SOVIET ATOMIC ENERGY VOLUME 15, NO. 5

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• Document Creation Date: December 23, 2016
• Document Release Date: February 25, 2013
• Sequence Number: 3
• Publication Date: November 1, 1963
• Content Type: REPORT

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Volume 15, No. 5
November, 1963
SOVIET.
ATOMIC
ENERGY
ATOMHAA 3HEPrwR
(ATOMNAYA ENERGIYA)
'TRANSLATED FROM, RUSSIAN
CONSULTANTS; BY REAU
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MECHANICAL TWINNING Of CRYSTALS
by M.V. Klassen-Neklyudova
In addition to studies of reorientation in response to mechanical
stress, this comprehensive new work includes many effects related
to mechanical twinning such as formation of reoriented regions in
response to high temperatures, and to electric and 'magnetic fields.
Discussions include experimental evidence on 'twinning with and
without change of shape, lattice reconstruction in martensite type
transformations, formation of twins by recrystallization, formation
of reoriented regions in inhomogeneous deformation, and the
macroscopic and microscopic theories of twinning.
228 pages
EFFECTS OF ULTRASOUND
ON THE. KINETICS OF CRYSTALLIZATION
by A.P. Kapustin
The'first detailed survey of the more important experimental as-
pects of crystallization and dissolution -ins ultrasonic fields: Topics
covered embrace all aspects of the effects of various frequencies
and strengths of ultrasound bn crystallization, emphasis being on
experiments and methods that provide an understanding of the
mechanisms involved. Primary topics are: Methods and Apparatus
for Studying Crystallization and Dissolution in'Ultrasonic Fields;
A Brief Review of Work on the Interaction of Ultrasonics with
Crystallizing or Dissolving Material; Crystallization Processes in
.Organic Compounds; Effects of Various Agents on Nucleation in
an Ultrasonic Field; The Growth and Dissolution of Monocrystals.
65 pages A Special Research Report $12.50
CRYSTAL CHEMISTRY 'OF LARGE-CATION SILICATES
by N.V. Belov, et. al.
An expansion of the basic lectures which Academician Belov de-
livered in the United States - updated for the English edition' A
lucid presentation by one of the world's greatest crystallographers
of the systematics of silicates with Na, K, Ca, and other large
cations-The Second "Chapter" of the crystal chemistry of sili=cates. Papers exclusively by Belov are: V.I. Vernadskii and Silicate
Crystal' Chemistry; The Second "Chapter" of Silicate Crystal
Chemistry; Isomorphism Relations, between Zirconium an&Titan-.
ium; Oxygen-Silicon Chains and Ribbons in the Second "Chapter"
of the Crystal Chemistry'of Silicates; The Crystal Structure of
Rhodonite MnS.03 Oxygen-Silicon Networks Based on, Wollan-
stonite Chains and Xonotlite; and Molecular Sieves.'The basic text
is appended with 16 pertinent papers by Prof. Belov and his col-
leagues, reprinted from'the cover-to-cover translation journals.
168 pages $12.50
CONTENTS UPON REQUEST
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ATOMNAYA ENERGIYA
EDITORIAL BOARD
A. I. Alikhanov
A. A. Bochvar
N. A. Dollezhal'
K. E. Erglis
V. S. Fursov
I. N. Golovin
V. F. Kalinin
N. A. Kolokol'tsov
(Assistant Editor)
A. K. Krasin
I. F. Kvartskhava
A. V. Lebedinskii
A. I. Leipdnskii
M. G. Meshcheryakov
M. D. Millionshchikov
(Editor-inz-Chief)
I. I. Novikov
V. B. Shevchenko
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
M. V. Yakutovich
A. P. Zefirov
Vol. 15, No. 5
SOVIET ATOMIC
ENER,GY
A translation of ATOMNAYA ENERGIYA
A publication of the Academy of Sciences of the USSR
01964 CONSULTANTS BUREAU ENTERPRISES, INC.
227 West 17th Street, New York 11, N. Y.
CONTENTS
November, 1963
P A G E
ENG. I RUSS.
The Effect of a Strong Magnetic Field on the Magnetohydrodynamic Stability of Plasma
and the Containment of Charged Particles in the "Tokamak"-E. P. Gorbunov
and K. A. Razumova ............................................ ; . 1105
Methods for the Calculation of the Radiational Thermal Output in the Body and Shielding
of a Nuclear Reactor-D. L. Broder and K. K. Popkov ........................ 1113
Measurement of the Thermal Neutron Density Distribution Along the Radius of Sleeve-Shaped-
Fuel Elements-V. F. Belkin, B. P. Kochurov, and O. V. Shvedov.................. 1121
Calculation of y-Ray Energy Absorption in Heterogeneous Macro-Systems-B. M. Terent'ev,
V. A. l l'tekov, and D. I. Golenko .................................... 1127
Measurement of Neutron Tissue Dose Outside Reactor Shielding-I. B. Keirim-Markus,
V. T. Korneev, V. V. Markelov, and L. N. Uspenskii .. ..................... 1132
Kinetics of the Swelling Produced in Fissionable Materials by the Separatioh of the Gaseous
Phase from a Supersaturated Solid Solution- V.?M. Agranovich, E. Ya. Mikhlin,
and L. P. Semenov ..................... .......................... 1140
Theory of the Coalescence of Gaseous Pores Under Swelling Conditions-L. 2. Semenov...... 1155
LETTERS TO THE EDITOR
The Motion of Isolated Charged Particles in a Magnetic Field with Helical Symmetry
-V. M. Balebanov, B. I. Volkov, V. B. Glasko, A. L. Groshev, V. V. Kuznetsov,
A. G. Sveshnikov, and N. N. Semashko ................................. 1162
Inelastic Scattering of 14-MeV Neutrons by Light Nuclei-E. M. Oparin, A. I. Saukov,
and R. S. Shuvalov .............................................. 1165
On the Design of a Neutron Spin Rotator-Yu. V. Taran ........................... 1168
Measurement of the U2as and Th232 Capture Cross Sections for Neutrons with Energies
of 5-200 keV-V. A. Tolstikov, L. E. Sherman, and Yu. Ya. Stavisskii ........... . . 1170
Cross Sections of the Inelastic Scattering of Neutrons with Energies of 0.4-1.2 MeV on Medium
and Light Nuclei-N. P. Glazkov ..................................... 1173
Dependence of the Mean Kinetic Energy of Fragments on the Fissionable Nucleus Mass
-V. N. Okolovich, V. I. Bol'shov, L. D. Gordeeva, and G. N. Smirenkin . . . . . . . . . . . . 1177
Energy Distribution of y-Radiation in a Material Medium-A. M. Sazonov and V. I. Sirvidas. . . 1179
Obtaining the Radioactive Isotope Be 7 from Cyclotron Targets-I. F. Kolosova and I. V. Kolosov 1182
The Solubility of Uranium Tetrafluoride in Aqueous Solutions of Acids-Yu. A. Luk'yanychev
and N. S. Nikolaev .. ........................................... 1184
Annual Subscription: $ 95
393
404
411
413
419
420
422
Single Issue: $30 Single Article: $15
All rights reserved. No article contained herein may be reproduced for any purpose what-
soever without permission of the publisher. Permission may be obtained from Consultants
Bureau Enterprises, Inc., 227 West 17th Street, New York City, United States. of America.
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CONTENTS (continued)
An Apparatus for Determining the Solubility of Radioactive Substances at Elevated Temperatures
and Pressures-V. V. Ivanenko, G. N. Kolodin, B. N. Melent'ev, and L. A. Pamfilova....
The Preparation of Certain Sulfides of Thorium by the Interaction of Th02 with Hydrogen
Sulfide-G. V. Samsonov and G. D. Dubrovskaya . . . . . . . . . . . . . . . . . . . . . . .. . ..
Estimation of the Dose of Neutron Irradiation Capable of Changing the Mechanical Properties
of Pure Metals-V. K. Adamovich ........... . ......... . .. ? . . .
Aerial Surveys of Uranium Deposits in Wooded Regions-V. I. Balabanov and A. L. Kovalevskii.
NEWS OF SCIENCE AND TECHNOLOGY
Conference on Reactions of Complex Nuclei-S. M. Polikanov ......................
Conference on Interactions of High-Energy Photons-B. B. Govorkov and A. I. Lebedev ......
The Second European "Vakuum" Symposium-E. Fischer .. ................... .
Modernization of the VVR-S Reactor ..................................... .
Brief Communications . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . ............... .
Commissioning of the World's First Reactor Power Station with an Organic-Moderator
and Organic-Coolant Reactor-Yu. Arkhangel'skii and I. Kovalev .................
P A G E
ENO. I RUSS.
