MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF NUCLEAR ENGINEERING
Cambridge 39, Massachusetts
MIT- 2344-3
M IT N E- 60
HEAVY WATER LATTICE PROJECT
ANNUAL REPORT
September 30, 1964
Contract AT (30-1) 2344
U.S. Atomic Energy Commission
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
DEPARTMENT OF NUCLEAR ENGINEERING
Cambridge 39, Massachusetts
MIT-2344-3
MITNE-60
AEC Research and Development Report
UC-34 Physics
(TID-4500,
36th Edition)
HEAVY WATER LATTICE PROJECT ANNUAL
September 30,
REPORT
1964
Contract AT(30-1)2344
U. S. Atomic Energy Commission
Editors
D. D. Lanning
I. Kaplan
F. M. Clikeman
Contributors
J. Barch
N. Berube
F. M. Clikeman
W. H. D'Ardenne
J. W. Gosnell
J. Harrington III
I. Kaplan
B. Kelley
D. D. Lanning
B. K. Malaviya
L. T. Papay
E. E. Pilat
E.* Sefchovich
A. Supple
T. J. Thompson
G. L. Woodruff
ii
DISTRIBUTION
MIT-2344-3
MITNE-60
AEC Research and Development Report
UC-34 Physics
(TID-4500,
36th Edition)
1.
USAEC,
New York Operations Office (M. Plisner)
2.
USAEC, Division of Reactor Development (P.
Hemmig)
3-5. USAEC, Division of Reactor Development (I. Zartman)
6.
USAEC, New York Patents Office (H. Potter)
7.
USAEC, Division of Reactor Development, Washington, D. C.
(S. Strauch)
8.
USAEC, New York Operations Office,
Research and Development Division
9.
USAEC, Division of Reactor Development,
Reports and Statistics Branch
10.
USAEC, Maritime Reactors Branch
11.
USAEC, Civilian Reactors Branch
12.
USAEC, Army Reactors Branch
13.
USAEC, Naval Reactors Branch
14.
Advisory Committee on Reactor Physics (E. R. Cohen)
15.
ACRP (G. Dessauer)
16.
ACRP (D. de Bloisblanc)
17.
ACRP (M. Edlund)
18.
ACRP (R. Ehrlich)
iii
19.
ACRP (I. Kaplan)
20.
ACRP (J. Chernick)
21.
ACRP (F. C. Maienschein)
22.
ACRP (R. Avery)
23.
ACRP (P. F. Zweifel)
24.
ACRP (P. Gast)
25.
ACRP (G. Hansen)
26.
ACRP (S. Krasik)
27.
ACRP (L. W. Nordheim)
28.
ACRP (T. M. Snyder)
29.
ACRP (J. J. Taylor)
30-32.
O.T.I.E., Oak Ridge, for Standard Distribution
33-100.
Internal Distribution
iv
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. In the past year, measurements
have been made in heavy water moderated lattices fueled with 1/4-inch,
1.03% and 1.14% enriched uranium rods. Research programs are also
under way to take and correlate data from single-rod measurements,
two-region lattice measurements, fast neutron distribution 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.
v
TABLE OF CONTENTS
1.
Introduction
1
2.
Fast Fission Measurements
5
I.
II.
III.
3.
II.
III.
Experimental Procedures
7
A.
1/4-Inch Rods
7
B.
1.01-Inch Rods
10
Results and Comments
11
15
Experimental Technique
15
Results
23
Theoretical Methods
35
Studies of Epithermal Neutrons in Uranium,
Heavy Water Lattices
I.
II.
5.
5
Fast Neutron Distributions
I.
4.
Theory
37
Cadmium Ratio Measurements
39
The Measurement of the Ratio of Capture in U-238
to Fission in U-235, C*
41
III.
The Fast Fission Ratio
46
IV.
Resonance Activation Measurements
48
V.
Analysis and Comparison of Results
48
Pulsed Neutron and Control Rod Research Studies
of Reactivity and Related Parameters
I.
II.
III.
IV.
V.
55
Experimental Set-Up for Pulsed Neutron Studies
55
Pulsed Neutron Experiments on Non-Multiplying Media
62
Pulsed Neutron Experiments on Unperturbed
Multiplying Systems
70
Determination of Lattice Parameters
81
Pulsed Neutron Experiments on Perturbed
Multiplying Systems
VI.
91
Exponential Experiments with Control Rods
in Multiplying Assemblies
A.
6.
Examination of the Flux Spectrum:
Measurements on Poisoned Lattices
I. Definition of ko,
II.
Introduction to Theory of Measurement
98
Radial Runs
103
109
109
109
vi
7.
III.
Poisoning Method Selected
111
IV.
Experiments and Analysis
113
Single Rod Measurements and Theory
115
I.
II.
8.
Theory
115
B.
Experimental Thermal Data
116
Resonance Energy Region Theory
122
125
Formation of Assemblies
125
Gold-Cadmium Ratios
127
III.
U-238 Cadmium Ratios
127
IV.
628 Measurements
134
Axial Buckling
134
Discussion of Results
136
II.
V.
VI.
Oscillating Neutron Source Experiment
I.
Theory
II. Experimental Setup
III.
10.
115
A.
Two-Region Lattices
I.
9.
The Thermal Energy Region
137
137
138
A.
Modulating Assembly
139
B.
Instrumentation
143
C.
Experimental Assembly
143
Discussion of Experiments
146
A.
Semiconductor Detector
146
B.
Calibration of Oscillator
150
C.
Study of Neutron Source
150
Material Buckling and Intracellular Thermal
Neutron Distributions
I.
Buckling Measurements
A.
Experimental Methods
B. Results
II.
Thermal Utilization Measurements
155
155
155
157
157
A.
Experimental Methods
157
B.
Theoretical Calculations
160
C.
Results
161
Appendix A.
References
165
vii
LIST OF FIGURES
2.1
Vertical Section of the Subcritical Assembly
2.2
Foil Packet Arrangement for Measurement of 628
2.3
Ratio of Fission Rate in U-238 to Fission Rate in U-235,
3.1
3.2
8
628, for Uranium Rods, 1/4 Inch in Diameter
13
Fuel Button for Surface Foils
17
Foil Holder for Moderator Foils (Dimensions Variable
with Lattice Spacing)
3.3
18
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.4
24
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.5
25
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.6
26
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.7
27
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.8
28
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.9
29
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.10
30
Relative Activation versus Distance from Center
of Fuel (Rod to Rod)
3.11
31
Relative Activation versus Distance from
Bottom of Fuel
3.12
34
Relative Activation versus Distance from
Center of Fuel (Rod to Rod)
36
239
4.1
Effect of Catcher Foils on Depleted Uranium Np
4.2
Effect of Depleted Uranium Catcher Foils on Depleted
Activity
41
Uranium Fission Product Activity
43
4.3
p2
44
4.4
Values of C for Heavy Water Lattices with 0.25-InchDiameter, 1.03% U-235 Fuel Rods
45
Comparison of Present Results for the Resonance Escape
Probability with Miniature Lattice Results
50
4.5
4.6
4.7
8
versus VM/F
Values of k, for Heavy Water Lattices with 0.25-InchDiameter Fuel Rods
51
Spatially Averaged Neutron Flux Spectrum for the 1.25Inch Lattice Obtained from GAM-1 and THERMOS Output
53
viii
5.1
Pulsed Neutron Source, Accelerator Tube
57
5.2a
Detection System Using Small BF 2 Counter (N. Wood Model,
Active Volume 4 Inch X 1/2 Inch, 40 cm Hg Filling Pressure)
Running in an Aluminum Thimble Along Axis
59a
5.2b
5.3
5.4
5.5
Detection System Using Long External BF
3
Proportional
Counter (N. Wood Model, Active Volume 20 Inch X 2 Inch,
40 cm Hg Filling Pressure)
59b
Schematic of Over-All Pulsing, Detection and Analysis
Circuitry
61
The Control Panel of the Accelerator and the Associated
Equipment
63
Thermal Neutron Decay Curves in Pure Moderator (D 0)
2
Assembly (36-Inch-Diameter Tank), with and without a
Thermally Black Rod Along Axis
5.6
Aa.2 /a
Fractional Buckling Change
Black Rods in Pure Moderator
68
2 Caused by Thermally
0 (D 2 0) Assembly, by
the Pulsed Neutron Method
71
Measured Extrapolation Distance of Thermally Black
Cylinders as a Function of Radius
72
5.8
Configuration of Fuel Rods in the Lattice
74
5.9
Thermal Neutron Decay Curves in the Multiplying
Assembly with Different Detection Systems
75
5.10
Variation of the Measured Decay Constant with "Waiting
5.7
Time" in the Multiplying Assembly, with Different
5.11
5.12
Detectors
76
Thermal Neutron Decay Curves in Multiplying Assembly
with Different Detector Locations Along Central Axis
77
Variation of the Prompt Neutron Decay Constant with
"Waiting Time" in Multiplying Assembly for Different
Detector Locations Along the Central Axis
5.13
79
Spatial Thermal Flux Distribution in Axial Direction
*(z, t) at Different Times t after Burst in the Multiplying
Assembly
5.14
Prompt Neutron Decay Constant X as a Function of
Buckling B 2 , for the Lattice of 0.25-Inch Diameter, 1.03%
U-235 Rods in Heavy Water with a Triangular Spacing of
1.75 Inches
5.15
5.16
5.17
80
83
Variation of the Measured Decay Constant X with
Geometrical Buckling B 2 for a Multiplying and a NonMultiplying Assembly
84
Fractional Buckling Change Produced by Cadmium Rods
in the Multiplying Assembly, by Pulsed Source Method
94
Reactivity Worth Ap of Central Cadmium Rods as a
Function of Radius a, Measured in the Subcritical
Assembly by Pulsed Neutron Method
96
ix
5.18
5.19
5.20
5.21
5.22
Axial Flux Distribution in the Exponential Assembly with and
without a Control Rod
99
2 2
Fractional Change in Buckling a2 /a2 Produced by Cadmium
Rods of Different Radii a, in the Subcritical Assembly
102
Location of the Foil Holder for Radial Flux Mapping in
the Exponential Assembly
104
Radial Flux Distribution (with Bare Gold Foils) in the
Exponential Assembly with and without a Control Rod
105
Radial Flux Distribution (with Cd-Covered Gold Foils)
in the Exponential Assembly with and without a Control
Rod
5.23
7.1
106
Variation of the Gold-Cadmium Ratio c2 /
of the Exponential Assembly with and
Thermally Black Rod Along Axis
1 Along
a Radius
without a
Axial Traverses in D 2 0 at Two Radii from 1-InchDiameter, Natural Uranium Rod at Center of Tank
7.2
117
Ratios of Corresponding (Same Height) Foil Activities
from Three Axial Traverses at Different Radii
7.3
108
118
Relative Activity of Gold Foils in D20 Around a Single
1-Inch-Diameter, Natural Uranium Rod at the Center
of Exponential Tank
7.4
119
(Relative Gold Foil Activity) + J 0 (ar) Around a Cadmium
Control Rod at the Center of the
D 2 0-Filled Exponential
Tank
7.5
120
(Relative Gold Foil Activity) +- J(ar)
Diameter, Natural Uranium Rod
Around a 1-Inch-
at the Center of the
D 2 0-Filled Exponential Tank
121
Assembly III (Four Ring, 2-1/2-Inch Pitch in 1-1/4-Inch
Pitch)
126
8.2
Cadmium Ratio in Three-Ring Assembly (Assembly II)
128
8.3
Cadmium Ratio in Four-Ring Assembly (Assembly III)
129
8.4
Gold Foil Activities in Three-Ring Assembly
(Assembly II)
130
Gold Foil Activities in Four-Ring Assembly
(Assembly III)
131
8.6
Cadmium Ratio in Six-Ring Assembly (Assembly IV)
132
8.7
Gold Foil Activities in Six-Ring Assembly (Assembly IV)
133
8.8
Ratio of Axial Foil Activities in Three-Ring Assembly Assembly II (First Foil Position 32 cm above Bottom of
Fuel)
135
9.1
Cut-Away View of the M.I.T. Research Reactor
140
9.2
Cross-Sectional View of Neutron Source Modulator
141
9.3
Main Structure
142
8.1
8.5
x
9.4
The Modulation Assembly
144
9.5
Instrumentation for Oscillating-Neutron-Source Experiment
145
9.6
Experimental Setup in Place
147
9.7
Fission Spectrum Obtained with Surface Barrier Detector
148
9.8
Decrease in Pulse Height as a Function of nvt Continuous
Irradiation
149
9.9
Calibration of Motor Speed Control
151
9.10
Relative Source Strength about Source Modulator
152
9.11a Time Variation of Neutron Source at a Frequency of
159.8 cps
154
9.11b Time Variation of Neutron Source at a Frequency of
78.2 cps
154
10.1
Axial Buckling vs. Extrapolated Height
156
10.2
Foil Holder Arrangement for Microscopic Flux
10.3
10.4
Measurements
159
Microscopic Gold Activity Distribution in Lattice of
1/4-Inch-Diameter, 1.03% U-235 Uranium Rods on a
1.75-Inch Triangular Pitch
163
Microscopic Gold Activity Distribution in Lattice of
1/4-Inch-Diameter, 1.143% U-235 Uranium Rods on
a 1.25-Inch Triangular Pitch
164
xi
LIST OF TABLES
2.1
3.1
3.2
Average Values of 628 Measured in the M.I.T. Lattice
Facility
12
Experimental Parameters for Threshold Detectors
20
Lattice Height and Ratio of Activity with U-235 Included
to Normal Activity
33
4.1
Measured Microscopic Parameter Data
38
4.2
Reactor Physics Parameters for Three Heavy Water
Lattices Containing 0.25-Inch-Diameter, 1.03% U-235
Uranium Metal Rods
40
Correction Factors for the Fission Product Activity of
Depleted Uranium Foils Used to Measure the Fast
Fission Rate
46
4.4
Resonance Activation Data
49
5.1
Comparison of the Thermal Neutron Diffusion Parameters
of Heavy Water
67
4.3
5.2
Measured Decay Constant of a Cylindrical Pure Moderator
Assembly with Thermally Black Rods of Different Radii
Along the Axis
5.3
Measured Prompt Neutron Decay Constant as a Function of
Buckling for the Lattice of 0.25-Inch-Diameter, 1.03%
U-235 Uranium Rods with a Triangular Spacing of 1.75 Inches
5.4
82
Comparison of the Values of Lattice Parameters Obtained
by the Pulsed Neutron Method with Those Obtained by Other
Methods, Lattice with 0.25-Inch-Diameter, 1.03% U-235
Metal Rods in a Triangular Spacing of 1.75 Inches
5.5
69
90
Measured Prompt Neutron Decay Constant and the Change in
Buckling Due to Cadmium Rods of Different Radii Along the
Axis; Lattice of 0.25-Inch-Diameter, 1.03% U-235 Uranium
5.6
5.7
Rods in Heavy Water, with a Triangular Spacing of 1.75 Inches
92
Prompt Neutron Lifetime and Reactivity for the Perturbed
Lattices, Measured by the Pulsed Neutron Method
95
Buckling Change Produced by Axial Cadmium Rods of
Different Radii in the Multiplying Assembly, Measured
in Exponential Experiments
5.8
100
Comparison of the Fractional Buckling Change Caused by
Axial Cadmium Rods of Different Radii in the Lattice, by
Pulsed Neutron and Steady-State Experiments
101
8.1
Two-Region Assemblies in the M.I.T. Lattice Facility
125
8.2
Axial Relaxation Lengths in Two-Region Assemblies
136
Measured Values of the Buckling for Slightly Enriched
Uranium Rods in Heavy Water (99.6% D 2 0)
158
10.1
10.2 Relative Absorption Rates Computed by Using THERMOS
161
1
1.
INTRODUCTION
I. Kaplan, D. D. Lanning, and T. J. Thompson
This report is the fourth annual progress report of the Heavy
Water Lattice Project of the Massachusetts Institute of Technology.
For the convenience of the reader, some of the main features of the
lattice facility are described as needed with the individual sections of
this report.
If
desired,
a more complete description of the project
and features of the facility can be found in the first progress report
(NYO-9658,
September 1961).(-
The second and third progress
reports(2',3) describe the experimental methods adopted or developed
and the application of these techniques to three lattices of 1-inchdiameter, natural uranium rods in heavy water and two lattices of
0.25-inch-diameter rods of uranium containing 1.03% U 2
3 5
Review of Progress to Date
During the period between April 1959 and September 1961, the
basic experimental arrangement was designed, constructed, and tested
at the M.I.T. Nuclear Reactor.
This arrangement provides a method
for transmitting thermal neutrons from the reactor core to the base of
the lattice assembly by utilizing a cavity or hohlraum.
provides a high-intensity source of neutrons - up to 10
within a lattice assembly of vertical fuel rods.
9
The design
2
n/cm -sec -
The fluxes are high
enough so that microscopic lattice measurements can be made in this
facility as well as, or better than, they can be made in critical experiments.
be in
The reactor lattice fuel is positioned vertically - as it would
a power reactor -
thus permitting accuracy in
experimental
measurement since no fuel element sagging occurs (as it would in a
horizontal position) and permitting ease in the handling of the experimental equipment and in the interpretation of the experimental results.
The development of this method for providing a neutron source has been
carried out both experimentally and theoretically, -4 and the method
itself represents an innovation permitting the transmission of thermal
neutrons around corners and in varying source arrangements with
2
minimal attenuation.
The design, construction, and proving out of this
entire arrangement - including concrete shielding blocks, the graphite,
the heavy-water piping system, the tank system, nuclear instrumentation, and the testing of all items and equipment -
required approxi-
mately two and one-half years.
The first experimental measurements utilizing this new arrangement were made in September of 1961.
The initial set of fuel elements
tested were 1-inch-diameter, natural uranium rods.
This choice of
natural uranium rods was made mainly to obtain comparisons with
results on similar rods which had previously been made in other laboratories in order to prove the validity of the measurement procedures
which we intended to use in our lattice studies.
this goal was achieved and even more.
As discussed below,
Techniques were developed
for measuring epithermal neutron capture rates.
These measurements
have provided a new insight into the experimental determination of the
effective resonance integral of the fuel rod. ()
Experimental analytical
bases of the determination of the material buckling were carefully investigated and effective techniques were developed for buckling
measurements. (-
A technique for measuring the fast effect utilizing
lanthanum-140 without chemical separation has been developed.(7)
After the natural uranium fueled lattices had been tested and
proven to compare satisfactorily with the results from other laboratories, and after sufficiently refined techniques had been developed,
the experiments on lattices of 0.25-inch-diameter, 1.03%o-enricheduranium rods were started. Measurements of thermal neutron distributions in the tight-packed lattices of these rods were instrumental in
leading to refinements of the THERMOS code which was initially developed at M.I.T. and later extended and refined at Brookhaven.
-
A technique has been developed for measuring resonance capture by
the use of foils in the moderator only.(12 ) It is important to note that
in BNL-8253, "The Physics of Heavy Water Lattices," by H. C. Honeck
and J. L. Crandall, it is clearly shown that there is a dearth of microscopic measurements of the type just described, even for natural
uranium lattices. Because of the importance of developing sound techniques for these measurements and because it is necessary to understand the experimental and theoretical implications of the parameters
3
leading to the neutron multiplication factor of the lattice, considerable
attention has been devoted to work in this area. The available high
fluxes in the lattice at M.I.T. have made this work possible and have led
to several methods of calculating and measuring k , in order to try to
establish as sound as possible a base for comparison between the various methods. The microscopic parameters, combined with the over-all
buckling measurements, are important in order to have the detailed
experimental information for comparison of the various theoretical
studies. In addition, by the use of pulsed neutron studies on heavy
water enriched uranium lattices, the project has made measurements
of parameters such as diffusion coefficient (D) and prompt neutron
lifetime (1), and a technique has been developed for the derivation of
the value of the infinite-medium multiplication factor (ko) and the
thermal neutron diffusion length (L) directly from the experimentally
measured, pulsed neutron die-away constant for the lattice.(li' 5 4 )
At the same time, measurements have been continued on the
standard microscopic and macroscopic lattice parameters of the
slightly enriched uranium lattices of 1.03%, 1/4-inch-diameter rods
in 3-foot- and 4-foot-diameter tanks and 1.143%, 1/4-inch-diameter
rods. A total of ten different lattice spacings have been investigated
as of September of 1964. We have also carried out investigations
aimed at discovering the minimum size lattice which can successfully
be used to predict the behavior of large-scale practical reactor
lattices. 8)
Appendix A contains a listing of technical reports which have
been published as part of this project.
The project staff, as of
September 1964, is as follows:
I. Kaplan, Professor of Nuclear Engineering
T. J. Thompson, Professor of Nuclear Engineering
D. D. Lanning, Associate Professor of Nuclear Engineering
F. M. Clikeman, Assistant Professor of Nuclear Engineering
H. Bliss, AEC Fellow
W. D'Ardenne, Research Assistant
D. M. Goebel, Naval Postgraduate Student (JLOASEP)
J. Gosnell, Research Associate (not charged to contract)
4
J. Harrington, AEC Fellow
B. K. Malaviya, DSR Staff
S. G. Oston, Research Assistant
L. T. Papay, AEC Fellow
E. E. Pilat, Sept. 1963 - June 1964 - Research Assistant
June - Sept. 1964 - Doctoral Thesis Student
C. G. Robertson, AEC Fellow
E. Sefchovich, Sept. 1963 -June 1964 -
Teaching Assistant (not
charged to contract)
June -Sept.
1964 - Research Assistant
G. Woodruff, DSR Staff and Research Assistant (not charged to
contract)
J. H. Barch, Senior Technician
A. T. Supple, Jr., Technician
N. L. J. Berube, Technician
Miss B. Kelley, Technical Assistant
D. A. Gwinn, Part Time Electronics Supervisor
J. Cornwell, Part Time Design Engineer
5
2. FAST FISSION MEASUREMENTS
L. T. Papay
Introduction
The results of earlier work at M.I.T. on measurements of 628'
238
235 , have
to the fission rate in U
the ratio of the fission rate in U
been reported in Refs. 7, 8, and 12. That work was done with 1-inchdiameter, natural uranium rods and with 0.25-inch-diameter rods
23523
containing 1.03% U
or 1.14% U 2 3 5 . The present report gives additional results for lattices of 0.25-inch, 1.14% U235 rods and for
single rods in air.
I.
Theory
The theory for 628 measurements has been given in previous
reports (7,56), but the basic equations and definitions will be repeated
here for convenience. The equation defining 628 is:
6
28
-whre
= P(t) (EC)ay(t) - S=
- a (t)
11
P(t)F(t) ,
(2.1)
where
P(t) is the experimentally determined ratio of fission product
activity per U235 fission to the fission product activity per
U238 fission;
T(t) is the experimentally measured ratio of fission product
activity from a foil depleted in U235 content to the fission
product activity from a foil of natural uranium (or, if available, from a foil of the same fuel content as the fuel) where
both foils have been irradiated in the same neutron flux for
the same length of time;
(EC) is an enrichment correction factor of the form
N 28
(N
25
densities;
where the N's represent number
N)25 N28
S is defined as the ratio
-;
3
N2
6
and
W2
N2 28
a =
m) ,
(2.2)
where the W's represent foil weights, and m is a correction factor to
account for the replacement of fuel adjacent to the detector foils used
in the experiment.
The subscripts 1, 2, and 3 refer to the depleted detector foil,
second (natural uranium for all cases reported here) detector foil,
and fuel material, respectively. The superscripts 25 and 28 refer to
U235 and U 2 3 8 , respectively. Note that (EC) is unity if the second
detector foil and the fuel material are of the same composition.
In order to evaluate 628, it is necessary, therefore, to evaluate
P(t) and T(t) in two separate experiments. The general procedure is
to determine the absolute value of 628, designated as 628, by some
method. Then y(t) is determined for the same fuel rod configuration
*
by a different method. After 628 and -y(t) have been determined, P(t)
may be evaluated by using Eq. 2.1. This value of P(t) may then be
used for all subsequent determinations of 628, provided that the rod
diameter and counting setup for y(t) are unchanged; thus 628 may be
determined experimentally by measuring F(t) and multiplying it by the
previously determined value of P(t).
4140
For all determinations reported here, the L140 technique
developed by J. R. Wolberg (7) was used in the determination of the
*
absolute value of 628. The equation giving 628 is:
628 28(28
6
28 ~
5
8
(c~~S
(EC)a-y - S
_ 1 -ay
23
(2.3)
where
28
is the ratio of the fission product yield of Ba
U235 to the fission product yield of Ba140 in U238
and
-y is the ratio of the La140 activity of the depleted foil to the
in
7
La140 activity of the natural foil, corrected for background and
decay.
All the other quantities have the same meaning as in Eq. 2.1.
II. Experimental Procedures
A. 1/4-Inch Rods
All the single-rod determinations made in air were carried out
in the graphite-lined cavity (hohlraum) located at the end of the M.I.T.
Reactor thermal column and directly below the heavy water lattice
tank (see Fig. 2.1). The values reported for 628 for various rod
spacings in heavy water moderator came from determinations made
in the heavy water lattice.
Figure 2.2 shows the foil packet arrangements used in the experiments. All the runs and results reported by H. S. Olsen ( 7 ) were
measured by using the foil packet configuration shown in Fig. 2.2a,
while the runs and results reported by this author were measured by
using the configuration shown in Fig. 2.2b. The two arrangements
differ in the type of catcher foils employed. The advantage of using
aluminum catcher foils is to decrease the fast source perturbation
factor, m (Eq. 2.2), as reported by H. Bliss$
The disadvantage of
using the aluminum catcher foils is that a fission product contamination correction has to be applied to the experimental results.
The depleted and natural uranium detector foils were 0.25 X
0.005 inch. The aluminum catcher foils were 0.25 X 0.001 inch. In the
cases where depleted and natural uranium catcher foils were used,
the foils were of the same composition and size as the respective
detector foils.
