8 inch or 1/16 inch in diameter,
supported in aluminum foil holders. The foils were counted with
Throughout this report, the references to more detailed M.I.T.
reports are to those listed in the Introduction.
7
either a NaI scintillator counter or a proportional flow counter. The
resulting data were analyzed with the help of computer codes described
in other reports (3, 16).
A. Axial Buckling of the 4-Foot Diameter Lattice
This lattice contained 1285 rods. The determination of the
extrapolated height of the lattice prescribed a problem which was
solved in the following way. In fitting observed relative flux plots with
the hyperbolic sine function, all points less than 30 cm from the bottom
of the tank were rejected. Least-squares fits were made (with inverseflux weighting) with all the remaining points; points were then dropped
successively, starting at the top of the lattice. For each measured
distribution, the fitting process was triqd for various assumed values
of the extrapolated height, H0 , taken at intervals of two centimeters.
The "best value" of H for each distribution (denoted by H ) was taken
to be that which gave the lowest value of the sum of the squares of the
differences between the experimental and fit values at each point. A
graph of the "best value" of H as a function of the number of points
used in the fitting prdcess generally looked like Fig. 3.1. When all
the data points were used, the value of H was only a centimeter or
two greater than the actual length of the rods (121 cm); as points
were dropped, H increased to 128 cm, where a plateau was observed.
When still more points were dropped, the value of H increased, possibly because an attempt was being made to fit a nearly exponential distribution to a hyperbolic sine function. Although all the individual
experiments did not yield a plateau, most of them did, with the plateau
near 128 cm. Accordingly, the value of the extrapolated height was
taken as 128 ± 1 cm. This method seems to offer a consistent and
reasonable criterion for the choice of the points to be used in the
determination of the axial buckling.
Another requirement, used for both the axial and radial flux
traverses, was that the experimental results analyzed come from a
region in the lattice in which the cadmium ratio was constant to within
a few per cent. In the case of the axial data, this requirement was
nearly always consistent with obtaining the plateau discussed above.
8
134
Ho
128
122
of points
distribution
FIG. 3-1
"BEST VALUE"OF THE EXTRAPOLATED
AS A
FUNCTION
USED
IN FITTING
TRIBUTION.
OF THE NUMBER
THE AXIAL
HEIGHT H0
OF POINTS
ACTIVATION
DIS-
9
About 16 data points were used per run in the analysis.
2
Values of the axial buckling (y ) were obtained from four runs
with bare gold foils and three runs with cadmium-covered gold foils.
The runs were those free of experimental difficulties, e.g., with foil
holders or rod positioning.
The results are:
Bare gold foils:
Cadmium-covered
gold foils:
Y = (239.7 ± 10.0) X 106 cm
2
2
-6
-2
2 = (238.4±7.3) X 10
cm
The uncertainties given are, in each case, the product of the standard
deviation from the mean and the "Student's" T-factor. The latter was
used because of the relatively small number of runs used to determine
the buckling. The uncertainty is, therefore, a measure of the reproducibility of the individual experiments.
Since the results obtained with the bare and cadmium-covered
foils agreed well, they were averaged to give:
2
Axial buckling, in 4-foot tank: y
(239
5.5) X 10
-6
cm
-2
B. Radial Buckling of the 4-Foot Diameter Lattice
The radial buckling of the 4-foot lattice was determined from
data obtained in four experiments.
In one experiment, only bare gold
foils were used; in the three other experiments, bare foils were alternated with cadmium-covered gold foils. Because of the close packing
of the lattice, the number of cells in the radial direction was relatively
large and with one foil per cell, the number of foils which could be used
in a single experiment was still appreciable. The results of the individual runs are listed in Table 3.1. The values of the uncertainties
quoted are those associated with the least-square fit to the function
J (ar) and serve merely as an indication of the validity of the fit to
that function.
The average values of the radial buckling obtained from the runs
with bare and cadmium-covered gold foils are
Bare:
a2 = (1398.6 ± 14.7) X 10-6 cm-
Cd-covered:
a 2 = (1393.5± 5.9) X 10-6 cm-2
2
.
10
TABLE 3.1
Radial Buckling of a Lattice With 0.25-Inch Diameter, 1.03 Per Cent
U235 Metal Rods With a Triangular Spacing of 1.25 Inches
Condition of
Gold Foils
Run
Number
Number of
Data Points
Radial 2
Buckling, a
(cm 2 X 10 6
5
Bare
15
1385.1 ± 4.5
602
Bare
16
1407.1 ± 6.8
652
Cd-covered
15
1402.3 ± 9.0
702
Bare
17
1420.9± 41.2
752
Cd-covered
13
1385.6 ± 10.5
802
Bare
15
1381.2 ± 6.3
852
Cd-covered
15
1392.5 ± 70
The values of the radial buckling obtained with bare and cadmiumcovered gold foils agree well.
2
a=
The average of all the results is:
(1396.1±7.6) X 10
-6
cm
-2
This value seems to be slightly smaller than the smallest value,
(1411± 6) X 106 cm 2, obtained in the same exponential tank for a
lattice of 1.0-inch diameter rods with a (triangular) spacing of 4.5
inches.
But the difference is probably not significant, in view of the
fact that the difference between the two values is nearly bridged by
the experimental uncertainties.
C.
Radial Buckling of the 3-Foot Diameter Lattice
The research program of the Lattice Project includes measurements to be made with fuel rods containing a greater concentration of
U
235
than 1.0 per cent.
Preliminary calculations indicate that some
of the more enriched lattices would be critical in the 4-foot tank.
tank three feet in diameter was therefore fabricated.
Since it
A
is
available, it was thought desirable to make some measurements in
both the 4-foot and 3-foot tanks to see if the experimental values of
11
any of the lattice parameters depend on the size of the subcritical
assembly. The lattice in the 3-foot tank contained 691 rods.
The diameter of the 3-foot tank was found, by direct measurement, to be 36 ± 3/16 inches, as a function of height. The lattice of
rods was shifted 1/4 inch off-center in a direction away from the
reactor and parallel to the axis of the thermal column. These deviations from the ideal cylindrical configuration are of approximately
the same magnitude as the differences obtained between fitted values
of the extrapolated radius, from flux traverse measurements. No
attempt was made to reshape the neutron flux entering the tank. The
tank was wrapped in cadmium sheet, as was the 4-foot tank, and surrounded by an annulus of air with an inner diameter of three feet and
outer diameter of six feet.
Before the insertion of the lattice into the 3-foot tank, the shape
of the radial flux distribution was determined at different vertical
levels between 11 cm and 108 cm from the bottom of the tank. At
11 cm, the flux distribution was somewhat flatter than a J (ar)
function; at 60 and 108 cm, good fits to a J (ar) function were obtained with an average value of the radial buckling of 2540X10 cFm,
corresponding to an extrapolated radius of 47.73 cm. The last value
agrees with the radius of 18.0 inches (45.72 cm) plus the extrapolation
distance of 0.71 Xtr with Xtr = 2.6 cm.
Some difficulties were experienced with the radial foil holders
in the 3-foot tank with the result that the value of the radial buckling
to be reported must be regarded as preliminary. Improvements are
being made and better values should be obtained. With this precaution,
the value obtained from three radial flux distributions in the 1.25-inch
spaced lattice was:
Bare gold foils:
a2 = (2362.8± 18.2) X 10-6 cm-2
The uncertainty is again the product of the standard deviation from
the mean and the "Student's" T-factor. The value obtained with the
lattice in the tank is significantly smaller than the value obtained with
the tank fitted with moderator.
12
D.
Axial Buckling of the 3-Foot Diameter Lattice
Three axial flux distributions were measured, each consisting
of 33 bare gold foils. The experimental data were analyzed as in the
case of the 4-foot tank. All data points below 30 cm from the bottom
of the tank were rejected. The same point-dropping scheme was used
and plateaus of varying length were again observed for H = 128 ± 1 cm.
The result obtained from the three experiments was:
Bare gold foils:
2
-6
-2
'Y = (1167.4± 13.1) X 10
cm
E. Material Buckling Values (Summary)
The results obtained thus far for the lattices of 0.25-inch diameter,
1.03% U235 , uranium rods are summarized in Table 3.2.
TABLE 3.2
Material Buckling of the Lattice of 0.25-Inch Diameter, 1.03% U 2 3 5
Uranium Rods in Heavy Water, With a Triangular Spacing of 1.25 Inches
DLateter
DaeeFol2 Foil
(fe et)
Condition
4
3
II.
Axial
Buckling
-2
6
(y2;cm X106)
Radial
Buckling
2
-2
6
2;cm X106)
Material
Buckling
2
-2
6
(B2; cm X10)
239.7 ± 10.0
1398.6 ± 15
1159 ± 18
(b) Cd-covered Au
238.4 ± 7.3
1393.5 ± 5.9
1155 ± 9
Average of
(a)and (b)
239.0 ± 5.5
1396.1 ± 7.6
1157 ± 9
Bare
1167.4 ± 13.1
236 2.8 ± 18
1195 ± 23
*(a) Bare Au
Lattice With 2.5-Inch Triangular Spacing
The measurements on this lattice, of 313 rods, were made and
analyzed by Mr. H. Kim (15) and re-analyzed by Professor F. Clikeman.
The experimental and analytic methods were essentially the same as
those used for the lattice with 1.25-inch spacing. Measurements were
made only in the 4-foot diameter tank.
13
Axial Buckling of the 4-Foot Diameter Tank
The extrapolated height of the lattice was determined by means
of the method described in the discussion of the lattice with 1.25-inch
spacing, and was 128 ± 1 cm, as in that lattice. The data points which
were used in the analysis were located between 30 cm and 108 cm above
A.
the bottom of the tank.
Five sets of measurements of the axial activity distributions
obtained with bare gold foils yielded the value,
Baegodfol:
2
Bare gold foils:
-
-6
(506.8± 14.2) X 10
cm
-2
2
.
Two sets of measurements with cadmium-covered gold foils gave:
Cd-covered gold foils:
y
2
(510.6 i 14.1) X 10
-
6
cm
-2
A single set of cadmium-covered natural uranium foils gave:
Cd-covered uranium foils:
y
2
506.0 X 10
-
6
cm
-2
Since the various results agreed well, they were averaged, with the
result:
-2
-6
2
cm
(507.7 ± 9.2) X 10
y
B. Radial Buckling in the 4-Foot Diameter Tank
The analysis of seven radial flux distributions measured with
bare gold foils yielded the result:
Bare gold foils:
2
i6 -
= (1392.5± 4) X 10
cm
-2
,
in good agreement with the value obtained for the lattice with 1.25-inch
spacing.
One flux distribution obtained with cadmium-covered gold foils
yielded the result:
-2
-6
2
cm .
Cadmium-covered gold foils: a = 1378 X 10
One flux distribution obtained with cadmium-covered uranium
foils yielded the result:
Cadmium-covered uranium foils:
a2
1371 X 10
-
8
cm
-2
14
The average for all the radial flux traverses was:
a2 = (1390.9± 3.8) X 10-8 cm-2
The values of the material buckling of the lattice of 0.25-inch
diameter uranium rods containing 1.03% U 235, on a triangular lattice
spacing of 2.5 inches, are listed in Table 3.3.
TABLE 3.3
Material Buckling of the Lattice of 0.25-Inch Diameter, 1.03% U 2 3 5
Uranium Rods in Heavy Water, With a Triangular Spacing of 2.5 Inches
Axial
Buckling
(- 2 :cm- 2 X106
Radial
Buckling
( 2 :cm- 2 X10 6 )
Material
Buckling
(B 2 :cm 2 X10
Lattice
Diameter
(fe et)
Foil
Condition
4
Bare Au
506.8 ± 14.2
1392.5 ± 4
886 ± 15
Cd-covered Au
510.6 ± 14.1
1378
867 ± 23
Cd-covered U
506
1371
865 ± 27
507.7 ± 9.2
1390.9 ± 9.2
883 ± 10
Average
6
15
4.
FAST FISSION MEASUREMENTS
AND RELATED STUDIES
H. Bliss
The methods developed in our earlier work on the ratio, 6 28
238
of
235
(4,14) and on the ratio of epito fissions of U
235
thermal to thermal fission of U
(4) have been extended and applied
fissions of U
to the 1/4-inch diameter uranium rods.
Results will be reported here
of the following experiments:
A.
Preliminary results of measurements of 628 in three lattices
of 0.25-inch diameter rods, containing 1.03% U 235, in heavy water, at
(triangular) lattice spacings of 1.25, 1.75, and 2.5 inches,respectively;
B.
Preliminary results of measurements of 625 in the same
three lattices;
C.
Results of a study of the perturbation of the fast flux in a
test rod by the presence of different types of foils in the test rod.
I.
Theoretical Basis of the Measurements
For the convenience of the reader, some of the formulas and
definitions underlying the method (4) will be repeated.
A.
628
For the general case in which the isotopic U
235
contents of the
two detector foils and the fuel material being studied are all different,
628 is:
(
628 = P(t)
5
28Ay(t) - S
1
-
Ay(t)
=NP(t)F(t)
(4.1)
.
The terms in Eq. 4.1 are defined as follows:
23
P(t) is the ratio of measured fission product activity per U
fission to the measured fission product activity per U
238
5
fission.
-y(t) is the ratio of measured fission product activity from a foil
depleted in U
235
content to the fission product activity from a foil of
natural uranium (or from a foil of fuel material if such material is
16
available) when both foils have been irradiated in the same neutron flux.
N25 N28
NN
NF
is an enrichment correction which is equal to unity
when the fuel material and second detector foil have the same U2 3 5
content.
A is the ratio
28 where the W's represent detector
foil weights and the N's represent numbers of atoms per cubic centimeter.
25
28
S is the ratio ND
ND
25
NF
~
NF
The subscripts D, N, and F refer to the depleted detector foil,
second detector foil (natural uranium in all measurements to be reported), and fuel material, respectively.
To determine 628, both P(t) and y(t) in Eq. 4.1 must be measured.
In all the methods used so far, this requires two experiments. First,
an absolute value of 628 is determined for a particular lattice configuration by using a fission chamber experiment or the La 140 counting
technique discussed in Ref. 4. Then, the quantity y(t) is measured in
the same lattice and Eq. 4.1 solved to obtain P(t). Once P(t) has been
determined, it will remain the same for different lattice pitches, providing the counting arrangement remains unchanged. Hence, further
determinations of 628 only require the measurement of -y(t), which,
when inserted in the expression F(t) and multiplied by P(t), yields 628.
B. 625
As a measure of the degree of thermalization of the neutron
spectrum, the quantity 625, defined as the ratio of epicadmium to sub-cadmium fissions in U 2 3 5 , is of interest. An expression for 625 may
be written by using the observed fission product activities of cadmiumcovered depleted and natural uranium foils and bare depleted and natural uranium foils, all of which have been exposed to the same flux.
The fission product activity of the cadmium-covered natural
uranium foil may be written as:
17
NCd =NT
EN
f
f2(E)(E)dE + (1-EN
c
f28r(E)*(dE]
E
A epicad+( 1 -EN)
=N
f
E
C
icad
(4.2)
In Eq. 4.2, EN is the weight per cent of U235 in the foil, NT is the total
number of uranium atoms in the foil (assumed to be constant for all
foils after normalizing for differences in foil weights), and Ec is the
cadmium cutoff energy. Similar expressions may be written for the
other three foils:
DCd
N
=N
2
TDEDA
Dec +(1-ED)A28]
ec
Je
N(A 25+A25
b = N TL'N\
sc ecl
(4.3)
+ (1-E)(A 28 +A28
ecj
,
(4.4)
Db = N
A 2sc5 +A 2eD+(1D)k
+(1-E
A sc+ecI'
+A
NTED(
T
,
(4.5)
EN
sc
Equations 4.2 through 4.5 may be solved to obtain 625
A2 5
25
A ec
sc
6225
N
-aD
Cd
Cd
(N -aD)-(N
-aD
b
b
Cd
Cd
(4.6)
where
a
C.