1188
426
1191
428
1194
430
1197
432
1201
435
1202
436
1206
438
1209
439
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THE EFFECT OF A STRONG MAGNETIC FIELD ON THE
MAGNETOHYDRODYNAMIC STABILITY OF PLASMA
AND THE CONTAINMENT OF CHARGED PARTICLES
IN THE "TOKAMAK"
E. P. Gorbunov and K. A. Razumova
Translated from Atomnaya L`nergiya, Vol. 15, No. 5,
pp. 363-369, November, 1963
Original article submitted November 24, 1962
Results of an investigation of plasma in the toroidal apparatus TM-2 in a strong longitudinal mag-
netic field (up to 22 kOe) are described. It is shown that increasing the magnetic field sharply de-
creases the low frequency oscillations in the oscillograms of the loop voltage and discharge current
derivative, and also weakens the interaction between the plasma and the walls of the discharge
chamber.
For a large enough ratio of the longitudinal field intensity to the intensity of the current self-
field. oscillations are not observed. According to radiointerferometric measurements, the mean elec-
tron density in this case hardly alters during the course of the operations. The conductivity reaches
a value of about 1016cgs.
1. Introduction
Studies of electrodeless discharges in a strong longitudinal magnetic field, carried out on the stellarator [1-3]
and the "Tokamak"[4], have shown that in such systems the plasma becomes unstable for currents appreciably less
than the critical current of Shafranov-Kruskal. It was established by a microwave probe method that the charged
particles passed anomalously quickly from the body of the chamber to the walls.
In one of the most recent experiments carried out on the stellarator [5], it was shown that the electron den-
sity fall-off rate in the plasma was proportional to 1/H, where H is the intensity of the longitudinal magnetic field.
The inclusion of supplementary stellarator windings did not alter this rate, although it reduced the amplitude of
regular oscillations. The maximum value of the density was substantially higher for large magnetic fields. All this
led to the conclusion that current-bearing plasma in a strong longitudinal magnetic field diffuses to the walls at an
anomalously high rate from the very beginning of the process.
According to Spittser this increase in diffusion may be caused by the setting up of ionic waves.
A series of experiments on the "Tokamak" [6, 7] cast doubt on the existence of increased diffusion to the
chamber walls. An explanation of the nature of the observed oscillations and the anomalously swift movement of
particles from the current-bearing plasma stabilized by a strong longitudinal magnetic field constitutes a most im=
portant problem.
2. Experimental Arrangement
The measurements were carried out in the toroidal chamber TM -2 with a strong longitudinal magnetic field.
The electrical scheme of the set-up is given in [8]. The vacuum chamber, as usual, was made of copper with two
transverse and one longitudinal insulated joint. The inner diameter of the chamber was 25 cm and the outer 80 cm.
Inside was located a bellows liner of stainless steel capable of independent evacuation.
The discharge aperture was limited by one stainless steel diaphragm with aperture diameter 16 cm. The
center of the aperture was displaced 5 mm outwards from the chamber axis. The outer part of the diaphragm on
the side bombarded by electrons was covered by a tungsten layer 0.5 mm thick. The liner was degassed by heating
and discharges twice per minute.
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l I . I
500 WO 1500 2000 2500 t, psec
The primary winding of the transformer was connected so
that all the change in resistance of the gaseous loop showed up
in the loop voltage, while the current in the majority of cases
had a sinusoidal form. Hence we used the initial value. of the
gas current derivative as a parameter characterizing energy im-
parted to the discharge, rather than the electric field strength.
The discharge parameters could be changed within the
following limits: initial hydrogen pressure p from 5 ? 10-4 to
3 ? 10-3 mm Hg; initial current derivative iinit from 0.2 ? 107 to
8.10 7 amp/sec (electric field intensity Einit immediately after
breakdown from 0.08 to 0.25 V/cm); longitudinal magnetic field
intensity from 5 to 22 kOe.
Leakage. fields within the chamber were not specially meas-
ured. They were apparently determined by the leakage field from
the current in the liner and the field from the backward loop of
the magnetic windings. The direction of the current in the back-
ward windings was chosen so that the force acting on the plasma
loop was directed towards the center of the torus.
The current, voltage, and light intensity of hydrogen and
e impurity lines were measured; hard X-radiation with quantum
energy greater than 200 keV was recorded.* The fluctuating
magnetic field was measured with the help of four coils disposed
outside the liner at the inner surface of the copper chamber.
The method of determining the mean electron density in
the plasma in "Tokamak" systems was described in[9]. Meas-
urement was carried out in the millimeter wavelength range by
radiointerferometry in the manner proposed by Warton for the
study of plasma.
Fig. 1. Oscillograms for a typical unstable
arrangement with p = 5 ? 10-4 mm Hg; linit
= 2.6 ? 107 amp/sec (Einit = 0.15 V/cm),
longitudinal magnetic field intensity H = 11
koe: 1) mean electron density; b) probe sig-
nal measuring the derivative of the azimu-
thal magnetic field; c) loop voltage; d) dis-
charge current; e) light intensity of the spec-
tral lines of hydrogen H8(X = 4860 A), car-
bon CII (X = 4650 - 60 A), chromium CrI
(X = 4252 A); f) integrated intensity of illu-
mination in the visible part of the spectrum,
measured by photomultiplier.
density followed by a fresh rise.
loop voltage and the magnetic
gestion that the second rise in
chamber walls.
3. Description of a Characteristic Discharge
Set-Up
Figure 1 shows typical discharge oscillograms for an arrange-
ment with a fairly small magnetic field. The value of the mean
electron density was calculated on the assumption that the plas-
ma filled the whole inner aperture of the diaphragm evenly. A
discharge of this kind may be separated into two characteristic
stages in time.
After discharge in the gas, there are no strong oscillations
in the circuit voltage for 500-800 psec, although small fluctua-
tions are observed in the magnetic probe. The mean electron
density reaches a maximum value and for some time remains
almost constant, while the spectral lines H8 and CIII are ex-
cited and then extinguished.
The second stage is characterized by the appearance of
sharp oscillations in all the oscillograms, an increase in the
light intensity of the impurity lines, and a fall-off in electron
good synchronization of the separate sharp breaks in the oscillograms of the
probe with the bright flaring up of the wall material spectral lines leads to the sug-
the electron density is linked with interaction between the plasma and the discharge
The hard X-radiation was measured by V. V. Matveev, A. D. Sokolov, and L. A. Suchkov.
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U loop
5 0 0 1000 t, ? s ec
Fig. 2. Correlation between oscilla-
tions in electron density, magnetic
probe, x-ray intensity, and loop volt-
age (p = 0.9.10-3 mm Hg; Iinit = 1.8
? 107 amp/sec (Einit = 0.1 V/cm); H
= 11 koe).
After some thousands of discharges the side of the diaphragm far-
ther from the axis of the torus appeared considerably fused, and in places
scorched with uniform indentations. The results of measuring the space
distribution of x-ray intensity leads to the conclusion that the outer edge
of the diaphram is the chief source of the radiation. In the oscillogram
the change in x-ray intensity during the process takes the form of surges
synchronized with the oscillations on the probes (Fig. 2), breaking out
before the appearance of the strong vibrations in the circuit voltage.
The larger the magnetic field, the longer the x-rays continue and the
greater is their intensity. The same is observed on lowering the longi-
tudinal electric field. On increasing the hydrogen pressure or adding
a certain percentage of other gases (helium or argon) to the hydrogen
the x-ray output rises appreciably. Thus the x-ray intensity appears
greater under those conditions for which the oscillations have lower
amplitudes and appear later.
With increasing longitudinal magnetic field (Fig. 3) the oscilla-
tions and the second maximum in the mean electron density appear
later. For an initial current derivative Iinit = 1.8 ? 107 amp/sec and
longitudinal magnetic field H ? 16 kOe oscillations in the loop voltage
are not seen at all. The hard X radiation is observed in these condi-
tions up to the end of the current, and the mean electron density hardly
changes during the whole operation. In this case the integrated light
intensity in the visible region, after an initial surge at the beginning of
the discharge,fell considerably towards the end. This is apparently
linked with a reduction in the interaction between the plasma pinch
and the chamber walls.
The absolute magnitude of the mean electron density on the flat
part of the curve differs from the maximum possible magnitude (ionic
contribution drawn from regions near the walls in the "shade" of the diaphragm included) by three-five times. This
discrepancy can be completely explained as being due to neutral-hydrogen atoms leaving in the process of dissocia-
tion and ionization at the wall.
There remains the uncertain question of what determines the fall in electron density which coincides in time
with the growth of oscillations in the magnetic probes.
The microwave interferometer measures the phase shift of electromagnetic waves passing through the plasma.
This shift appears in time form on the oscillogram. It depends not only on the electron density ne but also on the
length of the beam path in the plasma. The following explanations of the observed radiointerferometer results are
thus possible:
1) A significant reduction of the phase shift in the discharge process may be caused by a change in the concen-
tration of charged particles in a constant plasma-occupied volume. For this the life-time of the charged particles
seems to be several orders less than the classical. Noting a similar phenomenon in stellarator-type systems, the
authors of [1, 2, 5] came to the conclusion that for ohmic heating in electrodeless systems with strong magnetic fields
there was an anomalously swift diffusion of plasma across the magnetic field.