The two detector foils and the four catcher foils were wrapped
in mylar tape along with 0.25 X 0.060-inch fuel slugs at each end to
construct the foil packets shown in Fig. 2.2a,b. The depleted uranium
foils have an average U235 concentration of 18 ppm. The mylar tape
served to align the foils within the foil packet and to center the foil
packet within the fuel rod.
In each run, no more than four nor less than two foil packets
were irradiated at one time. In all of the runs carried out in the
cavity, the foil packets were located in a fuel rod near the center of
&
CONCRETE SHIELDING BLOCKS
-
-
STE
El
R,
0__
72" TANK
THERMAL COLUMN
LEAD SHUTTER
CADMIUM SHUTTER 7
48" TANK
ROD
UNE
STEEL SHIELDING DOORS
GRAPHITE
Fig.
2.1
REFLECTED HOHLRAUM
Vertical Section of the Subcritical Assembly
9
FUEL SLUG
0.060 "FUEL
0.001"
AL
7
,f
CATCHER
0.028" AL CLAD
0.003" MYLAR
TAPE
O.05"1 DEP. U.
DETECTOR
CATCHER
DETECTOR
CATCHER
FUEL SLUG
0.006" AIR GAP
lh
0.060"FUEL
CATCHER
DETECTOR
r .--
0.005" NAT. U.
0.060"FUEL
CATCHER
CATC HER
DETECTOR
CATCHER
0.060"FUEL
FUEL SLUG
FUEL SLUG
0
4
a. FUEL PACKET WITH ALUMINUM
CATCHER
FOILS
b.FOIL PACKET WITH DEPLETED
AND NATURAL URANIUM
CATCHER FOILS
FIG. 2.2. FOIL PACKET ARRANGEMENT FOR MEASUREMENT
OF 828
10
the cavity where the flux is reasonably flat.
For the determinations
carried out in the lattice, the foil packets were located between 8 and
20 inches above the bottom of the active fuel region. The spacing between adjacent foil packets was 4 inches.
Irradiation times of one week in the lattice and 40 hours in the
cavity were used in the determination of 6 28 These irradiation times
28
140
counting. Prior to irradiation,
gave sufficient activity for the La
each foil was cleaned, weighed, and background-counted.
A delay of
one week after irradiation was used before the La 10 counting began.
This delay allows the La140 to come to equilibrium with its parent,
140
The La 10 counting was done by using the 1.60-Mev La
Ba 140.
gamma-ray peak and counting the foils with a y -sensitive scintillation counter connected to a multichannel analyzer. All counting passes
were made within five weeks after the end of irradiation.
Irradiation times of 12 hours in the lattice and 3 hours in the
cavity gave sufficient activity for the determination of y(t). Longer
irradiation times were not used in order to avoid a problem of a gain
shift in the counting equipment with high fission product activity.
Prior to irradiation, each detector foil was cleaned, weighed, and
background-counted.
After irradiation, the foils were allowed to cool
approximately 4 hours before counting.
An integral gamma-ray count
was taken with a baseline setting of 0.72 Mev.
The 4-hour cooling time
was used to reduce the dose rate at the surface of the fuel rod to an
acceptable level. It also allowed for the beta decay of the U239 formed
This decay process, with a 23-minute half-life, has associated with it bremsstrahlung radiation of 1.20-Mev end point energy. If
cooling times of less than 4 hours were used, a correction due to the
to Np 239.
presence of this non-fission radiation would have to be made.
B.
1.01-Inch Rods
The procedures for the 1.01-inch, natural uranium rods in the
determination of 6 8 were exactly the same as for the 0.25-inch rods.
The foil packets were similar to those in Fig. 2.2b with the depleted
and natural uranium foils being 1.01 X 0.005 inch. Owing to the difference in foil diameters between the 1.01- and 0.25-inch foils, an irradi14 0
ation time of 10 hours was sufficient to give the required La
activity.
11
III. Results and Comments
The results of the determination of 6
for a single 0.25-inch rod
235 irdaeinte28
irradiated in the cavity yields a value of 628 of
0.0147 ± 0.0004. The function F(t) was determined for the same rod
located in the cavity. By using these values, the value of P(t) was deterenriched to 1.03% U
mined as given in Eq. 2.1. The result is P(t) = 1.16 ± 0.03. This value of
P(t) was used by the author for the evaluation of the single rod value of
(37)
235
. H. S. Olsen
in air for the 0.25-inch rod enriched with 1.14% U
6
(56)
28
used a value of P(t) of 1.14 ± 0.03 previously reported by H. Bliss.The value of 1.16 for P(t) reported here is in agreement with the value
of P(t) reported by Bliss (stated above) and with the value reported by
Wolberg(7 ) of 1.19. All of these values were determined by the same
methods.
Table 2.1 lists all the results reported.
These results agree
favorably with those reported earlier by Bliss, Peak, and Wolberg at
M.I.T. for similar rod diameters, rod spacings, and U235 enrichments
(Refs. 56, 7, 8), with one possible exception.
enriched U 2 3
5
The 0.25-inch, 1.03%
data seem to be consistently higher than those for the
1.14% enriched U235 rods with the same rod diameter.
This difference
exists also when the M.I.T. results for 0.25-inch rods are compared
with the results for similar rods moderated by light water as reported
by Brookhaven National Laboratory.(42)
in Fig. 2.3.
These comparisons are shown
Although the deviations are not much beyond the experi-
mental uncertainties, there appears to be a consistency which would
indicate some, systematic differences.
These investigations are being
continued.
The result for the 1.01-inch natural uranium rod lies below the
value of 0.0559 reported by Wolberg for a single rod moderated by
heavy water.
-
Clearly, more determinations are required before any
definite conclusions can be drawn; however, it may be possible to explain this difference in terms of a moderator backscattering effect.
A
continuing evaluation of 628 in both the air and heavy water moderated
conditions is planned for the 1.01-inch rods and will be reported in the
future.
The evaluation of 628 in the cavity at the M.I.T. Reactor serves
a twofold purpose.
In addition to extending the experimental data on
TABLE 2.1
Average Values of 628 Measured in the M.I.T. Lattice Facility
28
Number of
Determinations
Standard
Deviation (f)
of the Mean
Total
Errors (g)
00
0.0147 (c)
4
0.0003
0.0004
Air
00
0.0129
4
0.0004
0.0005
1.14
Air
00
0.0130 (c)
2
-
0.0005
0.25 (b)
1.14
Air
00
0.0133 (d)
3
-
0.0015
0.25 (b)
1.14
D 20
1.25
0.0265 (d)
9
0.0007
0.0042
0.25 (a)
1.14
D 20
1.25
0.0253 (c)
2
-
0.0023
0.25 (b)
1.14
D20
2.50
0.01639 (d)
12
-
0.0010
1.01 (a)
0.7 (e)
Air
00
2
-
0.0005
Rod
Diameter
(Inches)
Enrichment
Moderator
Rod
Spacing
(Inches)
0.25 (a)
1.03
Air
0.25 (a)
1.14
0.25 (b)
6
0.0519 (c)
(a) Reported by L. T. Papay.
(b) Reported by H. S. Olsen.
14 0
technique.
(c) Absolute value determined by La
(d)
Used a value of 1.14 for P(t).
(e)
Natural uranium.
(f)
The standard deviation of the mean of n measurements.
It reflects the uncertainty due to counting
statistics and is a measure of the reproducibility of the stated values.
(g)
It includes the effects of
The total error represents the over-all uncertainty in the values of 628.
in the fast flux perturuncertainty
the
and
P(t),
in
uncertainty
reproducibility, counting statistics,
bation factor.
0.14
I
- -II-- 9 0.14
o0
N~
to
I
1 1 1 1 1i
I
I
I
-
I
FT
1 1
-- IT I I I 1I |
~
o BNL (H2 0-MODERATED, 1.140% U2 3 5 )
0.12
o BNL (H 2 0-MODERATED, 1.03% U2 3 5 )
0
0
z
z 0.10 F_
+MIT (D2 0-MODERATED, IN MINIATURE LATTICE, 1.14%
U235)
0
e MIT (D2 0-MODERATED, IN EXPONENTIAL ASSEMBLY,
U)
1.030%
0
0 0.08
z
z
I I I Ill
U2 3 5 )
v MIT (D O-MODERATED, IN EXPONENTIAL ASSEMBLY,
8
0.06
1.14% U2 3 5 )
X MIT (AIR -MODERATED,
IN HOHLRAUM, 1.14%
U2 3 5 )
* MIT (AIR - MODERATED, IN HOHLRAUM, 1.03 % U2 3 5 )
0
U)
U)
LLZ
L.
0.04
++
0
0 0.02 I-
+
eY
Hr
I
FIG. 2.3
I
I I I [ I l1
I
I
I
I I 11 1 1 1
VOLUMEf|I'|l
100
10
RATIO OF MODERATOR VOLUME TO URANIUM VOLUME
I
RATIO OF FISSION RATE IN U 2 3 8 TO FISSION RATE IN U 2 3 5 828, FOR
URANIUM RODS, 1/4-INCH IN DIAMETER
~~-
14
628 and serving to investigate the backscattering phenomenon, it affords
the experimenter a less burdensome method of evaluating P(t). The
quantities 628 and y(t) may be determined in the cavity for a particular
235
concentration, and, therefore, P(t) may be
fuel rod diameter and U
in the cavity
calculated by using Eq. 2.1. The evaluation of 628
28 and y(t)
does not require the use of the lattice and does not require as long an
irradiation time as similar determinations in the lattice. In addition,
the higher, flatter neutron flux in the cavity should yield better statistical results. Thus, once P(t) has been determined in this manner, only
y(t) need be determined in the lattice for various rod spacings to determine 628. subject to the requirements that fuel rod diameter and counting setup remain unchanged.
3.
FAST NEUTRON DISTRIBUTIONS
G. Woodruff
Introduction
Fast neutron distributions have been studied by using threshold
detector foils in five types of lattices:
1.25-inch, 1.75-inch, and 2.50-
inch spacings of 1.03% U 235, 0.25-inch-diameter fuel rods, and 1.25inch and 2.50-inch spacings of 1.14% U 2 3 5 , 0.25-inch-diameter fuel
rods.
The reactions used thus far include Zn
64
(n,p)Cu 6 4 , Ni
5 8 (np)Co 5 8
In 115(n,n')In 1 1 m, U23 8 (n,f), and Th 2 3 2 (n,f). Efforts were made to use
2 0 4 (nn')Pb2 04n reacthe Rh 1 0 3 (nn')Rh10 3 m, Nb9 3 (p,n')Nb 9 3m, and Pb
tions, but these efforts were unsuccessful owing to insufficient activa-
tion for counting. Although it appears doubtful that these three reactions
can be used at present in the sub-critical lattice, some or all of them
might be used at higher source levels or in a critical assembly.
For
reasons given below, however, the rhodium reaction is by far the most
interesting, and further efforts will be made to measure it when larger
fuel rods are used in the MITR lattice and/or when the power level of
the M.I.T. Reactor is raised to 5 Mw, thereby increasing the lattice
source strength by a factor of 2.5 over its present level.
I.
Experimental Technique
The microscopic cell distributions were studied by irradiating
1/16-inch-diameter foils inside the fuel and 1/4-inch-diameter foils
in the moderator.
The moderator foils were cadmium-covered in
every case to minimize competing thermal reactions.
The fuel foils
were left bare because cadmium would have significantly affected the
thermal flux distribution and consequently the local fast flux, and
because, in any event, the fast-to-thermal flux ratio is most favorable
inside the fuel.
The fuel buttons used to position the fuel foils were of
The inner four positions were in a 0.060-inch-thick fuel
When the data from the
button of the type described by Simms.
two types.
earliest runs were analyzed, it was found that the steepest gradients
in the fast flux distributions came near the boundaries of the fuel and
16
It was desirable, therefore, to have additional foils
moderator.
positioned in this vicinity. At first, 1/16-inch-diameter foils were
placed in the 0.006-inch air gap between the fuel and clad.
This pro-
cedure, however, was handicapped by the small space available.
Only
very thin foils could be used, there were frequent difficulties loading
and unloading the fuel rods, and there was insufficient space for
catcher foils between the detector foils and the fuel.
It was found necessary to use catcher foils to prevent fission
product contamination in all cases.
Previously, it had been found by
to be important to have catcher foils for measurements
Wolberg (-
which were integrally counted for fission products, but this was not
necessary when counting gamma photopeaks resulting from thermal
activation.
1
)
In the case of the threshold reactions, however, the
activations are so low that the count rates from fission product contamination are not negligible if catcher foils are not used, even when
the counting is limited to the gamma photopeak of the energy desired.
The error resulting from this effect varies, depending on the reaction,
but is generally about 20 to 30% of -the total count rate when only one
side of the detector foil is not covered with a catcher foil.
Presum-
ably, it is twice this amount if catcher foils are not used and both
sides of the detector foil are exposed to fuel.
To circumvent the difficulties associated with placing foils between the fuel and the clad, an additional type of fuel button was prepared when the 1.14% U235 fuel slugs were made.
is illustrated in Fig. 3.1.
This type of button
With this arrangement, thicker foils could
be used at the edge of the fuel, catcher foils could be included, and
difficulties in loading and unloading fuel rods were minimized.
The 1/4-inch-diameter moderator foils were mounted on holders
of the type illustrated in Fig. 3.2.
An additional 1/4-inch bare moder-
ator foil was placed flat between the fuel cladding and the moderator
holder when the holder was strapped in place.
The cadmium covers
used were assembled from a 0.060-inch-thick ring and two 0.020-inchthick, 0.254-inch-diameter discs.
sarily "neutron tight,
This arrangement, while not neces-
minimized the amount of cadmium used and per-
mitted quick disassembly.
Since the only purpose of the cadmium cover
was to reduce thermal activation (no cadmium ratios were computed),
17,
.005 or
.010 in.
0.25"
16
FIG. 3.1
FUEL BUTTON FOR SURFACE FOILS
18
.032" 1100 Al
.010" 1100 Al POSITIONING
STRIPS EPOXED IN PLACE
0
-
0
O
.010" 1100 Al STRIPS BOLTED IN
PLACE OVER POSITIONING STRIPS
FIG. 3.2
FOIL HOLDER FOR MODERATOR FOILS (DIMENSIONS
VARIABLE WITH LATTICE SPACING)
19
the type of cover used was satisfactory.
In order to use 1/4-inch-diameter foils in the moderator, it was
necessary to position the foils diagonally so that they were not all at
the same height.
A height correction proportional to the axial depend-
ence of the thermal flux was used to normalize the heights.
Experi-
ments are in progress to confirm the validity of this correction.
Also,
in most cases the fuel foils and the moderator foils were located in
different fuel rods, so that a similar correction for radial dependence
of the thermal flux was used, although in practice this correction was
usually in the neighborhood of two per cent or less.
The detailed procedures for the different types of runs varied
with the reaction used.
Some of the parameters are included in
Table 3.1 for the five reactions used.
tions are those previously discussed (3)
activity calculation.
The thermal calibration reacin connection with absolute
Some additional remarks concerning the experi-
mental techniques are given below.
The In115(n,n')In115m reaction is complicated by the competing
thermal reaction, In1 1 (n,-y)n
1 16
. The thermal reaction has a cross
section of approximately 150 barns plus substantial resonance activa(T1/2 tion above the cadmium cutoff. The resulting In116 activity
54 min) is,
therefore, detectable even 8 to 12 hours after the end of the
irradiation when the counting of the In115m activity must begin.
Since
the In116 activity consists of gamma rays with energies greater than
the 0.335-Mev In 115m activity, there are Compton effect counts underneath the 0.335-Mev photopeak.
Although the contributions from the
two decay schemes could be resolved by analysis of the 0.335-Mev photopeak data alone, an alternative scheme has been found to be desirable.
Consider the following:
AT(t) = A 1 (t) + CA 2 (t)
(3.1)
where
AT(t) = total count rate under 0.335-Mev photopeak at time t,
A (t)
= count rate under 0.335-Mev photopeak resulting from
In115m activity at time t,
TABLE 3.1
Experimental Parameters for Threshold Detectors
Thermal
Calibration
Approx.
Threshold
Approx. Fission
Spectrum Cross
Irrad.
Cool.
-y Radiation
Counted
Reaction
(Mev)
Section (mb)
Time
Time
(Mev)
In115(n,n')In115m
0.5
290
8-12 hr
8 hr
0.335
4.5 hr
U 238(n,f)
1.0
580
1 wk
3 hr
fiss. prod.
-
U235 (nf)
Th 232(n,f)
1.2
140
1 wk
3 hr
fiss. prod.
-
U235 (n,f)
5858
Ni58n,p)C 058
2.0
550
1 wk
3 d
0.81
71.3 d
Mn
Zn64 (n,p)Cu64
3.0
269
12 hr
4 hr
0.551
12.8 hr
Cu 63(ny)Cu64
T
Reaction
1/2
Cr
50
(n,y)Cr
55
(n,-y)Mn
51
56
21
A 2 (t) = total count rate under a higher energy photopeak
(resulting from In1 1 6 decay) at time t,
and
C = constant relating A 2 (t) to the count rate under the
0.335-Mev photopeak resulting from In 1 1 6 activity.
(3.2)
A 1 (t 2 ) = A 1 (t 1 ) e
A 2 (t 2 ) = A 2 (t 1 ) e
2-t
(3.3)
2
Since AT(t) is measured and T and 2 are known, we have three equations in three unknowns, once a foil has been counted at two different
times. The value of C depends only upon the counting setup; when it
has been determined, it can be used to correct the counts of all the
other foils counted with the same technique. By counting one of the
foils more than twice, a redundant set of equations can be obtained,
values of C can be averaged over several determinations, and an estimate of the accuracy is available. In practice, a photopeak at 0.46 Mev
was found convenient for the higher peak (Eq. 3.3 was checked and
found to be valid), the value of C ranged from approximately 0.3 to 0.5,
depending upon the details of the particular count, and the reproducibility
was approximately 3% for a given count. It should be pointed out that
any or all of the higher peaks can be used for this calculation, and C
will vary accordingly and can even exceed 1.0. The method is not limited to two decay schemes and the general case is as follows with the
terminology similar to Eqs. 3.1 - 3.3:
AT (t) = Aj(t) + C 2 A 2 (t) + C 3 A 3 (t) +
A y(tn= A y(t
A 2 (tn)
=
(t n-t1 Ir
_)e
A 2 (t) e-n-t
1)
An(tn) = An(t 1)e -(tn-t)n
2
.
.
+ CnAn(t)
22
Finally, this method can be expected to be more accurate than methods
utilizing only one photopeak since more information is utilized to reduce
the experimental uncertainty.
The Zn 64(n,p)Cu64 reaction is also accompanied by a thermal
reaction that is troublesome, Zn 68(n,y)Zn 69.
The difficulty results
from the almost equal gamma energies (0.511 Mev and 0.44 Mev) and
half-lives (12.8 hr and 14 hr) of Cu64 and Zn 69.
When the y activities
of these foils are counted, the two peaks can easily be resolved by
standard scintillation counting, but they overlap at the lower edges and
It was found that
care must be exercised in interpreting the results.
by restricting the portion of the photopeaks counted, the activities
could be resolved into two components that followed the two half-lives
accurately and which gave reasonable fast neutron distributions.
serious limitations occur.
Two
The first is that the counting is very sensi-
tive to gain shift in the counting equipment, so that both high count
rates and long counting sessions must be avoided.
The second limi-
tation is that the fast-to-thermal flux ratio must be favorable.
In a
typical lattice, the ratio of the height of the Zn69 peak to the height of
the Cu64 peak varies from approximately 1 in the fuel to approximately
2 in the moderator, depending on the lattice spacing.
Measurements
made in the MITR pneumatic tubes and the MITR Medical Therapy
Room, however, show that the Cu64 peak is only a bump on the side of
the Zn 6 9 peak, even when the foils are cadmium covered.
It is doubt-
ful, therefore, that analysis is possible except in spectra where the
fast-to-thermal ratio is very favorable.
In counting the fission products resulting from the U238 (n,f)
reaction, integral counts above 0.72 Mev were made as described by
(7)
Wolberg. -
In counting the fission products of the Th
232 (n,f) reaction,
however, a minimum energy of 0.57 Mev could be used without introducing error from the decay of Pa
2 3 3
Th232 and subsequent decay of Th 233).
of thorium is
(formed by thermal capture in
Since the fission cross section
comparatively small, this would seem to be an attractive
way of increasing the count rate.
sulting from the decay of
Th 2 3 2
However, the background activity re-
has a large peak just above 0.57 Mev
apparently resulting from one of the members of the thorium decay
chain, Tl 208
.This
increased background reduced to some extent the
23
gain of the increased count rate, and efforts to find the optimum cutoff
energy are continuing.
II.
Results
An IBM 7094 computer code has been written to correct the foil
count rates data for background, decay time, foil weight, lattice position, and counting time.
Since fission product activity has no fixed
half-life for decay time corrections, it was also necessary to fit the
time dependence of this activity by a least squares code.
degree polynomial was found to give a reasonable fit.
A third-
W. D'Ardenne
has also tried semi-log and log-log fits of the fission product activity
time dependence and found that differences in the three types were
negligible for counting periods of a few hours.
The results of the first four microscopic distributions measurements described above are plotted in Figs. 3.3 through 3.10.
thorium data are not included.
The
Analysis is incomplete, but the data
are generally rather poor because of very large experimental errors,
especially counting statistics.
The data are normalized so that the average of the last four
points is taken as unity.
While normalization in the fuel might be pre-
ferred on physical grounds, the greater accuracy of the moderator
foils provides a normalization that is more representative of the distribution.
The scatter in the data, particularly in the fuel positions,
make it difficult to observe systematic trends.
In particular, it is
difficult to say, pending further analysis, whether or not there are systematic trends among the different reactions for any given lattice, or
whether all the reactions show the same microscopic cell distribution.
If the latter is true, there is little incentive for additional efforts to
develop the use of the Nb and Hg inelastic scattering reactions mentioned above, since analysis of the cross sections shows that the
neutron energies involved on these reactions are effectively covered
by the reactions already measured.
The Rh 103 (n,n')Rh 103m reaction, on the other hand, is potentially
very useful.
The theoretical energy dependence of the cross section
(53)
for this reaction --
shows that it exceeds 10 mb at 0.1 Mev and at
0.5 Mev is greater than 100 mb.
While no measured absolute values
24
8.8
8.4
7.:
0
()
Lu
5
4.
4.
cc.
3.
2.
I
0.8 '
0
0.2
FIG. 3.3
0.4
0.6
0.8
1.0
1.2
DISTANCE FROM CENTER OF FUEL (IN.)
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
25
8.8
8.0
7.2
6.4
z
0
5.6
4.8
U
F: 4.0
wj
3.2
2.4-
1.6
a8L
0
0.2
FIG. 3.4
1.2
1.0
0.8
0.6
0.4
DISTANCE FROM CENTER OF FUEL (IN.)
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
26
8.E
I
I
I
Zne4( n , p ) Cu6 4-(RUNS 10, 20, 25)1.03% ENR ICHMENT
o 1.25 IN. SPACING
a 1.75 IN. SPACING
x 2.50 IN. SPACING
I
8.0 -X
x
7.2
FUEL EDGE
6.4 A-
CLAD EDGE
z
0
5.6
C-)
STANDARD DEVIATION-±5.5%
4.8
LUi
1~
4.0
Ld
3.2
I
CC~
2.50 IN. MIDPOINT
2.4
1.75 IN. MIDPOINT
)
1.6
1.25 IN. MIDP OINT
X
X
0
0.8
)
OC
0.2
FIG. 3.5
0
I
I
I
OIx
0.4
0.6
0.8
DISTANCE FROM CENTER
x a
1.0
1.2
OF FUEL (IN.)
XX
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
27
8.8
x
II
U2 3
(nf)-(RUNS 15, 22, 17)
1.03% ENRICHMENT
o 1.25 IN. SPACING
L 1.75 IN. SPACING
x2.50 IN. SPACING
8.0-
7.2FUEL EDGE
z
6.4 -
C CLAD EDGE
0
5.6C)
LU
4.8-
LUJ
4.0
STANDARD DEVIATION - ±5% - IN F UEL
±3% -IN MOD.
x
3.2
2.50 IN.MIDPOINT1.75 IN. MIDPOINT
2.4-
1.25 IN. MIDPOINT
1.6
o0
x
x
XI
x
0.8
0
0.2
FIG. 3.6
I
x
0.4
0.6
0.8
1.0
1.2
DISTANCE FROM CENTER OF FUEL (IN.)
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
28
8.8
8.0
7.2
6.4
z
0
5.6
4.8
4.0
Lu
3.2
2.4
1.60
0.8
0
0.2
0.4
0.6
0.8
DISTANCE FROM CENTER
FIG. 3.7
1.0
1.2
1.4
OF FUEL (IN.)
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
29
I
x
I
I
i
U 2 3 8 (n ,f)-(RUNS 29,32)
1.14% ENRICHMENT
8.0
o0.25 IN. SPACING
x 2.50 IN. SPACING
7.2FUEL EDGE
6.4--
z
0
0
x
CLAD EDGE
x
x
5.6STANDARD DEVIATION - ±5% - IN FUEL
±3% -IN MOD.
4.8-
uJ
4.0
LuJ
ix
3.2
2.50 IN. MIDPOINT
2.41.25 IN. MIDPOINT
0
QP
)
1.6-
x
0
6
0.80
0.2
FIG. 3.8
0
10
OXx
X
X
0.6
0.4
1.2
0.8
1.0
DISTANCE FROM CENTER OF FU EL (IN.)
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
30
8.8
8.0
7.2
6.4
z
0
5.6
C)
4.8
LUJ
I
-ij
4.0
WU
3.2-
2.40-
1.6-
0.8
0
0.2
FIG. 3.9
1.2
1.0
0.8
0.6
0.4
DISTANCE FROM CENTER OF FUEL (IN.)
1.4
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
31
8.81
Zn 4(n,p)
8.0K
Cu6 4 -(R UN 35)
1.14% ENRICHMEN1
x
x 2.50 IN.