D
Effect of Various Types of Foils on the Fast Neutron Flux in
the Test Rod
The third area of work to be discussed involves the effect of the
presence of foils of depleted uranium, natural uranium, or aluminum
on the observed fission product activity of a depleted uranium foil. The
fission product activity in a depleted uranium foil arises almost
entirely from fast fissions of U 238. Consequently, any mechanism, such
as a perturbation in the fuel rod composition, which reduces the fast
18
flux in the region of the depleted detector foil will reduce the observed
fission product activity in the detector foil.
There are two sources of fast neutrons in any given lattice fuel
element. One source is fast neutrons from fissions within the fuel
element. The other is fast neutrons which leak out of neighboring fuel
elements and reach the given rod with sufficient energy to cause fast
fission (the so-called interaction effect). The second source is not
affected by a local perturbation in the fuel composition. However, the
introduction of aluminum, natural uranium, or depleted uranium in
place of fuel material (see Figs. 4.1 and 4.2 for a typical experimental
arrangement) lowers the thermal fission rate in these areas, which, in
turn, lowers the available supply of fast neutrons at the location of the
depleted detector foil. Experiments were designed to study this effect
and determine the magnitude of the factor needed to correct the fission
product activities. Experiments performed by Wolberg and reported
in Ref. 4, as well as subsequent experiments performed in the lattices
being reported here, indicated that the fission product activity in a
natural uranium foil was not affected, within the limits of experimental
error, by the presence of a fuel perturbation in the neighborhood of the
foil. This result is not surprising in view of the fact that almost all of
the activity in a natural foil is due to thermal fission. Thus, no correction factor is needed for the count rates of the natural uranium foils.
II. Experimental Procedures
A.
625 and 628
In all runs, these two quantities were measured together. In
addition, U238 cadmium ratios and initial conversion ratios were
measured in all runs by W. D'Ardenne, with the results presented elsewhere in this report. Figure 4.1 shows the location in the lattice of the
two fuel rods used, and the location within the rods of the foil packets
containing the natural and depleted uranium detector foils. Figure 4.2
is an enlarged view of the foil packets, showing the detector foil arrangement. It will be noted that the fuel rods are in equivalent radial positions.
Gold monitor foils were placed in the fuel rods, 10 inches above the foil
packets, to normalize any differences in axial flux at the detector
I
19
CENTRAL
BARE
FUEL
ROD
ROD
CADMIUM
COVERED
FUEL
ROD
FUEL
FUEL
FOIL
PACKET
FUEL
FIG.4.1
AXIAL AND RADIAL LOCATION OF DETECTOR
FOIL PACKETS FOR MEASUREMENTS OF
828 AND 825
20
"CADMIUM" ROD
0.028"Al
CLAD
0.006" AIR GAP
0.005" TEFLON
SLEEVE
0.005" NAT. U.
FUEL SLUG
/
-I
0020"CADMIUM
N
0.005" DEP U.-
0.060" FUEL
CATCHE R
DE TE CTOR
CATC HER
DE TECHOR
CATC HR
0.060 " FUE L
0.020" THICK
CAMIUM SLEEVE
I" LONG
OOZ'02C),,CADM,1UM"
FUEL SLUG
FIG.4.2
FOIL ARRANGEMENTS
828 AND 825
FOR MEASUREMENTS
OF
21
foil locations (see Fig. 4.1).
Catcher foils of the same thickness and composition as the
detector foils were placed on either side of the detector foils to eliminate the need for making fission product contamination corrections on
the surfaces of the detector foils.
The two detector foils and four catcher foils were inserted in
0.125-inch X 0.250-inch I.D. X 0.260-inch O.D. teflon sleeves along
with two 0.060-inch pieces of fuel material to make a foil packet as
shown in Fig. 4.2. The depleted uranium detector foil contained a
-6
235
concentration of 18 X 10 . The second detector foil was natural
U
uranium. Since the inside diameter of the aluminum cladding is 0.262
inch, the teflon served to keep the foils aligned horizontally within the
fuel rod. The aluminum or cadmium foils at either end of the foil
packet were made slightly oversize (0.258 inch) to prevent slippage
along the fuel of the teflon sleeve when the foil packets and fuel were
inserted in the aluminum cladding.
The foils were irradiated for 12 hours in the M.I.T. lattice
facility after first having been counted for background. After completion of the irradiation, the fuel rods were left in the lattice for approximately four hours and then integral gamma-counted with a baseline
setting equivalent to 0.72 Mev. This 4-hour cooling period reduced
the dose rate at the fuel rod surface to an acceptable level (about
1 r/hour) and allowed the U239 formed, with its 23-minute half-life,
239
. The decay process is accompato decay almost completely to Np
nied by a 1.2-Mev p ray (with associated bremsstrahlung radiation),
which would introduce activity corresponding to capture rather than
fission and would necessitate a correction if the U 2 3 9 were not allowed
to decay.
In addition to the normal measurement in which two fuel rods
were used, radial and axial determinations of 625 and 628 were made
in some of the lattices studied. The foil packets were constructed
exactly as described above.
For a radial measurement, cadmium-
covered and bare foils were placed in several (usually five) equivalent
radial positions at a height of 20 inches.
For an axial determination,
bare and cadmium-covered foil packets were located at 4-inch
22
intervals, beginning at 4 inches from the bottom of the fuel and extending to 28 inches, in two rods at the radial position shown in Fig. 4.1.
A diagram of the counting equipment used is shown in Fig. 4.3.
The scintillation detector was a 1-3/4-inch X 2-inch NaI(Tl) crystal.
B. Fast Source Perturbation
Figure 4.4 shows the location of the foil packets used to investigate the effect of removing fuel material from a region near the
depleted detector foils. The six rods were all located in equivalent
radial positions about the center rod of the lattice. Figure 4.5 shows
an enlarged view of the three types of foil packet construction used.
At a height of 10 inches from the bottom of the lattice, six
depleted foils were irradiated with varying thicknesses of depleted
catcher foils on both sides (see Fig. 4.5a). The thickness varied from
0.005 inch to 0.030 inch in steps of 0.005 iach.
At a height of 12 inches, four foil packets, each containing three
depleted uranium foils (two catcher foils and one detector foil) and two
0.060-inch pieces of fuel, were located (see Fig. 4.5b). On each end of
the packets were aluminum foils varying in thickness from zero to
0.060 inch in steps of 0.020 inch.
In addition, two of the rods contained packets (at 12 inches) consisting of 0.015 inch of depleted uranium (two catcher foils and one
detector foil) and 0.015 inch of natural uranium on one side of the depleted uranium (see Fig. 4.5c). No aluminum was placed at the ends of
these packets.
The rods were irradiated for 18 hours and gamma-counted as
described in the preceding section (II, A). From the obtained three sets
of foil count rates, it is possible to determine the count rate which
would have been obtained, had the fuel composition not been perturbed.
To check the correction factor obtained from the above experiment, a minimum error determination of 628 was made. This involved
minimizing the amount of fuel removed by the foil packet. Six rods
were used in equivalent radial positions (see Fig. 4.4). The foil packets
were all located at 20 inches. Three of the packets contained one 0.005inch depleted uranium detector foil with varying thicknesses of aluminum
23
BAIRD ATOMIC
NO. 815 BL
SCINTILLATION
PROBE
'/8" Al
BETA
SHIELD
FOIL
EIG. 4.3
EQUIPMENT FOR MEASURING GAMMA ACTIVITY OF
DEPLETED AND NATURAL URANIUM FOILS
24
CENTRAL ROD
FUEL
FOIL
PACKET
2' t
FUEL
FOIL
PACKET
10" FROM
BOTTOM OF
FUEL
REGION
FIG.4.4
FUEL
AXIAL AND RADIAL LOCATION OF
DETECTOR FOIL PACKETS FOR MEASUREMENT
OF FAST SOURCE PERTURBATION
25
FUEL
0.000"-0.060" Al
FUEL
0.060 " FUE L
0.005"-0.030" DEP U
O.OO5"DEP U
O.OO5" DEP U DETECTOR
O.OS"DEPU DETECTOR
0.005" DEP U
O.005"-0.030" DEP U
0.060" FUEL
FUEL
0.000"-0.060" Al
FUEL
TYPE A FOIL PACKET
(a)
TYPE B FOIL PACKET
(b)
FUEL
0.015" N AT U
0.005" DEP U
O.005"DEPU DETECTOR
0.005" DEP U
FUEL
TYPE C FOIL PACKET
(c)
FIG.4.5
FOIL PACKET COMPOSITION FOR MEASUREMENT
OF FAST SOURCE PERTURBATION
26
on either side. The thicknesses were 0.001 inch, 0.005 inch, and 0.010
inch, respectively. The other three packets each contained one 0.005inch natural uranium detector foil with the same three thicknesses of
aluminum. An enlarged view of the foil packets is shown in Fig. 4.6.
III. Results
A.
628
The La140 counting technique gave a result of 0.0179 ± 0.0004 as
235
the absolute value of 628 for a 1.03% U
, 1/4-inch diameter rod in a
lattice with a 2.50-inch spacing. The function F(t) in Eq. 4.1 was also
determined at the same locations in the lattice as were used to
measure the absolute value of 628.
Equation 4.1 was then solved for
P(t) to give:
P(t)
628
F(t)
1.12
0.03 .
Figure 4.7 is a graph of P(t) vs. time, from which it can be seen that
P(t) stayed nearly constant over the times of interest. Since P(t) is
also a calibration of the counting system used, the above value can only
be used if the counting arrangement remains unchanged.
The above value of P(t) was used to determine 628 for three
lattices and a single rod immersed in heavy water.
All measurements
were made at a height of 20 inches and at the radial location closest to
the central rod. The results are listed in Table 4.1. The correction
factors for the depleted foil activities (discussed in sections I., C and
II., B and results given in section III,,C) have been applied to the values
given in Table 4.1.
Radial measurements of 628 were made in the 2.50-inch and
1.75-inch lattices, and an axial measurement was made in the 1.75inch lattice. The results are shown in Figs. 4.8a, 4.8b, and 4.9,
respectively.
27
FUEL
FUEL
0.001"-0.010" Al
0.001"-1 0.O0O0" A I
0.005"DEPU DETECTOR
O.OO5"NAT U DETECTOR
0.001"-0.010" Al
0.001" 0.010" A
FUEL
FUEL
FIG. 4.6
FOIL
PACKET
COMPOSITIONS
ERROR DETERMINATION
FOR
OF 828
MINIMUM
r\)
1.20 1.15 1.10 1.05 P(t)
1.000.95 0.900.85 0.80
-
0
FIG.4.7
100
200
300
400
500
TIME AFTER IRRADIATION -MINUTES
DETERMINATION
OF THE FUNCTION
600
-+
P(t) = 8 2 8 / F (t)
700
29
TABLE 4.1
Average Values of 628 Measured in the M.I.T. Lattice Facility
Rod Spacing 6
28
(Inches)
Standard Deviation(b)
of the Mean
Number of
Determinations
Total(d)
Error
1.25
1.75
0.0259
0.0232
0.0007
0,0014
2
4
0.0011
0.0016
2.50
0.0181
0.0003
6
0.0007
2.50
0 . 0 17 9(a)
0.0002
0 . 0 0 0 5 (c)
6
1
0.0004
0.0008
oo
0,0176
(a) Absolute value of 628 determined in 2.50-inch lattice by La14 0
counting.
(b) The standard deviation of the mean of n measurements includes
reproducibility among a set of determinations; it also reflects
the uncertainty due to counting statistics.
(c)
This value is computed as the standard deviation of a set of
measurements; there can be no estimate of the reproducibility
error for a single determination.
(d)
The total error is an estimate of the over-all uncertainty in the
values of 628. It includes the effects of reproducibility and
counting statistics as well as the uncertainties in P(t) and the
depleted foil correction factors.
B. 625
Values of 625 were determined in the three lattices studied.
Because all four detector foils were counted at different times and had
different weights, the resulting count rates were normalized to the
count rate of the cadmium-covered natural uranium detector foil. The
results are listed in Table 4.2.
Radial and axial determinations of 625 were made in the 1.75inch lattice. The results are given in Figs. 4.10 and 4.11, respectively.
I
I
I
I
I
I
I
I
I
I
I
0.028
0.024
828
I
I
0.020
0.016
I
I
0.0 12 0.00 8
0.00 4 10000
0
I
I
2
4
FIG.4.8 a
I
I
I
I
I
16
14
12
10
8
6
RADIAL LOCATION IN INCHES
828 AS A FUNCTION OF RADIUS
AXIAL LOCATION-20 INCHES,
2.50 INCH LATTICE
I
18
I
I
20 .22
--
w
30b
I
l
I
I
I
-I
-{
0.0280
0.0240
0.0200
t
828
0.0160
0.01 20
0.0080
0
RUN I
0
RUN 2
0.0040
0.00000
II
2
4
I
I
i
6
8
10
RADIAL LOCATION
FIG.4.8b
i
12
IN INCHES
14
16
-
828 AS A FUNCT ION OF RADIUS
AXIAL LOCATION - 20 INCHES , 1.75
INCH LATTICE
0.02800.02400.02008280.01600.01200.00800.0040-
0.0000
4
FIG.4.9
8
LOCATION FROM
24
20
16
12
BOTTOM OF LATTICE IN INCHES --
28
828 AS A FUNCTION OF HEIGHT
RADIAL LOCATION -175
1.75 INCH LATTICE
INCHES,
t-j
32
TABLE 4.2
Average Values of 625 Measured in the M.I.T. Lattice Facility
Standard Deviation (a)
of the Mean
Rod Spacing
(Inches)
625
1.25
0.0522
0.0060
1.75
2.50
0.0303
0.0184
0.0010
2
2
0.0023
4
2.50
0.0120b
0. 0 0 1 0 (c)
Number of
Determinations
(a) The standard deviation of the mean is a reflection of counting
statistics and reproducibility of the results.
(b) Substituted lattice - see note (a) on Table 4.1.
(c)
This value is computed as the standard deviation of a set of
measurements.
C.
Fast Source Perturbation
The effect of removing fuel from the region near a depleted
detector foil is shown in Figs. 4.12 and 4.13. Figure 4.12 shows the
effect of depleted uranium and Fig. 4.13 shows the effect of natural
uranium and aluminum.
The curves were extrapolated to find the
expected count rate with no fuel removed. A correction factor was
determined for each of the three materials and the results summed
to find an over-all correction factor for the depleted foil count rates.
It should be noted that the over-all correction factor is different for
each lattice spacing because the interaction effect varies with lattice
spacing.
Table 4.3 lists the correction factors which were determined.
TABLE 4.3
Depleted Foil Correction Factors
for Foil Configurations Shown in Fig. 4.2
Lattice Spacing
Correction Factor
1.25 inch
1.08 ± 0.02
1.75 inch
1.09 ± 0.02
2.50 inch
1.10 ± 0.02
1.12 ± 0.02
o
33
I
1
1
1
I
I
I
I
0.0440
0.0400
0.0360
t
825 0.0320
-I
0.0280
0.0240
0.0200
I
I
0
2
4
RADIAL
FIG.4.10
I
I
I
I
14
12
10
8
6
LOCATION IN INCHES --
I
6
AS A FUNCTION OF RADIUS
AXIAL LOCATION -20 INCHES,
8 25
1.75 INCH LATTICE
w)
0.03600.0320-
0.0280
t
825 0.02400.02000.0160-
0.0120L
4
8
12
16
20
LOCATION FROM BOTTOM OF LATTICE IN INCHES
FIG.4.II
825
AS A FUNCTION OF HEIGHT
RADIAL
LOCATION - 1.75
1.75 INCH LATTICE
INCHES ,
24
--
28
1.2
z
0
w
H
w
-j
1.0
H
0
O
Q)
0
LU
z
0.9
0
C')
c,)
a:~0.8_
40
30
0
20
10
URANIUM,
DEPLETED
OF
CKNESS
TOTAL THI
FIG. 4.12
60
50
IN. X 103
70
EFFECT OF DEPLETED URANIUM CATCHER FOILS ON DEPLETED
URANIUM FISSION PRODUCT ACTIVITY
"-p
I
I
A
B
FUEL
SLUG
FUEL
SLUG
AL
FUEL
CATCHER_
DETECTOR
DEP U.