For a magnetic field of 22 kOethe electron density falls slowly during the course of the discharge. If we sup-
pose that the electron density curve forms part of an exponential, the life-time r of the electrons is 3-4 msec for
this case. It is interesting to compare this value of r with those corresponding to the Bohm diffusion coefficient
(D ~ 0.6. 106 Te/H, cm2/sec) and the diffusion coefficient obtained in stellarator experiments (D ~ 2. 104 Te/H
cm2/sec) [5]. In these empirical formulas TP_ is expressed, in electron volts and H in kilo-oersteds. For the first case
the quantity r = (1/ d)(a/ 2.4)2 in the TM-2 should be about 1 msec and for the second 0.3-0.4 msec (in these calcula-
tions the electron temperature is taken as 50 eV and the radius of the plasma pinch a = 8 cm).
As shown in [5], in stellaratorV-3 the maximum value of the mean electron density depends substantially on
the longitudinal magnetic field strength. From this fact we may conclude that the anomalously rapid passing out of
JA
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ne ,CrT3
44- +0,3
(2
Uloop
0 1 2 0 1 3 I 2 3 t, ?sec
Fig. 3. Oscillograms of electron density, hard x-ray intensity, spectral line in-
tensity of hydrogen H6 (X = 4860 A) and chromium CrI (X = 4254 A), loop volt-
age and gas current( in kA) for three arrangements with different longitudinal
magnetic field intensities (p = 0.9. 10-3 mm Hg; unit = 1.8 ? 107 amp/sec; Einit
= 0.1 V/cm).
Fig. 4. Example of a voltage oscillogram with
regular oscillations in the form of short-term
negative throws (above: oscillogram of current
discharge) for initial hydrogen pressure (with
small additions of argon - about 3(7) p = 1.4
10-3 mm Hg; li.nit = 2.6 ? 107 amp/sec (Emit
= 0.15 V/cm); H = 15 koe.
x ~)
1
? x
?
1X10"3 2S1r'3p, mm Hg
Fig. 5. Mean conductivity a at the moment of
maximum current as a function of initial hydrogen
pressure: 1) no voltage oscillations throughout the
process, Iinit = 1.8. 107 amp/sec (Einit = 0.1 V
V/cm), H = 16 koe; 2) clearly unstable arrange-
ment: Iinit = 2.6 ? 107 amp/sec (Es.nit = 0.15 V/cm),
H = 14 koe.
particles takes place from the very beginning of the process. In our experiments the maximum electron density does
not depend on the magnetic field intensity. All this makes one doubt the correctness of the hypothesis regarding the
determining role of anomalous plasma diffusion in systems with strong longitudinal magnetic fields.
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6c gs
s 110,:
1X10L
0,8
0,6
44
42
Ii
Sl II
0
,.
/
V o
`~
1
C I
~3
2
I
-
5
x
1
~
rt
1 2 3 4 5 6
8Imit - 107 amp/sec
Fig. 6. Mean conductivity calculated at the moment
of maximum current as a function of the initial cur-
rent derivative. 1) p = 6.5 ? 10-4 mm Hg, H = 11 kOe;
2)p=6.5.10-4 mmHg, H =22 kOe;3)2=1.10-3
mm Hg, H = 22 kOe.
dcgS
to f
0 S 10 1S 20H,kOe
Fig. 7. Mean conductivity calculated at the moment of maxi-
mum current as a function of the magnetic field strength for
p = 1 ? 10-3 mm Hg; linit = 0.8. 107 amp/sec (Einit = 0.009
V/cm).
2) If the electrons leave only from the outer regions of the discharge, the effective radius of the plasma falls.
A reduction of phase shift will also be observed in the radiointerferometer on account of the diminution of plasma
volume at constant concentration. Such a phenomenon may take place not only on account of anomalous diffusion
in the colder outer parts of the plasma but also because of the i;iteraction between the plasma pinch surface and the
discharge chamber walls, which is determined by magnetohydrodynamic instability.
3) If the effective radius of the plasma is much less than the inner dimensions of the diaphragm, small changes
in the outside radius of the pinch will lead to a marked change in the length of the microwave path in the plasma.
A displacement of the current pinch was actually observed in the "Tokamak-2" [10].
The electron density was measured with one vertical channel at the center of the chamber. No special investi-
gations of the electron density distribution with respect to'cross-section were carried out, so that at the moment we
have insufficient facts by which to assert preference for any one of the three suggested explanations for the interfero-
metric observations.
4. Oscillations in the Plasma
For arrangements in which the loop voltage remains smooth during the whole process, oscillations of compara-
tively small amplitude in the magnetic probe and uneven output of hard x-rays show that in such cases also the plas-
ma is unstable, although it interacts with the walls less strongly. For less stable discharge systems there are moments
[of time] when the oscillations grow rapidly in amplitude, or even change their qualitative character. The moment
at which appreciable oscillations begin at the magnetic probe coincides with the beginning of weak oscillations in
voltage. The moment at which very strong oscillations appear coincides with the cessation of X radiation, the appear-
ance of negative throws in the loop voltage, and bright flashes of the spectral lines of the wall material (see Figs. 1
and 2).
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The sharp drops in voltage (Fig. 4), in some cases leading to a sign
reversal, correspond to an increase in the current derivative. This may
be explained by a rapid drop in the induction of the current pinch, for
example, during a short-term widening of the current flow region.
In [7] the conclusion was reached that the low frequency plasma os-
cillations observed in the "Tokamak" determining the whole behavior
of the discharge, had a magnetohydrodynamic nature. This hypothesis
was confirmed by the existence of a correlation between the bursts of
hard X radiation and the oscillations in the probes, and also by the cessa-
tion of X radiation on the appearance of sharp surges on the loop volt-
age oscillograms. Actually, the effectiveness of the interaction of elec-
trons with small scale fluctuations must fall rapidly with increasing
0 S 10 1S 20 H, kOe electron velocity, and relativistic electrons must intereact essentially
Fig. 8. Mean conductivity calculated
at the moment of maximum current as
a function of magnetic field intensity
forp=1.10-3 mm Hg;Iinit=1.8.107
only with the magnetic field of the current, which does not cause them
to pass out to the outer wall of the chamber. Thus the separate bursts
of X radiation must correspond to large scale displacementsof the plas-
ma pinch.
amp/sec (Einit = 0.1 V/cm). 5. Conductivity of the Plasma
Careful consideration of the processes taking place in a plasma
for various external discharge parameters (see Fig. 3) leads to the conclusion that the magnetohydrodynamic insta-
bility arising in the plasma influences its activity to a marked extent.
Figure 5 shows the relation between the mean` conductivity at the moment of maximum current and the ini-
initial hydrogen pressure for cases with and without voltage oscillations. In the first case the energy reaching one
particle drops with increase in the total number of particles, which leads to a drop in conductivity. In the second
case the interaction'with the walls, to which the instability arising in the plasma leads, takes away a significant
part of the energy to the wall, so that the change in the number of particles taking part in the discharge has little
effect on the mean conductivity.
Figure 6t shows the relation between the mean conductivity at the moment of maximum current and the
value of the initial current derivative. Curves are given for various values of initial hydrogen pressure and longi-
tudinal magnetic field. The first steep rise in the curve ends when, for the given magnetic field,there is a substan-
tial interaction of the plasma with the wall due to the hydromagnetic oscillations arising. Calculation of the energy
balance shows that the heating of the particles in this part of the curve expends about 30'/o of the energy put into
the discharge. The second part of the curve is characterized by adropin conductivity as the energy contributed
grows. Here there occurs an increase in the amplitude of the oscillations in the plasma, and its interaction with the
walls increases. Naturally that part of the energy going into heat in this case rapidlydrops. The third part of the
curve is characterized by a growth in conductivity with a rise in the amount of energy, but considerably more slowly
than in the first part. Less than $o of the energy is here used in heating the plasma.
If in the arrangement without substantial oscillations in voltage the magnetohydrodynamic instabilities do not
lead to marked energy loss, the conductivity of the plasma must depend slightly on the longitudinal magnetic field.
This is confirmed by Fig. 7. The slight fall in a for increasing magnetic field may perhaps be linked with a
change in the leakage magnetic field intensity, which leads to a displacement of the equilibrium position of the
plasma pinch in the chamber. For unstable arrangements, that is, those with large initial current derivative, a linear
rise in the mean conductivity with increasing longitudinal magnetic field strength is observed (Fig. 8).
6. Arrangement without Voltage Oscillations
In discharges with parameters corresponding to the first rise in the curve of Fig. 6 there are no oscillations in
the oscillograms of voltage and current derivative. The conductivity of the plasma depends in a reasonable way on
the initial concentration of particles and the energy imparted to the discharge.
Mean conductivity here and later means conductivity calculated on the assumption that the current flows evenly
throughout the whole cross section of the aperture in the diaphragm.
tFigures 6-8 relate to experiments with somewhat less discharge aperture and worse vacuum conditions. This has
no effect on the qualitative discharge characteristics, but leads to a smaller conductivity at maximum current.