SPACING
7.2
_-FUEL EDGE
6.4
CLAD EDGE
z
0
C)
x
5.6
STANDARD DEVIATION-±5.5% -IN FUEL
±4 % - IN MOD.
4.8
uJ
a-
4.0
3.2
x
2.50 IN. MIDPOINT
2.4
1.25 IN. MIDPOINT
1.6
x
0.8
-
x
x
I
Ix I
I I I! I
,
0
1
I
0.2
0.4
0.6
0.8
1.0
1.2
1.4
DISTANCE FROM CENTER OF FUEL (IN.)
.. - I
0
x
FIG. 3.10
I
RELATIVE ACTIVATION VERSUS DISTANCE FROM
CENTER OF FUEL (ROD TO ROD)
32
have been found in the literature, an experimentally measured relative
shows that at 0.5 Mev, the cross section is greater than 10%
curve
and at 1 Mev, greater than 50% of its peak value.
Since the fast flux
can be expected to show a generally logarithmically decreasing dependence with energy, the rhodium inelastic scattering reaction rate should
be substantial at energies below 1 Mev, and this reaction should be a
useful tool for investigating the lower energy portion of the fast spectrum.
The neutrons below 1 Mev are especially interesting, not only because
of the large values of the flux in this energy region, but also because
the scattering-in from higher energies undoubtedly constitutes a major
source for this group.
It is quite clear from the plots of the cell distributions that there
is
a marked dependence upon rod spacing.
in the fuel with increased rod spacing.
There is increased peaking
If, by analogy with the thermal
flux disadvantage factor, we define a fast flux advantage factor as done
by Price,47
the distributions can be integrated and the advantage factor
computed for the different rod spacings.
This has not been done as yet
for the present data because no satisfactory representation of the data
has been obtained for interpolation and integration.
Attempts have been
made to fit the data with least squares fits of even-powered polynomials and with cosine functions having as periods multiples of the rod
spacing.
These efforts have not been successful because the gradients
in the distributions have been such that high-ordered functions were
required to follow the distributions, and these high-ordered functions
frequently oscillated between data points and were therefore objectionable on physical grounds.
No further efforts to fit curves to the data
are planned until further theoretical analysis is
completed, perhaps
indicating a better class of functions to use in the fitting process.
A few efforts have been made to measure the radial buckling by
the indium reaction for comparison with thermally measured values.
Analysis is incomplete, but it is somewhat doubtful that the accuracy
required for a meaningful comparison can be obtained by using the fast
reactions.
Several perturbation experiments have been performed.
viously discussed, (3
As pre-
reference foils are used in conjunction with the
fission reaction measurements.
These are 0.25-inch-diameter foils
33
of the same material as the run being performed.
They are irradiated
between two highly enriched uranium foils at the bottom of the fuel rod
containing the fuel foils.
To investigate the possibility of perturbation
resulting from the presence of the enriched foils, axial plots of the
thermal flux in the fuel rods were measured with gold foils placed at
intervals from 1.5 inches to 12.5 inches from the bottom of the fuel rod.
TABLE 3.2
235
Lattice Height and Ratio of Activity with U
Included to Normal Activity
R atio
Height (Inches)
1.5
1.0
2.5
0.996
4.5
0.999
6.5
0.979
8.5
1.011
10.5
0.990
12.5
0.937
Table 3.2, above, gives the ratios of the foil activities for the
two cases.
It is clear that the presence of the U235 is not a signifi-
cant perturbation.
Another possible source of experimental error is the presence
of the cadmium covers used with the moderator foils.
Any perturba-
tion of the thermal flux in the adjacent rod disturbs the source distribution for the fast flux being measured.
this effect were employed.
Two methods of investigating
First, the axial dependence of the thermal
flux in a fuel rod holding the moderator foils and cadmium covers was
measured with bare gold foils and then compared to a normal axial
buckling plot. A typical result is plotted in Fig. 3.11.
The second
method involved the use of a different type of moderator foil holder
and runs without cadmium covers.
Although the nickel moderator foils
were cadmium covered to be consistent with the other reactions used,
there is no other reason not to use bare foils, since thermal activations
do not complicate the counting process.
Accordingly, a run was made,
34
10
I
I
I1
I
I
I
9
GOLD FOIL ACTIVATION IN FUEL
MODERATOR HOLDER ATTACHED
x
CADMIUM COVERS AT INDICATED POINTS WITH
DISTANCE FROM CENTER OF FUEL (IN.) IN PAREN.
8
7
ROD WITH
o
6
5
0
z
0
0
4
0
0
Lli
\
3
(0.284)
(0.284) o 0.378)
(0.378) 9, (0.503)
LLI
(0.503)
\
(0.659)
(0.659)
2 --
(0.815)
(0.815)X
0
I
10
12
FIG.3.I I
I
I
I
14
16
18
DISTANCE FROM
I
I
|I
I
20
22
24
26
BOTTOM OF FUEL (IN.)
RELATIVE ACTIVATION VERSUS
FROM BOTTOM OF FUEL
I
28
DISTANCE
30
35
using no cadmium covers and using a moderator foil holder constructed
of very thin 1100 aluminum, such that the total mass of the holder was
less than 1 gram. The use of this type of holder served to also eliminate any perturbation caused by the use of the greater mass of the
normal moderator foil holders. The results are plotted in Fig. 3.12,
along with the previous run for the same lattice. It appears that this
perturbation is not a negligible one but that it is probably limited to the
foils closest to the fuel rod and amounts to a maximum depression of
approximately 10%. Further measurements must be made to verify
these conclusions, particularly since the magnitude of the correction
will probably vary with the particular lattice being studied.
III. Theoretical Methods
Future plans include comparison of the experimental results with
results obtained from MOCA II, which has previously been shown to give
good agreement with some experimental results, particularly fast effect
measurements.
In addition, if it is true that the distributions made so far are the
same for all the reactions used, it would indicate that the results are
probably due to an uncollided fission spectrum. This offers the possibility that a reasonably simple analytical derivation based on transport
theory could be obtained in agreement with experiment. Obviously, such
a theory would be valid only for neutrons above some cutoff energy
below which "scattering-in" sources are significant. However, the establishment of such a cutoff energy, even approximately, and the validity
of the analytical treatment for neutrons above this energy would be of
substantial value, both with respect to multigroup methods and to fast
neutron damage studies.
36
I
I
I
I
I
I
I
I
I
I
I
2.4 0
2.2 -
Ni 5 8 (n,p)
|0o
0
C058-(RUNS
31, 31P)
o CADMIUM-COVERED-MODERATOR
o BARE-MODERATOR RUN
0
2.0 1--
RUN
z
0
8 H_
0
I-
w
0r
STANDARD DEVIATION-
0 IN FUEL
5%
±3% IN MOD
1.6
1.4
0
1.2
00
0
e0
1.0 F-
I
V00
0
0 0
0
0
0
0
00
0
I
I
I
I
I
0
I
I
I
I
0.2
0.4
0.6
0.8
1.0
DISTANCE FROM CENTER OF FUEL (IN.)
FIG. 3.i2 RELATIVE ACTIVATION VERSUS DISTANCE
FROM CENTER OF FUEL (ROD TO ROD)
1.2
37
STUDIES OF EPITHERMAL NEUTRONS
4.
IN URANIUM, HEAVY WATER LATTICES
Walter H. D'Ardenne
Measurements related to reactor physics parameters were made
in three heavy water lattices.
The three lattices studied contained
1.03% U235 uranium metal rods in triangular
0.250-inch-diameter,
arrays spaced at 1.25-, 1.75-, and 2.50-inches.
The following four
microscopic parameters were measured in each of the three lattices
studied:
1) the ratio of the average epicadmium U238 capture rate in the
fuel rod to the average subcadmium U238 capture rate in the
fuel rod (P28
2)
the ratio of the average epicadmium U 235 fission rate in the
fuel rod to the average subcadmium U235 fission rate in the
fuel rod (625);
3)
238
the ratio of the average U
capture rate in the fuel rod to
the average U 2 3 5 fission rate in the fuel rod (C');
4) the ratio of the average U238 fission rate in the fuel rod to
the average U235 fission rate in the fuel rod (628).
The microscopic parameter, p 2 8 , is related to the cadmium ratio of
238
the average U
capture rate in fuel, R 2 8 :
1
p
28
R
28
-
(4.1)
1
The results of these measurements are listed in Table 4.1.
These results provide new experimental reactor physics data to which
the results of theoretical treatments may be compared.
Previous
studies of heavy water lattices have been restricted almost entirely to
large (1.0 inch in diameter or more), natural uranium fuel rods. (-8
Hence, the results of the measurements reported here are particularly
useful in that they extend the experimental data into the region of small,
slightly enriched fuel rods, thus broadening the base against which the
presently available theory may be tested.
An investigation of systematic
TABLE 4.1
Rod
Spacing
(Inches)
1.25
1.75
2.50
Single
Volume
Ratio
Vm/V
Measured Microscopic Parameter Data(a)
R28
25.9
52.4
108.6
C
625
628
2.183
0.8453
0.8137
0.0525
0.0274
±0.010
±0.0071
±0.0075
±0.0100
±0.0012
3.287
0.4373
0.6436
0.0310
0.0217
±0.016
±0.0031
±0.0032
±0.0013
±0.0007
5.402
0.2272
0.0188
0.0183
±0.029
±0.0014
±0.0023
±0.0007
-
00
P28
-
0.05544
±0.0018
-
-
Rod
Pos.#13
0
(d)
(e)
(f)
2 (d)
0.452
0.001224
0.244
0.001229
0.147
0.000875
-
-
2.93
0.521
±0.06
±0.016
-
-
-
0.275
The uncertainties are the standard deviations of the mean of two or more determinations.
(b) The values of
(c)
0.0130(
PAu
2
Bm em
±0.0005
MITR
(a)
(c)
(c)
*(b)
28
25)
used were obtained from THERM(OS results and are listed in Ref. 12.
SC
Results include measurements made by H. Bliss (56).
Results of Harrington (51), Kim (46), and F. Clikeman et al. (36).
The values quoted are an average of measurements made at heights of 14.5 inches and 21.0 inches
above the bottom of the sample thimble.
Preliminary results from measurements made by Olsen (37).
cc
39
errors associated with the above measurements has led to many changes
and adjustments in the experimental technique and procedure, which have
improved the general precision of the experimental results.
The experimental results of the microscopic parameter measurements were combined with theoretical results obtained by using the computer programs THERM(S and GAM-I, in order to determine the following reactor physics parameters for each of the three lattices studied:
the resonance escape probability, p; the fast fission factor, E ; the multiplication factor for an infinite system, k.;
ratio, C.
and the initial conversion
The final results are listed in Table 4.2.
2
The value of the effective resonance integral of U
3 8
(ER12 8 ) was
measured by a new method. This method involves the results of measurements made in an epithermal flux which had a 1/E energy dependence
combined with the results of measurements made in a lattice.
Methods were developed to measure that portion of the activity of
a foil which is due to neutron captures in the resonances in the activation
cross section of the foil material.
A new method has been developed to
determine the resonance escape probability by using the resonance activation data.
I.
Cadmium Ratio Measurements
The subcadmium and epicadmium U235 fission product activities
and the subcadmium Np239 activity of foils irradiated within a fuel rod
were found to be insensitive to perturbations within the fuel rod,
as the replacement of fuel material with aluminum catcher foils.
such
How-
ever, because of the extremely short mean free path within the fuel of
a neutron whose energy corresponds to one of the U238 resonances, any
perturbation in the surface of the fuel will permit neutrons to stream
into the interior of the fuel rod.
Hence,
the measured epicadmium
Np239 activity (which was directly proportional to the U238 capture
rate) was found to be very sensitive to perturbations in the U
238
con-
centration in the fuel rod, particularly at the rod surface where the
neutron flux varies rapidly.
foils within the fuel rod is
The use of aluminum or aluminum alloy
an example of such a perturbation which was
found to affect the measured results as shown in
cadmium Np239 activity and the epicadmium
Fig. 4.1.
U2 3 5
The epi-
fission product
TABLE 4.2
Reactor Physics Parameters for Three Heavy Water Lattices
Containing 0.25-Inch-Diameter,
1.03% U 2 3 5 Uranium Metal Rods
Rod
Spacing
(Inches)
Moderator to
Fuel Volume
Ratio
Thermal
Production
Factor
Thermal"
Utilization
Factor, f
Resonance
Escape
Probability, p
Fast
Fission
Factor, e
Multiplication
Factor, koo
Initial
Conversion
Ratio, C
1.25
25.9
1.472 ±
0.971 ±
0.849 ±
1.020 ±
1.239 ±
0.665 ±
0.015
0.002
0.004
0.002
0.018
0.007
1.481 ±
0.963 ±
0.923 i
1.016 ±
1.336 ±
0.532 ±
0.015
0.002
0.005
0.002
0.019
0.005
1.485 ±
0.947 ±
0.960 ±
1.013 ±
1.369 ±
0.466 ±
0.015
0.002
0.005
0.001
0.020
0.005
1.75
2.50
*
52.4
108.6
From the combined results of THERM()S and GAM-I calculations.
0
I
-
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
1
I
A DEP. U. CATCHERS, BARE DETECTOR; NORMALIZED TO THEIR OWN AV.
v Al CATCHERS, BARE DETECTORS; NORMALIZED TO ABOVE AV.
2.4 o DEP. U. CATCHERS, CAD. CO. DETECTOR; NORMALIZED TO OWN AVG.
Al CATCHERS, CAD. COV. DETECTOR; NORMALIZED TO ABOVE AVG.
2.2 -o
2.6-
-2.0-
~I.8<
.6
--
.4
2
w 1.2 S1.0
--------
O-----
:0.80.60.40.2
0
FIG.4.I
4
8
12
CATCHER
EFFECT OF CATCHER
28
24
20
16
FOIL THICKNESS, INCHES x10
32
36
239
ACTIVITY
40
3
FOILS ON DEPLETED URANIUM Np
H
42
activity were found to be slightly sensitive to perturbations in the high
energy neutron flux. The depression of the thermal flux caused by the
use of cadmium also depresses the high energy flux in the cadmiumcovered foils. The values of p2 8 as a function of VM/VF are shown in
Fig. 4.3. The values of p2 8 and 625 were corrected for this high energy
239
activity due to resonance capture
flux depression. The epicadmium Np
was not found to be affected by the presence of cadmium; however, many
other laboratories have reported such effects (cf., Ref. 40), and further
study of this problem is recommended to seek the possible causes of
this disagreement. In contrast to the results obtained at the Brookhaven
(43) no effect upon the measured Np 239 activity due
National Laboratory, to nonuniform activity distributions was observed. Continued study of
this problem is also strongly recommended. In addition, a program
should be undertaken to compare the many methods of measuring the
value of the U238 cadmium ratio which have been developed at various
laboratories.
The Measurement of the Ratio of Capture in U238 to Fission
in U 2 3 5 , CF
The relation between the value of C* and the measured quantities
has been discussed in an earlier report. (5)- These values of C , listed
in Table 4.1 and shown in Fig. 4.4, were calculated by using the relation
II.
28
C
P28)(a
1 + 6 25
(4.2)
-
225
'
SC
where (z28
235alfS
25S
is the ratio of the U238 capture rate in the fuel to
fission rate in the fuel for neutron energies less than about
the U
0.4 ev.
It should be noted that the value of the initial conversion ratio "C"
is defined as the ratio of captures in U238 to the ratio of absorptions in
235
. Hence the value of C is derived from the value of C by using
U
the ratio of the U235 fission rate to the U235 absorption rate.
1.'
DEP. U.
5 MIL
DER U.
5-30 MIL
DETECTOR
Z
r
|-
~-FUEL
SLUG
1.00
00
N-
0.9
-J
Z
20
30
40
0
10
TOTALTHICKNESS OF DEPLETED URANIUM,
60
50
IN. X 103
70
FIG.4.2 EFFECT OF DEPLETED URANIUM CATCHER FOILS ON DEPLETED
URANIUM FISSION PRODUCT ACTIVITY
4Ck)
1.6
I
Iy
I
I
I
I
I
]
V 1.14 %,0.25 IN.-DIA. RODS, S.D.52.4%
1.4
1.03%, 0.25 IN.- DIA. RODS,S.D.'0.7%
a 0.72%, 1.00 IN.-DIA. RODSS.D.SI.6%
1.2
1.14%,
I.0 -
P2 8
\0
0 8 1-
0.6 11.03%,
\
0.72%, I "
U
0.4
0
0.2
0
I
10
20
30
I
40
I
50
70
60
MODERATOR TO FUEL VOLUME
RATIO,
VMF
FIG. 4.3
p2 8 VERSUS
VF
I
80
vM
VF
90
100
110
1.0
I
*
I
I
I
I
0
cr
0.81-
0
cl)
LI
r?)
0
H
0
I
0.61-
0.4 I-
0.2
0
0
I
20
I
I
100
40
80
MODERATOR TO FUEL VOLUME RATIO, VM/VF
|I
I
60
FIG.4.4 VALUES OF C* FOR HEAVY WATER LATTICES WITH 0.25-INCH
DIAMETER, 1.03 w/o U23 5 FUEL RODS
120
~J1
46
III.
The Fast Fission Ratio
The fast fission ratio was found to be quite sensitive to perturba-
tions of the high energy neutron flux in the vicinity of the uranium
detector foils used to measure this quantity.
The effect which replacing
fuel material by depleted uranium has on the U238 fission product activity is
shown in Fig. 4.2.
On the one hand, this effect is unexpected
because the mean free path of a high energy neutron is large (of the order
of 10 cm); but, on the other hand, this effect is reasonable because high
energy neutrons born within, and in the immediate vicinity of, the detec-
tor foils have the highest probability of causing a U
foils.
238
fission in those
The importance of these neutrons increases as the fuel rod diame-
ter decreases and as the distance between the rods increases;
hence, in
the lattices which contained small fuel rods on wide spacings, a change
in the U 2
3 5
fission rate in or near the uranium detector foils signifi-
cantly affected the U 238 fission rate in those foils.
The experimental
methods currently used to measure the fast fission ratio require the
use of two uranium foils whose U235 contents differ significantly;
there-
fore, these methods inherently contain a source of systematic error.
Correction factors were experimentally determined for the results obtained in the 1.75-inch lattice and an analytical method was developed
to convert these results into the proper correction factors for the other
lattices.
These correction factors, which are listed in Table 4.3, should
be verified, preferably by using measurements made in single rod experiments to maximize the perturbation.
TABLE 4.3
Correction Factors for the Fission Product Activity
of Depleted Uranium Foils Used to Measure the Fast Fission Rate
Lattice Spacing
Correction Factor
1.25 inches
1.08 ± 0.02
1.75 inches
1.09 ± 0.02
2.50 inches
1.12 ± 0.02
The method used during the present work to make the fast fission
measurements had the disadvantage of requiring an auxiliary experiment.
47
The formulation of the fast fission ratio 628 from experimental values
is given by the relation:
628
628
=
F(t)
P(t) F(t) =
(4.3)
,
F(t)
where F(t) is
a function of the measured relative foil activities, P(t) is
a factor to convert the measured relative foil activities to relative
reaction rates, t is the time after irradiation, and the superscript, *
refers to a reference position.
tions of the irradiation time.
The factors F(t) and P(t) are also func-
This method has three disadvantages:
1) F(t) and F"(t) must be measured at different times, perhaps separated by many months; 2)
time; 3)
F(t) and P(t) are functions of the irradiation
F(t) and P(t) are functions of the time after irradiation.
These three disadvantages could be eliminated by measuring 6 28 and
F (t) in the graphite-lined cavity of the facility. Then the measurements of F(t) and F (t) could be made simultaneously, thus eliminating
all time dependence:
628
(4'4)
28
In Eq. 4.4, the value of 628 in the cavity is assumed to be constant and
28
not affected by the presence or absence of a lattice in the exponential
tank.
This independence of conditions in the exponential tank should
be verified experimentally.
The value of 628 was determined by means of the La
140
counting
technique developed by Wolberg (7 ) et al. It is recommended that this
method be compared with the double fission chamber methods, particularly the method recently developed at the Brookhaven National
Laboratory. (
Finally, the graphite-lined cavity and the exponential
tank provide excellent facilities for a study of the fast fission ratio in
single rods as a function of rod size, U235 content, and moderator.
Portions of this study are under way.
48
IV.
Resonance Activation Measurements
A new method of determining the resonance escape probability
has been developed.
This method involves the measurement of that
portion of the activity of a foil which is due to neutron captures in the
resonances in the activation cross section of the foil material.
The
resonance escape probability was determined by using the resonance
activation data to calculate the ratio of the slowing-down density in the
moderator to the U238 resonance absorption rate in the fuel.
This new
method has the advantage that the use of cadmium is not necessary and
the value of p determined by means of this method should be less sensitive to experimental uncertainties in systems which have a large
epithermal flux relative to the thermal flux.
The methods developed
to determine the resonance activation of a foil are similar to methods
used at other facilities.(4 1,56)
The resonance activation data, which
are listed in Table 4.4, may also be used to measure the relative neutron
flux or slowing-down density as functions of position at various energies
in the resonance energy region, which would provide experimental data
to which sophisticated theoretical treatments of this energy region could
The experimental methods may also be used to determine
be compared.
the effective resonance integral of U238 in the fuel rod.
It was assumed
that the irradiation sample thimble at position 13 of the MITR provided
a good reference position with a 1/E epithermal flux.
The results of
the resonance activation measurements made at that position supported
this assumption.
Some of the results of the measurements in the MITR
indicate that some of the resonance integral data appearing in the literature may be in error.
This possible discrepancy, plus the complete
lack of information for many nuclides, indicates that a program to accurately measure the resonance activation integrals of various nuclides
could yield some useful basic data.
V.
Analysis
and Comparison of Results
The experimental results of the measurements made during the
present work show good agreement with the results of measurements
by Peak -
et al. in the M.I.T. miniature lattice facility.
p, 628, and k,
The values of
are compared in Figs. 4.5, 2.3, and 4.6, respectively.
This agreement indicates that the miniature lattice can be used to make
TABLE 4.4
Resonance Activation Data
Resonance Integral
Ratio RI/o
Measured Activation Ratios
Peak Energy
Nuclide
of Dominant
Resonance,
E 0, ev
RL
R (b)
R c(b)
R res
In
1.46
2.91 ± 0.01
0.158±0.003
0.0546±0.0055
0.0435±0.0057
6.17
Au
4.9
2.41 ± 0.09
0.228±0.021
0.0944±0.0047
0.0985±0.0049
3.80
W
18.6
2.74 ± 0.02
0.184±0.013 0.0672±0.0054
0.0629±0.0056
4.74 11.3
As
47
2.51 ± 0.01
0.188 ± 0.006
0.0745 ± 0.0045 0.0684 ± 0.0047
4.30
12.9
8.1
Ga
95
3.52±0.07
0.196±0.030
0.0557±0.0078
0.0634±0.0080
6.21
8.0
2.4
Br
101
2.05 ± 0.02
0.246 ± 0.015
0.1202 ± 0.0084 0.1203 ± 0.0086
3.38
18.1
18.2
Mn
337
21.4 ± 4.1
0.118 ± 0.011
0.0059 ± 0.0024 0.0037 ± 0.0026
28.0
1.15
Na
2850
62 ± 19
assumed 0
95.0
assumed 0
~0
U238
-
3.306 ± 0.013 0.1982 ± 0.0005
0.0600 ± 0.0003
0.0570 ± 0.0004
-
-
-
U235
-
33.2 ± 1.7 0.1408 ± 0.0041
0.0042 ± 0.0002
assumed 0
-
-
(a)
(b)
0.123 ± 0.009 0.0022 ± 0.0004
a
R
Measured
Value
Reported
Value
12.3
8.0
1 5 . 3 (assumed
15.3
9.5
0.67
Measured at the bottom of the sample thimble at position 13 of the MITR.
For foil irradiated in *'entral cell at height of 20 inches above the bottom of the fuel region.
0
RESULTS OF PRESENT WORK FOR 1/4"-INCH DIA.,
1. 03 w/o U2 3 5 FUEL RODS.
A RESULTS OF PEAK ET AL (P2) FOR 1/4"-INCH DIA,
1.14 w/o U2 3 5 FUEL RODS IN MINIATURE LATTICE
CD
0.
awd
C-
0
(0
W1
z
0
U)
0.
010
2
LVd
0.71
0
20
0
MORA
06
TRT
0
ULVLM
V
0
2
100
120
AI,-
40
60
80
VM
MODERATOR TO FUEL VOLUME RATIO,T
FIG 4.5 COMPARISON OF PRESENT RESULTS FOR THE RESONANCE ESCAPE
PROBABILITY WITH MINIATURE LATTICE RESULTS
0
I
I
I
I
I
I
1.4 F0
LL
z
I-
1.3
235
1
0
F-
/
1.2 1I
I
w
H-
z
EL
/
/
0 1.03 w/o U
0
/
,PRESENI WUK
PULSED NEUTRON MEASUREMENT (11)
1.03 w/o
1. 14 w/o U235, MINIATURE LATTICE (8 )
U2 3 5 ,
1.1
z
1.0
0
20
I
40
60
iVM
80
I
100
I
120
MODERATOR TO FUEL VOLUME RATIO,
FIG.4.6 VALUES OF k,
FOR HEAVY WATER LATTICES WITH 0.25-INCH DIAMETER FUEL RODS
~31
H
52
microscopic parameter measurements.
The feasibility of using the
miniature lattice for other measurements is
The value of k,
currently being studied.
obtained by Malaviya ( 1 1) et al. from pulsed neutron
experiments made in the 1.75-inch lattice, which is also shown in
Fig. 4.6, is in good agreement with the result of the present work.
2
(11)
The results for the values of f, fm, L , and vZa of Malaviya et
al. also showed reasonable agreement with the results obtained from
the output of the computer programs THERMOS
and GAM-I.
The theoretical results obtained from the output of computer
programs THERM(S and GAM-I were used to aid in the analysis and
interpretation of the experimental results.