0-60 MIL
60 MIL
NAT. U
CATCHER
DEP. U.
5 MIL
CATCHER
FUEL
AL
DETECTOR
CATCHER
o- 0-15MIL
>-
5 MIL
FUEL
SLUG
60 MIL
0-60 MIL
FUEL
SLUG
u-
5
NATURAL URANIUM
W-
CA)
ON
I
o ARRANGEMENT
A ALUMINUM
0 ARRANGEMENT
B URANIUM
1.0
00
wcr
ALUMINUM
NO- 0.9
-jz
0
0L
I
0.8
0
FIG. 4.13
10
THICKNESS
I
I
40
20
30
OF ALUMINUM OR NATURAL
I
50
URANIUM,
I
60
IN. X 103
EFFECT OF ALUMINUM SLEEVE HG LDERS AND NATURAL URANIUM
DETECTOR ON FISSION PRODUCT ACTIVITY OF DEPLETED
URANIUM DETECTOR
37
The uncertainties in the correction factors were obtained from the
uncertainties in the coefficients of the least-square straight-line fit
to the data shown in Figs. 4.12 and 4.13.
By minimizing the amount of fuel removed in the region of the
depleted detector foil, a minimum error estimate of 628 was obtained
for the 1.75-inch lattice. Figure 4.14 shows 628 as a function of
aluminum catcher foil thickness. Extrapolating this curve to zero
aluminum thickness and also correcting for the .005-inch depleted
detector foil yields a value of
628 = 0.0233 ± 0.0007 .
The uncertainty shown is the total uncertainty which includes the estimated errors in P(t), least-squares fit of Fig. 4.14, and the correction
factor for the 0.005-inch depleted uranium detector foil. This uncertainty is approximately one half that given in Table 4.1 for the 1.75inch lattice.
IV.
Discussion of the Results
The results obtained in the present study are compared in
Fig. 4.15 with earlier results obtained at M.I.T. in the Miniature
Lattice Facility (5), and with results obtained at the Brookhaven
National Laboratory with 0.25-inch diameter rods in lattices moderated with ordinary water . The results indicate some discrepancies
between the two sets of M.I.T. results. In particular, the value obtained
for 628 in the exponential lattice with the 1.75-inch spacing seems too
high, and the value obtained in the present study for the single rod in
heavy water is significantly higher than that obtained in the earlier
study (4). As a result of the above analysis for correction factors, it
is expected that some additional corrections could be made to the previous miniature lattice measurements which will raise the values
slightly. The causes of these discrepancies are now being sought.
R. L. Hellens and H. C. Honeck, A Summary and Preliminary Analysis
of the B.N.L. Slightly Enriched Uranium, Water-Moderated Lattice
Measurements, Proceedings of the IAEA Conference on Light Water
Lattices, Vienna, June, 1962.
0.032
wA
0.0 2 8
0.024
828
0.020k
~mmEi
I
.~
0.0 16 K
FUEL
AL
FUEL
+-
1-10 MIL-+
AL
DEPU.
NAT. U.
AL
AL
FUEL
FUEL
0.0 12 -
0.008
0
2I
4
6
AL CATCHER
FIG. 4.14 828 VERSUS
I
8
FOIL
10
THICKNESS,
ALUMINUM
CATCHER
14
12
IN. X 103
FOIL
THICKNESS
I
16
0.14
II
I
I
I
I
I
,
,
,
i
i i i
I
0
i
i
i
i
i
i
I
0 BNL (H 2 0- MODERATED, 1.14 % U2 3 5 )
0.12
o BNL (H2 0-MODERATED,1.03% U 235)
D
v , x MIT (D2 0- MODERATED, IN MINIATURE
LATTICE, 1.14 % U 2 3 5 )
0
0
z 0.10 -
o MIT(D
0
in
i
I I I I
2 0-
MODERATED, IN EXPONENTIAL
ASSEMBLY, 1.03 % U 2 3 5 )
03
0.08
0
c-
E0
0
0.06 1-
z
0
(I)
0.04
H-
x
LiL
0
2
X0
0.02
0
I-
I
x
-4
I
I
FIG. 4.15
I
I
I
I
I I II
I 1I I11111i
I
I
I
I I II
I II II I11111
I
I
I
~
10
100
RATIO OF MODERATOR VOLUME TO URANIUM VOLUME
RATIO OF FISSION RATE IN U238 TO FISSION RATE
URANIUM RODS, 1/4-INCH IN DIAMETER
IN U 235'
I ~ I II II II II II
828, FOR
40
Apart from the result for the 1.75-inch lattice, the results obtained in
the miniature assembly and in the exponential assembly agree reasonably well and indicate that the miniature lattice may be a satisfactory
assembly for the study of the fast fission effect. The results obtained
for the heavy water lattices are not inconsistent with those obtained in
the more closely packed B.N.L. lattices, moderated with ordinary
water. In view of the different natures of the lattices, and the, as yet,
unresolved internal discrepancies in the M.I.T. results, no attempt was
made to draw a smooth curve through all the results.
Further work is in progress on 628 and 625, and the results
given in this report are preliminary in nature. Further details of the
work reported will be given in a Master of Science thesis to be completed shortly by Mr. Henry Bliss.
41
5.
STUDIES OF EPITHERMAL CAPTURE IN U 2 3 8
W. H. D'Ardenne
Introduction
Earlier work (2) on the capture of neutrons in U
2 38
has been
extended to the lattices of slightly enriched rods in heavy water.
238
cadmium ratio, R 28 and
Measurements have been made of the U
235 .
238
fission rate, C
capture rate to the U
of the ratio of the U
capture223
The intracellular distributions of neutron capture rates in
U2
38
and copper were determined with both bare and cadmium-covered
foils.
Considerable
effort was put into studies of technique:
(1) of the effect of the amount of cadmium used on the measured activities of cadmium-covered foils; (2) of the effect of different types of
catcher foils on the measured activities of detector foils;
(3) of the
effect on the value of the cadmium ratio of nonuniform distributions of
radioactivity in detector foils.
Finally, work has been continued on
measurements of the effective resonance integrals of various nuclides.
I.
The U238 Cadmium Ratio and the Conversion Ratio
A.
The U 2 3 8 Cadmium Ratio
The average U238 cadmium ratio was measured by irradiating
two 0.005-inch-thick, depleted uranium foils containing 18 parts U 2 3 5
per million at equivalent positions in the lattice with one foil surrounded
by 0.020-inch-thick cadmium.
inch-thick fuel buttons.
Each foil was placed between two 0.060-
Depleted uranium foils identical to the detector
foils were put between the fuel buttons and the detector foils to prevent
U2
3 5
fission products in the fuel from reaching the detector foils. The
stacks of foils and fuel buttons were placed inside sleeves of "Teflon",
0.125 inch long and with a wall thickness of 0.005 inch.
At either end
of these packets, there were placed 0.020-inch-thick "holder" foils
which kept the "Teflon'
sleeves in position.
The holder foils were
made of aluminum for the bare detector foil and of cadmium for the
42
cadmium-covered detector foil. The holder foils were 0.258 inch in
diameter, 0.008 inch larger than the diameter of the fuel or catcher and
detector foils, and 0.004 inch smaller than the internal diameter of the
aluminum cladding. These assemblies were placed between two fuel
slugs in a lattice fuel rod. In the case of the cadmium-covered detector
foils, a 0.020-inch-thick, 1-inch-long cadmium sleeve was positioned
outside the 0.028-inch-thick aluminum cladding of the fuel rod so that
the midpoint of the cadmium sleeve was located adjacent to the
cadmium-covered detector foil. A compressive force was applied to
the fuel inside the fuel rod to ensure that the foils were kept tightly
together. A schematic of the foil arrangements is shown in Fig. 5.1.
Normally, the bare detector foil and the cadmium-covered
detector foil were irradiated at a height of 20 inches from the bottom
of the fuel (the length was 48 inches) and 4n two fuel rods diametrically
opposed to each other and adjacent to the central fuel rod of the lattice.
The usual length of each irradiation was 12 hours with a cooling period
2 39
of at least four hours to permit the U239 produced to decay into Np
before the first count was taken. The 103-key peak of Np239 was
counted by a single-channel analyzer with a 1/2-inch-thick, 1-1/2-inchdiameter NaI(Tl) crystal. The window of the analyzer accepted gamma
rays ranging in energy from 84 key to 122 key. The 84-key gamma ray
of Tm 170 and the 122-key gamma-ray peak of Co 57 were used to calibrate the window settings each time the system was used and also to give
a sensitive indication of any drift during each counting session. At least
four sets of foils were irradiated for each fuel rod spacing, and each set
of foils was counted at least four times.
The results for the three lattices with rod spacings of
1.25 inches, 1.75 inches, and 2.50 inches (0.25-inch-diameter fuel rods
containing 1.03% wt. U 235), are listed in Table 5.1 and are compared in
Fig. 5.2 to measurements made in a miniature lattice at M.I.T. by
J. Peak (5). The quantity plotted as ordinate is actually
_
28R
1
28 - 1
_ epicadmium activity of U 238foil
subcadmium activity of U 238 foil
43
"BARE"
ROD
0.028" AI CLAD
0.006" AIR GAP
0.005" T E F LO N
SLE EVE
0.060" FUEL
0.005" NAT. U.
0.005"
CATCHER
DETECTOR
CATCHER
DE R U.CATCHER
DER UDE TEC TOR
CATC HER
0.060" FUEL
/0.020" Al
FUEL SLUG
FIG. 5.1
FOIL ARRANGEMENTS FOR CADMIUM RATIO
AND CONVERSION RATIO MEASUREMENTS
1.6
_r=
1.4
1.2
1.0
P2 8
0.8
0.6
0.4-
0.2-
0.
0
10
20
30
40
50
60
MODERATOR TO FUEL VOLUME
FIG.5.2
P2 8
VERSUS
VM
VF
70
80
RATIO, V
90
100
110
45
TABLE 5.1
Values of the U2 3 8 Cadmium Ratio in Lattices of 235
0.25-Inch-Diameter Uranium Rods Containing 1.03% U
L attice
Ratio of
Average Cadmium
Spacing
Moderator Volume
Ratio, R 2 8
(Inches)
to Fuel Volume
Average Value of
1
P28 R23 ~
1.25
2.188 ± 0.010
0.8416 ± 0.0071
1.75
25.9
52.4
2.50
108.6
3.308 ± 0.016
5.47 2 ± 0.029
0.4333 ± 0.0030
0.2236 ± 0.0014
The results obtained in the exponential and miniature lattices
agreed reasonably well, in view of the large theoretical corrections
(up to 25 or 30 per cent) which had to be applied to the results obtained
in the miniature lattices to permit comparison with the results expected
Those theoretical corrections were derived
in an exponential assembly.
(5) on the basis of age-diffusion theory, and the results indicate that a
better theoretical treatment of the correction seems worthwhile and that
satisfactory results for R 2
8
and p 2
8
may be obtained from measure-
ments in a miniature lattice.
The U 2
3
-cadmium ratio was measured as a function of radial
the results are
position and as a function of axial position in the lattice;
shown in Figs. 5.3a and 5.3b. The value of R 2 8 was constant radially except
near the edge of the lattice, i.e., to within a few inches of the tank wall.
The axial measurements hint at the existence of a minimum value of
R28, in qualitative agreement with the theoretical treatment by Peak
et al. (5); the effect, however, is quite small, and further work is
required.
B.
The Conversion Ratio, C
The measured conversion ratio, designated by C
,
is the ratio of
the U238 capture rate to the U235 fission rate in the fuel. The method
first used at M.I.T. (2, 8)
has been extensively modified and is
now
I
I
I
I
I
I
I
0
1.0
I
Go 0.8
c'J
cr-
'4
LL
'4
I
0
-LJ
0.6 [-
-)
Lli
'4
'4
'4
'4
I
'I
I
0.4 H
*
1.75 IN.-PITCH,3FT. TANK
A
2.50 IN.-PITCH,4FT. TANK
0.2 I-
0
0
I
4
RADIAL
FIG.5.3a
I
8
DISTANCE
R 2 8 VERSUS
I
12
16
CENTRAL
FROM
RADIAL POSITION
I
24
20
ROD, INCHES
IN LATTICE
"or
14
I
I
e 1.75
A 2.50
INCH-PITCH,3FT TANK
INCH- PITCH,4FT TANK
1.3 -
11
o 1.2
C,)
w
-J
cLI
1.0 k-
I
I
0.9
0
4
8
HEIGHT
F IG.5.3 b
12
FROM
-0-_
-
0
I
I
24
16
20
BOTTOM OF FUEL , INCHES
R2 8 VERSUS AXIAL POSITION
28
32
47
basically the same as a method recently reported by Tunnicliffe et al!a)
of Chalk River.
*
With the new method, the ratio C was obtained by irradiating
four foils, a 0.005-inch-thick natural uranium foil and a 0.005-inchthick depleted uranium foil in the lattice at the same position as was
used in the determination of R 2 8 , and, at the same time, a 0.005-inchthick natural uranium foil and a 0.005-inch-thick depleted uranium foil
in the thermal flux of the graphite-lined cavity beneath the lattice.
Since the flux in the cavity has been shown to be Maxwellian with a
-4
Wescott "r"
value of less than 10
,
there is no necessity for cor-
rections for resonance activation.
The arrangement of the foils irradiated in the lattice was the
same as the bare foil arrangement used for R 2 8 except that three
0.005-inch-thick natural uranium foils, one detector foil, and two
cataher foils were placed between one depleted uranium catcher foil
and one 0.060-inch-thick fuel button. In the cavity, three natural
uranium foils and three depleted uranium foils were placed inside an
aluminum sleeve 0.125 inch long with a 0.005-inch-thick wall. This
packet was taped to the end of a 6-foot-long, 0.5-inch-diameter polyethylene rod. The rod was inserted into a 5/8-inch-diameter aluminum
tube which protrudes into the cavity by 3-3/8 inches.
The foils were usually irradiated for 12 hours and allowed to
cool about four hours before they were counted. All four foils were
counted for fission product activity above 720 key, at the same time
and on the same equipment used for the measurement of the fast
fission ratio. After fission product counting was completed, the two
depleted uranium foils were counted at least four times to determine
their Np 2 3 9 activity, with the same counting equipment as that used
for determining R '
28
activity of the depleted uranium foil irThe ratio of the Np
239
activity of the depleted uranium
radiated in the lattice to the Np
foil irradiated in the cavity, designated as RN, was divided by the ratio
(a)P. R. Tunnicliffe, D. J. Skillings, and B. G. Chidley, Nuclear Sci.
Eng., 15, 268 (1963).
48
of the U 235 fission product activity of the natural uranium foil irra.diated in the lattice to the U2 3 5 fission product activity of the natural
uranium foil irradiated in the cavity, RF. The U 238 capture rate and
235
the U
fission rate of fuel material irradiated in a thermal flux were
calculated from known atom concentrations and thermal cross sections.
These calculated ratios were used to convert the ratio of (RN/RF) to
the conversion ratio, C . Results of these measurements will be published in a doctoral thesis by W. H. D'Ardenne.
II. Microscopic Distribution of Intracell Activations
The intracellular distribution was measured by using depleted
uranium foils, irradiated both bare and cadmium-covered, and by
using copper foils, both bare and cadmium-covered. The copper foils
and the depleted uranium foils were 0.005 inch thick and 1/ 16 inch in
diameter. The depleted uranium was used to determine the distribution of the U 2 3 8 capture rates, and the copper, which closely approximates a 1/v absorber, was used to simulate the 1/v portion of the
U238 captures.