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In such systems the mean conductivity at the moment of maximum current reaches the value 5 ? 1015 cgs. A
considerable induction shift of the current relative to the voltage is observed, corresponding to a mean inductance
of 1.0-1.2 pH during the discharge. It is only possible to explain this value of inductance if one assumes that the
current flows not through the whole cross section of the diaphragm aperture but through a narrower channel, the
actual conductivity when not being less than 1016 cgs. For a Maxwellian electron velocity distribution this would
correspond to an electron temperature of Te ~ 100 eV.
The existence of a Maxwellian electron velocity distribution in the plasma may raise doubts, as we do not
know the part of the current determined by escaping electrons. According to a simple calculation [11], the energy
of the escaping electrons in our apparatus cannot exceed a few MeV. If the acceleration process is similar to that
proposed in [12], then for our parameters a substantial part of all the electrons (0.116) must be accelerated to such
energies in a time of the order of 1 msec, and this may give a current of 10-20 kamp. In actuality, however, fast
electrons do not apparently determine all the discharge current. This follows from the fact that in arrangements
with large voltage oscillations hard X radiation, as shown earlier, vanishes immediately after the first voltage surge
but the conductivity remains practically the same as it was up to the appearance of oscillations. Beside this, a coarse
calculation of the relativistic electron current by the intensity of hard X radiation shows that it is negligibly small
(less than 100 amp). Probably something interferes with the electron acceleration. This is indicated by the anomal-
ous dependence of the hard X-ray output (over 200 keV) on the parameters of the discharge described in Section 3.
What part of the current is determined by the direct motion of low energy electrons cannot at present be stated.
Let us suppose that the conductivity is not determined by escaping electrons, and consider the energy balance
without voltage oscillations. In time t, energy W(eV) reaches one particle in the plasma. Towards the end of this
time interval the plasma conductivity reaches a magnitude corresponding to electron temperature Te. The "en-
ergetic' containment time rW = tTe/W-Te equals 300-400 psec on condition that all the original energy is
carried by particles to the wall. Probably, of course,a substantial part of the energy inparted to the discharge passes
out in the irradiation of impurity atoms and ions. However even such an energetic containment time has,for our
conditions,the same order as the theoretical time for the equalization of the temperatures of the electronic and ionic
components. It is therefore to be expected that the temperature of the ions will be close to the that of the electrons
if the phenomenon of charge exchange does not play a significant part in the heat exchange process.
7. Conclusions
Summarizing the results thus set out, we establish the following conclusions:
1) The low frequency oscillations excited in the discharge to a great extent determine its characteristics.
Correlation of the oscillations with surges in x-ray intensity confirm their magnetohydrodynamic nature.
2) Up to the appearance of the oscillations in the discharge, the following processes appear to be observed.
Hydrogen is being ionized all the time its lines are showing. The moment the Hg line disappears, the electron
density stops growing and from then on stays constant. Escaping electrons are accelerated up to energies of some
MeV and pass out to the outer wall of the diaphragm. At the end of the hydrogen ionization the conductivity be-
gins to increase with time, while the part of the energy transferred to the plasma forms some tens of a percent of
the energy imparted to the discharge. The plasma interacts comparatively weakly with the walls, but the observed
oscillations in the magnetic field of the current and the unevenness in time of the x-ray output do now allow the
discharge to be considered completely stable.
3) After the appearance of the oscillations in loop voltage and current derivative, the picture change sharply.
The magnetohydrodynamic instabilities, developing large amplitudes, lead to a strong interaction with the walls.
The spectral lines of the wall material and the gases adsorbed thereon make their appearance. Electrons accelerated
to large energies as a result of large scale displacements of the plasma pinch hurl themselves into the diaphragm
wall. Thereupon it appears that conditions for effective electron acceleration are no longer found in the unstable
plasma, and the plasma conductivity ceases to increase. The character of the dependence of the mean conductivity
on the initial gas pressure and the energy imparted to the discharge shows that this energy is not accumulated in the
plasma, but is given up at the diaphragm and the discharge chamber walls.
4) For sufficiently large containing magnetic fields the voltage and current derivative remain smooth through-
out the process. If we suppose that the velocity distribution of electrons is close to Maxwellian, the electron tem-
perature is of the order of 100 eV. The electron density in such arrangements scarcely alters up to the end of the
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current flow. The dependence of its maximum on the longitudinal magnetic field strength seems extremely slight.
All this casts doubt upon the existing idea that in longitudinal current discharges, stabilized by a strong magnetic
field,the reduction in phase shift measured by the radiointerferometer indicates a substantial rise in the diffusion of
charged particles to the chamber walls. At present we have no grounds for supposing the existence of such diffusion,
although there is also no conclusive proof of its absence.
In conclusion the authors express gratitude to L. A. Artsimovich for valuable discussions and interest in the
work, and also to their unfailing assistants, A. A. Kondrat'ev, L. S. Efremov, G. N. Ploskirev, and E. Yu. Frolov,
who performed a great part of the technical work. The work was carried out under the initiative and immediate
direction of Natan Aronovich Yavlinskii.
1. Kur et al. In the book: Transactions of the Second International Conference for the Peaceful Uses of Atomic
Energy. Collected reports of foreign scientists, Vol. 1, Atomizdat, Moscow (1959), p. 523.
2. R. Ellis, L. Goldberg, and J. Gorman, Phys. of Fluids, 3, 468 (1960).
3. W. Bernstein, A. Kranz, and F. Tenney, Phys. of Fluids, 3, 1019 (1960).
4. E. P. Gorbunov et al. "Zh. tekh. fiz.," 30, 1152 (1960).
5. V. Stodiek et al. Report No. 10 131, presented to the International Conference on Plasma Physics and Con -
trolled Thermonuclear Synthesis, Salzburg, MAGATI (1961).
6. E. P. Gorbunov et al. Report No. 10/223, presented to the International Conference on Plasma Physics and
Controlled Thermonuclear Synthesis, Salzburg, MAGATE (1961).
7. D. P. Ivanov and K. A. Razumova. Report No. 10 222, presented to the International Conference on Plasma
Physics and Controlled Thermonuclear Synthesis, Salzburg, MAGATL` (1961).
8. V. S. Vasil'evskii et al. "Zh. tekhn. fiz.," 30, 1137 (1960).
9. E. P. Gorbunov, In the collection: Diagnostics of Plasma, Moscow, Gosatomizdat (1963), p. 68 (in the press).
10. L. A. Artsimovich and K. B. Kartashov, "Dokl. AN SSSR," 146, No. 6 (1962).
11. E. Meservey and L. Goldberg, Phys. of Fluids, 4, 1307 (1961).
12. Dreiser. See [1], p. 170.
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to.
cover English translations appears at the back of this issue.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
METHODS FOR THE CALCULATION OF THE RADIATIONAL
THERMAL OUTPUT IN THE BODY AND SHIELDING OF A
NUCLEAR REACTOR
D. L. Broder and K., K. Popkov
Translated from Atomnaya Energiya, Vol: 15, No. 5,
pp.-370-376, November-1963
Original article submitted November 1, 1962
The radiational thermal output in the body and protective shields of energy-producing reactors is
very dangerous, since it can lead to the explosion of these reactors. In order to lower the amount
of heat escaping into the body and the most strongly stressed structural sections of reactors, heat
screens, are usually used.
In the present article we describe methods for the calculations needed in the design of ther-
mal shields. Expressions are given that can be used for the calculation of the thermal output due
to the penetrating radiation in various shielding setups, including those with the most commonly
used geometry.
The absorption of neutrons and y radiation heats the body of reactor, the shield, and also the protecting struc-
ture that is in the field of radiation. In powerful nuclear reactors, the energy flux in the body of the reactor reaches
1013-1014 Mev/cm2 ? sec, and so the specific power of the thermal output often reaches several watts per cm3, and it
can even attain the value of 102 W/cm3 in shields in the active zone.
For thick-walled reactor bodies, designed for a pressure of 100 atm or higher, intense radiation could cause
supplementary thermal stresses which must be taken into account in strength calculations.
In the determination of radiational thermal output, we must take into account 1) the y radiation of the fission
products, 2) the capture y radiation generated in the structural and protective materials (those in the body of the
reactor included), and 3) the reaction B10 (n, a)Li7 in boron-containing material.
Other processes, in particular y -radiation generated by the inelastic scattering of fast neutrons or the losses in
the elastic scattering of neutrons by the relatively heavy nuclei of iron, contribute only insignificantly to the thermal
output, and so their effects can be neglected. With these simplifications, the total thermal output Q is the sum of
two terms, the first of which Qy is due to the absorption of y radiation and the second Qa to the absorption of a -
particles generated by the reaction B10(n, a)Li7:
Q=Qv?Qa W;'cm3. (1)
The determination of the y component of the thermal output can be reduced to the calculation of the energy-
space distribution of the y radiation flux. If Iy (E, r) dE is the strength of the y radiation energy in the interval from
E to E + dE at the point r, then the specific thermal output Qy(r) can be calculated from the formula
Qv (r) = k ~ Iv (r, E) ?n (r, E) dE, (2)
where ? n(r, E) is the linear energy-absorption coefficient for the y radiation of energy E at the point r; k is a pro-
portionality coefficient determined by the dimensions of the quantities in the expression (2):
k = 1.6 ? 10-t3 W -sec/ MeV = 3.82. 10-14 cal/MeV.