The spatially averaged
neutron flux spectrum obtained for the 1.25-inch lattice by means of
these programs is
shown in Fig. 4.7.
There were some significant
discrepancies between the values of the microscopic parameters calculated from the theoretical results and the experimental values of
these parameters, particularly for the more closely packed lattices.
The discrepancies are most likely due to an error in the assumptions
for the spatial homogenization used with the GAM-I computer program
to account for the effects of lumping the fuel and of the interaction of
neutrons between fuel rods.
final results were small.
The effects of those discrepancies on the
A more sophisticated theoretical treatment
would be necessary in order to perform design calculations of similar
heavy water assemblies.
In summary, the usual microscopic lattice parameters were
measured in the three lattices studied.
The general precision of these
measurements was improved as a result of the extra care and precautions introduced into the experimental techniques and procedures.
An investigation of systematic errors was carried out and the sources
of those errors found to be significant were avoided or, where this was
not feasible, correction factors were developed.
developed to measure the ratio C
A new method was
which simplified the experiment,
reduced the experimental uncertainty associated with the measurement,
and avoided systematic errors inherent in the method used to measure
C* in earlier work.
A new experimental method was also developed to
measure the effective resonance integral of U238 in a fuel rod in the
lattice.
Methods to measure the resonance activity of a nuclide were
53
-j
z
:D
cE
uj
z
0
w
z
Li
-J
wr
5
0
10
FIG. 4.7 SPATIALLY AVERAGED
THE
15
20
LETHARGY
25
30
FOR
GAM - I
NEUTRON FLUX SPECTRUM
1.25 INCH LATTICE OBTAINED FROM
AND THERMOS OUTPUT
54
developed, and these methods were used in a new approach for finding
the value of the resonance escape probability. This new method had
the advantage of avoiding the use of cadmium.
The final results obtained
are consistent and in good agreement with earlier work done at M.I.T.
55
PULSED NEUTRON AND CONTROL ROD RESEARCH STUDIES
OF REACTIVITY AND RELATED PARAMETERS
B. K. Malaviya
A new pulsed neutron set-up has been brought into operation for
use in conjunction with the Lattice Facility.
One phase of research,
involving pulsed neutron experiments with multiplying and nonmultiplying assemblies, has been completed.
Control rod studies by
both pulsed neutron and steady-state methods have also been made.
A new important technique has been developed for the study of lattice
parameters by means of the pulsed neutron method.
This technique
makes possible the direct determination of such lattice parameters as
k,
and L2 in far subcritical lattices - measurements which have hither-
to been possible only by complicated and elaborate experiments on
critical or near-critical systems.
Measurements of large negative
absolute reactivities have also been undertaken and comparisons made
between experimental results and theoretical calculations.
In this
section, the experimental set-up and the new techniques will be briefly
described and the results presented.
has also been prepared.
I.
A detailed report of these studies
-11)
Experimental Set-Up for Pulsed Neutron Studies
The basic pulsed neutron experiment of the die-away type
involves the irradiation of a test assembly by a burst of fast neutrons;
the decay of the resulting thermal neutron population is recorded as a
function of time by means of a detector analyzer system.
For source
intensities generally available, it is necessary to make this a repetitive process to obtain good statistics.
The decay curve is then ana-
lyzed to extract the decay constant of the fundamental thermal flux
mode.
The essential components of the equipment for such an experi-
ment are a pulsed neutron source, the experimental assembly, a
thermal neutron detector, and a multichannel time analyzer with the
associated instrumentation.
56
The pulsed neutron source selected for this set-up is a small,
compact, sealed tube -Model
A-810 built by Kaman Nuclear of
Colorado - in which a Penning ion source produces deuterium ions
and these are accelerated to strike a tritiated titanium target and
generate neutrons by the (D,T) reaction.
The whole tube is mounted
in an aluminum cylindrical container (11 inches long by 5 inches in
diameter) filled with dried Shell Oil Company Diala-AX insulating oil
(Fig. 5.1).
The target pulse of negative accelerating potential -
variable between 0 and 120 kilovolts - is obtained from a Carad
Corporation step-up (1:25) pulse transformer;
the shielded, flexible,
high-voltage cable (Times Wire and Cable Company, Inc., Jan Type
RG-19/U-04145) from the transformer to the source-tube
5 feet long.
about
is
The accelerator assembly and the transformer are located
in the shielded lattice room at the top of the exponential assembly,
while the entire control unit is placed on the reactor floor about 18 feet
below.
The control unit supplies pulse voltages for the neutron tube
ion source and the step-up pulse transformer to the target.
The control
unit is versatile and can also be used with other types of tubes.
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 1 pps to 10 pps, while the pulse
width at half amplitude (shape triangular or approximately Gaussian on
a time scale) can be set at approximately 9, 12 or 15 microseconds.
The neutron yield is estimated to be about 107 neutrons per burst.
For pulsed neutron work, the lattice facility was isolated
from its reactor environment by closing the boral-lined steel
doors which separated the facility from the reactor neutron flux.
It was found that there was no effect of the transients or of pulser
operation upon the reactor safety system.
However, the neutron back-
ground during reactor operation was high enough to cause appreciable
pulse pile-up with a medium-sized BF3 detector.
The M.I.T. Reactor
operates on a 24-hour weekday basis and it was decided to make the
pulsed neutron runs during periods of reactor shutdown, on the weekends.
The exponential tank was covered on the sides and top with
0.020-inch-thick cadmium.
A circular cadmium plate, 0.020 inch thick
r
Fig. 5.1
Pulsed Neutron Source, Accelerator Tube
58
and clad in aluminum, was used to cover the bottom face.
For each
pulsed neutron run, this plate was placed at the bottom of the tank.
Thus, the entire assembly was surrounded by cadmium to reduce roomreturn background and to define the slow neutron boundary condition,
basic to the definition of the geometrical buckling.
In some experiments,
a 1.25-inch-O.D. aluminum thimble was installed along the axis,
positioned at the top by means of plastic adapters.
The source was located, on top of the assembly on the axis of the
cylindrical symmetry, so that the harmonic modes having radial modal
planes through the axis were not excited.
An attempt was made to
reduce the effect of the axial harmonics by using long BF 3 counters
and positioning them in such a way as to span a large part of the fundamental mode while at the same time integrating out the other harmonics.
Since the source was located on the top-center of the assembly and the
bottom was inaccessible because of the presence of the shielding,
pedestal, etc., the detector had to be located either inside the tank or,
outside, along the lateral periphery.
Several detector arrangements
were investigated.
A bank of eight long (25 inches X 2 inches) BF
3
counters fixed vertically along the side of the experimental tank proved
to be too sensitive and gave rise to considerable pulse pile-up.
A
single, small (0.5 inch by 4 inches) BF3 tube, running vertically in a
channel on the side of the tank, failed to provide an adequate detection
efficiency.
Finally, a 1-inch-I.D. aluminum thimble was fixed along
the axis of the cylindrical assembly and the small BF3 counter was
moved inside it.
This arrangement proved to be most satisfactory,
giving flexibility and good detection efficiency.
Thus, two detection systems are provided;
Fig. 5.2.
these are shown in
The long BF 3 counter (N. Wood Model G-20-20, active volume
20 inches by 2 inches diameter, B
10
enrichment 961o, filling pressure
40 cms of Hg) is mounted on the side of the tank so as to be exposed to
a narrow slot in the cadmium surrounding the tank and covered on the
outer side with 0.020-inch-thick cadmium.
This detector uses an RIDL
(Model 31-7) pre-amplifier located about three feet from it.
The other
arrangement employs a small BF 3 tube (N. Wood Model, 0.50 inch
diameter, 4.0 inches active length, B
enrichment 96%0 and 40 cms Hg
filling pressure) guided by a thin aluminum thimble (1.0 inch I.D.) fixed
59a
D-
PULSED
NEUTRON
SOURCE
FIG. 5.2a
DETECTION SYSTEM USING SMALL BF 2 COUNTER
(N. WOOD MODEL, ACTIVE VOLUME 4 INCH X 1/2 INCH
40CM Hg FILLING PRESSURE) RUNNING IN AN
ALUMINUM THIMBLE ALONG AXIS
59b
D
PULSED
NEUTRON
SOURCE
FIG. 5.2b
LONG EXTERNAL BF 3
(N. WOOD MODEL,
PROPORTIONAL COUNTER
ACTIVE VOLUME 20 INCH X 2 INCH, 40 CM Hg
FILLING PRESSURE )
DETECTION SYSTEM
USING
60
along the axis of the tank.
The BF 3 tube is wrapped in thin plastic to
insulate it from the thimble and the tank. A 7-foot-long cable, well
shielded with braided wire, passes through an air-tight stopper plugged
in a hole on the upper side of the tank and connects the detector to a
pre-amplifier placed just outside the tank; the pre-amplifier is also
insulated from tank-ground.
The amplifier-scaler (RIDL Models
30-19 and 49-30) and the high-voltage supply (RIDL Model 40-9) are
located on the reactor floor 18 feet below.
The pulses from the
detector system was determined to be of the order of 2 microseconds.
For moderator and simple lattice runs, when the heavy water is at full
height in the tank, both the detection systems can be used and compared.
When the runs are made with a control rod located along the
axis, only the long external detector can be used.
For runs where it
is necessary to vary the level of heavy water, the small BF3 tube in
the thimble alone is to be used and the effect of positioning it at differ-
ent heights along the axis can be studied.
The decaying neutron population is recorded as a function of
time by means of a TMC-256 channel analyzer coupled with the
Model CN-110 digital computer and a Type 212 pulsed neutron plug-in
unit.
This analyzer consists of a 16-binary scaler for buffer storage
of incoming signals, a ferrite-core magnetic memory with a storage
capacity of 256 words of 16 binary bits each, and appropriate switching
circuitry.
"Live" analogue display of the memory contents is provided
via a built-in oscilloscope.
The purpose of the Type 212 plug-in unit is
to convert the usual energy scale of the analyzer into a time scale, so
that the 256 memory addresses are sequentially sensitized to become
time channels with a total count capacity of 1,048,575.
Data are
extracted from the memory via a transmission system and recorded
by a Hewett-Packard digital recorder which prints out the counts and
channel number on a tape.
Continuous live data display on the analyzer
oscilloscope conveniently allows observation of the progress of an
experiment.
Figure 5.3 shows a block diagram of the experimental arrangement and the data recording system.
operation is as follows.
The time sequence of the logic
The initiating master-sync signal for the
pulsing sequence is generated by an external oscillator (consisting of
LATTICE
FIG. 5.3
ELECTRONICS
ROOM
SCHEMATIC
OF
OVERALL
PULSING,
DETECTION
AND
ANALYSIS
AREA
(REACTOR
FLOOR)
CIRCUITRY
GV
62
a Tektronix Type 162 waveform generator and Type 163 pulse gener-
ator; the latter shapes the trigger pulse).
This system trigger signal
is applied to the Type 212 plug-in unit of the analyzer and immediately
sensitizes its pre-burst background (first) channel; the width of this
background channel is variable, independent of the other channels.
Upon closing of the background channel, the analyzer sends out a pulse -
the source trigger - which is used to fire the pulsed neutron source.
Simultaneously, a variable time delay of duration 2nA (when n= 1,2, ... 8
Thus,
and A is the channel width) is initiated in the time analyzer.
after the neutron source is
fired, an appropriate
"waiting time"
(variable as 2nA) is provided to allow a stable spatial flux distribution
to be established.
There is also a target delay variable continuously
from 0 to 100 psec between the firing of the source and the appearance
of the target pulse (and, therefore, the neutron pulse), and the net or
actual waiting time is reduced by the pre-set target delay.
Thereafter,
the remaining channels open in succession and accept counts from the
detector.
As the last channel in the memory is sensitized, the entire
pulsing sequence is terminated.
The cycles are repeated at the pre-
set repetition rate defined by the oscillator.
The data from successive
cycles are accumulated and summed in the analyzer;
the analyzer cir-
cuit prevents overlapping of sweep time with the repetition period.
A
photograph of the control panel and a part of the associated equipment
is shown in Fig. 5.4.
The fabrication of the control rods used in these experiments was
discussed in the last Annual Reports. ('
3
These rods consist of hollow
cylindrical tubes of aluminum on which two layers of 0.020-inch-thick
cadmium is
wrapped and the edges soldered.
The stationary flux
mapping equipment and the gamma counting set-up have been described
in detail elsewhere.
II.
Pulsed Neutron Experiments on Non-Multiplying Media
The first experiments with the new accelerator and pulsed neutron
instrumentation were made with only heavy water in the tank of the expo-
nential facility.
The 36-inch-diameter, aluminum tank was in place at
the time and the sides and top were covered with 0.020-inch-thick
cadmium;
the aluminum-clad circular plate of cadmium covered the
63
Fig. 5.41
The Control Panel of the Accelerator
and the Associated Equipment
64
bottom of the tank during the use of the facility for pulsed neutron work.
The level of heavy water could be read on an external sight-glass indicator, and its temperature is continuously recorded by means of a platinum resistance thermometer.
The first few experiments were devoted to establishing a systematic procedure for the determination of the characteristic decay constant
of the fundamental thermal flux mode and to an examination of the effects
of some of the experimental variables on the measured decay constant.
The standard die-away runs also gave information about the diffusion
parameters of heavy water. The effects on the decay constant due to
changes in the following quantities were measured.
1. "waiting time" and detector position (which affects the quality
and content of the higher harmonics),
2.
channel width (which enters in the dead-time correction),
3. repetition rate (which affects the delayed neutron and background correction),
4.
discriminator setting (which reveals if there is any significant pulse pile-up), and
5. the perturbation introduced by the thimble and detector when
these are placed inside the assembly.
The set of raw data from the analyzer, consisting of the total
number of counts in successive channels, is treated by an IBM-7090
code, EXPO, which has been written as part of this program to facilitate the reduction of the data from pulsed neutron experiments. This
code fits the corrected experimental counts as a function of time to a
single exponential plus a constant background, i.e., to an expression
of the form:
n = Ae
+ B,
(5.1)
and a weighted, least-squares iterative technique is used to compute
the values of the parameters X, A and B together with their associated uncertainties. The counting loss for each channel (Ith) is calculated by using the relation:
Corrn(I)
=
(Tdead)(Q(I))
(Pulsno)(Width)
(5.2)
65
where Q(I) is the experimental number of counts in Ith channel, Tdead
is the dead time, Pulsno is the total number of bursts (trigger pulses)
and Width is the channel width. The corrected number of counts is
then given by:
P()
(5.3)
QM
1 - Corrn(I) '
The code uses the time, T(I), at the middle of each channel as determined by:
T(I) = (Chdel) X (Width) - Tdel + (Spac) X (I - 0.5)
(5.4)
,
where Chdel is the delay multiplier, Tdel is the "target delay" and
Space (=Width+ gap) is the total spacing between channel ends. The
weights are based on the Poisson statistical errors in the numbers
of counts and are given by:
WT(I) =
1
(5.5)
.
P(I)1/2
The code then fits P(I) against T(I) in a three-parameter fit of the form
of Eq. 5.1 and computes the decay constant, X, together with the standard
errors. In analyzing the data, the code has provisions to drop the initial
channels one by one and to calculate the decay constant for fewer
channels each time, thus effectively varying the "waiting time" between
the injection of the burst and the start of the data analysis. Thus the
effect on the decay constant of dropping the points from the other end
can also be studied with the code.
In all the runs, the delay multiplier on the time analyzer was set
at its minimum value and the target delay at its maximum value,
100 Itsec, so that almost the entire decay curve was obtained.
For
example, with a channel width of 80 sec and the maximum target delay
100 sec, only the first 60 sec (= 80X2 -100) of the decay curve were
left out. On the basis of an over-all dead time of 2 isec, the count-loss
corrections amounted to a maximum of less than 1.0 per cent. The
investigation of the effect of some experimental variables on the
measured decay constant will be considered in the next section.
The measurement of the diffusion parameters of heavy water at
room temperature involves the standard type die-away runs on moderator assemblies of varying dimensions. The size of the assembly (in
66
the 36-inch-diameter tank) was varied by changing the moderator
heights.
When the level had to be varied, the external BF3 counter
was not suitable and the small BF 3 detector tube in a central position
was used, at a position of half the moderator height in each run.
The
geometrical buckling was calculated in each case from the inner tank
radius R (= 45.72 cm) and the indicated heavy water height H according to the relation:
B
2
2
=(2.405 2
.
+ (H+2d
= \ R+d)
(5.6)
The extrapolation distance d is assumed to be given by:
d = 0.710X
tr
;
r
tr
3D
v
(5.7)
where the value of D is derived from the experimental data.
The set
of values of X and B2 are fitted to an expression of the form:
X = va
+ vDB
2
- CB
4
,
(5.8)
and an iterative weighted least-squares procedure is used to yield the
values of the coefficients vZ , vD and C.
The results for the diffusion
parameters of 99.60 per cent heavy water at room temperature are
shown in Table 5.1 and compared with the values obtained by other
authors.
The values of the diffusion parameters of the moderator are then
used to evaluate the geometrical buckling of cylindrical moderator
assemblies modified by placing individual absorbing rods along the
central axis.
In these experiments, the 36-inch-diameter exponential
tank was filled with heavy water to the overflow line and its level
maintained constant.
In all the runs, the long, external BF3 counter
was used for the detection of thermal neutrons.
The rods were fixed
at the top and bottom so as to be located exactly along the vertical axis
of the assembly.
The thermal neutron decay curves of the assembly with and without a typical rod (8.0 cm diameter) along the axis are shown in Fig. 5.5.
A significant change in the decay constant is evident. Altogether, rods
of seven different sizes were investigated; the results are summarized
in Table 5.2.
The addition of the control rod along the axis is considered
TABLE 5.1
Comparison of the Thermal Neutron Diffusion Parameters of Heavy Water
Brown and
Hennelyl
(Steady State)
Ganguly and
Waltner 2
Meister and
Kussmaul 3
Present Work
Buckling Range, m-2
-
630 - 1000
13 - 470
30 - 55
Temperature, *C
20
20
22
21
99.30
99.88
99.82
99.60
27.0 ± 5.0
Mole % D 20
x
0
=v~
D
=
a
sec-
vD X 10-5 cm2 sec
-
-
19.0 ± 2.5
(2.051 ± 0.025)*
2.08 ± 0.05
2.000 ± 0.009
1.967 ± 0.023
3.72 ± 0.50
5.25 ± 0.25
4.87 ± 0.31
C X 10-5 cm 4 sec~ 1
D
From the value of D=
1
.
= (0.827 i 0.010) cm,
using v = '-2 X 2.2 X 105 cm sec
-
.
v
H. D. Brown and E. J. Hennelly, Proc. of the Brookhaven Conf. on Neutron Thermalization, Vol. III,
BNL-719 (C-32), 879 (1962).
2N. K. Ganguly and A. W. Waltner, Trans. Am. Nucl. Soc. 4 (2), 282
(1961).
3 Private
communication to A. E. Profio from J. L. Shapiro.
M)
68
o
_
-
0
0
-
e
O
0
_
00
0
00
0000
0
.
0
0.00e
-4
U
000
0
0g
0
z
z
Oo
0
0
00
00
0
0.
0
U
0~
0
.
0
0
0
S S.
00
C,.)
0
00
00
H
z
0.
0.
00
~0
0
S
0
0
0
0
0
00
00
.
o
0
FIG. 5.5
DECAY IN ASSEMBLY
WITHOUT ROD
Oc
0000
0
DECAY IN ASSEMBLY WITH
AN 8.0 CM DIAMETER BLACK
ROD ALONG AXIS
I
10
20
I
40
30
CHANNEL NUMBER
I
50
60
70
THERMAL NEUTRON DECAY CURVES IN PURE MODERATOR
[D2 0] ASSEMBLY (3 6 INCH DIAM TANK), WITH AND WITHOUT
A THERMALLY BLACK ROlD ALONG AXIS.
TABLE 5.2
Measured Decay Constant of a Cylindrical Pure Moderator Assembly
with Thermally Black Rods of Different Radii Along the Axis
Rod
Radius
cm
Decay
Constant
X, sec-
Fractional Change
of Buckling
Aa
X 10-2
Geometrical
Buckling
Change of
Buckling
B2, m-2
AB2, m-2
a2
None
594.1 ± 4.0
29.02 ± 0.22
0.635
670.3 ± 4.3
33.12 ± 0.24
4.10 ± 0.32
16.11 ± 1.2
1.295
728.5 ± 4.2
35.97 ± 0.24
6.95 ± 0.32
27.12 ± 1.2
1.714
757.3 ± 5.1
37.49 ± 0.25
8.47 ± 0.33
33.05 ± 1.3
2.209
789.8 ± 5.4
39.22 ± 0.26
10.20 ± 0.34
39.80 ± 1.3
2.667
813.7 ± 6.0
40.58 ± 0.26
11.56 ± 0.34
45.10 ± 1.3
3.327
848.1 ± 6.4
42.37 ± 0.27
13.35 ± 0.35
52.08 ± 1.4
3.969
875.5 ± 6.4
43.83 ± 0.28
14.81 ± 0.36
57.78 ± 1.4
CO
70
as a change in the boundary conditions of the assembly; hence, a change
in the geometric buckling. When the rod is inserted into the tank, the
22
buckling B2 are found by solving Eq. 5.8 as a
values of the geometrical
2
quadratic in B . All the other values of the parameters in Eq. 5.8 have
been determined experimentally as described above. Figure 5.6 shows
a graph of the change in buckling produced by the rod as a function of
its radius and compares the result with a theoretical curve given by
-The agreement is fair, although one-group theory
one-group theory. (11)
somewhat overestimates the effectiveness of the rod in changing the
buckling.
The change in radial buckling produced by the control rod can be
used to evaluate the thermal extrapolation distance for the black
cylindrical rod. In a bare cylindrical assembly of moderator of extrapolated radius R, with a black cylindrical rod placed along its axis, the
radial flux is given by thermal diffusion theory as:
4(r)
= A Jo(ar) - Y0 (aR) Y(ar)
.
(5.9)
When this expression is inserted in the equation defining the extrapolation distance d, the result is:
d0(r)
0'(r) r=a
1 Y (aR)J (a a) - Y 0 (aa)J 0 (o.R)
a Y1 (aa)J0 (aR) - Y0(aR)J0(aa)
(5.10)
Thus, if a is known, Eq. 5.10 gives d for a rod of radius a. The
parameter a is obtained from the measured buckling change a2 (=AB 2
since the moderator height is maintained constant) produced by placing
the rod in the unperturbed assembly.
The values of the extrapolation distance for rods of different radii,
determined in this way, are shown in Fig. 5.7. The theoretical curve,
which is based on an interpolation of the curves for large and small radii,
is taken from Ref. (32), together with a value of the transport mean free
path Xt = 2.47 cm for 99.60 per cent heavy water.
III. Pulsed Neutron Experiments on Unperturbed Multiplying Systems
The first multiplying system to be fully investigated by the pulsed
neutron die-away technique was a lattice of slightly enriched uranium
71
f
EXPERIMENTAL
-THEORETICAL
POINTS
CURVE
ONE -GROUP
BY
THEORY
50 -
40-
x
N
<4
N
o
30
20-
10-
1.0
FIG.5.6
FRACTIONAL
2.0
BUCKLING CHANGE
3.0
4.0
ROD RADIUS, a cm-*
CAUSED BY THERMALLY
a
0
BLACK RODS IN PURE
PULSED
NEUTRON
MODERATOR [D2 0] ASSEMBLY, BY THE
METHOD
72
4.0
EXPERIMENTAL POINTS
-
THEORETICAL CURVE
4
0
w 3.0
0
z
{
0
cr
H
w
2.0
1.0
2.0
ROD
3.0
RADIUS
4.0
5.0
CM
FIG. 5.7 MEASURED EXTRAPOLATION DISTANCE OF THERMALLY BLACK
CYLINDERS AS A FUNCTION OF RADIUS
73
fuel rods moderated by heavy water;
the U235 concentration was 1.03
per cent and the 0.25-inch-diameter fuel rods clad in aluminum of
0.028-inch thickness were arranged in a triangular lattice with a spacing
of 1.75 inches.
The actual fuel length was 48 inches, so that in the
lattice there was a bottom reflector of 2.5 inches, including aluminum
and plugs, adapter and the grid plate.
The lattice was placed in a tank
of 36-inch inner diameter, and the over-all experimental arrangement
and detection system employed were the same as in the moderator runs.
When the small BF3 counter was used along the axis in the assembly, the
central thimble replaced the single central fuel element and was surrounded by six fuel rods as shown in Fig. 5.8.
The change could be
made with the aid of a hole in the top plastic adapter especially fabricated for this purpose and for control rod experiments.
The decay constant was first measured as a function of the
detector location and the waiting time.
Figure 5.9 shows the thermal
neutron decay curves (corrected for counting losses and background)
obtained with the long external detector (Fig. 5.2b) and with the small
detector placed axially at half the moderator height inside the assembly.
Although the initial slopes are markedly different, each gives the same
asymptotic decay constant after the initial flux stabilization region is
excluded from the analysis.
This result is shown in Fig. 5.10, in which
the decay constant for each run is
time.
shown as a function of the waiting
The decay constant approaches the constant asymptotic value
from different directions and the delay time is about the same in the
two cases.
The effect of placing the small BF 3 counter at several heights
along the axis was also studied.
Only when the detector is
at half the
moderator or assembly height, does the decay constant approach a
constant value with a reasonable waiting time, and this constant value
is the same as that obtained with the long external detector.
Figure 5.11
shows thermal flux decay curves in three typical cases - with the small
detector at the midway point and 7 inches above and below it.
It is
seen
that in the latter two cases a very long time is needed for the flux to
show a persisting single exponential behavior.
Also, in the upper posi-
tion, the proximity of the fast source interferes with the quick establishment of a fundamental mode.
These observations are strengthened
FIG.5.8
CONFIGURATION
OF FUEL RODS IN THE LATTICE
SMALL CENTRAL HOLE IS FOR AXIAL THIMBLE
LARGE CIRCLE REPRESENTS
ROD, INSERTION .