Figure 5.4 shows the bare and epicadmium copper activation
distributions. In Fig. 5.5, bare and epicadmium activation distributions of 0.0025-inch-thick, 1/ 16-inch-diameter gold foils, as measured
by R. Simms (17), are shown. The bare and epicadmium depleted uranium
activation distributions are given in Fig. 5.6. The epicadmium distributions for gold, copper, and depleted uranium are compared in Fig. 5.7.
The epicadmium copper distribution is nearly the same as the
epicadmium gold distribution. Neutrons, whose energies lie between
238
the cadmium cutoff and the lowest U
resonance at 6.7 ev, cause
about 75 per cent of the epicadmium 1/v copper activation and nearly all
of the epicadmium gold activation is due to the 4.96-ev resonance.
The epicadmium depleted uranium distribution shows that the
U 2capture rate in the fuel rod is sharply peaked at the surface of
the rod. This steep gradient at the rod surface implies that the epi239
cadmium Np
activity of a uranium foil placed between two fuel slugs
in a rod may be sensitive to any perturbations in the rod surface. Such
perturbations include:
1.1
1.0
0.9
0.80.70.6
0
IL
wL
0.50.4 -
Hd
-J
0.3 0.20.1
0
0
0.2
0.4
DISTANCE
FIG.5.4
FROM
0.6
0.8
1.0
CENTER OF CENTRAL ROD, INCHES
INTRACELLULAR COPPER ACTIVITY
DISTRIBUTIONS
1.2
'Ji
0
1.0
0.8
I-
C,
-J
a
0.6
LL
w
I-J
0.4
uJ
0.2
0
0.2
DISTANCE
FIG.5.5
0.4
0.6
0.8
1.0
1.2
FROM CENTER OF CENTRAL FUEL ROD, INCHES
INTRACELLULAR
GOLD
ACTIVITY
DISTRIBUTION
1.0
I-
0.8-
0.6-
5
0.4-
0.2
0
0
FIG. 5.6
0.2
DISTANCE
0.4
0.6
0.8
1.0
1.2
FROM CENTER OF CENTRAL FUEL ROD, INCHES
INTRACELLULAR DEPLETED URANIUM ACTIVITY DISTRIBUTION
I-a
A/
LL
o
0.8
Lu
<
<
0.6-
_0.4 -
e COPPER
>
A GOLD
a
ui
AIR GAP
-i
CLAD
MODERATOR
>O.211
u
a
FUEL
O
FIG.5.7
0.2
0.4
0.6
0.8
DEPLETED URANIUM
1.0
1.2
1.4
INCHES FROM ROD CENTER
INTRACELL ACTIVITY DISTRIBUTIONS OF CADMIUM COVERED COPPER,
GOLD, AND DEPLETED URANIUM IN THE 1.25 INCH -PITCH LATTICE
-1
.r4.
440,
wpm
lo".~~o
W__
53
1. Misalignment among foils and fuel slugs;
2.
Foils and fuel slugs having different diameters;
3.
Burrs, chips, cracks, etc. on the edges of the foils or the
fuel slugs;
4. Gaps between the foils and the fuel slugs caused by tapered
foils, crowned foils, unsquare fuel slug ends, or a uranium
oxide layer on the surface of the foils or slugs;
5.
Deviations due to the use of materials whose resonance
cross sections depart significantly from that of the fuel
material such as U 2 3 5 , gold, aluminum or aluminum
alloys, etc.
The attempt was made either to eliminate or correct for each of the
above possibilities in performing the experiments.
III. Studies of Techniques
A. Effect of Cadmium on Epicadmium Activity
Two experiments were performed to determine whether the
presence of cadmium, which depresses the thermal flux and thus the
fast flux, perturbs the resonance energy neutron flux.
First
distributions 1239
of the Np
activity induced in
First, microscopic
cadmium-covered, 0.005-inch-thick, 0.0625-inch-diameter, depleted
uranium foils were measured in the moderator between two bare rods
and between a bare rod and a rod containing a cadmium sleeve. A
schematic diagram of the arrangement is shown in Fig. 5.8. The resulting distributions were essentially identical, as shown in Fig. 5.9.
Second, six 0.005-inch-thick depleted uranium foils were irradiated in equivalent positions in the lattice, with the cadmium-covered
foil arrangement for R28 except that the cadmium sleeve length was
varied from 0.250 inch to 1.5 inches.
The results are shown in Fig. 5.10; there seems to be no significant trend in the results.
B. The Effect of Foreign Material in the Fuel Rod
Several experiments were performed to determine the following:
1. The effect of using aluminum catcher foils or aluminum alloy
detector foils.
Ul
CADMIUM
PILL BOX
ALUMINUM
FOIL
ALUMINUM
FOIL
HOLDER
HOLDER
BARE -TO -CADMIUM
BARE -TO - BARE
ROD TRAVERSE
ROD TRAVERSE
OF CADMIUM
COVERED FOILS
OF CADMIUM
COVERED
FOILS
FUEL ROD
CENTR AL
CONTAINING
CADMIUM
PILL BOX
FUEL
ROD
FIG.5.8
"BARE"
FUEL
ROD
DIAGRAM OF THE EXPERIMENTAL ARRANGEMENT FOR MICROSCOPIC
DISTRIBUTIONS TO STUDY EFFECT OF CADMIUM ON EPICADMIUM ACTIVITY
55
-1--1-
I
1I
1.03% ,1/'4
I
I
I
I
"
.i
I
Ii
lii
I
DIA.
1'/4" PITCH
0
-
3
A
6
A
0
0
a-
A
6
2
CLAD
FUEL
A
a -AIR
IL
FUEL
MODERATOR
GAP
I---
w
CLAD
-.
,
I&
AIR GAP
>:
I
A ROD TO ROD
o ROD TO CD. ROD
0
I It I
0
FIG. 5.9
I
I
I
I
I
0.4
0.2
DISTANCE
I
I
I
I
I
I
I
I
II
II
1.2
1.0
0.8
0.6
FROM CENTER OF CENTRAL ROD,
I
1.4
1.6
IN.
MICROSCOPIC Np239 ACTIVITY OF CADMIUM-COVERED DEPLETED
URANIUM FOILS, 1/16 INCH DIAMETER, 0.005 INCH THICK
Ul
0'~
I
LLZ
0-Q <
I.2 [-
c:
I
*
INTERNAL SLEEVE
A
EXTERNAL SLEEVE
I
I
I
I
o w
w 1. 1 - O
0
z
cr
ow 1.0
A
A
A
> 0
-o
w
a:
A
0.9
0
I
I
1/4
1/2
CADMIUM
FIG.5.IO
EFFECT
OF CADMIUM
I
I
3/4
I
SLEEVE LENGTH,
iI
I '/4
I V2
INCHES
ON CADMIUM COVERED
w4 -
FOIL ACTIVITY
fffflml*
57
2.
The effect of substituting depleted or natural uranium for fuel
materials.
3.
The effect on the detector foil activity of the use of the 0.020inch-thick aluminum holder foils.
To investigate these effects, the following set of experiments
were made:
1. Six bare depleted uranium detector foils were irradiated in
similar positions with aluminum catcher foils ranging in
thickness from 0.001 inch to 0.040 inch;
2. Six cadmium-covered depleted uranium detector foils were
irradiated in similar positions with aluminum catcher foils
ranging in thickness from 0.001 inch to 0.040 inch;
3. Six bare depleted uranium detector foils were irradiated in
similar positions with depleted uranium catcher foils ranging
in thickness from 0.005 inch to 0.030 inch;
4. Six cadmium-covered depleted uranium foils were irradiated
in similar positions with depleted uranium catcher foils
ranging in thickness from 0.005 inch to 0.030 inch;
5.
Six bare depleted uranium detector foils, using 0.005-inchthick depleted uranium catcher foils, were irradiated in
similar positions with the aluminum holder foils ranging in
thickness from 0.020 inch to 0.060 inch in three rods and
with no aluminum present in the other three rods. Mylar
tape was used instead of the teflon sleeves for this experiment.
The results are shown in Figs. 5.11a, 5.11b, and 5.12.
Figures 5.lla and 5.1lb show that the presence of aluminum adjacent to either bare or cadmium-covered depleted uranium detector
foils perturbs the Np 2 3 9 activity induced in the detector foil, and that
up to 0.030 inch of depleted uranium used as a catcher foil does not
239
activity
affect significantly either the bare or cadmium-covered Np
of the detector foil.
Figure 5.12 shows that the presence of up to 0.060 inch of aluminum, with 0.065 inch of uranium separating it from the detector foil,
has no effect upon the Np 239 activity of the detector foil.
i
I
I
I
I
I
I
* BARE DETECTOR, AL CATCHERS
1.8
A CADMIUM COVERED DETECTOR,
AL CATCHERS
BARE AND CADMIUM
COVERED DETECTOR,
DEPLETED URANIUM
CATCHERS
l.7 > 1.6 0
41.5 o. 1.4 -
z
S 1.3 S1.2 1.1
II.I
1.0UU
4
0
FIG.5.1 la
EFFECT
8
CATCHER
OF CATCHER
12
16
FOIL THICKNESS,
FOILS ON
24
20
INCHES x 103
Np239 ACTIVITY OF DEPLETED
32
28
URANIUM
FOILS
2.62.4
2.2 -
A DEP. U. CATCHERS, BARE DETECTOR; NORMALIZED TO THEIR OWN AV.
v Al CATCHERS, BARE DETECTORS; NORMALIZED TO ABOVE AV.
o DEP. U. CATCHERS CAD. COV. DETECTOR ; NORMALIZED TO OWN
AVG.
1 Al CATCHERS, CAD. COV. DETECTOR; NORMALIZED TO ABOVE
AVG.
-2.0-
-
l.8 --
<
1.6
1.4i.2--------
<1.0
O--------O----
uj
cr 0.80.60.40.2-
0O
A
0
FIG.511b
4
8
12
CATCHER
EFFECT OF CATCHER
I
I
16
20
24
28
FOIL THICKNESS, INCHES x10
32
I
I
36
3
FOILS ON DEPLETED URANIUM Np
23 9
ACTIVITY
I
40
I
I
I
I
I
I
I
I
I
I
I
I
1.2
o
AVG.
1.0
CL
0.8
0.
z
w 0.6
- I--
-
--
-
- -
- -
-
- -
-- -
- -
-
- -
-
-
- -
0.4
w
(r 0.2
0
0
5
10
15
ALUMINUM
FIG.5.12
20
25
30
35
40
45
50
55
HOLDER FOIL THICKNESS, INCHES xIO
60
3
EFFECT OF ALUMINUM HOLDER FOILS ON DEPLETED
URANIUM Np 2 3 9 ACTIVITY
u-l
60
C. The Effect of Counting Geometry
As can be seen in Fig. 5.6, the distribution of the Np 239 activity
in a cadmium-covered foil is sharply peaked at the edge of the foil
while the thermal activity distribution in a bare foil is more nearly
uniform. These two different activity distributions in the foil could
result in a different counting efficiency for each foil, which would
directly affect R 2 8 and indirectly affect C
.
To investigate this possibility, three different methods of counting
were used to count several sets of foils:
1. The distance between the NaI(Tl) crystal and the foils was
varied from 0.5 inch to 2.5 inches.
2.
The radiation emitted by the foils was collimated by a 5/16inch-diameter hole through 2-inch-thick lead so that all the
gamma rays reaching the crystal would have the same
detection efficiency.
3. The foils were homogenized by dissolving them in equal
amounts of nitric acid and counting the solutions.
The results are given in Table 5.2 and shown in Fig. 5.13. There
seems to be no significant difference among the three different methods;
further work is in progress on this problem.
TABLE 5.2
Values of R
Determined in Various Counting Arrangements
Distance from
NaI(Tl) Detector
(Inches)
(B.
Average Value
of R 2 8
0.5
3.311 ± 0.019 (±0.57%)
2.5
3.344 ± 0.024 (±0.72%)
2.5 + Pb
3.266 ± 0.039 (±1.2%)
HNO3 soln.
3.332 ± 0.027 (±0.81%)
Arcipiani et al., Nuclear Sci. Eng. 14, 317 (1962).
61
1.03% LATTICE WITH 2.50 INCH SPACING
AND 19 RODS OF 11.-5%WT U 2 3 5 SUBSTITUTED
CC
" 1.2
0
U)
1.1
<
1.0
20.9
cr
O.8
)
1.0
FOIL DISTANCE
3.0
2.0
FROM CRYSTAL, INCHES
1.03%LATTICE WITH 2.50 INCH
u-
0
o)
SPACING
1 .2
1.1
2
-
1.0
D
0.9
0.8
0
3.0
2.0
1.0
FOIL DISTANCE FROM CRYSTALINCHES
1.03% LATTICE WITH
1.75 INCH SPACING
1I.2
o
Lu
- -o-----Q-
-- - - 0- ---
w 1.0
HNO, SO'N
--
0
Pb COLLIMATOR_
0.9
J
0.8
I
0
I
I
1.0
2.0
3.0
FOIL DISTANCE FROM CRYSTALINCHES
FIGURE 5.13 RELATIVE VALUES OF R2 8 FOR DIFFERENT
COUNTING METHODS
62
D. Work Related to Effective Resonance Integrals
Work in this area is still in progress and it is too early to give
any results. The objectives of the work are:
1. To determine the U238 effective resonance integrals;
2. To determine the relative slowing-down density at various
energies;
3.
To determine the ratio of the U2 3 8 resonance capture rate
to the slowing-down density of neutrons entering the reso-
nance region;
4. To measure the neutron diffusion coefficient at various
energies;
5. To investigate the possibility of making a resonance detector
foil which will not perturb the epithermal neutron flux by
matching the slowing-down power of the detector foil to the
slowing-down power of the medium in which the foil is used.
The effective resonance integral of a nuclide may be determined
by two basic approaches: by means of a cadmium ratio measurement
or by the 1/v-subtraction method.
The cadmium ratios of several isotopes which are readily
available in foil form or as an aluminum alloy have been measured.
For other nuclides of interest, a convenient method has been developed
to fabricate detector foils from powders. A powder containing the isotope of interest is mixed with powdered aluminum and then compressed
into foils. Foils which are to be used inside the fuel rods have boron
carbide added to the mixture to match the macroscopic 1/v-absorption
cross sections of the detector foil and the fuel material.
63
INTRACELLULAR THERMAL NEUTRON DISTRIBUTIONS
AND ASSOCIATED PROBLEMS
6.
R. Simms
Introduction
The work to be discussed in this section continues and extends
work discussed in earlier reports (6, 10). The topics to be treated
include: experimental and theoretical determinations of the thermal
neutron density (or flux) distribution in the unit cell of lattices of
slightly enriched uranium rods in heavy water; difficulties arising
from the assumed cylindricalization of the unit cell in the theoretical
analysis; the use of improved energy exchange kernels in the theoretical analysis; modification of the THERMOS code to include the
effects of radial and axial leakage; the effect of flux perturbation in a
detector foil; and an experimental and theoretical analysis of the cadmium ratio of gold in the lattices.
The material to be presented is treated in greater detail in
Ref. 17, of the general Introduction to this report, based on a Doctoral
thesis submitted by Mr. Richard Simms.
I.
Intracellular Thermal Neutron Distributions
A.
Experimental Methods
235
The lattices studied consisted of 1/4-inch-diameter, 1.03% U
uranium metal rods on a 1.25-inch or 2.5-inch triangular spacing in a
3- or 4-foot-diameter, exponential tank, moderated by 99.7% D 20. The
height of the active fuel was four feet. The experiments required the
preparation of detector foils, the development of foil holders and cadmium covers, and procedures for counting and data reduction.
Nine sets of 1/16-inch-diameter foils were used in the experiments; the foil materials were gold (four sets), lutetium (two sets),
Now at Atomics International, Canoga Park, California.
64
europium, depleted uranium, and copper. The foils in a set were all
punched from the same sheet by means of a punch and die. The small
diameter of the rods and the small lattice spacings made the accurate
positioning of the foils difficult. After considering several alternative
schemes, a satisfactory design for foil holders and cadmium covers
was developed. The holder (uranium) for the foils irradiated in the
fuel rod is shown in Fig. 6.1. The holder (aluminum) for the foils
irradiated in the moderator is shown in Fig. 6.2. The cadmium box
used is shown in Fig. 6.3. The foil holders used in the moderator were
attached to a special three-rod cluster, as shown in Fig. 6.4. The foils
irradiated in the fuel rod were placed in the central fuel rod.