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In practical calculations, the integral in (2) is replaced by the sum
Qv (r) _ k; 1, 1F,' (r, E) Eli n (r, E
where cp (r, E) is the scalar flux of the y -radiation of energy E at the point r. The sources of y radiation can be
divided into two classes: primary sources, related directly to the fission process, and secondary sources originating
with the interactions of neutrons with nuclei of elements in the heat-transfer agent, in the moderator, and also in
the structural materials of the reactor and shield. In the present work, we are interested in instantaneous and de-
layed y radiation (primary radiation) and in capture y radiation (secondary radiation).
The calculation of the scalar energy flux of y radiation cpy (see the diagram) reduces mathematically to the
calculation of the integral
1, 9y (r) e-Fla (1) sa-N,n (E) 6`B (E, S S) dL
~ E=E s s, nL
v
4.,r (rm - rs)2 s,
Va
where qy (rs) is the distribution function of the specific source strength of y radiation of energy E; ?sE and pm(E)
are the linear attenuation coefficients of y radiation of energy E in the source and shield material respectively;
B(E, bs, 6m) is a measure of the accumulation of the energy of scattered y -radiation of energy E in the material
of the sources (in the region b s) and in the material of the shields (in the region S M). The integration it taken over
the volume of the sources Vs .
The space-distribution of the specific strength of
the primary y?radiation sources is completely determined
by the integral of the fissions kf(rs).
f (r.,) = \ nv (rs, E) I, (r? E) dE
(5)
= 3,1.101pp (rs) graduations/cm -sec,
Location of radiation sources in shielding layers.
where nv(rs, E) dE is the flux of neutrons with energy be-
tween E and E + dE at the point rs; E f(rs, E) is the macro-
scopic cross section of nuclear fission corresponding to the
neutron heating energy E at the point rs; p(rs) is the spe-
cific thermal power at. the point rs in W/cm3. In some
cases it can be assumed that p(rs) = P/Va, z = const (here
P is the thermal power of the reactor and Va, z is the
volume of the active zone). Knowing the value of `f{rs),
we can calculate the specific strength of the sources of the primary (instantaneous and delayed) y radiation q Y1 (rs).
If the reactor has been operating for a long period with constant power,* then
qy1 (rs) _ (r,,) v.,S, (E),
where v is the number of photons of instantaneous and delayed y radiation referred to a single fission (v = 14.7
[1]) and S(E) is the share of y quanta of energy E in the spectrum of the primary y radiation. Values of the pro-
duct vy Sy(E) obtained from [1] and [2] for various energies are given in Table 1.
The specific source strengths of capture y radiation gy2(rs) can be calculated if the space energy distribu-
tions of the neutrons and the dependence of the radiation capture on the energy are known. In this case, the capture
integral t '(rs) for the ith isotope can be obtained from the formula
? The specific source strength for the delayed y -radiation is determined from the integral of the fissions xf(rs, t) and
is specified for any instant of time. In a reactor operating with constant power, the specific source strength for the de-
layed radiation depends only on the time to of operation of the reactor. In practical calculations it is usually assumed
that ta .0.
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TABLE 1. The Energy Spectrum of Instan-
taneous and Delayed y -Radiation
Energy of vySy(E) Energy of v S (E)
y radix y radia Y Y
tion v-ouanta/ tion v -quanta/!
(Mev) fission E (MeV)1fission
Y_
~i (r,)' _ nv (rs, E) (rs, E) dE,
where z' (rs, E) is the macroscopic cross section of radiation cap-
ture of neutrons of energy E for the ith isotope.
I.0
1..i
(1.024
The quantity qy2 (rs) is obtained from the relation
1.5
I.34
5,0
0.019
0
2
1
17
5
5
017
0
E
.
2.5
.
().71
.
0.n
.
0.007
),
9yz (rs) _C (rs) sv, (
3.))
0.102 ,
h-.-
0.01)4
a
3
0t)
0
1
.
.
where S c (E) is the mean number of y quanta of energy E gen-
y
the absorption of a single neutron by a nucleus of the
erated b
ith isotope. Table 2 gives values of St (E) taken from [3].
The main difficulty in the calculation of sources of capture y -radiation is the determination of the space
energy distribution of the neutrons, i.e., the function nv (rs, E) in the expression in (5).
Recently, in the calculation of neutron distribution in shielding, the multigroup method [4] has often been used,
in which the neutron spectrum is divided into several energy groups. Within each group, all the characteristics of the
materials under consideration are assumed to be independent of the energy. For every ith group of neutrons, we can
write the differential equation in the diffusion form
I rl a clrPj _ f
where a = 0 for plane geometry, a = 1 for cylindrical geometry, and a = 2 for spherical geometry; coj is the distri-
bution function for neutrons of the jth group; Dj the effective diffusion coefficient for neutrons of the jth group; E j
the effective cross section of departure of neutrons from the jth group. The right-hand side of (9) determines the
sources of neutrons of the jth group.
The multigroup method is discussed in more detail in [4-7]. In [4], a seven-group method is proposed for the
calculation of biological shielding in the diffusion-growth approximation. The results of using this method are found
to be in satisfactory agreement with the experimental results given in [4], and this method can thus be recommended
for engineering calculations.
Knowing the space neutron-energy distribution we can calculate the capture integral (7):
(r) _ nv, (r) ~vl (r)+
where E Y (r) is the mean macroscopic cross section of radiation capture of neutrons of the jth group by nuclei of the
ith isotope.
Table 3 gives the means with respect to the energy of the cross sections of radiation capture for some elements
for the seven-group calculation. The table gives the cross sections of the seventh (thermal) group averaged over the
Maxwellian spectrum for the normal temperature 20?. If this last condition is not satisfied, then we must introduce
a temperature correction. In practical calculations, we can assume [10] that
6v (T) = 6: (To) T , (10)
where o (T) and a (To) are the cross sections of radiation capture for the absolute temperatures T and To of the
material Y Y
It must be noted here, however, that absorption (stronger for lower energies) displaces the maximum of the
Maxwellian distribution into the region of higher energies. This effect can be taken into account in the calculations
by introducing into the formula (10), in place of the actual temperature T, an effective temperature Tn for the
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TABLE 2. Mean Number of y -Quanta -of .Energy E Gen-
erated by the Absorption of a Single Neutron by Various
Elements S , C(E), y -quanta/capture
1) Il I.))0
Il 0 0 0
1.1
11 11 11
li '._II. iO -0.6011
R
u li n
0.51 )).7:{I 0 O
l.r
>).8,5 U. It II 11.21
0.12 0.23 O :UJftIl(ii
Mit
i>l 251 0. Ili 11.(u(ll
it .il) O i,, 0 171)
FU
!` (1 7 1).60 1(
O 2'-~. O 23 O rS~O.I)21
V'i
>O 84 i 0.40 I 0.23
4, I ~ : , i ( 1 3{) 6 8 ' 0 .1!11 {
Flo
>1 .37i, O.l8'
n.8'i 0.26' 0.03'0.000".
l b
Il (1 1)
ll 0.07 0?);'+"I
1238
_ ' . 5 4 1 . 7 8 1 1 ) . !1I
i
11.3i! 0 0 1()
i
TABLE 3. Seven-Group Cross Sections of Radiation Capture for Some Elements, Barn
Energy Interval
t
It
)u
I-v
}}
(-Y- ? .5 MeV)
(0.o-1 .5 MeV) (u.5 _.11eV 45 keV)
(45--s keV)
-
I 1'll
(3keu-3.;ieV {3.seV--~';gr) (1,gr.-
i
i
--
0.03285 ~
0.012368
0.0:182
It. 17,8
O, 0:;:;7
00:14:;
(),03738
11.02366
0.1122370
((.0271
n
I-,
03!)
(1.022133
1
0,02252
(1.02'16
0?(1''0)
.
11.O'ING:;
(1.11663
0.0828
11. 799
8,
0.112;,111
O.O'327
0.02-((71
0. 1 7
- 1 : 8
7. 1 1
(1.021/2
0.0220 .i
!
0.0`2((82
(1.067., (1.6(i)
3. 1 23
11,(12!4
(1.02?6 _'
(1.(12:113
0.0':18;1;
(1.3U.i
1
06
1.0:
(t (r2 .43's
0.02(3(2
).nl:;(-;
(LO;;lil 0.:361(
.
I.37
(1=211
11,(3=`.11;:,
((.1)11/)
(I.UI.~..
l.ll. l '
O. 110
0. 1
i
11.231 ,
I. ,ti
For boron, the cross sections are given for the reaction 1310(n, a) Liz, taking into account the isotope composition
of the natural mixture.
neutron gas. From the empirical formulas in [11], the value of Tn for light materials (A < 25) is found to be
Ta= To [1 1,91A`"("')
as OeV) -l;
J
while for heavy materials it is
Tn=TO [1-r-0,6A?(k70)
US (leV),
where a (kT0) is the absorption cross section for neutron energy kTO, os (1 eV) is the scattering cross section for neu-
trons wits energy 1 eV. The formulas (11) and (12) yield correct results for 0 < A ac(kTO)/as(1 eV) < 0.5.