REGION OF CONTROL
75
_J
z
z
cr-
Z
-)
F-
z
D
0
u)
0
10
20
50
40
CHANNE L NUMBER
30
FIG.5.9 THERMAL NEUTRON
DECAY CURVES IN THE
MULTIPLYING ASSEMBLY WITH DIFFERENT
SYSTEMS.
60
DETECTION
70
+ P
o Q
800-
DATA
DATA
+
D
ARRANGEMENT P
+
700[k
0
+
0
0
0
0
0
0(
+
+
z
0
+ +
0
u-
+
+1
+I
0
0
E)
0
600|-
T
0
0
0
ARRANGEMENT Q
0
I
0
0.2
I
I
0.4
0.6
I
I
I
1.0
1.2
08
TIME AFTER BURST
I
I
1.4
1.6
MILLISECOND
I
I
I
1.8
2.0
22
FIG 5.10 VARIATION OF THE MEASURED DECAY CC)NSTANT WITH 'WAITING TIME'
ASSEMBLY, WITH DIFFERENT DETECTORS.
2.4
IN THE MULTIPLYING
0>
77
r0
00
0
0
0
0®
00
U
3
0
0
0
U
0
0
2
0
0
0**0*00 0
4 zi
0
e6
0
0.
0
*S
*
(I)
so 0
-i
Ul
z
z
o
*0
0
*5.0
I
C-)
@0*ejo
S
0 e0
0
Uf)
z
0 0
:D
0
C)
000
@00
0500.0
-0
000.
©
00500.
0
__
O*
S
S
0
-4
*0..
-0
0
00
0e~
00
0
I
0
lO
**
00
I
20
40
30
CHANNEL NUMBER
50
0
60
70
FIG.5.11 THERMAL NEUTRON DECAY CURVES IN MULTIPLYING
ASSEMBLY WITH DIFFERENT DETECTOR LOCATIONS ALONG
CENTRAL AXIS.
78
by considering the variation of the decay constant with waiting time in
the three cases, as shown in Fig. 5.12.
While the decay constant for
the central position assumed a constant value at about 2.2 msec, in the
other two cases it continues to vary slowly and appears to tend to the
constant value of the middle curve.
The effect of harmonics was further investigated by mapping the
axial flux at different stages of the stabilization of the flux in the
assembly.
By moving the small BF 3 counter successively to five dif-
ferent positions along the axis and measuring the prompt neutron flux
decay in each case, the axial flux distribution
different times.
4(Zit) was
obtained at
An attempt was made to normalize these runs by
keeping the total number of bursts the same and maintaining the absolute source strength constant.
The axial flux distribution at different
heights after the burst is shown in Fig. 5.13, which brings out several
interesting features.
Just after the injection of the fast neutron burst
from the source (at t = 105 [isec), there is a highly skewed flux distribution which peaks near the top of the tank, i.e., near the location of the
source.
The peak gradually moves towards the center of the tank and
the distribution approaches a symmetrical normal mode. This phenomenon begins at about the value t = 2.3 msec and confirms the earlier
independent observation of a waiting time of about 2.2 msec at the full
heavy water height.
The delayed neutron decay was studied by locating
the small BF 3
detector at half the core height and running at a repetition rate of one
pulse per second with a channel width of 1280 [isec.
The pulsed source
was in operation for some time before this run was started.
Since the
assembly was far below critical, the statistics of the delayed neutron
tail were very poor and no significant delayed neutron contribution
from the assembly was noticeable.
The over-all variation in the delayed
neutron tail was less than 3 per cent within a 100-msec timing cycle
and could be considered as a constant background to be subtracted from
the observed counts.
The background intensity can be determined from
the pre-burst background (i.e., the first) channel of the time analyzer
and the corrected prompt flux 4(t) can be determined.
The background
intensity can also be obtained from the code EXPO, which yields the
constant B of Eq. 5.1 from the least squares fit.
1000-
900Lu
f 800-
z
700 -
5600-
T
500-
400 -
0.2
FIG.5.12
THE
0.4
0.6
1.8
1.4
1.6
1.0
1.2
0.8
TIME AFTER BURST MILLISECONDS
VARIATION OF THE
PROMPT NEUTRON
2.0
2.2
2.4
DECAY CONSTANT WITH " WAITING TIME"
IN MULTIPLYING ASSEMBLY FOR DIFFERENT DETECTOR LOCATIONS ALONG THE
CENTRAL AXIS.
80
z
z
I
0
0
15
20
-~
25
30
Z (INCHES)
35
40
FIG.5.13 SPATIAL THERMAL FLUX DISTRIBUTION IN AXIAL DIRECTION
<4(z,t) AT DIFFERENT TIMES t AFTER BURST IN THE
MULTIPLYING ASSEMBLY
81
IV.
Determination of Lattice Parameters
After these auxiliary studies, the main runs were made and the
prompt neutron decay constant X was determined as a function of geometrical buckling B 2, corresponding to different dimensions of the
multiplying assembly.
In every case, the small BF 3 counter was
located at half the moderator height and the asymptotic decay constant
was determined by the methods described above.
points were obtained for the (X,B 2) data.
Eleven different
The results are shown in
Table 5.3 and the X vs. B2 curve is plotted in Fig. 5.14.
The points
are found to lie approximately on a straight line - especially in the
lower buckling range - thus supporting qualitatively the conclusions
drawn from the theoretical study.(11,54)
In Fig. 5.15, the (X vs. B 2 )
curves for the pure moderator assembly and the subcritical lattice
are shown on the same graph.
This figure brings out the mutually
counteracting effects of additional absorption and multiplication due
to the introduction of the lattice in the pure moderator tank.
The fundamental mode of the prompt neutron decay, in a subcritical multiplying assembly irradiated by a fast neutron burst, can
be shown to be given by:
X=vZ +vDB
a
-1-
2
- va(1-_)
a
k 0 e-B 2
,
(5.11)
where Z a is the total absorption cross section, B2 is the geometrical
buckling, r is the neutron age to thermal, and other symbols have their
usual meaning.
For large assemblies,
2
-B 2r
~
B2 +
72B4
2
so that we can write
X =-m + nB
2
4
-qB,
(5.12)
where
m
n
=
((1-
=
vD + V2a(1-P)kor
)k-1)vra'
q va(1z=
)k
2 ,(5.13a,b,c)
The prompt critical buckling B
2
pc
corresponds to X=0 and is
directly determined from the experimental data by means of Eq. 5.12.
82
TABLE 5.3
Measured Prompt Neutron Decay Constant as a Function of
Buckling for the Lattice of 0.25-Inch-Diameter, 1.03% U235 Uranium Rods
with a Triangular Spacing of 1.75 Inches
Moderator Height
H cm
Buckling
B2 m-
2
Prompt Decay Constant
x sec~
130.2
31.26
713.6 ± 6.5
122.0
31.95
741.5 ± 6.4
110.7
33.31
787.3 ± 7.0
101.5
34.50
826.2 ± 7.2
90.7
36.89
902.5 ± 8.1
80.5
39.78
1001.0 ± 8.9
75.4
41.71
1052.2 ± 8.7
70.6
43.81
1126.1 ± 10.0
65.8
46.48
1199.5 ± 11.1
60.8
49.78
1294.5 ± 11.8
55.6
54.22
1427.0 ± 13.1
1500
1
1400-
1300-
1200-
1100T
100C-
90C-
80C-
700-
0
10
FIG. 5.14 PROMPT
20
30
NEUTRON DECAY CONSTANT
40
50
60
70
B2
ni2
X AS A FUNCTION OF BUCKLING B2 , FOR THE LATTICE
OF 0.25-INCH DIAM, 1.03 % U235 RODS IN HEAVY WATER WITH A TRIANGULAR SPACING OF 1.75
INCHES
-*-MULTPLYING
1300[-
---
ASSEMBLY
m--PURE MODERATOR
ASSEMBLY
1200-
Il00=
IOocL
T
/
900/
/
800/
/
U
700/
/
6000
FIG.5.15
/
U
/
p
'U
10
20
VARIATION OF THE MEASURED
MULTIPLYING
30
40
50
60
70
82
m~2
DECAY CONSTANT X WITH GEOMETRICAL BUCKLING B2 FOR A
AND A NON-MULTIPLYING ASSEMBLY.
85
Further, if a correction is made - based on some theoretical model for the difference between prompt and delayed criticality, then we obtain
the usual material buckling. The quantities p and r appearing in
Eqs. 5.13a, b, and c can be calculated for any particular lattice from
known delayed neutron and slowing-down characteristics. For a system
with VM
1, it is found that D ~ Dm, where Dm is the diffusion coefvU
2
ficient of the moderator. If, therefore, the (X,B ) data for a lattice are
fitted to an expression of the form (5.12), then Eqs. 5.13a, b, and c can
be solved to yield the values of k. and vZ a and other parameters of interest can be derived therefrom.
The first step in applying the above analysis is to fit the values of
X as a function of B2 obtained from the experiments on the subcritical
lattice (Table 5.3) to an expression of the form (5.12); this yields:
m = (467.2 ± 23.7) sec-
,
n = (4.203 ± 0.048) X 105 cm
2
1
sec
q = (13.2 ± 2.5) X 106 cm4 sec
.
(5.14a,b,c)
The geometrical buckling for prompt criticality, B2 , corresponding to X = 0, is given by solving Eq. 5.12 as a quadratic in B with the
values of m,
n, q from Eqs. 5.14:
2
B PC = (1152 ± 53)[IB .
(5.15)
If we use the relation
2 + aB2
B2 = 2 + 'B2 (Ak) = B
dc
pc
ak
pc +k
B2
PC + L22 +- r ,
(5.16)
then we obtain the delayed critical buckling:
2
B ddc = (1180 ± 60)[iB
It is necessary for further analysis to obtain the value of the effective delayed neutron fraction j3 and of the neutron age to thermal, T,
for the lattice studied. The parameter f is calculated by taking into
account, also, the delayed photoneutrons in heavy water; r is corrected
86
for light water contamination, inelastic scattering and the reduced
'154) The following values are obtained:
moderator volume.
I3=
0.00783 ,
r= (120.0 ± 3) cm
2
(5.17a,b)
.
From the earlier moderator runs, the value of vz a and vDm was found
to be:
vzm = (27.0 ± 5.0) sec~
,
a
= (1.967 ± 0.023) X 105 cm2 sec~
vD
(5.18a,b)
.
Now, from Eqs. 5.13a and 5.13b, the total absorption cross
section in the lattice is given by
v-
a
= n - vD
T
(5.19)
-
and by using the values given above:
vZa = (1396.1 ± 65.5) sec-
.
(5.20)
From Eqs. 5.20 and 5.18a, the macroscopic absorption cross section
for the fuel is:
vz
a
= vz
a
m
a
- vzm = (1369.1 ± 65.7) sec
-1
.
(5.21)
The diffusion area in the moderator is given by:
L
mm
-
v
vZm
a
=
(7280 ± 138) cm 2
.
(5.22)
Now it is assumed that va vDm and thus we get the diffusion area in
the lattice:
2
2 vD
L
= (141 ± 7) cm .
(5.23)
vz
a
We also have from Eqs. 5.13a and 5.13b the expression for the
prompt infinite multiplication factor
(1-I)k
=
n(n-vD) - m
,
(5.24)
87
which can be written as:
1-
1
-
(1-p)ko
m
(n-vD)
(5.25)
Putting in the values of the constants m, n, vD and r, we get:
(1-T)ko, = 1.335 ± 0.026 ,
(5.26)
from which, by using Eq. 5.17a, we get:
k,
= 1.345 ± 0.026
(5.27)
.
It is important to note that what is measured directly in terms of the
or nearly
experimental data (Eq. 5.25) is the quantity (1 - (1-)k
(k,-1), and hence we can expect good accuracy in the value of k0 .
Continuing the analysis further, we can evaluate several other
parameters of the lattice. The moderator thermal utilization, fm, is
given as:
f
0.0037
= L2 =0.0193
m
(5.28)
,
m
so that
1
fU + fAl
-
f
=
0.9807 ± 0.0037
,
where fAl represents the neutron absorption by the cladding.
(5.29)
The cal-
culated value of the "thermal utilization" for the cladding given by the
THERMOS code
-
is
(5.30)
fAl = 0.015
Thus, the thermal utilization for the lattice becomes
f = 1 - fAl
-
fm = 0.9657 ± 0.0037 .
(5.31)
Again, the basic equation for the decay constant of the subcritical
system is:
-B
;Xv + :DB 2 -vZ(1-)ke
0
a
a
(5.32)
(.2
and the measured value of X for the subcritical assembly with full heavy
water height, from Table 5.3, is:
88
X = (713.6 ± 6.5) sec- 1 ,1
where
2
B
= 31.26 X 10~4 cm -2
By using these values and those of vD and vZa from Eqs. 5.20 and 5.18b
in Eq. 5.32:
(1-I3)k00e-B2
= 0.929 ± 0.064 .
(5.33)
Also, from the value of L2 in Eq. 5.23, the thermal non-leakage factor
is
1 2=
1 + L2B
0.694 ± 0.011
(5.34)
Hence, from the last two equations, the prompt multiplicative factor
(effective) is
-B 2 ,
(1-3~)ko
e
2
2 = 0.645 ± 0.046
(5.34a)
1 + L B
whence,
-B 2,
k
eff
=k
1 + L2 B2
= 0.650 ± 0.046.
(5.35)
Furthermore, the prompt neutron lifetime is:
1
v7-
+ v7DB
2 = (497.3 ± 16.4) [isec.
It is also possible to obtain the material buckling B 2
(5.36)
from the
two-group equation:
B2
-
1
T+L 2)+{(T+L2
) +4(kO,-1) rL2}1/2 ;
(5.37)
2L
with the values obtained earlier:
r = (120 ± 3) cm2 ,V
L2 = (141
±7) cm2
= (1.345 ± 0.025) ,
k
we get:
B
2
= (1250 ± 72) B
.
(5.38)
We can also use the age theory transcendental equation instead of
Eq. 5.37 to evaluate the material buckling.
89
Finally, the last of Eqs. 5.13 can be used to obtain a rough value
for the neutron age in the lattice.
If we put the values of
a , (1-p)k,
etc. from the above, in Eq. 5.13c, we get:
(5.39)
T = (118 ± 20) cm
The uncertainty is large, but this does show that the value Tr=(120 ± 3),
that has been used, is reasonable and consistent.
The values of some of the parameters obtained above are listed
in Table 5.4 and compared, wherever possible, with the values obtained
from other sources - either the THERMOS code (39) or steady-state
experiments on the subcritical lattice.
The value of k,
is compared
with the value of 1.35 ± 0.03 obtained from the four-factor formula,
with the value of r obtained from the THERMOS code (corrected for
the epithermal contribution by the GAM code), f from THERMOS, and
p and E from quantities related to these parameters, measured in
steady-state exponential experiments by D'Ardenne et al.
material buckling B 2
m
(12)
-
The
is also compared with the result of steady-state
exponential experiments.
(36)
-
As seen from Table 5.4, the values of the
lattice parameters obtained by the pulsed neutron method agree, within
experimental uncertainties, with the values from other sources whereever these are available.
An important question bearing on the application of this technique
concerns the range of bucklings needed to be covered and the size of
the multiplying assembly that is adequate for the investigation of the
lattice parameters by the pulsed neutron method.
The size of the
assembly and the buckling range affect the degree of precision in the
final values of the derived parameters and the type of analysis to be
Very small assemblies are unsuitable
used in the reduction of data.
for several reasons.
At very large bucklings, the effect of diffusion
cooling becomes increasingly significant.
If we suppose that the dif-
fusion cooling coefficient for the multiplying system is the same as
for pure moderator, the effect is significant at sufficiently large values
of the geometrical buckling.
The diffusion cooling effect in the thermal
spectrum is caused by the preferential leakage of faster neutrons and
results in a decrease of the average diffusion constant vD, as it is
known from a pure moderator.
In a multiplying medium, diffusion
cooling may also have some effect on other parameters, such as I and
TABLE 5.4
Comparison of the Values of Lattice Parameters Obtained by the Pulsed Neutron Method
with Those Obtained by Other Methods, Lattice with 0.25-Inch-Diameter, 1.03% U2 3 5
Metal Rods in a Triangular Spacing of 1.75 Inches
Value Obtained
Parameter
k
L2 cm2
fm
Value Obtained
by the
by
Pulsed Neutron Method
Other Source
1.345 ± 0.026
1.35 ± 0.03
140.9 ± 6.9
134.7
THERMOS
0.0193 ± 0.0037
0.016
THERMOS
0.015
THERMOS
0.9657 i 0.0037
0.9673
THERMOS
497.3 ± 16.4
-
1396.1 ± 65.5
-
fAl
fU
I psec
va
sec
k
0.650 ± 0.046
-
B 2 cm-2
pc
1152 ± 53
-
B 2 cm-2
m
1250 ± 72
1235 ± 25
SSEE stands for Steady-State Exponential Experiments.
Name of Source
THERM'S and SSEE
SSEE
91
ko, in addition to vD.
For very high bucklings, it is expected that the
neutron spectrum changes and approaches the moderator spectrum,
since multiplication and absorption are overcome by thermal neutron
leakage.
It is well to limit the measurements to the range of bucklings
for which the diffusion cooling effect can be ignored.
Further, in small
assemblies in which the fuel concentration is low (VM/VU " 1), the
multiplicative contribution to the thermal neutron decay rate becomes
less important and the decay constant is relatively insensitive to the
parameters characterizing multiplication.
It is expected, from general
considerations, that assemblies between 10 and 30 dollars subcritical
for any system should provide results with good accuracy.
V.
Pulsed Neutron Experiments on Perturbed Multiplying Systems
The next set of experiments involved the measurement of the
prompt decay constant of the subcritical assembly, perturbed by the
full insertion of a single control rod along the axis.
The same lattice
was used as for the measurements described in the previous section.
However, to make room for a control rod along the axis, the seven
central fuel elements were removed and a 4.0-inch-diameter circular
hole was opened in the special plastic adapter (Fig. 5.8).
The control
rods in all these runs were hollow and empty, being closed at the bottom.
The heavy water level was maintained constant at the overflow line
(filled with nitrogen).
The detection system with the long, external BF 3
counter fixed longitudinally on the side of the tank (Fig. 5.2b) was
employed throughout these runs.
on top lid of the tank.
The pulsed neutron source was placed
At the end of each run, the time analyzer was
allowed to sweep for about 10 minutes after the source was shut off so
(11,50)
these same
as to ensure the conditions for quasi- equilibrium,
1 1 ,5 0 )
runs could then be used for the application of the kp/1 method.(
The repetition rate was 10 pulses per second and the time-analyzer
channel width was 80
sec.
The delay multiplier of the time-analyzer
was set at X 2 and the target delay at its maximum value, 100
1 Jsec,
so
that all but the first 60 pLsec of the decay curve could be mapped.
Cadmium control rods of seven different sizes were used and the
decay constant was determined in each case.
Table 5.5.
The results are shown in
The prompt neutron decay constant X of the fundamental
TABLE 5.5
Measured Prompt Neutron Decay Constant and the Change in Buckling Due to Cadmium Rods of
Different Radii Along the Axis; Lattice of 0.25-Inch-Diameter, 1.03% U 2 3 5 Uranium Rods in
Heavy Water, with a Triangular Spacing of 1.75 Inches
Rod
Radius
cm
Prompt Decay
Constant
-,
sec~ 1
Change in
Decay Constant
AX, sec-
Change in
Buckling
AB
2 =
Fractional
Buckling Change
A2 (104 cm- 2)
X 10-
2
a
None
689.9 ± 4.0
0.635
771.1 ± 5.1
81.2 ± 6.4
2.300 ± 0.18
8.97 ± 0.7
1.295
846.5 i 5.4
156.6 ± 6.72
4.436 ± 0.19
17.30 ± 0.7
1.714
879.7 i 6.1
189.8 ± 7.3
5.387 + 0.21
21.02 ± 0.8
2.209
935.0 ± 7.0
245.1 ± 8.0
6.943 ± 0.23
27.09 ± 0.9
2.667
963.9 ± 7.7
274.0 i 8.7
7.762 i 0.24
30.28 ± 0.9
3.327
997.5 ± 8.2
307.6 ± 9.1
8.714 ± 0.26
34.00 ± 1.0
3.969
1029.9 i 9.0
340.0 ± 9.8
9.632 ± 0.28
37.58 ± 1.1
93
mode in the unperturbed lattice is given by Eq. 5.11, and the change in
decay constant, AX, with respect to the unperturbed lattice, is related
to the change in buckling caused by the rod by the relation:(11,5 4 )
AX
AB2 =
2
(5.40)
vD + vr (1-p)kgr eB
The values of the parameters occurring in Eq. 5.40 have been obtained
earlier, as discussed in the previous sections, either through measurement or calculation. The buckling B2 refers to the unperturbed lattice.
Since the height of the core is maintained constant in all the runs, AB2
is also the change in radial buckling caused by the rod:
2
2 =
AB
_
2
.
(5.41)
The last column in Table 5.5 shows the value of the fractional change
2 2
in radial buckling Aa /a , caused by the rods of different sizes. In
0
2 2
a /a 0 is plotted against the rod radius. These results are
Fig. 5.16,
later compared with the results of steady-state experiments and twogroup calculations.
The value of the geometrical buckling from Table 5.2 and the
value of the prompt neutron decay constant from Table 5.5 may be used
to evaluate the prompt neutron lifetime i, the parameter I/l and the
negative reactivity of the assembly with the rod in place.(-1) The
results are shown in Table 5.6. The value of the parameter 1/l is seen
to vary from 15.6 sec~ to 17.6 sec~ over the range of reactivity
studied. The negative reactivity, or the degree of subcriticality of the
lattice in any configuration, is calculated from the prompt neutron
lifetime i and the measured decay constant by the relation: -1)
S
1
*(5.42)
Tx
The values of p for the lattice in the unperturbed state and with the
control rods of different sizes individually inserted, are shown in the
next to last column of Table 5.6. Finally, the last column of Table 5.6
shows the reactivity worth, Ap, of the rods as measured by the change
of subcriticality caused by the rod. The values of Ap are plotted in
Fig. 5.17 as a function of the control rod radius. The points lie on a
94
40
N
0
10-
1.0
2.0
3.0
ROD RADIUS
FIG. 5.16 FRACTIONAL
BUCKLING
4.0
a cm
CHANGE PRODUCED BY CADMIUM RODS
IN THE MULTIPLYING ASSEMBLY, BY PULSED NEUTRON METHOD.
TABLE 5.6
Prompt Neutron Lifetime and Reactivity for the Perturbed Lattices,
Measured by the Pulsed Neutron Method
Rod
Radius
(a:cm)
Geometrical
Buckling
(B
2
:m
2
)
Prompt
Neutron
Lifetime
Inverse
Lifetime
Parameter
(e: sec)
, sec~
Prompt
Decay
Constant
(X:sec
Negative
Reactivity
_
I
Rod
Worth
)P
None
29.02 ± 0.22
502.7 ± 16.3
15.58 ± 0.50
689.9 ± 4.1
0.519 ± 0.02
-
0.635
33.12 ± 0.24
490.3 ± 15.9
15.97 ± 0.51
771.1 ± 5.2
0.595 ± 0.03
0.076 ± 0.007
1.295
35.97 ± 0.24
475.0 ± 15.4
16.48 ± 0.53
846.5 ± 5.4
0.659 ± 0.03
0.140 ± 0.008
1.714
37.49 ± 0.25
469.4 ± 15.2
16.68 ± 0.54
879.7 ± 6.1
0.690 ± 0.04
0.171 ± 0.009
2.209
39.22 ± 0.26
463.3 ± 15.0
16.90 ± 0.55
935.0 ± 7.0
0.750 ± 0.04
0.231 ± 0.009
2.667
40.58 ± 0.26
458.2 ± 14.6
17.08 ± 0.55
963.9 ± 7.7
0.777 ± 0.04
0.258 ± 0.009
3.327
42.37 ± 0.27
451.1 ± 14.5
17.35 ± 0.56
997.5 ± 8.5
0.804 ± 0.04
0.285 ± 0.010
3.969
43.83 ± 0.28
445.9 ± 14.4
17.56 ± 0.57
1029.9 ± 9.0
0.835 ± 0.04
0.316 ± 0.010
(-0
.1
96
0
16 -
12 -
8-
4.|
2.0
1.0
ROD
RADIUS
4.0
3.0
a cm
-
FIG. 5.17 REACTIVITY WORTH Ap OF CENTRAL CADMIUM RODS AS A
FUNCTION OF RADIUS a , MEASURED IN THE SUBCRITICAL
ASSEMBLY BY PULSED NEUTRON METHOD.
97
smooth curve of the general shape expected from theoretical considerations.
An attempt was also made to interpret these data by the recently
proposed kP/1 method for the measurement of reactivity of an assembly
in the subcritical state. The method is based on the fact the equilibrium
neutron density N(r,t) in a pulsed subcritical system is composed of a
prompt neutron contribution Np and a delayed neutron part Nd, which are,
under certain conditions, related by the equation:
tdt
0N exp
- f0' Np dt =R
(5.43)
where R is the repetition rate of the source. Thus, knowing the prompt
neutron distribution N P(t) from the experimental curve, the above integral relationship determines kp/i, since Nd is known from the experiment. Once kp/1 is known, the reactivity in dollars can be obtained
from the relation:
$ =
.
(5.44)
In general, the restriction on the pulse repetition rate is such that
w < R < X, where o is the decay constant of the shortest lived precursor.
A preliminary application of this method to the above runs appears
to indicate that the method is not applicable to assemblies as far below
critical as the ones used here. In the application of this method, a precise knowledge of the delay tail is crucial. If the assemblies are too far
below critical, the delayed neutron contribution may be so insignificant
as to make an accurate determination of Nd in Eq. 5.43 difficult. However, this result bears further investigation, especially to check if the
theoretical conditions basic to the derivation of Eq. 5.43 are met experimentally. The repetition rate of 10 pulses per second used in these
runs may be too low; the Kaman pulsed neutron tube is limited to a
repetition frequency of about 10. It appears worthwhile to check the
applicability of this method in the far subcritical range by a wider range
of the choice of experimental parameters.