A sche-
matic diagram of the foil holder arrangement is shown in Fig. 6.5. The
foils were counted by a gamma-ray counter in conjunction with an automatic sample changer. Each experiment required the use of about 70
foils.
Data reduction was accomplished by means of a computer program,
ACTIVE, written for the IBM 7090.
made.
Routine counting corrections were
In addition, corrections were made for radial leakage and for
the axial position of the foils.
The latter corrections were based on
measured, macroscopic flux distributions.
B.
Experimental Results
Brown et al. (6, 16) showed that the THERMOS method (ref. a)
could predict the intracellular activation distribution for lattices of
1-inch-diameter, natural uranium rods in heavy water. The method,
however, gave poor agreement with experiment for a lattice of 1/4-inch-
diameter, 1.03% U 2 3 5 , uranium rods on a 1.25-inch triangular spacing.
Figures 6.6, 6.7, and 6.9 show the results of experiments made in the
lattice with the 1.25-inch triangular spacing.
Table 6.1 and Fig. 6.6
give the directions of the intracellular activity traverses in the cell.
In the figures, "1D THERMOS" refers to the one-dimensional code of
reference a;
"MODIFIED ID THERMOS" refers to a newer version
which will be discussed below. The theoretical curve in the fuel element falls significantly below the experimental points when the theoretical results are normalized to the experimental ones at the edge of
the cell. As part of a study of the effect of varying the thickness of the
65
TOP VIEW
1/16"
A
A
SIDE VIEW
SECTION AA
0.012"
0.06"
0.012"
I/4"
FIG. 6.1
THE HOLDER FOR THE FOILS IRRADIATED IN
THE FUEL ROD USED IN THE LATTICE WITH
THE .25-INCH TRIANGULAR SPACING.
66
TOP VIEW
CLAD
FOLD ALONG THE
CENTER ROD
FIG. 6.2
THE HOLDER FOR THE BARE FOILS IRRADIATED
IN THE MODERATOR USED IN THE LATTICE WITH
THE 1.25-INCH TRIANGULAR SPACING.
67
HOLDER
CADMIUM BOX'
(SIDE VIEW)
'S
CADMIUM BOX
(TOP VIEW)
1/32" DIAMETER
FIG. 6.3
THE CADMIUM BOX AND A SECTION OF THE HOLDER
USED TO POSITION THE BOX IN THE MODERATOR.
68
CENTER
ROD...
HOLDER
FOR THE
BARE
FOILS
CADMIUM
SLEEVE
HOLDER
FOR THE
CADMIUM
COVERED
FOILS
FIG. 6.4
THE THREE-ROD CLUSTER.
69
UR ANIUM ROD
1100 ALUMINUM
*
SET BS-
i
FOIL HOLDER (60 MILS) -t
4
FOIL HOLDER (60 MILS) -t
HOLDERS FOR THE
BARE FOILS
6.04
SET A'
/' 16" FOIL
CADMIUM (20 MILS)-~~'--1% U 2 3 5 SPACER (60 MILS)
FOIL HOLDER B (60 MILS)
5"
I%U 235SPACER (60 MILS)
FOIL HOLDER A (60 MILS)
1% U2 3 5 SPACER (60 MILS)
CADMIUM (20 MILS)
CADMIUM
BOX
SET B
FOR THE
FOILS
-'"-SET A
TEST POSITION
FIG.
6.5
POSITIONS OF THE FOIL HOLDERS IN THE EXPERIMENTS
IN THE LATTICE WITH THE 1.25-INCH TRIANGULAR SPACING.
ADJACENT ROD-TO-ADJACENT ROD
LEFT SIDE
RIGHT SIDE
40
ROD-TO- MODERATOR
ROD-TO-ROD
RIGHT SIDE
ROD-TO-ROD
LEFT SIDE
CENTER
FIG. 6.6
DIRECTIONS
TRAVERSES
ROD
OF INTRACELLULAR ACTIVITY
IN THE MODERATOR.
71
II0
w
I-J
w
OZ
0
FIG. 6.7
0.5
1.0
1.5
RADIUS
2.0
(CM)
2.5
3.0
3.5
GOLD ACTIVITY DISTRIBUTION FOR RUN A14; 2.5 MIL
THICK GOL D FOILS IN A LATTICE OF 1/4-INCH DIAMETER,
1.03% U-235, URANIUM RODS ON A 1.25- INCH
T RIANGULAR SPACING
72
I
I
i
1
1
SUBCADMIUM ACTIVATION
+a
(SD±O.4%)
1.00
0
x
0
ADJACENT
FUEL ROD
+
0
0.96-
x
0.92 -
/
--
/
0.88
MODIFIED I D TH ERMOS
ID THERMOS
3.8 MIL GOLD CFROSS SECTIONS
I/V-ACTIVATION
EQUIVALENT
CELL BOUNDARY
(I
2 0.84
D2 0
I-
ROD-TO-ROD
MIDPOINT
A
6-
w 0.80
-J
-/
w 0.76
A
-CLAD
1-
CENTRAL
-FUEL ROD
CLAD-4
-
0.40 EPICADMIUM
0.36 0.34
x
o0
MODERATOR
AVERAGE
oX
x
0.30L
0
FIG. 6.8
(SDi0.5%)
n
H
0.32
ACTI VATION
,
0.5
1.0
1.5
RADIUS
2.0
(CM)
2.5
,,
,
3.0
,
,
3.5
GOLD ACTIVITY DISTRIBUTION FOR RUN A 16; 4.3 MIL
THICK GOLD FOILS IN A LATTICE OF 1/4-INCH DIAMETER,
1.03% U - 235, URANIUM RODS ON A 1.25 - INCH
TRIANGULAR SPACING.
73
4-
I
x
0
+
0.92
--
ADJACENT
FUEL ROD
MODIFIED ID THERMOS
ID THERMOS
7.7 MIL GOLD CROSS SECTIONS
I/V-ACTIVATION
0.88
.&-EQUIVALENT
CELL BOUNDARY
0.84
D2 0
-- ROD-TO -ROD
MIDPOINT
CLAD-
CLAD
w O.80
CENTRAL
FUEL ROD
76
wO.
EPICADMIUM
I I
ACTIVATION
(SD±O.5%)
0.30
0.28
4
-
x
MODERATOR
AVERAGE
O.26XX
0
FIG. 6.9
0.5
1.0
1.5
RADIUS
2.0
(CM)
2.5
3.0
3.5
GOLD ACTIVITY DISTRIBUTION FOR RUN A13; 10 MIL
THICK GOLD FOILS IN A LATTICE OF 1/4-INCH DIAMETER,
1.03% U- 235, URANIUM RODS ON A 1.25 -INCH
TRIANGULAR SPACING.
74
TABLE 6.1
Nuclear Parameters for the Lattices With 1-.25-Inch
and 2.5-Inch Spacings Obtained by Means of
ID and Modified 1D THERMOS Calculations
Quantity
Cutoff
Energy
(ev)
1.25-Inch Lattice
Modified
1D
ID
S1/v(a)
0.4
1.260
1.178
1.228
1.211
Lu-176(a)
0.4
1.194
1.120
1.165
1.150
CEu-151(a)
0.14
1.304
1.215
1.265
1.250
f
0.78
0.9773
0.9782
0.9612
0.0616
n
0.78
1.504
1.506
1.510
1.510
2.5-Inch Lattice
Modified
1D
1D
(a) is the disadvantage factor defined by Eq. 6.1.
gold foils used, foils 2.5, 4.3 and 10 mils thick, respectively, were
used; this aspect of the experiment will also be discussed below.
When the lattice was increased to 2.5 inches, corresponding to a ratio
of moderator-volume to full volume of 108 instead of 25.9 for 1.25inch spacing, the one-dimensional THERMOS calculation gave results
in good agreement with experiment, as can be seen in Figs. 6.10, 6.11,
and 6.12.
Brown et al. (6) suspected the most likely cause of the discrepancy between theory and experiment in the case of the 1.25-inch
lattice. To investigate the problem further, a systematic study was
undertaken of those variables that could possibly affect the intracellular activation distribution. An analytical study, involving the use
of various energy exchange kernels, indicated that the details of the
kernel are not important for this type of measurement. (Some of the
kernels studied, the free gas and Nelkin kernels, are compared in
Fig. 6.13.) This result is, at first, surpr'ising, in view of the differences in the various models. But further consideration showed that
O.
i.-
I0.
w
>0.
.
0
0.5
FIG. 6.10
1.0
1.5
GOLD ACTIVITY
2.0
3.0
3.5
RADIUS (CM)
2.5
DISTRIBUTION
1/4-INCH DIAMETER, 1.03%
4.0
4.5
5.0
5.5
6.0
65
FOR RUN A4; 2.5 MIL THICK GOLD FOILS IN A LATTICE OF
U-235, URANIUM RODS ON A 2.5-INCH TRIANGULAR SPACING.
1.02
1
1
1
SUBCADMIUM ACTIVATION
1.00
(SD±O.2%)
o
+
0
CLAD
x
0.96
ADJACENT
FUEL ROD
x
+
MODIFIED ID THERMOS
ID THERMOS
0.92-
-3.8
MIL GOLD CROSS SECTIONS
O . 88-
EQUIVA LENT CELL BOUNDARY
RO D -TO-ROD
O. 84 _FUEL
MIDPOINT
CENTRAL
ROD
CLAD
D2 0
0.80)
u0. T6
MODERATOR AVERAGE
0.1 5-
0
I0.10
0.5
1.0
FIG. 6.11
EPICADMIUM ACTIVATION
I
1.5
|
2.0
2.5
3.0
3.5
RADIUS (CM)
4.0
(SD±O.4%)
|
|
4.5
5.0
0| -t
5.5
|
6.0
_
6.5
GOLD ACTIVITY DISTRIBUTION FOR RUN A 5; 4.3 MIL THICK GOLD FOILS IN A LATTICE OF
1/4-INCH DIAMETER, 1.03% U-235, URANIUM RODS ON A 2.5-INCH TRIANGULAR SPACING.
0.88
0.84
0.80
0
0.5
1.0
1.5
2.0
2.5
3.0
RADIUS
FIG. 6.12
3.5
4.0
4.5
5.0
5.5
6.0
6.5
(CM)
GOLD ACTIVITY DISTRIBUTION FOR RUN A9; IOMIL THICK GOLD FOILS IN A LATTICE OF
1/4-INCH DIAMETER, .03% U-235, URANIUM RODS ON A 2.5 -INCH TRIANGULAR SPACING.
0.20
0
WW
z
NO MODERATOR MOTION
-
j- 0
W
o z
FREE GAS MODEL
M =2
0. 10
FREE GAS MODEL
M =3.595
_
NELKIN
MODEL
au.
'w
wo
a
-_
0
_
_
1
2
3
Ef
,
4
5
6
FINAL ENERGY (UNITS
OF kTM)
7
8
9
FIG. 6.13 COMPARISON OF THE NELKIN AND FREE GAS ENERGY EXCHANGE KERNELS
FOR HEAVY WATER FOR NEUTRONS HAVING AN INTIAL ENERGY, Ei,0F8.4kTM.
79
the lattices are not strongly absorbing, and the spectrum should not be
very different from a Maxwellian distribution, independent of the kernel.
The kernels satisfy the principle of detailed balance, which places the
constraint on the kernel that, in the absence of absorption, the spectrum
in an infinite medium is a Maxwellian spectrum. Simple prescriptions
to approximate the effect of anisotropic scattering also did not change
the calculated intracellular activation distribution enough to account
for the observed discrepancy.
A systematic study of the flux perturbation due to the foil showed
that the analytical method developed (17) to treat this problem was adequate, so that such perturbations could not be responsible for the disagreement between theory and experiment. The possible effect of flux
perturbation in a foil was treated by defining effective activation cross
sections, as a function of energy, for the detecting foils. These
effective cross sections were then averaged over the spectra calculated by the THERMOS code. Figure 6.14 shows the effective cross
sections calculated for gold foils of different thickness. Experiments
were made with gold foils that were effectively infinitely thin, and with
foils 2.5, 4.5 and 10.2 mils thick. The results of these experiments are
shown in Figs. 6.7 to 6.17 and indicate that consistent results are obtained with foils of these three different thicknesses. The foils 2.5 and
4.3 mils thick, gave the best balance of irradiation time, count rate,
accuracy of foil weight and correction required for flux perturbation
for the range of conditions studied. The use of the "infinitely thin" or
"dilute" foils (Fig. 6.15) led to much more scatter in the experimental
results; the use of such foils would require more work on the conditions
under which they might give satisfactory results. In any case, the foils
2.5, 4.3, and 10.2 mils thick, respectively, gave the same results insofar
as concerns the agreement or disagreement between experiment and
theory.
C. Theoretical Methods: THERM!S and Cell Cylindricalization
The first version of the THERMOS method is based on a onedimensional treatment-of a unit cell in an infinite array, in which the
actual hexagonal or square cell is replaced by an "equivalent" cell of
o
b
10.0
o
0
b
z
0
0
0
LJ
1.0
U..
0
wL
N
0
z
0.I
I0-2
FIG. 6.14
EFFECTIVE
GOLD
ENERGY (EV)
-10~
ACTIVATION CROSS SECTIONS FOR METALLIC
Z 0A = 5.83 CM').
FOILS (NOTE: Zs =0.548 CM,
1.08
O4
l.
MLAven'.md
_
+
x
0
+
x
x
x
--
FUEL ROD
1.00 -+
0
0.96>-
x-
MODIFIED ID THERMOS
x
0.92
-
>x
+
+
THERMOS
IV-ACTIVATION
KID
EQUIVALENT CELL BOUNDARY
ROD-TO-ROD
+
MIDPOINT
+
CLA D--
0
0.88
0
D20
x
wCENTRAL> 0.84-FUEL ROD
w0.800
.
0.39 --
4"S
0 .3 5 -
0
x
xx
0.37 Lo +
0.5
FIG. 6.15
1
1.0
1
1.5
GOLD ACTIVITY
2.0
x
0
0
+
-- 1
(SD t 2%)
EPICADMIUM ACTIVATION
AVERAGE
MODERATOR
1
2.5
DIdTRIBUTION
1...1...I.I.?
3.5
3.0
RADIUS (CM)
4.0
45
5.0
5.5
I
6.0
6.5
FOR RUN A8; DILUTE GOLD FOILS IN A LATTICE OF 1/4 -INCH
DIAMETER, 1.03% U-235, URANIUM RODS ON A 2.5 -INCH
TRIANGULAR SPACING.
co~
p
82
FIG. 6.16
REFLECTION OF NEUTRONS FROM THE
HEXAGONAL AND EQUIVALENT CELL
BOUNDARIES.
83
FIG. 6.17
RESTRICTIVE PATHS FOR NEUTRONS
IN THE EQUIVALENT CIRCULAR CELL
(NOTE: WHEN 0 IS BETWEEN #c
AND 180 *-4)c , WHERE Oc EQUALS
ARCSIN (Ro/r), THEN NEUTRONS FROM
POINT P WILL NEVER INTERSECT THE
INNER CIRCLE .,THE FUEL ROD).
84
circular cross section. A consideration of the geometric arrangement
of the unit cell indicates how the assumption of a cylindricalized cell
may lead to error. In an infinite lattice, the condition that there is no
net leakage is expressed mathematically by assuming that the cell
boundary acts as a perfect reflector of neutrons. Neutrons are reflected from the actual cell boundary, the hexagon, in the case of the
triangular array, as shown in Fig. 6.16, with the angle of incidence
equal to the angle of reflection. In the usual analytical treatment of
the one-dimensional cell, similar reflection is assumed to occur at the
"equivalent" circular boundary. If a fuel rod is placed in the center of
the cell, then there are paths for which the neutron will never enter
the rod, regardless of the number of times that it is scattered at the
circular boundary of the cell. This possibility is shown in Fig. 6.17;
if the neutron passes through the point P at an angle + between *c and
180*-c
(
where cpc is a critical angle defined by
c = arcsin (R9/r),
and where R is the radius of the rod and r is the radial distance to
0
the point P, then the neutron will never enter the fuel rod. This effect
does not arise in the actual cell because of the corners.