The next step in the calculation of the thermal output is the determination of the total intensity of y radia-
tion of various energies at the points under consideration, i.e., the calculation of the integral (4). In most cases this
calculation, for reactor shields and bodies, can be carried out with the assumption that plane geometry can be used.
Since the shield thickness is usually considerably smaller than the radius of the active zone, this zone can be con-
sidered to be a radiating half-space with shielding. In this case, neglecting the accumulation of scattered y radia-
tion in the active zone, we obtain for steel shields, in agreement with [12],
( 1(E)) ??(l.,.r;
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v (E)
 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
where qE is the mean, through the volume of the active zone, of the specific source strength of y radiation of en-
ergy E, ?S is the linear coefficient of attenuation for y radiation of energy E in the active zone, E iiixi is the thick-
ness of the shielding layers (along relaxation paths) between the surface of the active zone and the point under con-
sideration, and E,, (x) = x" Stt dt, is the exponential-integral function [12].
It should be noted that, in calculations of thermal output, the energy factor for the accumulation of scattered
y radiation must be used in the determination of the y radiation flux. In (13) an exponential approximation for the
accumulation factor was used [13, 14]:
B(, r)= 'V A3 (E)e-uxaj(E)
i=t
Tables of graphs of the values of A](E) and ai (E) are given in many references [2, 12-16].
The neglect of the accumulation factor for the scattered y radiation in the active zone lowers the values of
(0 EE)1 by up to -406. By using the results in [17, 18], we can obtain a formula for numerical calculations in which
this accumulation is taken into account. The substitution in (4) of the accumulation factor expressed as the sum
(see [17] and [18] and (14)).
B (E, c5s, 6.) = Bs (E, usss) + B. (E, usss + ftmsm) - B. (E, usss)
A; (E) e6? AT (E) e-(wsa,+I~mdrn)?ajl(E)- \1 Am (E,) -l 6sa""(E)
j=1 j_1
qE E Al(E A. (E) r l
((pEE)1 2y S f s ( ) EZ ~' uzx`l 1 ~~ai e 1, E2[ 1 T are (E) Itzx` J
AFe(E)E2 `1+ae(E)) it`x!1 (15)
In most cases, the distribution function for the sources of capture y radiation for steel shields surrounded by
moderator can be expressed in the form of the exponential sum
9Y (x)-gv,e1'x+~yv?e-
where x is a coordinate measured from the shield surface nearest to the active zone.
Thus the strength of capture y radiation of energy E from the kth shield at the point under consideration, sepa-
rated from the source layer by a shield of total thickness E pExi (along relaxation paths), can be calculated from
the formulas r
((pV E)k = ((pY'E)k + ((p:: E)k;
~E' 9y 1J AFQ{e
a=1
( ?ixill
(d+ )E i l (1 +. aFe
+ ftixi i
J i
- e-"'Et [ (1 + CtFe) ttixi e"-' ld+ !ts ) E1 ([ (1 +aFe) + ?s J (ttsd + I ttixi
+ E1[(1+aFe) (Fid+ utxi)
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E" Z
" _ qv Fe -!J (d+ i ) / are (PV u? Ai r e ?s E1 [ (1 } aI ) - - ] ?ixi j
us
7=1
Gi ?ixi
(( t
- eEt [ (1 ? are) ?ixi ] - e-~" ld} us ) E1([ (1 + are) - u" j C.?sd ? xi
?E1 [(I+ are) ! g d+Y, uixi)]} .
where ps is the linear attenuation coefficient of y radiation in the material of the layer-source, k is the thickness
of the layer source. For thin shields, neglecting the variation of the function qy (x), we obtain
qV (x) = qy = const =
R2
qy (r) 2ltrdr
R1
R2
27t S rdr
R1
(r) rdr, (20)
where R1 and R2 are the radii of the internal and external surfaces of the layer source and r = Rt + x. For the kth
shield we have
qEF 2 AFe
((Pv E)k = 2?s 1 dare {E2 ((1 + a~ e) ?ixi E2 [ (1 + a e) ( ?i Ti T ?s
j=1
)]}.
This formula can also be used for the calculation of the radiation flux from thick shields if q (x) is expressed as a
step function. Y
In the determination of the strength of y radiation generated by the absorption of neutrons in thin layers of
water ( ?sd > 2), the radiating layer can be considered to be nonabsorbing. In this case
EdE 2
(q) EE), _ gy7 AreE1 (1 + al;,,) J (22)
7=1 i
For thick layers (?sd > 2), we must use formulas similar to (17)-(19) and (21). For example, for the exponent
q (x) = q'ez'x we have
I (1
(q) E)k = 9 ~, A, e {ex'dE1 r
(i-+-aFe) ?rx=
i +d) E
E1~(1+ale) ?ixi(l-}
us
(1 are) Z uia'i-4'usd
Fe ~1
(1 - 7 ) LJ uixi
?s +d E'
-t--e Et \~(1+are) ?ixifi?sd
For a uniform distribution, i.e., q(x) = qy = const, we have
C 1 - \}
?s / /
9E, 2
((P~ E)k = 2?s Ale lE2 [ (1 i aFe) ?ixi ] - E2 [ (1 -I- are)
=1 i
Fe
?ixi? usd]} .
(24)
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
The strength of capture y -radiation (;4Y
a sum:
at the point under cons ideration coming from all layers is obtained as
(V)'E)11 = (1)yE)a, (25)
where k is the number of layers, excluding the layer containing the point under consideration. The contribution
((pEE) of the capture y'-radiation from this layer can be obtained by using the formulas given below: for a point
at a distance x from the surface of a layer with constant specific y -radiation source strength we have qY
_T 2
((pyE)ij1=q~,l~ _ AJuji2-E2:[(1?aJ)?.sx]-E2[(1,_a.i)lls`(d-x)_]};
~=1
Ex
for a layer with an exponential distribution qy(x) = q0e
2
(FEE),, 1 = qn`, ~, A (- e--1:' 9it ~' eFxEj ('.ix) + Ej [(-?j-E) x]}.
I, I -I- e 1n p~N1 J r-` (,t-) {?i (d - x)] + E1 [(?d 1) (d - x)]
where p j = ? (1 + a j).
In many cases, we can use a simplified formula 119] obtained under the assumption that the accumulation
factor is linear: B(px) = 1 + Gix. For the exponent q(x) = q0e- Ex
?X ~d lt (d-X)
fill
(qy )II,-
_rx )
e- (1-x)E, [u, (d --, ) 1 E [(It ~) (d- x)1 - r lln Ft 1- e~xE1(ux,) -1- Et [(u - 1) x] j 28
T_ j
The total strength cpY E, occurring in the formula (3), is obtained for each point for which the calculation is
performed in the form of a sum
(p~,E=(q)E11 E)1 T ((pvE)11__(( E)11,.
The thermal output Qa due to the absorption of a -particles with a probability of 0.94 as a result of the reac-
tion B10(n, a)Li7 is given by the formula
7
Qa,=kE, Y'nt'1Lf~,
where E~ is the macroscopic reaction cross section for neutrons of the jth group (see Table 3); Ea is the energy of an
a -particle equal to 2.31 MeV.
During the reaction B10(n, a)Li7, in addition to an a-particle, a y -quantum of energy 0.478 MeV is also
emitted, which must also be taken into account in the calculations.
The method described above can be used in the calculation of the thermal output in the body and in other
structural parts of nuclear reactors with an error of less then 3c$%.
1. Reactor Physics Constants, ANL-5800 (1958).
2. G. Eterington, Nuclear Engineering Handbook. McGraw-Hill (1958).
3. E. Troubetzkoy and H. Goldstein, Nucleonics, 18, No. 11, 171 (1960).
4. D. L. Broder and others. Atomnaya 1`nergiya, 12, 129 (1962).
5. G. I. Marchuk, Numerical Methods for Nuclear-Reactor Calculations [in Russian], Atomizdat, Moscow (1958).
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 Declassified and Approved For Release 2013/02/25: CIA-RDP1O-02196ROO0600110003-4
6. D. L. Broder and K. K. Popkov, Inzh-fiz. Zh., No. 12, 118 (1961).
7. G. I. Marchuk, Methods for Nuclear-Reactor Calculations [in Russian], Gosatomizdat, Moscow (1961).
8. M. Clark, Nucl. Engng. 6, No. 56 (1961).
9. O. A. Barsukov and V. S. Avzyanov, Atomnaya L`nergiya, 10, 478 (1961).
10. Merrei, Nuclear-Reactor Physics [Russian translation], Izd-vo inostr. lit., Moscow (1960).
11. E. R. Cohen, Report No. 611 presented by the USA at the Second International Conference on the Peaceful
Uses of Atomic Energy (Geneva, 1958).