98
VI.
Exponential Experiments with Control Rods in Multiplying Assemblies
A set of steady-state exponential experiments have also been made
with the same set of rods and the same lattice to measure the change in
buckling caused by the rod and to examine the perturbation of flux
spectrum due to the rod.
For these experiments, the seven central fuel
elements were removed to make room for the control rod (Fig. 5.8);
the latter were introduced through a top plastic adapter and positioned
along the axis of the assembly in the manner described earlier.
An axial
foil holder of aluminum could be fixed in an off-center position in the
moderator region between fuel rods.
Gold foils, 0.010 inch thick and
1/8 inch in diameter, were attached to the foil holder.
The lattice was
irradiated with thermal neutrons from the thermal column of the MITR.
After irradiation, the foils were gamma-counted to straddle the 411-key
Au 1 9 8 gamma-ray peak with a window width of 60 key.
The experi-
mental counts were corrected for dead time, background, foil weights,
decay during counting, etc., and the final axial distribution was obtained
for the unperturbed lattice and for the lattice with each of seven different size rods individually placed along the axis.
distribution is shown in Fig. 5.18.
An example of the axial
In a large enough region, the harmonic
content is negligible and the data are fitted well by a single exponential.
The change in the relaxation length caused by the placement of the rod
is seen to be significant.
The value of the fundamental axial buckling -y2. is calculated in
each case by fitting the axial flux distribution #(z) to the function
A sinh y(h-Z), by means of a least squares fit. Thus the experiments
give directly the change in axial buckling produced by a control rod.
However, since the material buckling of the lattice remains unchanged,
the change of axial buckling is equal to the change of radial buckling.
The results are summarized in Table 5.7. The reactivity effect of the
control rod in terms of the fractional change in radial buckling Aa2
2
caused by the rod, as measured in this steady-state exponential experi-
ment, is compared in Table 5.8 and Fig. 5.19 with the results of pulsed
neutron experiments.
The results of the two methods agree within the
experimental uncertainties, although these uncertainties are somewhat
larger in the steady-state case.
a2 /a 2as
Figure 5.19 also shows the curve for
given by a two-group theory expression:
-
99
Lu
0::
~
O
0
~-----
FLUX WITHOUT ROD
FLUX WITH 2.7 INCH
DIAM. Cd ROD ALONG
AXIS
I
|
|
|
|
|
|
|
33 43 53 63 73 83 93 103 113
DISTANCE FROM THE BOTTOM OF THE TANK Z, CM
FIG.5.18
AXIAL FLUX DISTRIBUTION IN THE EXPONENTIAL
ASSEMBLY WITH AND WITHOUT A CONTROL ROD.
TABLE 5.7
Buckling Change Produced by Axial Cadmium Rods of Different Radii in the Multiplying Assembly,
Measured in Exponential Experiments
Rod Radius
(cm)
Axial Buckling
(Y 2
M-2
Change of Buckling
2
2
2
Fractional Buckling Change
2
A
0
-
None
12.148 ± 0.18
0.635
14.340 ± 0.21
2.192 ± 0.28
0.092 ± 0.012
1.295
16.188 ± 0.23
4.040 ± 0.29
0.170 ± 0.012
1.714
17.068 ± 0.25
4.920 ± 0.31
0.207 ± 0.013
2.209
18.513 ± 0.26
6.365 ± 0.32
0.268 ± 0.013
2.667
19.468 ± 0.28
7.320 ± 0.33
0.308 ± 0.014
3.327
20.365 ± 0.29
8.217 ± 0.33
0.346 ± 0.014
3.969
20.912 ± 0.29
8.764 ± 0.34
0.369 ± 0.014
I.
TABLE 5.8
Comparison of the Fractional Buckling Change Caused by Axial Cadmium Rods
of Different Radii in the Lattice, by Pulsed Neutron and Steady-State Experiments
Rod Radius
Steady-State Experiment
(cm)
Aa 2
0
Pulsed Neutron Experiment
A
0
0.635
0.092 ± 0.012
0.089 ± 0.007
1.295
0.170 ± 0.012
0.173 ± 0.007
1.714
0.207 ± 0.013
0.210 ± 0.008
2.209
0.268 ± 0.013
0.271 ± 0.009
2.667
0.308 ± 0.014
0.303 ± 0.009
3.327
0.346 ± 0.014
0.340 ± 0.010
3.969
0.369 ± 0.014
0.376 ± 0.010
102
THEORETICAL CURVE BY
TWO-GROUP THEORY (ZERO ABSORPTION IN FAST GROUP )
PULSED NEUTRON EXPERIMENT
EXPONENTIAL EXPERIMENT
40-
S30I0
20-
10 -
L.O
FIG 5.19
2,0
ROD RADIUS
a
FRACTIONAL CHANGE IN BUCKLING
RODS OF DIFFERENT
3.0
cm
-!
4.0
PRODUCED BY CADMIUM
RADII a ,IN THE SUBCRITICAL ASSEMBLY
103
=
2
-0 .820 Yo( La) +d. Y1 (pa)+ -
(K(va)+dv
9
Ki(va))j
- -1
1rS
(5.45)
based on flat boundary conditions for the fast neutron group (the
symbols have their usual meanings). The experimental points agree
with the theoretical curve for small values of the rod radius; for
large rods, the theory underestimates the worth of the rod by a few
per cent; this is believed to be due to the neglect of fast absorption
in the two-group treatment.
A. Examination of the Flux Spectrum: Radial Runs
A necessary condition for the results of exponential experiments
such as those described above, to be analyzed in terms of the properties of the lattice by simple theory, is that the neutron spectrum which
is perturbed near the rod should recover its asymptotic value within
the bounds of the assembly. To examine this condition, radial flux distributions were measured in the unperturbed and perturbed assemblies
with bare and cadmium-covered gold foils. The 0.010-inch-thick,
1/8-inch-diameter, gold foils were attached to a horizontal aluminum
foil holder placed along a chord of the tank so as just to graze the control rod in the perturbed assembly. This configuration and the setting
of the foils with respect to the fuel rods and the control rod are shown
in Fig. 5.20. Cadmium boxes providing a cadmium sheath 0.020 inch
thick were used to obtain the activities above the cadmium cut-off
energy. The foil holder was placed sufficiently far from the bottom
(neutron source) so that the measured flux distribution was representative of the lattice spectrum; in previous lattice exponential runs, it was
found that at 60 cm and 108 cm above the bottom of the tank, good fits
to a J (ay) distribution were obtained.
Figure 5.21 shows the radial flux distribution with bare gold
foils, in the assembly with and without the largest (8.0-cm diameter)
control rod along the axis. The distribution with cadmium-covered
gold foils is shown in Fig. 5.22. The effect of the rod on the flux distribution and the difference between the subcadmium and epicadmium
flux distributions are both evident from these two figures. The slight
bulging of the flux caused by the rod at the outer edge of the tank is
104
RADIAL
FOIL
HOLDER
FOIL POSITION
FIG. 5.20 LOCATION
HOLDER FOR RADIAL FLUX
MAPPING IN THE EXPONENTIAL ASSEMBLY
105
14
-
FIG.5.21
7
0
7
DISTANCE FROM AXIS r (INCHES)+
14
RADIAL FLUX. DISTRIBUTION (WITH BARE GOLD FOILS)
IN
THE EXPONENTIAL ASSEMBLY WITH AND WITHOUT A CONTROL ROD.
-
FLUX WITH NO CONTF
ROD
-
FLUX WITH CONTROL
ROD
EDGE OF CONTROL ROD
EDGE OF TANK
%
004
14
7
0
7
14
DISTANCE FROM AXIS r(INCHES)
FIG. 5.22 RADIAL FLUX DISTRIBUTION (WITH CD-COVERED GOLD FOILS) IN THE
EXPONENTIAL ASSEMBLY WITH AND WITHOUT A CONTROL ROD
H
107
also observed as predicted by theory.
To examine more clearly the influence of the rod on the cadmium
ratio, the gold-cadmium ratio was calculated from the measured flux,
at every point in the assembly with and without the rod. In Fig. 23, the
cadmium ratio is plotted as a function of the radial distance from the
axis. The hardening of the spectrum,as indicated by the decrease in
the cadmium ratio near the rod,is well illustrated; however, the cadmium ratio returns to its unperturbed value at about 7 inches from the
axis in this 18-inch-radius tank. Thus, the main condition for the
validity of the results, viz., the recovery of the unperturbed spectrum
(at least as indicated by the gold-cadmium ratio) within the bounds of
the assembly, is well satisfied. The small rise in the cadmium ratio
in the unperturbed case near the axis is due to the moderator region
left by the removal of the seven central fuel rods. There is also seen
in both the perturbed and unperturbed cases a significant hardening of
the flux near the outer edge of the tank, showing the variation of leakage with neutron energy.
108
-*--
---
POINTS IN UNPERTURBED ASSEMBLY
(NO ROD PRESENT)
0-- POINTS WITH 4.0 CM. RADIUS CADMIUM
ROD ALONG AXIS
1.0
0
D
I
/
2.
I
I
I
I~
I
I
I
II
0
FIG. 5.23
'4
I
I
I
I
I
I
10
7
DISTANCE FROM AXIS, r (INCHES)
I
ow
VARIATION OF THE GOLD CADMIUM-RATIO ±2 ALONG A RADIUS OF THE
EXPONENTIAL ASSEMBLY WITH AND WITHOUT A THERMALLY BLACK ROD
ALONG AXIS.
109
6.
MEASUREMENTS
ON POISONED LATTICES
J. Harrington, III
Exploration has been started of a new technique for the experimental measurement, in a subcritical assembly, of the neutron multiplication factor for an infinite lattice (k 0 ).
The objective of this work
is to develop the technique and use it to obtain values of k0, for lattices
of slightly enriched uranium in heavy water.
Work began in mid-April,
1964; the first series of experiments, in the 2-1/2-inch lattice, was
scheduled to begin shortly after the close of the period covered by this
report.
The following account will describe the objectives of the work,
and the planning and preparation for the achievement of those objectives.
I.
Definition of ko
In general, ko, is the ratio of the number of neutrons produced to
the number absorbed, in an infinite assembly.
It can be defined in
terms of the neutron cycle for a predominantly thermal reactor, as:
(6.1)
k, = repf
Here, ne is the total number of (fast) neutrons produced for one thermal
neutron absorbed in the fuel; ra is the number of neutrons produced by
fission for one thermal neutron absorbed, and E is the total number of
(fast) neutrons produced for each fission neutron; p is the probability
that a fast neutron escapes absorption, while slowing down to thermal
energies; and f is the probability that a neutron, once thermal, is captured in the fuel.
It is important that the various factors be defined
consistently, and that each process be counted once and once only in
the neutron cycle.
II.
Introduction to Theory of Measurement
The general approach will be to extend the technique developed at
Hanford (PCTR)(3',4)
for the measurement of k,
test region of a critical reactor.
by poisoning a central
Their procedure is based on poisoning
the central cell of the reactor down to the point where it has the same
110
effect on reactivity as an equal volume of void; under certain conditions,
the value of k, for the poisoned sample is taken to be unity, and the
value of k, for the unpoisoned sample is inferred from the amount of
poison necessary to reach this point. In a subcritical assembly, the
approach will be to poison the entire lattice or a section of the lattice
down to the point where the material buckling is zero, take the value of
k, for the poisoned lattice to be unity, and again infer the value of k,
for the unpoisoned lattice from the required amount of neutron poison.
Note that the equivalence of zero material buckling and a unit infinite
multiplication factor holds in all reactor models. Thus, the approach
is not dependent on a particular theory, such as age theory, groupdiffusion theory, etc.
The proposed measurement will afford a comparison with the
value of k, derived from pulsed neutron work, and that derived from
the values of p, f, E, and rl determined by other workers. Alternatively, the work, taken together with the experimental determination
of p, f, and E, may be treated as an experimental determination of Y7.
To date, this has not been done as part of the Lattice Project studies.
If a neutron-multiplying assembly were poisoned to such an
extent that k, were reduced to unity, then Eq. 6.1 would reduce to:
1
=
r'e'p'f' .
(6.2)
Primed quantities denote the various parameters in an assembly
poisoned to this extent. The use of a predominantly thermal poison
would result in changes in f, but relatively small changes in the other
three parameters. In fact, a purely thermal poison, that did not expel
any moderator, would not change E or p at all. In this case,
E =E
(6.3)
Ppp
If the change in neutron energy spectrum were negligible, then
One could then, by measuring thermal utilization in the clean and
poisoned lattices, determine k 0 as:
f
(6.5)
k -= f .
111
The advantage to this method of determining the value of k 0 o, as pointed
derives from
out by Donahue, Lanning, Bennett, and Heineman,(.,2
the fact that the quantity actually determined experimentally is (ko, - 1).
Note that:
abs
abs
f =
fuel
abs + abs
, _fuel
abs + Eabs
'
1oo
1abs
poison
mod
fuel
mod
fuel
(6.6)
+ Eabs
abs
poison
f -f1
(6.7)
+ Eabs
f
fuel
In cases where the value of k,
mod
is near unity, then the percentage
is markedly less than the percentage uncertainty
uncertainty in k,
in the right-hand side of Eq. 6.7.
The foregoing treatment only applies to a homogeneous reactor.
such as those under
Complications arise in heterogeneous systems,
study on the Project, but the hope is to obtain a practical technique,
while retaining the advantage just explained.
III.
Poisoning Method Selected
Various poisons and poisoning techniques have been used in the
past with both critical and subcritical lattices,
multiplying assemblies.
Differential parameters,
sections and mean free paths have been measured,
as well as nonsuch as cross
as well as
integral parameters such as the neutron age and the migration area
The technique developed at Hanford, discussed previously, has been used not only with solid moderators as in the original
(Refs. 29, 30, 31).
work, but also with liquid moderators.
52
The poison may be homogeneously distributed in the moderator;
this was done,
for instance,
in
work at Brookhaven on lattices of
slightly enriched uranium rods in light water.
poison.
-31) B203 was used as
Heterogeneous poisons are also used; one example of the use
of this technique is the work done at the Savannah River Laboratory in
an effort to determine an inhour equation for the Process Development
Pile. (
Rods of aluminum, copper, and stainless steel were inserted
both in the fuel clusters and in the moderator,
as part of this work.
It was decided at the outset of this work that poisoned moderator
experiments
would not be attempted.
The poison then had to be
112
heterogeneous, and it was clear that it should be axially contiguous, to
simplify interpretation of results. Rods, tubes, rod or tube bundles, and
sheets were considered. Rods were chosen for simplicity in handling,
and because the measurement of the absorption rate in the poison and
the interpretation of the results are considerably simplified.
Copper was chosen as the best material for use as a "thermal"
poison. Its neutron absorption cross section varies as 1/v, where v is
neutron velocity and has a value of 3.8 barns for 2200 m/sec neutrons.
This cross section permits convenient rod sizes in the lattices studied;
the rods are thicker than wire, which would be difficult to handle, but
are not so thick as to expel more than a few per cent of the moderator
from the lattice. There is little resonance-region absorption in copper;
its infinite resonance integral is 3.3 barns. Copper is obtainable at
reasonable expense ($1.50-$2.00 per lb) in the form and purity desired.
Its short half-life and mode of decay (almost entirely beta) will minimize radiation hazards to personnel.
A series of calculations, consisting largely of extrapolations from
past experimental work on the Project, was made to determine the size
of copper rod which would poison each of the lattices under consideration
to the null material buckling point. Calculations were also made of the
variation in buckling as a function of the amount of poison. Account was
taken, in the course of the calculations, of the effect of the poison on the
resonance escape probability of the lattices, due to expulsion of D2 0
and epithermal absorptions in the copper. The effect was calculated to
be, at worst, a change of a few per cent in p. The effect of the poison
on r7 and E was ignored.
A considerable saving in time and money was achieved by purchasing rods with diameters available from stock. One set of 750 rods,
6 feet long and 3/16 inch in diameter, has already been obtained. About
half of these were not of satisfactory straightness; steps have been taken
to remedy this situation with the second set of rods, which are 0.144 inch
in diameter. While cladding is apparently not strictly necessary when
dealing with copper and D2 0 of the purities involved, it is proposed to
coat all exposed surfaces with 0.00045 inch of KANIGEN to reduce the
possibility of copper causing corrosion of the aluminum tank and fuel
cladding.
KANIGEN is a trade name for a chemically-deposited coating
113
of nickel, containing 5-8% phosphorous.
It is non-crystalline, hard,
and very uniform in thickness over the plated area, and has superior
corrosion properties.
The cost is comparable to that of equivalent
thicknesses of less satisfactory electroplated coatings.
IV.
Experiments and Analysis
The previous discussion of the theory behind the work dealt only
with a lattice poisoned just enough so that k,
Actually, this
was unity.
Various amounts of poison
will not be attempted in the present work.
will be used, and the amount necessary to reduce k,
to unity, or equiv-
alently, to reduce the material buckling to zero, will be inferred in the
manner to be described.
The macroscopic and microscopic neutron density distribution
will be determined in each poisoned lattice.
This will be done via foil
activation techniques which are by now standard on the Project (Refs.
6, 9, 10, 51).
Both bare and cadmium-covered gold foils will be used.
2
, of the poisoned assemblies may be evalum
ated from the macroscopic distribution just as is done with unpoisoned
The material buckling, B
lattices.(6,51)
The thermal utilization can be calculated from the
microscopic distribution, by using the THERMOS code, --
in a fairly
straightforward extension of techniques described by Brown Simms
-() in previous reports.
any change in
and
This will also permit calculation of
r7, though none is expected.
The extension of the Simms-
Brown work is based in part on a paper on absorption rates in mixed
lattices by Suich. (--
Quantities related to E and p will also be
measured in some or all of the lattices.
It is intended to span a range of positive and negative material
bucklings.
A least squares fit of the data on thermal utilization of the
several poisoned lattices plotted vs. material buckling should then
yield the thermal utilization for a lattice with null material buckling.
A similar technique will be used with the experimental quantities
related to E and p, if it is found that they are affected by the poison.
In this way, the change in the four factors making up k,
can be calcu-
lated for a poisoned lattice with null material buckling.
As stated above, insertion of poison in the moderator, far from
fuel elements, is not expected to change
ri noticeably, since the neutron
114
energy spectrum in the fuel should not be affected.
and 6.4 apply and yield:
k
,.?
=
Then Eqs. 6.1, 6.2,
.PF)(
(6.8)
Since each of the factors on the right-hand side has the form
terms in nuclear constants]
and
experimentally measurable ratios
~
1+
it is still (k,- 1) that is being measured, and the chief advantage of the
method as described earlier has indeed been retained.
The results of the poisoned lattice work can be used not only in
the determination of the value of k,, but also for the determination of a
number of integral parameters which appear in various reactor models.
Migration areas, diffusion lengths, and the neutron age can all be
obtained. The anisotropy induced by insertion of the copper can be
studied. Although few specific plans have been made, our intent is to
make the fullest possible use of the poisoned lattice data.
115
SINGLE ROD MEASUREMENTS
7.
AND THEORY
E. E. Pilat
I.
The Thermal Energy Region
A.
Theory
The thermal neutron flux distribution around a single fuel rod
immersed in moderator satisfies, to a very good approximation,
(3)
-
the equation:
+
r+
(T 2-K2)0 + f(r) = 0,
(7.1)
r dr
dr2
where
4(r) represents the radial flux dependence,
f(r) represents the radial dependence of the source minus sink
term (exclusive of moderator absorption),
K2 = _L
-y
of the moderator, and
= reciprocal of the axial relaxation length.
A series solution of this equation has been found -3 in ascending powers
of r. It can be shown that the coefficients of the first few terms are
obtainable from a least squares fitting of experimental foil activities
measured around a single rod. These coefficients yield information
about the form of the source-sink term. However, the series solution
in purely ascending powers of r represents an analytic solution at the
origin and therefore omits the singularity at the origin which physically
corresponds to the existence of a neutron sink in the form of the fuel
While it may be possible to fit the analytic solution to the activation data at some distance from the rod, it is clearly more useful to
include the sink effect in the series solution. The complete solution is
rod.
therefore of the form:
27
00
00
=
where the
n r T
i=0
. and
4.
1:3
r1
+ z
3=0
r
are constants for a given fuel rod.
(7.2)
A Fortran pro-
gram is being written to least-squares fit the foil data to a function of
this form.
116
B.
Experimental Thermal Data
Radial and axial gold foil activations have been measured around
a single, 1-inch-diameter, natural uranium rod placed at the center of
a 3-foot-diameter tank filled with D 2 0.
Although the axial data were
expected to be exponential in character (proportional to e- TZ), it was
not obvious that the constant y so obtained would be independent of
radius, since the slowing-down density around the fuel rod is spatially
neither uniform nor of a J
form.
made at three different radii:
Axial foil activations were therefore
10.8 cm, 15.9 cm, and 22.2 cm.
The
results of the innermost and outermost runs, plotted on arbitrary scales,
It can be seen that over a fairly large region
are shown in Fig. 7.1.
away from the top and bottom of the facility, the thermal flux is, in fact,
exponential with a relaxation length independent of radius.
As a more
precise check on this, the activity of each foil from the two outer runs
was divided by the activity of the corresponding (same height) foil from
the innermost run.
In regions where y is independent of radius, the
result is a constant.
Figure 7.2 shows these curves and substantiates
the assumption that this
"asymptotic"
region exists, although its extent
decreases at larger radii.
Although the full analysis of the radial activations must await
completion of the previously mentioned computer code, it has been
possible to verify that a significant number of source neutrons are
generated so that the radial activity distribution is characteristic of
the source as well as the sink term.
This may be seen by comparison
of the measured foil activities with the results of Malaviya on foil
activities near control rods (where only a sink term is present).
First, the radial activity distribution, a sample of which is shown
in Fig. 7.3, was divided by J 0 (ar).
Here,
a = 2.405
R
(7.3)
and R is the extrapolated radius of the D 20-filled tank before the
central rod was added.
is
The result obtained with the control rod data
shown in Fig. 7.4 and the effect of the control rod neutron sink near
the center is evident.
The result obtained with the data around a fuel
rod, Fig. 7.5, also shows a flux decrease near the rod; but the curve
is much flatter, indicating that source neutrons from the rod have
117
1000
'
U 00 -
eg
-J
-
i
10-
AXIAL TRAVERSE
AT A RADIUS
OF 10.8 CM
0
10
F IG. 71
AXIAL TRAVERSES IN D20 AT TWO RADII FROM
I INCH DIAMETER NATURAL URANIUM ROD AT
CENTER OF TANK
20
30
40
FOIL POSITION
50
60
70
1.2
I
I
I
I
II
I I
I
X
(I)
1.1
I
I
I
x
x
z
D
I
X
1.0
X
X
x
x
x
V
x
x
x
x
x
X
X
x
X
X
X
X x
x
X
X
x
0.9
0.8-
00
0
o 00
0
0
0
0
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
->
0
0.7
0.60.5
Foil activity at radius of 22.2 cm
Foil activity at radius of 10.8 cm
t
0.4
-J
o
0.3
0
Foil activity at radius of
Foil activity at radius of
15.9 cm
10. 8 cm
0.2wr
0.1
0
1 2
4
6
8
10
12
14
16
18 20
AXIAL POSITION OF FOILS
FIG. 7.2 RATIOS OF CORRESPONDING (SAME HEIGHT)
AXIAL TRAVERSES AT DIFFERENT RADII
22
24
26
28
30
FOIL ACTIVITIES FROM 3
32
I
I
I
I
I
I
I
I
I
I
I
I
I I
I
I
I
I
I
61+
+
+
+
5 F-
+
+
+
+
+
4
+
+
+
+
+
+
+
3
+
+
F-
+
+
+
+
2 F-
+
+
+
+
I -
+
+
0
I
+
I
40
I
I
32
I
I
24
I
I
I I I I
I I I I
16
8
0
8
16
24
DISTANCE FROM CENTER OF TANK CM
I I I I I
32
40
48
FIG. 73 RELATIVE ACTIVITY OF GOLD FOILS IN D20 AROUND A SINGLE I INCH DIAMETER
NATURAL URANIUM ROD AT THE CENTER OF EXPONENTIAL TANK
120
1
I
I
I
'I
2[--
I
I
I
0
0
0
I
I
0
0
0
1.010
4c
0
.J
0t
0.8.
0
rz
0.6
N
0
<t
0.4 1_i
0.2H-
0
0
I
I
FIG. 7.4
II
10
F
I
I
I
I
I
I
I
I
20
30
40
50
DISTANCE FROM CENTER, CM
60
(RELATIVE GOLD FOIL ACTIVITY)+ Jo(ar) AROUND
A CADMIUM CONTROL ROD AT THE CENTER OF
THE D2O FILLED EXPONENTIAL TANK
w
-J
0
9.0
U)
x
8.5H
m
8 .0
Relative Foil Activity
JO(ar)
1-
2.405
Reff
a
7.5
Reff
= 47.5 cm (estimated from I ig. 73)
H
X --
7.00
uJ 6.5
6.0
-j
Iii
cr
0
5.5xx
w
N
5.04.5
0
z
x'II
I9
FIG. 75
20
22
24
26
283
0
INCREASING RADIUS (FOIL NO.)
32
34
36
40
(RELATIVE GOLD FOIL ACTIVITY)-Jo(ar) AROUND A 1 INCH DIAMETER NATURAL
URANIUM ROD AT THE CENTER OF THE D2 0 FILLED EXPONENTIAL TANK
PO
H
122
tended to "fill up" the space vacated by those neutrons absorbed in the
rod.
Second, an attempt was made to fit the radial data around a fuel
rod by using the method developed by Malaviya (--)
for control rods.