It is evident that the circular cell approximation can introduce a
significant error whenever the rod is close (in terms of mean free
paths) to the outer boundary of the cell. If the cell boundary is far
from the rod, neutrons will be scattered before they undergo many
reflections from the boundary. A mean free path in heavy water is
approximately an inch, and it seems likely that the poor agreement
between theory and experiment, observed by Brown et al. and confirmed
by the present work, results from the approximation of a cylindrical
cell. It has been shown (b) that similar considerations apply to the
closely packed lattices of uranium rods in ordinary water studied at
the Brookhaven National Laboratory.
Honeck has shown (b, c) that a two-dimensional (2D) THERM(S
calculation, in which the approximation of a cylindrical cell boundary
is not made, yields results in agreement with experiment. This calculation is, however, time-consuming and expensive; and Honeck has
85
shown (c) that a modified one-dimensional calculation, in which the equalangle reflection condition at the cell boundary is replaced by an isotropic
reflection condition, gives results which reproduce those of the 2D calculation for the intracellular neutron density or flux distribution, but without the corresponding increase in computer time.
A two-dimensional THERMOS calculation, for which the cylindrical cell approximation is not made (the calculation treats the actual
hexagonal cell), was made for the lattice with the 1.25-inch spacing. The
results of the calculation are shown in Fig. 6.18; the result indicates
that the one-dimensional calculation could lead to as much as an 8%
error in the level of the flux at the center of the fuel rod. The modified
one-dimensional calculations shown in Figs. 6.7 to 6.12 are equivalent
to the corresponding 2D calculations. It may be concluded that the cell
cylindricalization can lead to serious errors in the theoretical thermal
flux distribution in a cell of a closely packed lattice.
The THERMOS code, which has been extremely useful in the interpretation of intracellular flux distributions, was developed by Honeck
for an infinite lattice. The question arises as to the possible effects of
the axial and radial leakages in a finite lattice. The THERMOS code
was therefore modified and extended to take into account the exponential variation of the flux in the axial direction and the J -distribution
in the radial direction. The results indicated that the effects are very
small in both the 3-foot and 4-foot-diameter tanks used in the M.I.T.
Lattice experiments. It is possible, however, that future work in miniature exponential assemblies, such as those studied by Peak et al. (5),
may require significant leakage corrections.
A method of normalization of theoretical and experimental results
has been suggested, based on the prediction of the cadmium ratio of the
foils used in the measurements of the intracellular activation distribution. It was found, however, that uncertainties in the effective resonance
integrals of the foils are too large, so that the new method offers little
advantage at present over the usual methods of normalization of the
subeadmium activation at either the center or the edge of the cell. The
method should be useful when better values of the effective resonance
integrals are available.
86
CLAD
2 D, ROD-TO-ROD
1.00
2 D, ROD-TO-MODERATOR
0.96
0.92
ci
m
0.88-
0
cf)
0.84-
w
0.80-
-J
0.76-
0.72 0
0.5
1.0
DISTANCE FROM THE CENTER
FIG. 6.18
1.5
ROD (CM.)
2.0
COMPARISON OF THE ONE AN[ DTWO
DIMENSIONAL THERMOS CALCULATIONS FOR
THE LATTICE OF 1/4-INCH DIAMETER,1.03%
ENRICHED, URANIUM RODS ON A 1.25-INCH
TRIANGULAR SPACING.
87
The epicadmium intracellular activation distribution has received
little attention in the past. Measurements with foils of depleted uranium
provide some additional data. The distribution of foil activities with depleted uranium foils indicate that the resonance flux at the U
nance energies was depressed in the vicinity of the fuel rod.
238
reso-
On the
other hand, the measurement with gold foils indicated that the flux at
the gold resonance (4.9 ev) was spatially flat in the moderator.
Future
analytical and experimental work is indicated.
D.
Reactor Parameters
One of the reasons for measuring or calculating intracellular
neutron density or flux traverses is to derive values of the disadvantage
factor and thermal utilization for the unit cell.
The disadvantage factor
n' defined as
n
V
m
f
n(r) dr
mod
+f
f
fuel
(6.1)
,
n(r) dr =
nf
can be obtained directly from the experimental results.
The determi-
nation of the value of the thermal utilization from the experimental
neutron density distribution requires values of cross sections (of the
fuel, cladding, and moderator) averaged over the neutron energy
spectrum.
The energy spectrum is obtained by using the THERMOS
method or some other appropriate theoretical procedure.
Now,
THERMOS can also be used to obtain the values of the disadvantage
factor and the thermal utilization.
It seems reasonable, therefore, to
use THERMOS to calculate these quantities and to use the experimental
results to check the validity of the THERMOS calculations.
In
other
words, the main purpose of the measurement of the density distribution is to ensure that a version of THERMOS is being used which reproduces the density distribution and enables us to trust the results of
the THERMOS calculations of the disadvantage factor and the thermal
utilization.
The results of the experiments show that the "modified 1D"
THERMOS calculation predicts a neutron density distribution (gold
activation distribution) in
the lattice with 1.25-inch spacing which
88
agrees well with experiment. Either the "1D" or "modified 1D"
THERMOS calculation works for the lattice with 2.5-inch spacing.
These two versions of THERMOS were used (for the sake of comparison) to calculate values of the disadvantage factors and thermal utilization for the two lattices. In the calculation, the Nelkin-Honeck
energy exchange kernel was used, with the diagonal elements adjusted
so that the integrated value of the kernel corresponds to the transport
cross section. Values of the disadvantage factor were obtained for a
1/v-absorber (gold) and for two non-1/v absorbers (Lu176 and Eu 51
The results are significantly different in the 1.25-inch lattice, depending on whether the 1D or modified 1D THERMqS calculation is used;
the difference between the two values of f is much smaller. The results of these calculations are given in Table 6.1 (page 74). Values of
17 were also calculated and showed only a small difference. For the
2.5-inch lattice, the results obtained with the two versions of
THERMOS are much closer, as would be expected. Uncertainties in
f have been estimated to be ± 0.0006 to ± 0.0010 (6) and are due primarily to uncertainties in the cross sections of aluminum and deuterium.
Experimental values of 1.138 ± 0.011 for 1/v and 0.9760 ± 0.0006
for f were given by Brown et al. (6) for the 1.25-inch lattice. The value
of ,1/v is slightly smaller than that given by the modified 1D THERMOS
calculation; but the two should probably be considered to agree reasonably well, in view of the difficulty of assigning an accurate value to the
uncertainty of either the experimental or theoretical values. The
"experimental" value of f depended on the use of cross sections averaged over the 1D THERMOS spectrum since the more accurate modified
1D THERMOS was not available at that time.
Further theoretical studies will be made when more experimental
results are available.
89
References
a. H. C. Honeck, THERM(S, A Thermalization Transport Theory
Code for Reactor Lattice Calculations, BNL-5826 (1961).
b.
H. C. Honeck, The Calculation of the Thermal Utilization and
Disadvantage Factor in Uranium-Water Lattices, IAEA Conference on Light Water Lattices, Vienna (June, 1962); also
BNL-7047 (May, 1963).
c.
H. C. Honeck, Some Methods for Improving the Cylindrical
Reflecting Boundary Condition in Cell Calculations of the
Thermal Neutron Flux, Trans. Am. Nuclear Soc. 5 (2), 350
(1962).
90
7.
RESEARCH WITH MINIATURE LATTICES
E. Sefchovich
Introduction
The work on miniature lattices (5) has been resumed and is being
pursued along two lines.
First, measurement of reactor parameters
such as 628' P2 8 , and 625, with improvements in the experimental
arrangements and in the theoretical analysis.
Second, the possibility
of developing new methods of measuring material buckling is being
examined; in particular, an oscillating source method and a pulsed
neutron method are being investigated.
I.
Measurement of Reactor Parameters
Earlier in this report, sections 4 and 5, respectively, it was seen
that measurements of 628 and p 2 8 made in the miniature lattice facility
could be interpreted so as to yield results in reasonably good agreement
with results obtained in the exponential assembly.
The comparison is
sufficiently encouraging so that attempts are being made to improve the
theoretical analysis of the results of the measurements as well as the
experimental arrangement and methods.
To correct for source and leakage effects and to extrapolate the
results to critical assemblies, Peak et al. developed a theoretical
treatment based on the age-diffusion approximation.
Work is now
under way on the use of the GAM-1 and THERM(S codes instead of the
analytical age-diffusion method.
It is evident from the earlier results that a more accurate de-
termination of the axial and radial extrapolation lengths is required.
On the experimental side, work is under way on improving the boundary conditions.
For example, the assembly, in the earlier experiments,
was not surrounded by vacuum, but by shields consisting of alternate
layers of paraffin and B 4 C plastic.
Some of the fast leakage neutrons
may have been reflected back into the assembly, increasing the
measured extrapolation length.
The effect of the non-isotropy of the
91
source is also being examined.
Preparations are also being made to extend the measurements of
Peak et al. to lattices moderated by mixtures of heavy and light water
with greater concentrations of the latter, and to a wider range of lattice
spacings. So far, only one set of short uranium rods is available for
these measurements, containing 1.143% U 2 3 5 .
II. Buckling Measurements
The miniature assembly is being used in an attempt to investigate new methods of measuring the material buckling. In exponential
and critical assemblies, the buckling is nearly always determined from
measurements of the steady-state variation with position of the thermal
neutron flux.
The importance of the buckling concept makes it desirable to
have several means to determine its value. Another consideration,
although not so important, comes from the interest in having a method
to measure the material buckling "on-site; " this is clearly absent in
the foil-activation method. With these two goals in mind, two possibilities have been considered and are discussed below.
In the first method considered (ref. a), a plane oscillating neutron
source, S = S0+Se
1 e it is assumed to impinge on one of the plane faces
of the cylinder, which is assumed to be bare and of extrapolated dimensions R and H. The absence of delayed neutrons and the validity of agediffusion theory is likewise assumed.
Consider a solution to the age-diffusion equation of the form,
c(r,z,t) =
0 (r,z)
+ 4 1 (r,z) eiwt
(7.1)
where * 0 (r,z) is the solution of the steady-state age-diffusion equation,
V 2O(r,z) + B 2k(r,z)
=
0,
(7.2)
with
B
2
( -2, -1B
2
Fa (koe
D
T
(7.3)
92
Similarly, .
1 (r,z)
V2
will satisfy
+ p2
1 (r,z)
1 (r,z) =
0,
(7.4)
where
2
a k e-B2 TD 00
1
vD
= B2 - i
v
.(7.5)
For locations away from source and boundaries, so that source
and end effects may be neglected, the solutions of Eqs. 7.2 and 7.4
which go to zero at the extrapolated boundary can be written as:
2.405
e(r,z)
-Kz
(2.405
r)eFJ z
= C
(7.6)
,J
and
1 (r,z)
= C j
(7.7)
where
K2 _
2.405)
2
-B2
(7.8)
and
2 _ (2.405 2
2
Equation 7.9 can be solved for
=
+ if
2+
j±
.
(7.9)
to give
(7.10)
,
where
a
2
2 1/2
22_2 ,
)1/ 2
(7.12)
,
and
2 1/2
U4+
$2
(7.13)
Thus the total flux @(r,z,t) in Eq. 7.1 can be written as:
(r,z,t) = j
0o
2.405 r)
R
(Ceo1
Z+C
e-Oze1(tot z)}
(7.14)
93
Let T equal the time it takes the neutron wave to travel from the source
to the point z. T will be given by:
T = z
2 2 1/2
2 K) 1/
=
,
(7.15)
is the propagation velocity for the wave. If we now substitute
2
0
2
for L* in Eqs. 7.11 and 7.12 and solve for B , we get the following
relations:
where V
B2 _ 2.4052 +
0
)
B
B22 -( 2( 2.405)
+(
~7 2,
v
2
T)
2
(7.16)
(7.17)
Combining the last two equations, we finally get:
vD
W
=
(7.18)
and
B2
(2.405 2
2
2
From Eqs. 7.17 and 7.18, it is obvious that a measurement of (
and n and knowledge of the source frequency w/27r could lead to the
2
determination of vD and B . From Eq. 7.15, g can be determined by
measuring the phase difference, AO = wAT, between two points, z and
z2 as follows:
A
;(7.20) =
rl can be obtained by determining the relaxation length of the timedependent component of the total flux, as can be seen from Eq. 7.14.
At the present time, a series of experiments is being prepared
to assess the usefulness of the oscillating-source method and to learn
about the problems involved.
A relatively large lattice will be investi-
gated by using ordinary water as the moderator and 0.25-inchdiameter, 1.143% U 235, uranium fuel rods. Clearly, the values of vD
2
and B , so determined, must be independent of the source frequency,
so that a number of frequency values must be investigated.
94
The second possibility, which is still in a very early stage of
development, involves the use of pulsed neutron techniques (b). This
method has, so far, been used to determine thermal-neutron nuclear
constants by measuring the neutron flux decay constant and using a
calculated value of the geometric buckling. It seems feasible to invert
the process: if the thermal-neutron nuclear constants are determined
by some other independent method, then the decay constant, measured
directly, could be used to determine the buckling. At the present time,
further analysis is necessary before any conclusion, as to its possibilities, may be reached.
References
a.
R. E. Uhrig, "Neutron Waves in a Subcritical Assembly,"
Proc. Univ. Conf. Subcritical Assemblies, TID-7619 (1962).
b.
H. S. Isbin, "Introductory Nuclear Reactor Theory,"
Reinhold Chemical Engineering Series, 1963, chap. 9.
95
8. TWO-REGION LATTICES
J. Gosnell
Introduction
The "substitution technique" has been used quite widely, e.g.,
references (a, b), for the determination of material buckling because
of the possibility this method offers of obtaining information about
reactor lattices with small amounts of fuel. As part of the M.I.T.
Lattice Research Program, studies have been started on the measurement of various parameters in substituted or two-region exponential
lattices. The flexibility offered by the Lattice Facility, together with
the fact that several different types of fuel rods are available, makes
such a study desirable and feasible. The results can then be compared
with those obtained in the miniature assembly and in regular oneregion exponential assemblies.
Two-region lattices are formed in the MITR lattice tank by replacing a small central section of an existing lattice with a sublattice
of different enrichment and/or spacing. It is intended to investigate
whether the central lattice region will exhibit the properties characteristic of a full lattice of the same composition. If the investigation
demonstrates that this idea is feasible, new lattices can then be
studied by inserting them in the central position.
I. Experiments
The validity of parameter measurements in the central region
will depend largely on the degree with which its spectrum approaches
that of a full critical lattice of the same composition. Therefore, the
initial investigation has concentrated on measurements of spectral
change across the two regions.
The lattice chosen for initial study was composed of 0.25-inchdiameter, 1.03% U235 rods. The triangular spacing of the outer region
was 1.25 inches while the test region was 2.50 inches. Test regions of
two and four rings of rods about the central rod were formed in the
96
three-foot lattice tank. Macroscopic flux distributions in the radial
direction were made across the two regions with bare and cadmiumcovered 1/16-inch-diameter, 0.010-inch-thick gold foils in the moderator,
and with bare and cadmium-covered 1/4-inch-diameter, 0.005-inch-thick
depleted uranium foils within the fuel rods. The uranium foils were
counted for Np239
Cadmium ratios (cadmium coacti atiocivatio) are
shown in Fig. 8.1. It is seen that the cadmium ratios in the smaller test
region failed to achieve the values of the full lattice. (Displacement of
the foil holder in the small test region assembly gives an unsymmetric
distribution of activities which is reflected in an alternating effect on
238
the gold cadmium ratio plot.) In the larger test region, the U
cadmium ratio at the lattice center shows good agreement with the full
The gold ratio apparently exceeds the full lattice
The difference may be due to total experimental uncertainty
2.50-inch lattice.
value.
which cannot be estimated from the small number of presently completed
traverses; the uncertainties given in Fig. 8.1 are the standard deviation
estimated from the counting statistics only.