12. The Shielding of Nuclear Reactors [in Russian], lzd-vo inostr. lit., Moscow (1958).
13. G. Gol'dshtein, The Fundamentals of Reactor Shielding [in Russian], Gosatomizdat, Moscow (1961).
14. H. Goldstein and J. Wilkins, Calculation of Penetration of Gamma-Rays, NDA Report NYO-3015 (1954).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover- to-
coverEnglish.translations appears at the back of this issue.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
MEASUREMENT OF THE THERMAL NEUTRON DENSITY DISTRIBUTION
ALONG THE RADIUS OF SLEEVE-SHAPED FUEL ELEMENTS
V. F. Belkin, B. P. Kochurov, and O. V. Shvedov
Translated from Atomnaya Energiya, Vol. 15, No. 5
pp. 377-381, November, 1963
Original article submitted March 14, 1963
This article is devoted to an experimental investigation of the thermal neutron density distribution
along the radius of sleeve-shaped fuel elements consisting of natural uranium and an organic cool-
ant, monoisopropyldiphenyl. The thermal neutron density distribution for 23 types of fuel element
was measured by using the activation method. The theoretical neutron density distributions were .
determined for these fuel elements by solving the single-velocity kinetic equation by means of an
electronic computer. The experimental and theoretical results are given in the form of neutron
density distribution graphs, screening numbers, and neutron density jumps in the outside coolant
layer.
Introduction
The tendency to increase the coolant temperature without substantially increasing the pressure with the aim
of producing efficient power reactors brought about the use of coolants consisting of organic liquids with high melt-
ing points.
The thermodynamic and structural requirements imposed on systems with natural uranium (as the fissionable
material) and an organic coolant led to the development of multilayer fuel elements, to which the calculation meth-
ods suitable for simpler types of fuel element cannot be applied [1, 2]. This makes it necessary to use more com-
plex calculation methods, which must be checked experimentally.
Experimental Equipment
The thermal neutron density distribution was measured in fuel element mock-ups (fuel assemblies) whose
length was 75 cm. An assembly consisted of the following elements (Fig. 1). The sleeve 1, made of natural metall-
ic uranium (with a density of 18.7 g/cm3), was encased between the outside and inside aluminum jackets, 2 and 3,
respectively. A magnesium displacer 4, was provided at the center of the assembly. The inside layer of the mono-
isopropyldiphenyl coolant 5 (whose density was 0.986 g/cm3) was poured between the outside surface of the mag-
nesium displacer and the inside jacket of the uranium sleeve. The outside layer 6 of monoisoprophyldiphenyl was
poured between the outside jacket of the uranium sleeve and the screening Avial tube 7. An air gap 9, was provided
between the outside Avial jacket 8 of the assembly and the screening Avial tube. (In some experiments, monoiso-
propyldiphenyl was replaced by water.) The dimensions of all the fuel assemblies were the same: the inside diam-
eter of the uranium sleeves was 30 mm, the air gap was 3 mm, the thickness of the outside Avial jacket was 2 mm,
and the thickness of the screening Avial tubes and of the uranium sleeve jackets was 1 mm.
The fuel assemblies were characterized by the following dimensions: the outside diameter of the uranium
sleeves, the diameter of the magnesium displacer and, correspondingly, the thickness of the inside monoisopropyl-
diphenyl layer, and the thickness of the outside monoisopropyldiphenyl layer.
Each assembly was given a code designation which indicated the outside diameter of the uranium sleeve, the
thickness of the outside monoisopropyldiphenyl layer, and the diameter of the magnesium displaces. For instance,
in the 54-1.5-20 assembly, the outside diameter of the uranium sleeve was 54 mm, the thickness of the outside mono-
isopropyldiphenyl layer was 1.5 mm, and the diameter of the magnesium displacer was 20 mm. If the displacer was
not provided, then, depending on the material with which the inside cavity was filled, the last figure was replaced
by the letter A (air) or M (monoisopropyldiphenyl).
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4 re.. u,,,
u
Fig. 1. Thermal neutron density distribution q along
the radius R of the assemblies (the theoretical results
are given by the curves, while the points represent the
experimental results), a) For the 46-2-1\1 assembly;
b) 46-2-16 assembly; c) 46-2-A; ) and 0) experi-
mental values for the 46-2-M and 46-2-A assemb-
lies, respectively.
The neutron density distribution was measured by
means of detectors with a diameter of 4.2 mm and a
thickness of 0.4 mm, which consisted of a mixture of a
transparent plastic and dysprosium oxide (with a density
of - 3 mg/cm2). For the installation of the detectors,
grooves into which uranium prisms with detectors were
inserted during the experiment were milled in the uran-
ium sleeves. The slits in the prisms which were not
occupied by detectors were filled.with uranium plates.
The other detectors were placed in the recesses of the
aluminum jackets and tubes and. also in the grooves of
the magnesium displacer. The spacing of the detectors
is indicated by the positions of the experimental points
in Figs. 1-3..
The detector activity was measured by means of
an automatic eight-channel counting device, The
assemblies were irradiated in the A -O channel of a
heavy-water reactor [3] in a flux of 109 neutrons/cm 2sec.
There was an air gap between the outside Avial jacket
of the assembly and heavy water, since the inside diam-
eter of the AO channel was -100 mm. The position of
the detectors during the activation approximately coin-
cided w ith the center of the reactor core. The cadmium
ratio for dysprosium was not less than 100, so that the
detectors recorded only thermal neutrons.' The modera-
tor temperature was 293?K.
Experimental Results
Figures 1-3 show typical thermal neutron density
distributions along the assembly radius, which were ob-
tained experimentally and by solving the kinetic equa-
tion by means of a computer. The assemblies whose
neutron densities are given in the same figure differed
from each other only by the dimension of the inside
monoisopropyldiphenyl layer. In certain assembly
variants, the magnesium displacer was not provided,
and the inside hollow 'space of the uranium sleeve was
filled with monoisopropropyldiphenyl or air.
Table 1 provides the values of the screening number Q, * which were obtained by using different methods: 1)
processing our experimental data; 2) processing the results of the numerical solution of the kinetic equation; 3) using
the data provided in [1-2].
Table 2 provides the values of the neutron density jump 8, defined as the ratio of the neutron density at the
outside surface of the outside layer of monoisopropyldiphenyl or water to the neutron density at the surface of the
uranium sleeve. Since detectors could not be installed at the outside surface of the outside monoisopropyldiphenyl
layer under our experimental conditions, the experimental values in the determination of p were corrected in corre-
spondence with the neutron density curves obtained by solving the kinetic equation. With an allowance for
Ra
q (r) rdr
The value of Q is given by Q 1 = . _ _ , where Ro and Ri are the outside and inside radii of the uranium
sleeve.
q (Ro) \ rdr
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4, rel. i:n.
Fig. 2. Thermal neutron density distribution along
the radius of the assemblies (the curves represent
the theoretical results, while the points represent
the experimental results). a) For the 50-2.5-16
assembly; b) 50-2.5-24 assembly; c) 50-2.5-A
assembly; 0) and 0) experimental values for the
50-2.5-16 and 50-2.5-B assemblies, respectively.
q, rel, un.
1i
------ - .._1- _1..)-
1.1
0 5 10 15 20 25 30 35 R, mm
Fig. 3. Thermal neutron density distribution along
the radius of the assemblies (the curves represent
the theoretical results, while the points represent
the experimental results), a) For the 54-1.5-M; b)
.54-1.5-16 assembly; c) 54-1.5-A assembly; 0 ) and
O). experimental values for the 54-1.5-M and
54-1.5-A assemblies, respectively.
inaccuracies in mounting the detectors, the errors in measuring the distributions and jumps of neutron density were
equal to 1-1.51o.
The theoretical neutron density distributions were obtained by solving the single-velocity kinetic equation for
the multizone Wigner-Zeitz cell. The calculations were performed according to the program composed by F. M.
Filler and T. D. Bogdanova. By preliminary calculations, the dimensions of the equivalent cells for each assembly
were determined under the assumption that the neutron distribution in the internal monoisopropyldiphenyl layer is
close to the experimental distribution. In this, the sources of thermal neutrons in monoisopropyldiphenyl were as-
sumed to be 4.77 times as strong as in D20-
It was assumed that the neutrons have a Maxwellian distribution, the mean effective temperature Tn of which
may depend on the coordinates. The temperature Tm of neutrons in the moderator was assumed to be equal to the
n
temperature. Tn of heavy water, while the temperature of neutrons in uranium was assumed to be Tn = 1.3 Tn on the
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TABLE 1. Screening Numbers
Assembly type data bor-
experiment calculation ;rowed from
([1. 21
54-1.:;-II
S'I
41 -__u
54 1.5-10
50-2,j-21 50-2,5-20
50-2,5-1(i
50-2,5-M
41)-2,0-11
46-2.0-24.