It is shown by Malaviya that the diffusion theory expression,
J (atR)
<p r)=JO(ar) -
0 (aR) YO(ar),
(7.4)
accurately predicts the flux around a single absorbing rod if a is
defined by:
a
2
2
=BM +y
2
- a
2
2
2
- To + Y
(7.5)
where
2 is the axial buckling,
2
a2 is the radial buckling,
2o
BM is the material buckling of D 2O, and the
subscript zero refers to the tank containing D 2 0 but no rods.
This expression has been developed on the assumption that the addition
of a control rod changes only boundary conditions, but does not alter
the material buckling of the D 20 in the tank.
If the fuel rod at the center
produces appreciable neutrons, then this derivation will fail, since the
thermal neutron source distributed through the D20 corresponds to a
change in its material buckling.
The axial activation data previously
2
2
mentioned have been used to evaluate -y
and 7y . When this is done, the
resulting expression predicts a much smaller flux depression than is
found experimentally near the fuel rod.
This is again interpretable as
being due to source neutrons from the fuel rod.
They evidently are
present in significant enough numbers to affect the measured a and 7Y.
That is, since these equations do not allow for neutron production, the
results tend to compensate for it by decreasing the effective absorption.
II. Resonance Energy Region-Theory
Since the neutrons at any point in a reactor lattice are born in
the individual fuel rods, it might be assumed that the flux spectrum at
this point is the sum of individual flux spectra of neutrons around a
single fuel rod, the spectra being evaluated at the proper distances
123
from the fuel rod. (Spectra around single fuel rods are, of course,
functions of distance from the fuel rod as well as of energy.) The
implied assumptions are:
1. Negligible absorption by the fuel rods above the energy
considered.
2. The presence of all the fuel rods in the lattice does not
alter its moderating properties.
These should be excellent assumptions for all but the tightest D2 0
lattices.
Let f(rk,E) denote the flux per unit energy at energy E and at
a distance r k from a single fuel rod immersed in moderator. Let 4(E)
be the spectrum expected at a point in the lattice. Then, with the above
assumptions,
4(E)
nkskf(rk,E) ,
=
(7.6)
where
nk = number of fuel rods at distance rk from point being
considered, and
sk = relative source strength of rods at distance rk'
By using this equation to relate lattice and single rod spectra, it
becomes theoretically possible to measure, by means of experiments
at several distances from a single rod, epithermal quantities of interest
at a particular point in a lattice.
For example, ignoring for the moment the complication of 1/v
absorption, the activity "A" of a cadmium-covered foil is proportional
to its effective resonance integral Ieff'
(E)a ff(E) dE = CI ff.
A = b f
(7.7)
Thus, by using Eq. 7.6, "A" becomes:
A =
f
E
A =
b
nkskf(rk,E)u
nksk
k
(E) dE
,
(7.8)
bf(rk,E)a ff(E) dE
,
(7.9)
k
E
124
A = I nkskAk
(7.10)
k
where A k is the activity of a cadmium-covered foil at a distance rk
from the single fuel rod.
The proportionality constant between activity and ERI can be
determined if a foil of the same material with a known ERI is irradiated. For this purpose, it is convenient to use the known fact that the
neutron spectrum in an infinite homogeneous medium varies as 1/E.
Since in most lattice spacings of interest it has been found that the
neutron energy distribution is closely represented by the "1/E" dependence in the epithermal region, we can therefore use the relation:
~
Z
Nkf(rk,E)
,
(7.11)
k
where N k is the number of fuel rods at a distance r k from a point in an
infinite uniform lattice. For large distances, Nk is proportional to r.
For the continuous case, Nk becomes simply the element of area at
radius r, i.e., 27rdr. The sum in Eq. 7.11 may then be looked upon
either as what would be obtained physically in an infinite lattice of fuel
rods, or as a mathematical approximation to the integral obtained from
using an infinite homogeneous system. Thus, the proportionality constant between cadmium-covered activity and ERI can be evaluated if a
foil (of the same material) having a known ERI is irradiated at several
distances from a single rod and if the activities are added by using the
same weight function, Nk, as appears in Eq. 7.11.
Aside from requiring only a single fuel rod, the proposed method
has the advantage that once the constant of proportionality is known for
any foil material, only one set of irradiations around the single rod is
required. The results for all lattice spacings of a given fuel are obtainable from this data simply by changing the weight factors nk and sk to
correspond to the particular lattice spacing being studied. In addition,
such an approach can be extended to the treatment of multiregion lattices
where it may help provide some understanding of experimental data in
the epithermal region.
125
8.
TWO-REGION LATTICES
J. Gosnell
Investigations of the validity of lattice parameter measurements
in the center of two-region assemblies are being conducted by using
the M.I.T. lattice facility.
Determination of spectral changes across
the two regions has been the main object of the experiments.
In addi-
tion, axial buckling measurements were made at various radial
positions in the assemblies to ascertain whether or not the axial relaxation length is
I.
a function of radius.
Formation of Assemblies
The M.I.T. lattice facility offers the flexibility necessary for the
formation of two-region assemblies.
With the present girder system
in the facility, the easiest method of forming a test region in an existing lattice is to remove (or insert) alternate fuel rods, thus forming a
test region with a spacing different from the outer reference lattice.
This method has been used to form four assemblies with 0.25-inchdiameter fuel rods.
The four assemblies, listed in Table 8.1, were of one enrichFuture work will include the effects of
ment (1.031o U 235) throughout.
enrichment and rod size differences.
TABLE 8.1
Two-Region Assemblies in the M.I.T. Lattice Facility
(All assemblies formed of 0.25-inch-diameter, 1.03% U235 fuel rods.)
Assembly
Outer
Inner
Designation
Reference Region
Test Region
I
1-1/4-inch pitch
2 rings* - 2 -1/2-inch pitch
I
1-1/4-inch pitch
3 rings
- 2-1/2-inch pitch
III
1-1/4-inch pitch
4 rings
- 2-1/2-inch pitch
IV
2-1/2-inch pitch
6 rings
- 1-1/4-inch pitch
Rings about the central rod.
See Fig. 8.1.
126
FIG. 8.l
ASSEMBLY
III
( FOUR RING 2'/2 INCH PITCH IN I'/4 INCH PITCH)
127
II. Gold-Cadmium Ratios
In the previous report,
gold-cadmium ratios were given for
assemblies I and III for 1/16-inch-diameter, 0.010-inch-thick, gold
foils. It was noticed that the cadmium ratio in the center of the tworing assembly failed to achieve the value of the full lattice, while the
ratio in the center of the four-ring assembly apparently exceeded the
full lattice value.
It was decided to remeasure the four-ring assembly to better
determine if such an effect exists and to investigate, as well, a threering assembly. Because of the uncertainty in weight, and lower
activity of the 1/16-inch-diameter foils, it was decided to use 1/8inch-diameter, 0.010-inch-thick foils for the traverses.
Two traverses, each of bare and cadmium-covered foils, were
irradiated across the diameter of each assembly. In this way, since
the foil holder is symmetrical about the center, a total of four
measurements of each activity was obtained for each foil position.
The results are shown in Fig. 8.2 and Fig. 8.3.
It is seen that the cadmium ratio in the three-ring assembly
reaches 96% of the full lattice value while, in the four-ring assembly,
the full lattice value is, indeed, exceeded.
In Figs. 8.4 and 8.5, the epicadmium and subcadmium components
of the foil activities are shown. The flattening of the epicadmium flux
within the more highly moderated test lattice is evident. It appears
that spectrum equilibrium has not been reached in either assembly. In
a larger test region, the epicadmium flux should begin to rise, leading
to a region of constant cadmium ratio.
The last assembly analyzed to date had six rings of 1.25-inch
spacing in a 2.50-inch reference lattice (assembly IV). Cadmium
ratios were measured as before and the results are indicated in Fig. 8.6.
The epicadmium and subcadmium components of the activities
are shown in Fig. 8.7. Here the thermal flux actually decreases in the
central region and again an equilibrium spectrum has not been attained.
III. U238 Cadmium Ratios
The cadmium ratio of U238 was chosen as an indication of spectral
effects inside the fuel rods. Measurements in assemblies I and III
14
12
10
0
I-
8
6
4
2
0
2
F IG. 8.2
4
6
DISTANCE FROM
CADMIUM
8
10
12
14
LATTICE CENTER(INCHES)
16
RATIO IN 3 RING ASSEMBLY (ASSEMBLY.E)
18
1-j
ro
03
I
14
-I
I
I
I
I
I
I
I
CADMIUM
RATIO
FOR FULL 21/2 I NCH
LATTICE , 13.3 t 0.4
I
12
0
I
I
I
I
10 I-
I
I
8
I
I
0
()
6 k-
I
I
4
POSITION OF RODS
2[0
I
0
2
0
4
DISTANCE
I
6
FROM
0
0
L
1L
0o0
0
1
10
14
12
8
LATTICE CENTER (INCHES)
0
1
16
18
I-A
FIG.8.3
CADMIUM
RATIO IN 4 RING ASSEMBLY (ASSEMBLY
JIE)
12
10
cn
Iz
8
a:
a:
H
m 6
a:
I-
4
H
0
2
0
2
FIG.8.4
14
12
10
8
6
4
DISTANCE FROM LATTICE CENTER(INCHES)
GOLD
FOIL ACTIVITIES
18
16
IN 3 RING ASSEMBLY (ASSEMBLY
I)
0
10
U)
I.-
8
z
6
in
4
I0
2
0
2
FIG. 8.5
4
6
8
10
12
14
DISTANCE FROM LATTICE CENTER (INCHES)
GOLD FOIL ACTIVITIES
16
IN 4RING ASSEMBLY (ASSEMBLY JII)
18
I--
I
I
I
I
I
I
I
I
14
12
I
1 0 1-
I I
I I
I
I
POSITION
OF RODS
GOLD
I
I
0
8
I
I
6
I
I
4
-
GOLD CADMIUM RATIOFULL I-4 LATTICE
I
U-
2 38
I
I
I
2
U 238 RATIO-FULL IT LATTICE
ee
e
e
I
0
2
4e
e
-
4
FIG. 8.6 CADMIUM
6
DISTANCE
e
I
i4
I
12
10
CENTER
FROM LATTICE
8
RATIO IN 6 RING ASSEMBLY
16
14
(INCHES)
(ASSEMBLY
J3)
18
w
ro
12
10
z
8
I.-
6
4
2
0
2
FIG. 8.7
14
12
10
8
6
4
DISTANCE FROM LATTICE CENTER (INCHES)
GOLD
FOIL
ACTIVITIES
16
18
IN 6 RING ASSEMBLY (ASSEMBLY .)
1-
134
The 0.25-inch-diameter, 0.005-inch-
have been previously reported. (3)
thick, depleted uranium foils were irradiated within the fuel elements
at 24 inches from the bottom of the fuel at various radial positions in
assembly IV.
The techniques used for the measurements are described
by D'Ardenne in a previous report.
(3)
Results for two measurements in
each position are shown in Fig. 8.6.
The central position value agrees
with that of the full 1-1/4-inch lattice.
IV.
6
28
Measurements
The ratio of fissions in U
238
to fissions in U
235
,
it 28 "
6 , which is
an indicator of variation of fast flux in an assembly, has been measured
in assembly III as a function of radial position and in the central
position of other assemblies.
The data are being reduced at the present
time.
V.
Axial Buckling
Axial traverses with 1/8-inch-diameter, 0.010-inch-thick, gold
foils were made in assemblies II, III, and IV at various radial positions.
The foils were placed in aluminum holders within a fuel rod with 2-inch
lengths of fuel slugs separating the foils.
In assembly II, axial traverses were made in the central position
and in positions in rings 3 and 7.
(Ring 3 was the last ring of the test
region and ring 7 was the mid-point of the outer reference region.)
The
ratios of the foil activities in the center traverse to each of the offcenter traverses are shown in Fig. 8.8.
for the other assemblies.
Similar results were obtained
It appears that the axial relaxation length
may be considered constant over the radius of the assembly.
In the
case of the outermost traverse, only a small section exhibited an exponential decrease due to the large leakage effect close to the edge of the
core.
Within this exponential region (between foil positions 2 and 8),
the slope agreed with the center traverse.
With the exception of the outermost traverses, the results of the
axial measurements were analyzed with a computer code described in
other reports.
Table 8.2.
-
The average axial relaxation lengths are given in
The uncertainties in these values is of the order of
± 25 X 10 6 cm-2
135
1.04
1.02
I.00(
Cl)
0.98
1
w
1.04
12 13
10 I
9
8
7
6
4
5
3
FOIL POSITION FROM BOTTOM OF TRAVERSE
2
I
I
I
I
0
0
14
15
I
IIL0
0
1.02 1-
0
0
0
0
0
I.00I-
0
0
0
0.98
0
CENTER
0.96 k-
7
0
th RING
0.94
0.92
0
I
I
1
2
I
I
I
5
6
4
3
FOIL POSITION
FIG. 8.8
I
I
I
I
I
I
I
12 13
9
10 11
8
7
FROM BOTTOM OF TRAVERSE
I 0
14
15
RATIO OF AXIAL FOIL ACTIVITES IN 3 RING ASSEMBLYASSEMBLY 11 (FIRST FOIL POSITION 32cm. ABOVE
BOTTOM OF FUEL)
136
TABLE 8.2
Axial Relaxation Lengths in Two-Region Assemblies
VI.
Assembly Designation
Axial Relaxation Length
(cm- 2 X 106)
II
1183
III
1259
IV
1285
Discussion of Results
The cadmium ratio traverses of the several assemblies indicate
that, although complete equilibrium is not reached, the approach to the
full lattice values is sufficiently close to require only small corrections.
Calculations based on two or more neutron energy groups are now being
made to predict the necessary correction factors.
Additional axial traverses will be made as a function of radius to
better determine the constancy of the axial relaxation length in the
assemblies.
This constancy may be considered an indication of equi-
librium in the axial direction where the assembly behaves as infinitely
long.
Determination of the material buckling of the test region would
then be greatly simplified.
137
OSCILLATING NEUTRON SOURCE EXPERIMENT
9.
E. Sefchovich
Introduction
The theoretical basis of the oscillating-neutron-source experiment is briefly reviewed and the results of experimental work done up
to now are presented.
I.
Theory
Assume a time-varying neutron source of the form:
S = S
(9.1)
+ ReSI eiwt
where Re indicates the real part of the time-dependent portion of the
source.
Let this source impinge on one of the plane faces of a cylinder
of extrapolated dimensions R and H.
Then, under the assumptions of
absence of delayed neutrons and validity of age diffusion theory, it can
be shown(2) that the flux at every point in the assembly can be repre-
sented by:
z i(wt-z),
C e kz+ReC e 7-rl
<(r,z,t) = J (2.405 r
(9.2)
when it is assumed that boundary effects and higher harmonics can be
neglected.
In Eq. 9.2, the relations are:
k2 _
2.405 2 -
(9.3)
2
2 + k2 1/2
(2k2
2= - k 2 )1/2 ,(9.5)
where
2.-1/2
$2= [k4 +
]
,
(9.6)
w/27r is the frequency of the source, vD is the thermal neutron diffusion
coefficient, and B2 is the prompt material buckling.
138
Thus, the time-dependent part of the neutron flux will propagate
as an attenuated wave with an inverse relaxation length -0. The imaginary exponential can be written as iw(t-T), where T is the time for the
neutron wave to travel from the neutron source to a point Z and is
given by:
(9.7)
T = wz
From Eqs. 9.4 and 9.5, we obtain the relations:
(9.8)
,
vD =
and
B2 =2.405 2 + (2
2
(9.9)
It appears from Eqs. 9.8 and 9.9 that a measurement of ( and rl
and a knowledge of the source frequency, w/27r, could lead to the
determination of vD and B 2
can be determined by measuring the phase
From Eq. 9.7,
difference, AO=wAT, between two points as follows:
A=
AZ-
AT
AZ'
(9.10)
rj can be obtained by determining the relaxation length of the timedependent component of the total flux as can be seen from Eq. 9.2.
II. Experimental Setup
To test the feasibility of the method, it was decided first to perform the experiments on assemblies of pure, ordinary water and heavy
water and then on actual miniature lattices.
For pure moderator assemblies,
B2
(9.11)
1
L
where L is the thermal diffusion length, and for the miniature lattices
the material buckling is:
2
B=
kc exp(-B
2
2 -r)-1
(9.12)
139
The experiments performed so far have been done by using the
6-inch beam hole of the Medical Therapy Facility at the M.I.T. Reactor.
Figure 9.1 shows this facility and its location with respect to the M.I.T.
Reactor and the Heavy Water Lattice Experiment.
The experimental setup includes the modulating assembly, necessary to produce a sinusoidal neutron source, and the instrumentation
required for the experiment.
A.
Modulating Assembly
The source modulator was built by Laurence E. Demick of the
Physics Department at M.I.T. as part of his B.S. thesis.
The device
consists of a rotating aluminum cylinder, three inches long, in which
one-quarter of the circumferential area is covered with cadmium.
cross-sectional view is shown in Fig. 9.2.
A
As the cylinder rotates, for
each cycle of the cylinder the neutron source changes through two
cycles.
A Westinghouse "Magnaflow," 2-hp, 440-VAC, 3-cycle electric
motor is provided to drive the source modulator.
nal speed of the motor is 3400 rpm.
The maximum nomi-
The driving system is composed
of a 2:1 speed-up ratio of timing belts and pulleys, so that a maximum
rotation frequency of 6800 rpm is
attainable.
Since each rotation of the
cylinder develops two cycles, the maximum modulation frequency is
13,600 rpm or 226 cps.
In practice, the maximum frequency is
about
190 cps.
The position of the port in the ceiling of the Medical Therapy
Room presents special problems in driving the modulator.
The
structure must be rigid and strong enough to support the weight of the
160-lb motor as well as withstand any vibration which may result
during the experiment.
The assembly is actually composed of two
parts, which are designated as superstructure and modulation assembly.
The superstructure, Fig. 9.3, is the support for the motor,
moderator or miniature lattice, and the modulation assembly.
As this
structure is not in the direct path of the beam, it was built from
structural steel angles and channels for rigidity and strength.
Once in
the Medical Therapy Room, the structure is placed in experimental
position with wood timbers and braced to the ceiling to prevent as much
vibration and shifting as possible.
140
THERMALCOWMN
DOOR
LATTICE
MEDICALTHERAPY ROOM
Fig.e 9.*1 Cut-Away View of the MIT Research Reactor
141
0.020" CADMIUM
BOLTS
SHAFT
2.828"
2o = R(sin wt+coswt)
0
= /
1
2a
I+-- 2a --
Rsin(wtt
+I
S f
SI
So
l
n ,
"r/4
r/2 3r/4
n
r
57r/4 37/2 77/4
2r
FIG. 9.2 CROSS SECTIONAL VIEW OF NEUTRON SOURCE
MODULATOR
y)
142
MODULATION ASSEMBLY
MODERATOR OR
MINIATURE LATTICE
SUPPORT
I
FIG. 9.3 MAIN STRUCTURE
143
Figure 9.4 shows the modulation assembly.
Its main function is
to provide support for the bearings and shaft driving the cylinder and
for the borated plastic shield used to limit the source size.
All parts
of the modulation assembly which are in the path of the beam are constructed of 1100 aluminum and cadmium.
The borated plastic box is
separately removable. The entire assembly is
a unit in itself and is
bolted to the main superstructure.
B.
Instrumentation
The electronic equipment designed to carry out the experiment
is
shown in Fig. 9.5.
Some of the instruments were obtained com-
mercially, while others were built locally.
The TMC multichannel analyzer is used to record the time variation of the flux.
Each pulse from the neutron detector is
and fed into the proper channel of the analyzer.
amplified
The time width of a
channel can be set to any one required from 0.25 to 64
Lsec.
Thus,
each channel represents a point in the time variation of the flux
intensity, and a plot of the number of counts per channel vs. channel
number will then determine the variation of the flux intensity with time.
The phase shift and intensity attenuation of the sinusoidal beam can
then be obtained by comparing these plots for different frequencies of
modulation and detector position.
The multichannel analyzer is triggered by pulses from the photomultiplier.
The light cone of the microscope lamp impinges on the
photomultiplier tube.
The shadow produced by a 5-inch screw attached
to the large driving pulley, when it passes through this light beam,
gives the desired timing pulse.
The rotation velocity of the motor can, therefore, be obtained by
measuring the number of pulses coming from the photomultiplier per
unit time.
This procedure was used to calibrate the variac which con-
trols the motor.
C.
Experimental Assembly
The experimentation so far has involved the use of ordinary water.
An aluminum tank, 36 inches high and 11.5 inches in inside diameter, is
being used to contain the moderator.
A 25-inch-high tube, 0.5-inch I.D.,
144
ALUMINUM
ANGLES
MAIN
/
STRUCTURE
I
I
BORATED PLASTIC
COVERING OVER
ALUMINUM BOX
FIG. 9.4
THE MODULATION ASSEMBLY
BAUSCH AND LOMB
MICROSCOPE LAMP
BAIRD ATOMIC POWER
SUPPLY MOD 312A
8'
PHOTOMULTIPLIER AND
TRANSISTORIZED
PREAMPLIFIER
4
-
SURFACE
9 3 W/o
ENRICHED
U 2 3 5 NEUTRON
CONVERTER
RIDL AMPLIFIER
MOD30-19
TENNELEC-MOD 101
PREAMPLIFIER
,
LOW FREQUENCY
DISCRIMINATOR
I
TMC 256 CHANNEL ANALYSER >|-I
TIME OF FLIGHT UNIT
MODEL 211
FIG. 9.5 INSTRUMENTATION
BARRIER
SEMICONDUCTOR
DETECTOR WITH
I
TENNELEC POWER
SUPPLY-MOD 981 RM
6V DC
BATTERY
BAIRD ATOMIC AMPLIFIER
MOD 518
FOR OSCILLATING-NEUTRON-SOURCE
EXPERIMENT
I-'
Ul
146
is welded to the bottom plate and is a dry thimble used to guide the
detector.
The tank is surrounded by rings of cadmium, paraffin, borated
plastic, and paraffin, respectively, for shielding purposes and to avoid
the reflection of neutrons from the room.
A steel cart and a wooden table, which fits on the cart, were constructed to hold the whole assembly and to help transfer it from one
place to another. The picture in Fig. .9.6 shows the experimental setup
in place.
Discussion of Experiments
A series of preliminary experiments was needed prior to
measurements in a miniature lattice. These were made and are disIII.
cussed in this section.
Semiconductor Detector
Early in the planning of the experiments, it was found that surface
barrier semiconductor detectors would be very suitable because of
their small size and relatively large sensitivity. Semiconductors are,
however, plagued by two problems: their noise level may be high, and
they suffer severe radiation damage at relatively low fluxes.
The noise level problem was solved by using very thin, fully
enriched U235 foils as neutron converters. Fission products produce
A.
pulses which are very much larger than the noise, making its discrimination possible. A representative fission product spectrum obtained
with a semiconductor detector is shown in Fig. 9.7.
To assess the extent of the radiation damage problem, six surface
barrier detectors were obtained from the Radioactivity Center at M.I.T.
One of the detectors was damaged prior to being used and two others
were discarded because of their very thick window.
Two tests were then performed. One of the semiconductors was
subjected to continuous neutron irradiation. Fission spectrum
measurements were continuously taken to see if there was any effect.
The results are shown in Fig. 9.8, where the spectra of different exposures are plotted, the exposure and counting times being indicated.
Beyond nvt 10 12/cm2 a rapid decrease in pulse height is observed.
147
FIG. 9.6 EXPERIMENTAL
SETUP
IN PLACE
1600
1400
1200-
z1000 -
800-
z600-
400
200-
01
0
50
100
150
CHANNEL NUMBER
200
FIG. 9.7 FISSION SPECTRUM OBTAINED WITH SURFACE BARRIER DETECTOR
(20 MIN. COUNT)
250
c
I
1~49
III
hr, nvt = 8.4 x 1012
I hr, nvt = 6.6 x 1012
1 hr, nvt = 4.8 x 1012
I hr , nvt = 3x1012
-70/
-00
-. 00
.
.
X--.e
0
0*0
-No
1000
z
z
U
U
20 min,nvt=6x0l
20 min, nvt = 1.2 x 1012
0
U
z
0
0
100 |-
0
50
I
100
CHANNEL
I
150
200
250
NUMBER
FIG. 9.8 DECREASE IN PULSE HEIGHT AS A FUNCTION
OF NVT. CONTINUOUS IRRADIATION
150
This is most probably due to the fact that when fission products are
stopped in the semiconductor detector, they introduce impurities which
become trapping centers.
In the other test, another detector was subjected to periodic
neutron irradiations.
The detector was irradiated for 20 minutes and
then allowed to cool off for 10 minutes before being irradiated again.
In this fashion, it was found that reproducible spectra were obtained.
The test was stopped at an exposure of nvt ~3 X 10
12
/cm
2
. Thus, it
seems that when irradiated in this manner, the semiconductor
"recuperates" its characteristics.
As a result of the last test, it was decided to use semiconductor
surface barrier detectors and operate in this fashion.
B.
Calibration of Oscillator
The next step was to calibrate the motor speed control.
This
was done by taking the output from the RIDL amplifier in Fig. 9.5 into
an RIDL scaler and measuring the count rates for different variac
settings.
motor.
This resulted in a calibration curve for the speed of the
The source frequencies are obtained by recalling that for each
rotation of the motor, the neutron source goes through four cycles.
The calibration curve is shown in Fig. 9.9.
As can be seen, there is a
rather large portion of frequencies over which the variation is linear.
C.
Study of Neutron Source
To assess the adequate functioning of the source oscillator, a
study of the source was undertaken.
The neutron density distribution on the oscillating cylinder, itself,
was first measured.
This was done by irradiating 1/ 16-inch-diameter,
0.010-inch-thick, gold foils placed on an aluminum square plate,
2 inches on a side.
0.5 inch apart.
Recesses were milled on the plate to hold the foils
Upon removal of the foils, their activity was determined.