Additional experiments are planned with other lattice combinations
differing in number of rods in the central region, rod spacing, and U2 3 5
concentration of the rods.
Measurements of lattice parameters, e.g.,
628, will also be made as a function of radial position.
References
a. W. E.. Graves, Analysis of the Substitution Technique for the
Determination of D 2 0 Lattice Bucklings, DP-832, June, 1963.
b.
J. L. Crandall, Efficacy of Experimental Physics Studies on
Heavy Water Lattices, esp. pp. 17-20, DP-833, July, 1963.
12
o0
10-
8-
6
4
x
2
0
FIG. 8.1
10
20
DISTANCE
CADMIUM RATIOS
30
40
FROM LATTICE CENTER (CM)
IN A TWO - REGION
LATTICE
50
98
9.
SINGLE-ROD MEASUREMENTS
AND THEORY
E. E. Pilat
Introduction
One of the purposes of the Lattice Project is the investigation of
the possible use of simple and relatively cheap methods of measuring
reactor parameters.
A method which yielded some promising results
(a, b) but seems not to have been pursued with any vigorous interest
involves the use of a single fuel rod in a bath of moderator, or perhaps
of just a few rods.
The possibility of developing this method further,
together with the fact that experiments with a single rod or with a few
rods can easily be made in the M.I.T. Lattice Facility, has encouraged
the initiation of a program of research in this field.
The results of
such measurements can be compared both with results obtained in the
exponential assembly and in the miniature lattice.
I.
Theory
The single-rod approach to reactor lattice physics starts with
the assumption that a lattice can be thought of as the linear super-
position of a number of properly chosen sources and sinks embedded
in homogeneous moderator.
By "properly chosen," we mean that the
parameters characterizing the sources and sinks are chosen to give
correct values of the various physical lattice parameters, e.g., the
thermal flux distribution.
Most previous investigations of the relation
between single-rod parameters and lattice parameters have concentrated
on the thermal energy region.
If the source and sink strengths of a
single rod are known, the thermal utilization can be calculated.
This
has been done for two different choices of sink function by Galanin (c)
andStewart(d ).The source-sink parameters pertain to the individual
rods and are therefore obtainable from experiments on a single rod
immersed in moderator.
In the first experiments to be done, a single
rod will be placed at the center of the MITR lattice tank and radial and
axial flux traverses will be made around it.
(See Fig. 9.1.)
99
FOILS FOR
RADIAL
TRAVERSE
-Al FOIL
HOLDER
THERMAL
FIG.9.1
COLUMN
SINGLE ROD EXPERIMENT
IN MITR LATTICE FACILITY
100
If it is assumed that diffusion theory holds in the moderator
around the single rod, then the equation governing the rod-born thermal
neutrons is
V2
where
K2
24 + F = 0,
_
(9.1)
= 1/L2 of the moderator, and F = source strength minus sink
strength. Away from the ends of the lattice tank, the flux will have an
axial dependence of the form e-Y z; and if the same dependence is
assumed for F, then, denoting the radial dependence of the flux by +
and that of the sources and sinks by f(r), the equation governing radial
diffusion is
d2
d$ + (Y 2_ 2)
+ f(r) = 0.
(9.2)
dr
This equation may be solved by expanding the functions 4 and f in
*
power series about r = 0. If it is assumed that f is an even function
of r, the result is:
*o = arbitrary,
(This value depends upon the source strength and multiplication of the
particular facility used. The foil-counting efficiency may also be incorporated into this term so that all quantities will be determined relative to it.)
2
(a 2 +f )
(9.3)
4
+2 =1 { 2
L -(a
0
=
2
\
where a
2
= -y
2
-K
2
,
(9.4)
''5'
1 = 43 =
Thus, when the foil activities from a radial traverse around the single
rod are fitted to an even-order polynomial in r, the coefficients of the
** = 4
+
f= f
+
o
r+
2
r2 +.
f r 2+...
2
. .
101
first three terms will be 9,' $2, and $4. The interpretation of f and f2
depends on the particular source and sink functions used. For the
source, age theory is commonly used with the rod idealized to a line.
At least two different sink functions appear in the reports: a delta
function and a function of the form e-p 2 r 2 , where p is a constant. The
latter function is motivated by analogy to age theory because a sink is
a negative source. Since our purpose is to deduce the flux distribution
in the vicinity of, but not extremely close to, the rod, there is no a
priori reason for selecting either sink function.
For simplicity, we have first developed the equations with source
and sink, both of the age theory type; thus
2 2
2 2
f(r) = Ae-a r
-
Bep
r
(9.5)
,
so that
f
(9.6)
= A - B,
Bp
f2
2
2 _
-AA2
(9.7)
Since a 2 = 1/4-r, this, in conjunction with Eqs. 9.3 and 9.4, gives us two
equations for three unknowns, A, B, p. A third equation may be obtained
by integrating Eq. 9.2 over the cross sectional area of the tank which,
for the source and sink just mentioned, gives:
(,2 2
d*
27rR()+-y
2
R
-c)
f
0
R
2 R 2]
-7a
'rA
27rr dr +
rB
-2 R 2]
1-e
1-e
. =20 .
p
(9.8)
R
Now, r, is known for heavy water. p, (d*/dr)R, and f 27rr dr may be
obtained from the single-rod foil activation experiment; so the relation
(9.8) provides a third equation. In practice, this method will be difficult
because the equations involve differences of similar quantities, i.e.,
2_
2
A-B, BP -Aa . However, since only thermal activations are needed,
it should be possible to obtain highly accurate foil activations around
the single rod. The ultimate usefulness of this method can therefore
be determined only by experiments, which are now being planned.
A delta function sink term complicates the solution of the diffusion equation. This problem is now being examined, so that the
102
relative usefulness of the two types of sink functions can be evaluated.
If single-rod source functions are used in calculating lattice
bucklings, the age must be corrected to account for the presence of the
fuel. It has been observed that the age equation can be solved in an
infinite periodic slab lattice if the fuel region is assumed to act as a
void. The fuel is thus assumed to be a neutron source, but neither to
scatter nor to slow down neutrons once they have been born. The
effective age in such a lattice is
V
7 a
7
Mod
t
1 + 22
Fuel 1
VMod
C
-
1
Mod
+ (
V
Fuel
VMod
_
C2
2
Mod
(9.9)
where C
and C2 are small correction factors which depend on the
slowing-down density in the source slab. in ordinary heavy water
lattices, C 1 /'r and C 2 /T are negligible. The effective age therefore
becomes
TLat
(VTotal
_M:
.IMod
V Mod
which is exactly the correction that would be made in a homogeneous
medium. It is not known if this result can be precisely extended to
lattices of cylindrical fuel elements.
II.
Experiments
Experiments are being made to map the thermal flux around a
single fuel rod immersed in D 2 0 at the center of the MITR exponential
tank. Both radial and axial flux traverses are being made. The axial
traverses are done at several different radii to ascertain whether or
not the axial relaxation length is a function of radius for this system.
Experiments have so far been carried out with bare gold foils and a
one-inch-diameter, Al-clad, natural uranium fuel element. Future experiments will include the use of 1/4-inch-diameter, slightly enriched
uranium fuel rods in place of the natural uranium rod, as well as the
determination of flux plots using cadmium-covered gold foils. Data on
bare and cadmium-covered gold traverses have been obtained previously
103
with full lattices of these same 1/4-inch and one-inch rods in the MITR
exponential assembly. It should therefore be easy to correlate such
foil activity distributions in the full lattices with predictions about them
based on the single-rod experiments.
References
a.
L. W. Zink and G. W. Rodeback, The Determination of Lattice
Parameters by Means of Measurements on a Single Fuel
Element, NAA-SR-5392, July, 1960.
b.
R. W. Campbell and R. K. Paschall, Exponential Experiments
With Graphite-Moderated Uranium Metal Lattices,
NAA-SR-5409, September, 1960.
c . A. D.
Galanin,
Reactor,
The Thermal Coefficient in
a Heterogeneous
PICG 5, 477 (1955).
d. J. D. Stewart, A Microscopic-Discrete Theory of ThermalNeutron Piles, AECL-1470, 1962.
104
10.
ENERGY SPECTRA AND SPATIAL DISTRIBUTION OF
FAST NEUTRONS IN URANIUM-HEAVY WATER LATTICES
G. L. Woodruff
An investigation of fast neutron spectra in a lattice has been
undertaken, based on the activation of threshold detector foils. The
purposes of the investigation are to obtain, insofar as possible, the
energy spectrum above approximately 0.1 Mev at different points in
lattice cells, to study the effect of various lattice parameters such as
rod spacing on the fast neutron distribution, and to correlate experimental results with some form of theoretical treatment.
The threshold reactions currently in use include Zn 6 4 (np)Cu 6 4
Ni 5 8 (n,p)Co 5 8 , In
1 15
(nn'
)In
5
m
Th 2 3 2 (n,f), and U 2 3 8 (n,f).
An effort
is being made to incorporate additional reactions into the study and to
develop the use of heretofore untried reactions. These reactions include Rh 103(n,n')Rh103m Nb93 (n,n')Nb93m, Pb204(n,n')Pb 204m, and
199
199m
Hg
(n,n')Hg
. Some reactions which have previously been used
for fast neutron detection are not suitable for this study, primarily due
to difficulties in foil preparation for lattice irradiation, or to the requirement of a minimum half-life of the order of an hour for the me-
chanics of unloading the lattice and preparing foils for counting.
Since the data treatment to be effected requires absolute reaction
rates as input, the experimental method used provides for an absolute
calibration in addition to a relative lattice cell traverse. The relative
traverse is composed of small foils (1/ 16-inch diameter in the case of
1/4-inch fuel rods) spaced at various radial distances from the center
in the fuel rod.
Additional foils are then contained in foil holders in
the moderator at various distances from the fuel.
The moderator foils
are cadmium-covered in every case to minimize competing thermal
reactions which complicate the counting process.
The foils inside the
fuel rod are left bare, since the fast-to-thermal flux ratio is most
favorable in the fuel, and since cadmium covers on the fuel would significantly perturb the local flux distribution.
105
The absolute calibration procedure differs for fission and nonfission reactions.
In the case of the non-fission reactions, two addi-
tional foils are irradiated in the MITR Lattice cavity.
One of these
additional foils, hereafter referred to as the calibration foil, is to be
counted with the traverse foils, while the other, called the monitor
foil, is of a material conveniently used as a flux monitor.
ideas, consider the Zn(n,p)Cu reaction.
To fix
The two foils in the cavity
could in this case be copper, the calibration foil, and cobalt, the monitor foil.
By either absolute counting the cobalt foil in some manner,
or by counting it with a standard cobalt-60 source, the thermal cross
section for Co60 activation can be used to compute the thermal flux in
the cavity.
Since the flux in the cavity has been shown to be Maxwellian
with a Westcott "r"
value of less than 10~4, there is no necessity for
corrections for resonance activation.
Once the value of the cavity flux
has been computed in this manner, the absolute activity of the calibration foil, Cu in this case, can be computed.
This Cu foil then becomes
the standard to be counted with the Cu64 activity of the traverse foils
and their absolute activity can be obtained.
In the case of the fission reactions, the monitor foil serves the
same purpose.
The calibration foil used, however, is
some nuclide
furnishing a Lal40 source, either elemental La or U235 in some form.
In either case, a La140 source is obtained as described above.
This
La140 source could be counted with the traverse foils, except that in
every case, the fission. rate in the traverse foils is insufficient to produce enough Lal40 for counting.
To circumvent this difficulty, still
another foil is irradiated in the fuel rod along with the traverse foils.
This foil, called the reference foil, is placed in the same fuel rod as
the traverse foils but at a lower position..
The reference foil is placed
at a height corresponding to the bottom' of the fuel in the lattice (i.e.,
z = 0) where the local flux is higher than. at the higher equilibrium
lattice positions.
To further enhance the local flux, highly enriched
uranium foils are placed on either side of the reference foil.
When the
traverse foils are counted for integral fission product activity, a small
piece of the reference foil is punched out and counted in the same way.
The reference foil is later counted for Lal40 along with the calibration
106
foil.
The absolute fission rate of the traverse foils can then be calcu-
lated from that of the calibration foil by using the reference as an intermediate comparator.
The La140 counting is used as a standard because
integral fission product activity is not a linear function of fission rate
and time, and of all the individual fission products, La140 offers the
best combination of accurately known yield, long effective half-life, and
a gamma-ray energy high enough to produce a distinct peak above the
remaining fission products.
Even with La 1 4 0 as the basis, the above
procedure is by no means unique, and simpler, more accurate methods
can probably be developed with experience.
When several absolute reaction rates have been obtained, several
methods are available for computing a fast neutron energy spectrum.
Among the better known techniques are the Trice Method, least-squares
polynomial. methods, and orth-normal expansions.
All of these methods
have their advantages and disadvantages and no one method has been
shown to be superior in all cases.
It is planned to try some of these
methods with the experimental data obtained in an effort both to test
the methods and to obtain the neutron spectra in the various lattices.
In particular, it is to be expected that the data obtained will not be of a
high order of accuracy, since the fast flux in the MITR Lattice is too low
to produce, in most cases, reaction rates high enough to have sufficient
activity for highly accurate counting.
Thus, various semi-theoretical
calculations regarding error instability of the various methods can be
explored.
Finally, once neutron spectra and distributions have been obtained,
it is planned to compare the results with those obtained with some
method, probably a Monte Carlo computer code.
107
11.
CONTROL ROD AND PULSED NEUTRON RESEARCH
B. K. Malaviya, A. E. Profio
The program described in the last Annual Report (a) has been
continued.
Some phases of the work have been completed while others
have been brought to the stage where experimental results should soon
be forthcoming.
I.
Stationary (Exponential) Experiments
The first step toward the study of the reactivity effect of control
rods in exponential experiments was the measurement of the linear
extrapolation distance of thermally black cylinders.
distance is
The extrapolation
an input parameter in the calculations of control rod effec-
tiveness and is,
in general, an important quantity for describing the
absorption characteristics of a lumped neutron absorber.
Although its
theoretical evaluation has been considered by various authors (a, b, c)
for rod sizes of practical interest, to our knowledge, no exact values
are known and no systematic experimental measurements have been
reported.
The extrapolation distance of thermally black cylindrical rods of
various sizes was investigated by relating it to the change in the axial
buckling produced by the rod in an assembly of pure moderator (D 2 0)
irradiated by a stationary thermal neutron source.
In a bare cylindri-
cal exponential assembly of pure moderator of extrapolated radius R,
with a black cylindrical rod placed along the axis, the radial flux is
given by
(dr) = A J0 o2 (ar)
J
-
(aR)
J4
Y (oR) Y 0 (air)j,
0
(11.1)
where a is the radial buckling, which is related to the axial buckling
2
y by
2
Bm
2
a
-y
2
108
If the actual radius of the rod is a, the boundary condition at the
surface of the rod (which provides an internal boundary of the moderator assembly) is defined by the extrapolation distance
d = d
(11.2)
d
r=a
where d is the thermal extrapolation distance into the rod.
Equations
11.1 and 11.2 yield
d =1I
Y (aR) J (aa)- Y (aa) J (aR)
0
0
0
0
.(11.3)
Y (aa) J (aR) -Y
( aR) J (aa)
Thus, if a is known, Eq. 11.3 gives d for a rod of radius a.
parameter
The
a can be determined by measuring the axial buckling of
a pure moderator assembly with (y) and without (T
) the rod along
its axis, and observing that the material buckling remains unchanged
by the introduction of the additional boundary; i.e.,
aL 2
2
-Y 2 :a 2 - Y 2
2
2
a =a+ A-Y ,
(11.4)
0
where
/2.405).
The experimental assembly used for these measurements was
the 48-inch-diameter tank which forms part of the M.I.T. exponential
facility. The tank was filled with heavy water (99.8%) up to a height
of 52 inches and fed at the bottom with a thermal neutron flux from
the thermal column of the MITR.
The black absorbing rods were
fabricated (a) by wrapping two layers of 0.020-inch cadmium sheets
on aluminum tubes of varying radii; this thickness of cadmium ensures complete blackness to thermal neutrons.
The bottom of the rods
was closed by aluminum discs and the hollow rods could be fixed
exactly along the central axis of the tank by means of top and bottom
positioners.
The axial. bucklings were measured by mapping the axial
109
flux plots with the help of 0.25-inch-diameter, 0.010-inch-thick gold
foils attached to aluminum foil holders. After irradiation, the foils
were gamma-counted so as to straddle the 411-key gamma-ray peak.
Figure 11.1 shows the mapping of the axial flux in the pure
moderator tank without the rod (continuous curve) and with a typical
(2.10-inch-diameter) cadmium rod along the axis (dashed curve). The
measured flux is well represented in each case by a single exponential
in the region of measurement. The change in the rate of relaxation of
the flux (slope) produced by the rod is appreciable enough to be
measurable. The axial buckling was calculated from the axial flux
with the help of a code AXFIT. The errors given by the least-square
fit are of the order of 0.25%; the error in reproducibility, as determined from repeated runs, was of the same order.
The results are shown in Table 11.1. The corresponding radial
bucklings calculated from Eq. 11.4 and the values of the extrapolation
distance d calculated from Eq. 11.3 are shown. The errors in d are
due to uncertainties in the measurement of -y and amount to about 2%.
The values of d (cm) are plotted as a function of the radius (cm) of the
black cylinder in Fig. 11.2.
Figure 11.3 shows the variation of A2 / a 0 with rod radius. For
small values of the radius, the variation is approximately linear, as is
to be expected from a simple-minded theory.
The validity of the method depends on the accuracy with which the
parameter a can be determined from Eq. 11.4. To check this, the
radial flux was experimentally mapped with each of two typical rods
and was compared with that given by Eq. 11.1, using the value of a
calculated from Eq. 11.4. An example of the good agreement is shown
in Fig. 11.4.
Further exponential experiments with control rods have to do
with the measurement of the reactivity effect of the rod given in terms
of the relative change in buckling produced by the rod in a subcritical
assembly and also the investigation of the flux spectrum as a condition
for the results of the exponential experiments to be interpretable in
terms of a simple theory. These results will then be compared with
theoretical calculations and the results of the pulsed neutron experiments.
0
TABLE 11.1
Measured Extrapolation Distances for Black Cylinders of Different Radii
Axial Buckling
in Presence of
Control Rod
Change in
Radial
Buckling
Radial
Buckling
Parameter
2 _
Rod
Radius
72
(cm)
(10-6 cm-2)
(10-3 cm~
)
Extrapolation
Distance d
(cm)
2
(10-6 cm -2
0.635
1732 ± 4
41.43
238
2.82 ± 0.08
1.295
1882 ± 4.5
43.18
388
2.62 ± 0.07
1.714
1968 ± 3.5
44.19
474
2.44 ± 0.06
2.209
2055 ± 4
45.16
561
2.298 ± 0.05
2.667
2128 ± 5
45.96
634
2.20 ± 0.05
3.327
2225 i 5
47.01
731
2.11 ± 0.05
3.969
2315
47.96
821
2.02 ± 0.05
4
Y
= 0.001494 i
3.8 cm-2
111
10
I
_
-
I
0--
----
i
-
..
WITH 2.10 IN. CD. ROD ALONG AXIS
--
WITHOUT
I
i
I
ROD
'4
'0 '4
-
'4
'4
'4
-
X~N
bN
,'14 1
x
%0.
-LJ
\K
wL
0
0.1
Nr
0
XX
x
0
%
xx
0x'%
0.01E-
I
I
I
I
I
I
80
60
100
120
40
20
DISTANCE FROM TANK BOTTOMz (CMS)
FIG.II.I
AXIAL FLUX DISTRIBUTION
OF PURE MODERATOR
IN TANK
140
I-i
I-i
ro
3.0
U)
E
I
C)
a)
C.)
C
0
4U)
2.0 -
0
C
0
0
0
0.
0
h.
w 1.0
0
S
h.
0)
I.-
0
I
1.0
Measured Extrapolation
I
3.0
I
2.0
Rod Radius
Distance of
4.0
cms
Thermally
Black
FIG. 11.2
Cylinders as a Function of Radius
0'
400
0
z
300
02
200
z
w
z
r
00
0
-
3.0
2.0
ROD RADIUS (CMs)
1.0
FIG. 11.3
4.0
FRACTIONAL CHANGE OF RADIAL BUCKLING OF A PURE MODERATOR
TANK, PRODUCED BY CD. RODS OF DIFFERENT RADII
x al
|li
]|
|
||
|||U
5.0
H
H
50
40
30
.
Radial
Run
With
-
20
10
Radial
Distance
10
from
the
cms
2.60 Cm. OD. Cd Rod Placed
Axis
of the
Axially in Tank
FIG. 11.4
20
30
Tank
of
Pure
Moderator
40
50
115
II.
Pulsed Neutron Experiments
Pending the operation of the small, compact pulsed neutron source
for use in conjunction with the subcritical facility, a set of runs was
made with the existing Texas Nuclear Corporation accelerator to investigate the thermal neutron diffusion parameters of heavy water
based on small assemblies.
A knowledge of these parameters is needed
in the evaluation of the prompt neutron lifetime to be used in the measure-
ment of reactivity by the pulsed neutron technique.
The test assemblies were cylindrical jars of glass or aluminum
of diameters varying from 15.5 cm to 43.8 cm, filled with 99.8% D 2 0 to
heights of 17.8 cm to 48.3 cm, thus providing a buckling range of
140 m
- 2 to 855 m - 2 . The outer surface of the assemblies was covered
with 0.020-inch-thick cadmium sheets to provide a slow neutron boundary condition.
The heavy water was transferred from the storage vessel
to the test assembly in a nitrogen atmosphere to prevent degradation,
and the assembly was subsequently closed with plastic leak-tight covers
so that the heavy water remained in a nitrogen atmosphere throughout.
The pulsed neutron source was a 150-kv Cockcroft-Walton accelerator equipped to generate neutrons by the (D, D) reaction; the pulsing
was achieved by the deflection of the beam.
from 5
1.sec
670 pps.
The pulse width used varied
to 12 pLsec and the repetition rate from 500 pps to about
The fast neutrons from the source are thermalized, and the
asymptotic thermal flux emerging from the assembly is detected by a
5-inch Li6
-
ZnS plastic crystal mounted on a DuMont 6364 photo tube.
The detector is surrounded on the sides by a 0.020-inch-thick cadmium
sheet and mounted on the assembly-axis so as to be exposed to a 5-inch
circular window cut in the cadmium cover on the top of the assembly.
A block diagram of the equipment is shown in Fig. 11.5.
The target was located on the axis of the cylindrical test assembly
at the bottom, while the detector was on the axis at the top.
Thus, the
harmonic modes having radial modal planes through the axis were not
excited for reasons of symmetry.
The complete decay was examined
for the initial curvature (due to harmonics) in the plot of the backgroundcorrected count vs. time data.
Three runs were made with each buck-
ling value to test the consistency of the results.
ELECTRONICS
TARGET ROOM
AREA
HAMNER N361
PRE AMP
HV SUPPLY
HAMNER N338
LINEAR
AMPLIFIER
PHS OUT
PMT
SIGNAL IN
MODEL 212
TMC CN 110
MODEL 220
NEUTRON
PLUGIN)
256 CHAN NEL
ANALYZER
DATA OUTPUT
UNIT
(SYSTEM
IS(PULSED
EXPERIMENTAL
I--------A
GENERATOR
ASSEMBLY
I
SYSTEM
TRIGGER
TRIGGER
SCALER
___SCALER)
SOURCE TRIGGER
OUT
TRIGGER IN
ACCELERATOR
INITIAL PULSE
ELECTROPULSE
TRIGGER)
ACCELERATING (2p.SEC.DELAY AFTER SOURCE
AND
PULSING
FINAL PULSE
ACCELERATOR
UNIT
FIG. 11.5
ELECTROPULSE
ULAY= -ULS
IIOA
210A
WID
Ur)
OVERALL CIRCUITRY
----
PRINTER
117
An IBM-7090 code EXP() has been written for the analysis of the
data from the analyzer. It fits the experimental counts and time points
to a single exponential plus a constant background, i.e., to an expression
of the form:
n = Aet
+ B,
(11.5)
and computes, by a weighted least-squares procedure, the values of the
parameters X, A, B, together with their associated uncertainties (or
errors). Instead of varying the waiting time in each run, the delay between the injection of the burst and the opening of the first channel was
kept constant throughout at 20 NLsec; thus, almost the whole decay curve
was mapped over the 63 channels. In analyzing the data, the code successively drops the initial channels, one by one, and calculates the
decay constants for fewer channels each time, thus effectively varying
the "waiting time." This is shown for a typical run in Fig. 11.6. It
was found that as the waiting time is increased, the decay constant decreases and so does the error in the decay constant. When the point
is reached where the fundamental mode is established, the data represent a single exponential and the error is a minimum. Thereafter, on
dropping further points, the errors begin to rise. The "best" decay
constant value selected is the one corresponding to this minimum error;
this is verified by an actual graphical plot of the data. It was found that
a waiting time of about 120 pLsec (for the smallest assembly) to about
170 1 sec (for the largest assembly) was necessary. The asymptotic
mode was observed over three to five decay times and the uncertainties
(due to statistics) in the decay constant were between 1% and 2%. The
error in reproducibility was of the order of 1%.
The bucklings of the cylindrical assemblies (physical radius R
and height H) were computed according to the prescription:
B2 = (2.405
RW+Td
d = EXtr ,
tr'
X 3D .
t 3D
v
+\H H7+
2
+ 2d/
(11.6a)
(11.6b)
1.c
(11.6c)
II
I
II
II
I
I
I
I
I
I
o
0
8
0
I0
x
7
U
0
6K[
i
I
I
I
I
I
I
100
120
140
20
40
60
80
160
180
200
TIME FROM BURST END TO START OF ANALYSIS CHANNEL (MICROSECS.)
FIG.I11.6
460
VARIATION
OF DECAY CONSTANT WITH 'WAITING
TIME"
119
with
e = 0.71046.
The X vs. B2 data were then treated for a two-parameter fit of
the form
X = X + DB
(11.7)
- CB
where X9 = 17.5 sec~ (calculated vM a for 99.8% D2 0). This was done
by means of a new IBM-7090 code DEECEE which makes a leastsquares fit by using an iterative procedure and computes D and C
together with their probable errors. The code takes the actual physical dimensions of the assemblies as input data and the value of X as
an input parameter and calculates the geometrical bucklings from an
assumed initial value of D in Eq. 11.6c. A fit of these buckling values
against X then yields D and C; this new value of D is then used to
compute the bucklings again from Eqs. 11.6 and a new fit is made; the
process is repeated, yielding self-consistent values. The value of the
velocity characteristic of the spectrum is taken to be
v _
X 2.2 X 105 cm/sec.
2
The X vs. B2 experimental points are shown in Table 11.2 and
Fig. 11.7. There is appreciable diffusion cooling effect as seen from
the departure of the curve from a linear relation for larger bucklings.
The final values of the diffusion parameters for 99.80% D 2 0 at 21*C are:
D = 1.794 ± 0.016 X 10
5
2
cm /sec,
54
C = 3.198 ± 0.365 X 105 cm /sec .
The errors are derived, in the code, from the mean-squared deviation of the experimental points from the resulting interpolation curve
The weights used in the least-squares fitting are of
given by Eq. 11.7.
the form
W.1
1
AXki'
where AX. is the probable error in X .
120
20
,
I
I
I
I
i
I
18-
16
0
w 14Fcl)
0
ASYMPTOTIC CURVE
FOR SMALL BUCKLINGS
I2-
z IOFc/)
z
0
8[6HF
4FX=17.5+1.796 x 105 B 2 - 3.198 x IOB
5 4
2I
i
I
200
B2
FIG.II.7
DECAY
I
,
I
400
600
BUCKLING (m- 2 )
CONSTANT VS. BUCKLING
,I
i
800
121
TABLE 11.2
Experimental Results for Room Temperature (21*C) Heavy Water
R
cm
cm
B2
-2
m
21.907
19.367
12.224
48.260
40.640
40.640
140
180
347
2448.5
3154.4
5812.7
31.5
42.7
55.3
10.160
22.860
549
9045.8
10.160
7.779
17.780
17.780
623
854
10117.5
12520.9
112.8
184.3
H
sec
-1
AX
-1
sec
301.9
These experiments are being continued to cover a wider buckling
range based on larger assemblies, which should make possible a determination of the absorption cross section of heavy water by making a
three-parameter fit of the form
X= vT
+ vDB
- CB
(11.8)
to the (X, B ) data. Another IBM-7090 code DIFFN has been written
which does this fitting by a weighted least-squares technique.
For these and other pulsed neutron experiments with the subcritical facility, another small, compact pulsed neutron generator has
been brought into operation with the associated networks and equipment
designed by D. Gwinn. The source is a Type A-810 neutron generator
built by Kaman Nuclear of Colorado and utilizes the (D, T) reaction for
neutron production. The neutron generating tube consists of a P.I.G.
ion source, a miniature accelerating structure, a tritium target, and
two gas occlusion elements (the "reservoir and the "getter") all sealed
in a glass envelope; and the whole tube is housed in a 10-inch by 4.5inch-diameter cylindrical aluminum enclosure fitted with dried Shell
Oil Company Diala-AX insulating oil. The 120-kilovolt negative accelerating potential is obtained by a Carad Corporation step-up pulse transformer; the high voltage cable from the transformer to the tube is about
eight feet.
122
The accelerator assembly and the transformer are located in the
lattice room on top of the subcritical facility, while the entire control
unit is placed on the reactor floor, 25 feet below. The control unit
supplies pulse voltages for the neutron tube ion source and for the pulse
transformer to the target. The unit can be used in conjunction with
other types of tubes, also; it has three independent networks to generate
a target pulse, a plasma pulse and a magnetic field pulse (not needed for
the Kaman tube); a timer circuit fires the pulse networks at prescribed
delays relative to each other. The pulse rate is variable from one pulse
per second to ten pulses per second; the pulse widths can be approximately 9, 12 or 15 Lsec. The yield is estimated to be about 10 7 neutrons
per burst, having an energy of 14 Mev.
The experiments currently underway, using this equipment, have
to do with the determination of the diffusion parameters of heavy water
over a large buckling range, the pulsing of lattices of slightly enriched
uranium moderated with heavy water for the determination of the reactor parameters of the lattice, and a thorough investigation of the factors
affecting the experimental measurement of the decay constant for such
systems.
These will lead to the measurement of the reactivity effect of
control rods by several methods using subcritical assemblies and provide data for comparison with the results of steady-state experiments
and theoretical calculations.
References
a. M.I.T. Heavy Water Lattice Project Annual Report, September 30,
1962, NYO-10, 208.
b. B. Davidson and S. Kushneriuk, Linear Extrapolation Length for a
Black Sphere and a Black Cylinder, MT-214 (1946).
c.
W. P. Seidel, B. Davidson and S. Kushneriuk, Influence of a Small
Black Cylinder Upon the Neutron Density in an Infinite NonCapturing Medium, MT-207 (1946).
d.
L. TrLifaj, The Cylindrically Symmetrical Solution of Milne's
Problem Using Spherical Harmonic Analysis, PICG, 5 (1955).
e. B. K. Malaviya and A. E. Profio, Measurement of the Diffusion
Parameters of Heavy Water by the Pulsed Neutron Technique,
Trans. Am. Nucl. Soc. 6, 58 (June, 1963).