The distribution observed is shown in Fig. 9.10.
neutron density is not uniform.
As can be seen, the
The maximum deviation from uniformity
observed, however, is only about 8%.
A study was then made of the time dependence of the neutron
source.
Measurements were taken at various frequencies in the range
151
3000 r-
200
I
I
I
I
I
I
I
I
/
2250|-
x
150 X
0~
(I
xx
0
1500K- 0
[0n 1oo
0
Xx
Xx
750-
501Xx
0
0
0
I
20
40
60
80
VARIAC SETTING
100
FIG. 9.9 CALIBRATION OF MOTOR SPEED CONTROL
152
DIRECTION OF OSCILLATION
0.970
W-
0.992
0.963
m
0.5"
O.|952
918
FIG. 9.10
0.983
e
0.987
0
0.967
0
1.000
0
0.973
0
0.948
0
0.993
0
0.975
0
0.941
0.994
0
O. 966
934
RELATIVE SOURCE STRENGTH ABOUT
SOURCE MODULATOF
153
of interest, namely, between about 70 cps and 160 cps.
Typical results
at the two extremes of this range are shown in Fig. 9.11 (a) and (b).
As
can be seen, the source follows very closely a sinusoidal variation.
As a pure sinusoidal variation is highly desirable and the change
in phase is
to be obtained with good accuracy, a code was programmed
for the IBM-7094 digital computer to make a harmonic analysis of the
data.
The program calculates the coefficients of the Fourier series
which allows us to represent the data either as
f(t) = C + E (a
sin I wt + b
cos I wt)
or
f(t) = C + F p sin(U wt+)0 )
where 0
is the phase of the Ith harmonic.
The use of this code to analyze the source data showed the
presence of a prominent third harmonic, its magnitude ranging between
8% and 9% of that of the fundamental mode at practically all frequencies.
The other harmonics were found to be negligible.
154
5000
4000
z
z
0
3000
<n
2000
z
0oD
0
1000
240
210
180
150
120
90
60
30
CHANNEL NUMBER (64 MICROSECONDS PER CHANNEL)
0
FIG. 9.11(a) TIME VARIATIO N OF NEUTRON SOURCE
FREQUENCY OF 159.8 CPS
AT A
5000
-J
Li
4000H
z
z
* 0.
00
0
0
0
3000
000
0
0
0.
.00
0-
04
00
0
0.0
-
2000
0
0-.-
0
0
*.0.0
0...
0
1000
0
120
240
60
90
30
150
180
210
CHANNEL NUMBER (64 MICROSECONDS PER CHANNEL)
FIG. 9.11(b) TIME VARIATION OF NEUTRON
FREQUENCY OF 78.2 CPS
SOURCE AT A
155
MATERIAL BUCKLING AND INTRACELLULAR
THERMAL NEUTRON DISTRIBUTIONS
10.
F. Clikeman, J. Barch, A. Supple, N. Berube and B. Kelley
I.
Buckling Measurements
A standard system has been developed for the measurement of
the material buckling of lattices in the M.I.T. Lattice Facility.(',2
3
)
The following results have been obtained by using these techniques on
new lattice arrangements.
A.
Experimental Methods
Neutron flux distributions throughout the lattice assembly are
measured by activating gold foils, both bare and cadmium covered.
Special aluminum holders are used to position the gold foils in the
heavy water.
The relative activity is measured in both the axial and
radial directions in the tank.
The region of the assembly in which the
cadmium ratio is constant is used to determine the material buckling.
In this equilibrium region, the measured relative gold activities are
least-squares fitted to the functional relationship:
<0 = AJ (ar) sinh -y(H - Z)
(1)
,
where
a 2 is the radial buckling in the r direction,
2 is
the axial buckling in the Z
direction,
H is the extrapolated effective height of the assembly.
2
Then the material buckling, B,
2
2
2
Bm = a -y7
becomes:
(2)
.
The least-squares fitting process is accomplished by use of an
IBM 7094 computer.
The high computational speed allows the develop-
ment of data analysis by means of repeated computation with varying
parameters and numbers of experimental points for the input.
A useful
result of this technique can be seen in Fig. 10.1, where the effective
height (H) is varied and values of -y 2 are calculated for several cases
1360
1-3/4
1340
/
1320
1300
RUN 30 CD
COVERED FOILS
1280
(9
C-)
/
/
1260
z
zi
156
I
I
LATTICE 1.03%
1/4 U-RC DS
1240
D
m
-J
1226.5
1220
,,
x
1200
128
1180
1160
/
/
I
1140
I
1120
-
123
125
I
127
18 POINTS
16 POINTS
14 POINTS
I
129
I
131
I
133
135
EXTRAPOL ATED HEIGHT (c.m.)
FIG. 10.1
AXIAL BUCKLING VS. EXTRAPOLATED
HEIGHT
157
of fitting the axial data. It is found that the curves cross at a common
point.
This point is the correct value of the extrapolated height, and
thus the crossing point is used to determine the value of the axial
buckling.
B.
Results
2
The results of several measurements of a and y 2 for various
lattices are given in Table 10.1.
II.
Thermal Utilization Measurements
Introduction
The work reported in this section is
cussed in earlier reports
a continuation of work dis-
' 23) on the intracellular thermal neutron
distributions and the determination of the thermal utilization.
topics are treated in this section:
Three
(1) the experimental determination
of the subcadmium neutron density distribution throughout a unit cell
of slightly enriched uranium in heavy water; (2)
comparison of the
experimental distribution with the theoretical determination as given
by the modified 1D THERMOS code; and (3) the thermal utilization as
determined by the modified 1D THERMOS code.
A.
Experimental Methods
The lattices studied consisted of 1/4-inch-diameter, aluminum-
clad, uranium fuel rods on a triangular spacing in a three-feet-diameter,
exponential tank, moderated by 99.6% D 20.
the fuel was four feet.
In all cases, the height of
Two cases were studied.
The first used 1.031o
U235 fuel with a lattice spacing of 1.75 inches and the second, 1.141o
U 2 3 5 fuel with a lattice spacing of 1.25 inches.
The experimental techniques used were the same as those
reported by Simms et
.
The gold foils that were used as detectors
were 1/16 inch in diameter and either 0.0025 or 0.0043 inch thick.
The
foil holders and cadmium boxes were the same ones that were used by
Simms et al. (10)
Both bare and cadmium-covered foils were irradiated in the
lattice at the same time but in slightly different axial positions, as
shown in Fig. 10.2.
The activity of both the bare and cadmium-covered
TABLE 10.1
Measured Values of the Buckling for Slightly Enriched Uranium Rods in Heavy Water (99.6% D 2 0)
(Aluminum cladding thickness of 0.031 inches with an O. D. of 0.316 inches)
Values were measured in a 3-foot-diameter, Cd-covered exponential assembly.
Lattice
Triangular
Saig
Spacing
(Inches)
Temperature
fof 2 0
Type
off
Run
Type
of
fRn2
Detector
Run
Number
Radial
Buckling
2
a
6
cm 2 X10
Axial
Buckling
2
7Y
-2
6
cm X 10
Baerl
2
Bm
m
-2
2
cm X10 6
Values for 0.25-inch O. D., 1.027% enriched uranium rods (density of 18.898 gm/cm )
1.75
27 0 C
Axial
Radial
(H=45.2 cm)*
Radial
(H=53.8 cm)*
29
31
33
Average
15
Cd-covered Au
20
30
Average
10
Bare Au
11
Average
12
Cd-covered Au
13
Average
14
Bare Au
16
19
21
Average
17
Cd-covered Au
18
22
Average
1168
1174
1199
1183 ± 13
1191
1216
1250
1219 ± 17
Bare Au
2358
2427
2406 ±
2370
2394
2382 ±
2384
2421
2407
2413
2406 ±
2405
2421
2404
2410 ±
21
9
8
6
C.
Lattice
Triangular
Spacing
(Inches)
Temperature
of D20
Type
of
Run
Type
of
Detector
Run
Number
Radial
Buckling
am2
Axial
Buckling
cm-2 X 106
cm-2 X 106
Material
Buckling
B
m
cm-2 X 106
Values for 0.25-inch 0. D., 1.027% enriched uranium rods (density of 18.898 gm/cm 3 )
1.75
27 0 C
Radial
(H=61.4 cm)*
Bare Au
Cd-covered Au
37
39
44
46
38
42
Average
40
45
47
43
Average
Grand Average of Axial Measurements
Grand Average of Radial Measurements
2
Material Buckling a.
- 72
(H is the height above bottom of the fuel rods.)
27*C
27*C
2.50
180 C
180 C
27 0 C
27 0 C
27 0 C
60 0 C
60 0 C
18 0 C
27 0 C
60*C
Axial
Radial
Axial
Axial
Axial
Radial
Axial
Radial
Bare Au
Bare Au
Bare Au
Cd-covered Au
61
80
4
5
2397
2387
2386
2400
2424
2402
2399 ± 6
2378
2410
2416
2384
2397 ± 9
1200 ± 17
2400 ± 4
1200 ± 18
1509 ± 16
2418 ± 20
1538 ± 13
1512 ± 13
1525 ± 9
Average
Bare Au
8
Bare Au
63
Bare Au
62
Average Radial Buckling
2413
20
1570 ± 16
2418 i 20
2416 ± 12
Average value of radial buckling was used to
obtain the material buckling at each temperature:
(Note relative uncertainty for comparison of
temperature effect is smaller than the total
uncertainty quoted.)
907 ± 20
891 ± 17
846 ± 20
c-l
Lattice
Triangular
Spacing
(Inches)
Temperature
ofD O
2
o
Type
of
Run
Type
of
Detector
Run
Number
Radial
Buckling
2
-2
cm X10 6
Axial
Buckling
2
cm
Values for 0.25-inch O. D., 1.143% enriched uranium rods (density of 18.92 gm/cm
1.25
27 0C
Axial
Bare Au
Axial
Cd-covered Au
Radial
Bare Au
Radial
Cd-covered Au
75
67
72
81
Average
79
66
74
Average
64
82
83
73
77
84
Average
65A
65B
80A
80B
71A
71B
76A
76B
Average
2
X10 6
3)
969
929
916
987
943 ± 13
943
967
962
956 ± 7
2368
2402
2438
2430
2380
2392
2398 ± 10
2367
2402
2366
2422
2396
2362
2393
2358
2385 ± 8
Material
Buckling
B2
m
cm 2 X10 6
Lattice
Triangular
Spacing
(Inches)
Temperature
ofof
of D20
Type
Run
Type
of
Detector
Run
Number
Radial
Buckling
2
-2
cm-2 X 106
Material
Buckling
B2
m
cm- 2 X 106
Axial
Buckling
2
cm-2 X 10 6
Values for 0.25-inch O.D., 1.143% enriched uranium rods (density of 18.92 gm/cm 3 )
1.25
60 0 C
270C
27*C
27*C
Axial
Bare Au
85
86
Average
996
953
975 ± 15
Grand Average of Axial Measurements
Grand Average of Radial Measurements
1417 ± 17
948 ± 8
2392 ± 6
Material Buckling (a2
2)
1444 ± 10
0.
0
159
CENTER
ROD
.
HOLDER
FOR THE
BARE
FOILS
CADMIUM
SLEEVE
HOLDER
FOR THE
CADMIUM
COVERED
FOILS
Fig. 10.2
Foil Holder Arrangement for Microscopic
Flux Measurements
160
foils was counted on automatic sample changing scintillation counters
H98
g
Hg198*
set to count the 0.411-Mev gamma ray in the Au 1 9 8 decay. The measured activity was corrected for background, counter
deadtime, and the 2.7-day half life of the Au 1 9 8 activity.
The foil activity was also corrected for the different axial
positions of the foils by using the equation,
(.
= sinh -y(H' -Z.)
,
where Z. is the height of the foil position above the bottom of the fuel.
H' and y are the extrapolated height and the axial component of the
buckling, respectively, and were measured in a separate experiment
as reported in section A, page 155.
After all of the corrections have been applied to the activities,
the activities of the cadmium-covered foils are plotted as a function of
radial position from the center of one fuel rod. A smooth curve is
then drawn through the points by eye and the epicadmium activity is
determined at each point. The epicadmium activities are then subtracted from the bare foil activities to yield the subcadmium or
thermal activities. The thermal activities are then also plotted as a
function of radial position.
In all cases, two rod-to-rod and one rod-to-moderator foil
holders were used. In the moderator, no statistically significant
difference in the activity could be observed between the gold foils
irradiated in corresponding positions relative to the fuel rods. Therefore, in order to get better counting statistics, the activity of all of the
foils irradiated in the same relative position in the cell were averaged
together. It is this average that is plotted in Figs. 10.1 and 10.2. The
error due to the counting statistics is about the size of the points.
B. Theoretical Calculations
The one-dimensional computer code THERM(S, as modified by
Simms et al., was used to compute the neutron flux distribution in a
unit cell consisting of five regions: the fuel; a small air gap between
the fuel and cladding; the cladding; the moderator; and a scattering
region at the cell boundary. The computer code then used the computed
flux distribution and the Au 1 9 7 activation cross section to compute the
161
relative activity of Au198 for gold placed in the cell.
The cross sections
used were modified to take into account any self-shielding caused by
using a finite thickness of gold. As a result, a number of curves of the
Au
1 98
activity were computed using the thickness of the gold as a
parameter.
THERMOS also computes the total absorption of neutrons in the
cell for a number of different integrated energies.
By using the energy
range from 0.0 to 0.415 ev (the cadmium cut-off energy), the ratio of
the number of neutrons absorbed in the fuel to the total number absorbed
in the cell was determined and this value is reported as f, the thermal
utilization.
C.
Results
Both the experimental and theoretical subcadmium gold activities
are shown in Figs. 10.3 and 10.4 for the two lattices studied.
As shown
in the figures, the agreement between the computed curves and experimental points is good.
This leads one to believe that the modified ID
THERMOS code is a reasonably accurate description of the lattice cells
and that the values of the thermal utilization that it computes are accu-
The results of THERMOS are given in Table 10.2.
rate.
It might be
noted that the sum of the absorptions does not equal 1.0000.
This is
because the code was programmed to consider absorption up to 0.785 ev,
and the results given here are only for neutron energies up to 0.415 ev.
TABLE 10.2
Relative Absorption Rates Computed by Using THERMOS
1.14% U 235, 1-1/4'' Spacing
1.03% U235 , 1-3/4'' Spacing
Total Absorption
Region
Total Absorption
Volume
in Region
Volume
in Region
Fuel
0.3177
.96620
0.3177
.96233
Air Gap
0.0307
.00002
0.0307
.00002
Cladding
0.1644
.01569
0.1644
.01660
Moderator
8.2069
.00718
f
0.9769
±0.0010
16.572
0.9677
.01550
±0.0010
162
The error given for f is the same as that given by Brown et al. and comes primarily from uncertainties in the cross sections of aluminum and D 20. The quoted error has no relationship to the degree of fit
between the theoretical THERM(S calculation and the experimental
points or to the uncertainties in the experimental points.
19
163
18
17
16
I-
5 15
H
0
14
H
-j
U
-
5
4
3
0
0.5
1.0
1.5
2.0
2.5
3.0
RADIUS (cm)
FIG. 10.3
MICROSCOPIC GOLD ACTIVITY DISTRIBUTION IN
LATTICE OF 1/4-INCH DIAMETER 1.14% U2 35
URANIUM RODS ON A 1.75-INCH TRIANGULAR PITCH.
164
15
14
13
12
F-
5;
0
I
uJ
-J
Lu
6
5
4
3
0
0.5
1.0
1.5
2.0
2.5
RADIUS (c.m.)
FIG. 104
MICROSCOPIC GOLD ACTIVITY DISTRIBUTION IN
LATTICE OF 1/4-INCH DIAMETER 1.143% U2 3 5
URANIUM RODS ON A 1.25-INCH TRIANGULAR PITCH.
165
APPENDIX A
References
1.
Heavy Water Lattice Research Project Annual Report, NYO-9658,
September 30, 1961.
2.
3.
Heavy Water Lattice Research Project Annual Report, NYO-10,208
(MITNE-26), September 30, 1962.
Heavy Water Lattice Research Project Annual Report, NYO-10,212
(MITNE-46), September 30, 1963.
4.
Madell, J. T., T. J. Thompson, A. E. Profio and I. Kaplan, "Spatial
Distribution of Neutron Flux on the Surface of a Graphite-Lined
Cavity," NYO-9657 (MITNE-18), April 1962.
5.
Weitzberg, A., 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 1962.
6.
Palmedo, P. F., 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 1962.
7.
8.
Wolberg, J. R., 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 1962.
Peak, J., 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 1962.
9.
Brown, P. S., T. J. Thompson, I. Kaplan and A. E. Profio,
"Measurements of the Spatial and Energy Distributions of Thermal
Neutrons in Uranium Heavy Water Lattices," NYO-10,205
(MITNE-17), August 1962.
10.
Simms, R., 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.
11.
Malaviya, B. K., I. Kaplan, D. D. Lanning, A. E. Profio and
T. J. Thompson, "Studies of Reactivity and Related Parameters
in Slightly Enriched Uranium, Heavy Water Lattices," MIT-2344-1
(MITNE-49), May 1964.
12.
D'Ardenne, W. H., T. J. Thompson, D. D. Lanning and I. Kaplan,
"Studies of Epithermal Neutrons in Uranium, Heavy Water
Lattices," MIT-2344-2 (MITNE-53), in press.
13.
Hansen, K. F., "Multigroup Diffusion Methods," NYO-10,206
(MITNE-19), April 1962.
14.
Kaplan, I.,
"Measurements of Reactor Parameters in Subcritical
and Critical Assemblies: A Review," NYO-10,207 (MITNE-25)
August 1962.
166
15.
Kaplan, I., D. D. Lanning, A. E. Profio and T. J. Thompson,
"Summary Report on Heavy Water, Natural Uranium Lattice
Research," NYO-10,209 (MITNE-35), July 1963. (Presented at
the IAEA Symposium on Exponential and Critical Experiments,
Amsterdam, September 2-6, 1963.)
16.
Wolberg, J. R., T. J. Thompson and I. Kaplan, "Measurement of
the Ratio of Fissions in U 2 38 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), 1963. (Presented at the IAEA Symposium on
Exponential and Critical Experiments, Amsterdam, September 2-6,
1963.)
17.
Madell, J. T., T. J. Thompson, A. E. Profio and I. Kaplan, "Flux
Distributions in the Hohlraum Assembly," Trans. Am. Nucl. Soc.,
3, 420 (December 1960).
18.
Weitzberg, A., and T. J. Thompson, "Coincidence Technique for
U 2 3 8 Activation Measurements," Trans. Am. Nucl. Soc., 3, 456
(December 1960).
19.
Madell, J. T., T. J. Thompson, I. Kaplan and A. E. Profio,
"Calculation of the Flux Distribution in a Cavity Assembly,"
Trans. Am. Nucl. Soc., 5, 85 (June 1962).
20.
Weitzberg, A., J. R. Wolberg,
. Thompson, A. E. Profio and
I. Kaplan, Measurements of U
Capture and Fast Fission in
Natural Uranium, Heavy Water Lattices," Trans. Am. Nucl. Soc.,
5, 86 (June 1962).
21.
Brown, P. S., 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.
Am. Nucl. Soc., 5, 87 (June 1962).
22.
Malaviya, B. K. and A. E. Profio, "Measurements of the Diffusion
Parameters of Heavy Water by the Pulsed-Neutron Technique,"
Trans. Am. Nucl. Soc., 6, 58 (June 1963).
23.
Malaviya, B. K., T. J. Thompson and I. Kaplan, "Measurement of
the Linear Extrapolation Distance of Black Cylinders in Exponen-
tial Experiments," Trans. Am. Nucl. Soc., 6, 240 (November 1963).
24.
Brown, P. S., 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," BNL-719,
Vol. 2, 305-17, 1962.
25.
Simms, R., I. Kaplan, T. J. Thompson and D. D. Lanning, "The
Failure of the Cell Cylindricalization Approximation in Closely
Packed Uranium, Heavy Water Lattices,
Trans. Am. Nucl. Soc.,
7, 9 (June 1964).
26.
Malaviya, B. K., I. Kaplan, D. D. Lanning and T. J. Thompson,
''Measurement of Lattice Parameters by Means of the Pulsed
Neutron Technique." (Paper presented at the Winter A.N.S.
Meeting, November 30-December 3, 1964 at San Francisco.)
27.
Morse, P. M. and H. Feshbach, Methods of Theoretical Physics,
Part I, McGraw-Hill Book Company, Inc., New York (1953).
167
28.
Kash and Woods, "Transport Mean Free Path in D 2 0 by a Boron
Poisoning Method," Phys. Rev., 90, 564 (1953).
29.
Kouts, H., G. Price, K. Downes, R. Sher and V. Walsh, "Exponential Experiments with Slightly Enriched Uranium Rods in Ordinary
Water, Proc. Inter. Conf. on the Peaceful Uses of Atomic Energy,
Geneva, Vol. 5, P/600 (1955).
30.
Duggal, V. P. and J. Martelly, "A Study of the Slowing Down of
Neutrons in Graphite," Proc. Int. Conf. on the Peaceful Uses of
Atomic Energy, Geneva, Vol. 5, P/358 (1955).
31.
Kouts, H. and R. Sher, "Experimental Studies of Slightly Enriched
Uranium, Water Moderated Lattices (Part I)',' BNL-486 (T-111),
September 1957.
32.
Weinberg, A. M. and E. P. Wigner, The Physical Theory of Neutron
Chain Reactors, The University of Chicago Press, Chicago (1958).
33.
Hendrie, J. M., J. P. Phelps, G. A. Price and E. V. Weinstock,
"Slowing Down and Diffusion Lengths of Neutrons in GraphiteBismuth Systems," Proc. Int. Conf. on the Peaceful Uses of
Atomic Energy, Geneva, P/601 (1958).
34.
Donahue, D. J., D. D. Lanning, R. A. Bennett and R. E. Heineman,
"Determination of k from Critical Experiments with the PCTR,"
Nuclear Sci. and Eng., 4, 297 (1958).
35.
Finn, B. S., "Relationship Between Reactivity Changes, Buckling
Changes and Periods in a Heavy Water Reactor," Nuclear Sci. and
Eng., 1, 369 (1960).
36.
Clikeman, F. et al., private communication.
37.
Schmit-Olsen, H., private communication.
38.
Honeck, H. C., private communication.
39.
Honeck, H. C., "THERMOS, a Thermalization Transport Theory
Code for Reactor Lattice Calculations," BNL-5826 (1961).
40.
Engelder, T. C. et al., "Spectral Shift Control Reactor - Basic
Physics Program - Critical Experiments on Lattices Moderated
by D 2 0-H
20
Mixtures," BAW-1231 (December 1961).
41.
Carver, J. G. and W. R. Morgan, "Selection of a Set of Radioactivants for Investigating Slow Neutron Spectra," Proc. of 1961
Int. Conf. on Modern Trends in Activation Analysis, College
Station, Texas.(December 15-16, 1961).
42.
Hellens, R. L. and H. C. Honeck, "A Summary and Preliminary
Analysis of the BNL Slightly Enriched Uranium, Water Moderated
Lattice Measurements,
Proc. of the IAEA Conf. on Light Water
Lattices, Vienna (June 1962).
43.
Arcipiani, B., D. Ricabarra and G. H. Ricabarra, "A Note on the
Measurement of the U 2 3 8 Cadmium Ratio," Nuclear Sci. and Eng.,
14, 316 (1962).
44.
Hellens, R. L. and G. A. Price, Unpublished Brookhaven National
Laboratory Report.
168
45.
Lanning, D. D., "Determination of k,
from Measurements on a
Small Test Sample in a Critical Assembly, Ph.D. Thesis,
Nuclear Engineering Department, M.I.T. (May 1963).
46.
Kim, H., "Measurement of Material Buckling of a Lattice of
Enriched Uranium Rods in Heavy Water," M.S. Thesis, Nuclear
Engineering Department, M.I.T. (June 1963).
47.
Price, G. A. and R. L. Hellens, "Lattice Studies in Light Water
Moderated Systems," BNL-Memo (1963).
48.
Tribilach, R. J., "Fast Flux Measurements in Zero Energy
Reactors," Neutron Dosimetry, p. 565, IAEA, Vienna (1963).
49.
Bardes, R. G., J. R. Brown, M. K. Drake, P. U. Fischer,
D. C. Pound, J. B. Sampson and H. B. Stewart, "HighTemperature, Gas-Cooled Reactor Critical Experiment and
Its Application," GA-4496 (August 1963).
50.
Garelis, E. and J. L. Russel, Jr., "Theory of Pulsed Neutron
Source Measurements," Nuclear Sci. and Eng., 16, 263 (1963).
51.
Harrington, J., "Measurement of the Material Buckling of a
Lattice of Slightly Enriched Uranium Rods in Heavy Water,"i
S.M. Thesis, Nuclear Engineering Department, M.I.T.
(September 1963).
52.
Engelder, T. C. et al., "Spectral Shift Control Reactor Basic
Physics Program "~TAW-1283 (November 1963).
53.
Roy, J. C. et al., "Measurement of Fission Neutron Fluxes and
Spectra with Threshold Detectors," AECL-1994 (May 1964).
54.
Malaviya, B. K., "Studies of Reactivity and Related Parameters
in Subcritical Lattices," Ph.D. Thesis, Physics Department,
Harvard University (May 1964).
55.
Suich, J. E., "Calculation of Nautron Absorption Ratios in D 20Moderated Mixed Lattices," Trans. Am. Nucl. Soc., 7, 32
(June 1964).
56.
Bliss, H., "Measurement of the Fast Fission Effect in Heavy
Water Partially Enriched Uranium Lattices," M.S. Thesis,
Nuclear Engineering Department, M.I.T. (June 1964).
57.
Tassan, S., "Fast Fission Factors in Slightly Enriched Uranium,
Light Water Moderated Slab Lattices," Nuclear Sci. and Eng., 19,
471 (1964).