46-2,0-20
4G-'',0-1(i
46-2.0- it
1._'79 1.261
I.?..,1 1.218
I.,_139 ;1. 21'12
I . _2'i 1 . ':38
1..'-18 1.231
1.199 1.197
1.187 1.188
1.17(; 9.183
1.166, 1.179
1.1112
1.1'35 :1.147
1.130 '1.9:'17
1.125 1.'134
1.121) 1.131
1.913 1.119
Layer thickness,
mm
TABLE 2. Neutron Density Jump 8 at the Outside Layers
of Monoisopropyldiphenyl and Water
Assembly type iexperi- calcula-
ment tion
{
54-'1.5 A
51-1.5-24
1
292
_
.
,
t,~-1.5-20
1.284
54-1.5-16
1.
54-'1.5-A1
1.268
50-I.5-A
50-1.5 _ 1
A
9.3!1I
5n-2.5-24
1.492
30-2.5-16
1.398
50-.). 541
1. 47: {
1.163
0-3.5M
50-3.5- A`
I.52i
5(1 3.5-M
1.53:,
46-2- A
1.3(11;
46-9-94
1.:31.5
46-2-20
1.282
46-2-16
1.290
46-2-M
1.280
46-2- A*
1.349
46-2-M*
1.294
1.284 0. ():,
1.282 (1. 0,-)
1.3811
1.276
10
1.37.., .? ''.5 _-(l.10
1.31 '' ?0. I I I
50-4-0- 10
1. { :,o+u. 10
4-11. I I I
3.50 u. Ii)
1.288 2.00+u. 1u
1.283 2.09?0.11
1.279 2.(10?0.1()
1.277 2.00?11.10
1.262 2.00+0.90
-- 2.00-1-0.10
- 2.00?0.10
? The outside monoisopropyldiphenyl layer was replaced
by water.
basis of preliminary calculations [4, 5]. A good agreement between the experimental and theoretical values of the
screening number was observed in this case.
The scattering cross section E m of monoisopropyldiphenyl depends rather heavily on the neutron temperature
(in [7], this dependence was determined experimentally: yi' - v1.58 ? 0.12 in the temperature range from 18 to
250?C). From the preliminary calculations, it follows that much lower 13 values are obtained for Tn = Tn = 1.3.
Satisfactory agreement with experimental data is obtained if the Tn value is assumed to be close to T. The value
of 8 only slightly depends on the equivalent cell's dimensions and the filling of the inside space of the lump with
monoisopropyldiphenyl. Some of the results of preliminary calculations are given in Tables 3 and 4.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
Calculation I
46-2-B 50-2.5-A 54-2.5- A
With aluminum
1.288
1.383
1.290
Without aluminum}
1.301
1.401
1.306
Air gap
1.276
In order to determine the effect of the aluminum layer between uranium and the outside coolant layer, we
performed several calculations for the cases where the monoisopropyldiphenyl layer was in close contact with uran-
ium and where aluminum was replaced by an air gap. As can be seen from Table 5., 13 somewhat increases in the
first case and decreases in the second case.
It should be noted that a certain increase in the theoretical neutron density in approaching the assembly center
is observed in the case of hollow slugs. For instance, calculations of a cell with a 54-1.5-A assembly, where a ma-
terial with a very small cross section ( E = 0.0025) was placed in the hollow space inside the uranium sleeve, have
shown that the neutron density near the assembly axis increases by approximately 12% in comparison with the mini -
mum neutron density (see the dashed curve in Fig. 3). It can be assumed that this effect is caused by the anisotropy
of the angular distribution of neutrons [8].
For assemblies without a coolant inside the neutron sleeve, the screening number Q is also determined by using
the equation [1, 2]
Q=1 I A ~1?
Here A, a, and y are tabular functions of (2VU/Sout)EU.
ES
S )2
TABLE 3. Dependence of 13 on Em and the Thickness
t of the D20 Layer for a Cell with a 50-25-20 Assembly`
1.18 I 2. iii 2.20
1.'111 1 1.336
1.341
Ttr, c:tii >
1.361
1.367
1.400
1.405
TABLE 4. Dependence of Q and 13 on Tn for a Cell with
a 50-2.5 A Assembly
U o
T -T
it n
U- o
T -1,3T
n n
exFeri-
!~[n
enT
u o
TT
1
n n
7~=i,3TO
n
~xret]ri
en
1.230
1.197
1.199
1.424
1.383
1.391
TABLE 5. Effect of the Aluminum Layer on 13
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
The calculations were performed for the following cross sections (cm-1):
ES =0.392;
"a =0..27.5;
ss 1= 0.0842;
Al
= 0.0108;
Es1g = 0.1546;
s,alg = 0.0021;
sM=2.26;
L a =0.011;
ED20 = 0.397;
sa20 = 0.001.
In this, the absorption cross sections were averaged with respect to the Maxwellian spectrum:
S 6a (x) xe- dx
1 x.e-.c dx
where x = E/kTo.
It should be noted that the distribution of the neutron density, i.e., of the value of f n(E)dE is determined in
measurements (see, for instance, [6]) as well as in calculations with the accepted averaging. Therefore, in using
the obtained results for calculating the thermal utilization factor, one should use the absorption cross sections for a
constant temperature, for instance, Tn , introducing, however, temperature corrections for the deviation from the
1/v law.
For assemblies with uranium sleeves whose outside diameters were 4.6, 5.0, and 5.4 cm, the thickness of the
heavy water layer was equal to 5, 5.5, and 6 cm, respectively. Thus, the measurements performed and comparisons
between the experimental and theoretical results have shown that the experimental neutron density distribution in
fuel elements of heavy-water reactors with organic coolants are in agreement with the calculation results for the
single-velocity model with Tn = 1.3 To and Tn = T.
1. A. D. Galanin, In the coll.: Neutron Physics [in Russian], Gosatomizdat, Moscow (1961), p. 125.
2. A. Amouyal, P. Benoist, and J. Horowitz, J; Nucl. Energy, 6, 79 (1957).
3. V. V. Goncharov et al. In the book: Transactions of the Second International Conference on the Peaceful Uses
of Atomic Energy. Reports by Soviet Scientists. Vol. 2, Atomizdat, Moscow (1959), p. 243.
4. P. P. Blagovol, In the coll.: Neutron Physics [in Russian], Gosatomizdat, Moscow (1961), p. 56.
5. V. I. Mostovoi et al. In the book: Transactions of the Second International Conference on the Peaceful Uses
of Atomic Energy. Reports by Soviet Scientists. Vol. 2, Atomizdat, Moscow (1959), p. 546.
6. R. Deutsch, Nucl. Sci. and Engng, 10, 400 (1961).
7. L. N. Yurova et al. Atomnaya L`nergiya, 12, 331 (1962).
8. K. Case, F. de Hoffman, and G. Placzek, Introduction to the Theory of Neutron Diffusion, I. Los Alamos (1953).
' All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be. available in English translation. A complete list of the cover-to..
cover English translations appears at the back of this issue.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
CALCULATION OF y -RAY ENERGY ABSORPTION
B. M. Terent'ev, V. A. E1'tekov, and D. I. Dolenko
Translated from Atomnaya Energiya, Vol. 15, No. 5,
pp. 382-286, November, 1963
Original article submitted January 8, 1963
By means of the Monte-Carlo method, a determination was made of the fraction of y -ray energy
absorbed in the elements of a complex heterogeneous system formed by a cylindrical, irradiated
water-equivalent mass, cylindrical y -ray sources located inside or outside the mass, and units of
auxiliary equipment. From the results, various energy efficiencies (e.e) were determined depend-
ing on the y radiation from particular systems which were models of radiochemical equipment.
Results from corresponding experiments were in good agreement with the calculated data. The
program enabled one to find the e.e. for arbitrary macro-systems of a similar type.
One of the problems which arise in the carrying out of any radiochemical, radiobiological, and some medical,
investigations is the determination of total absorbed y -ray energy in the irradiated system. This quantity may be
obtained by integration of the absorbed doses in some volume, but determining the latter, even by approximate
methods [1], presents great difficulty, especially in the case of heterogeneous media, because of the necessity for
taking multiple scattering into account.
A semi-empirical method has been given r2] for the direct determination of total absorbed energy. This
method was based on an analytic determination of the primary, attenuated y -ray flux escaping from the system
(without considering scattering) and the introduction, after comparison with experimental results, of a correction
factor (build-up factor for total flux). This method is very satisfactory for doing engineering physics calculations,
but it is impossible to apply it universally since it is difficult to extrapolate data for a system with small dimensions
to a large-scale system.
An exact analytic solution for the problem of finding both the absorbed dose field and the total absorbed y -ray
energy is possible through the kinetic equation for y -quanta [3], but the techniques for solution have not yet been
completely developed. In cases of complex geometry, it is more convenient to use the Monte-Carlo method which
has been used before [4] for the computation of a similar set of problems.
In this paper, the method and results are given for a Monte-Carlo computation of the absorbed energy distribu-
tion among system components which was performed on the "Strela-3" computer. The calculations deal with models
of two typical radiochemical apparatuses of the "tubular heat exchanger" (Fig. la) and "fractionating still" (Fig. 1b)
types which are finite heterogeneous systems. Some of the calculated results are compared with experimental data
which was obtained with the K-60,000 equipment described in [5]. The initial energy for all quanta was assumed to
be 1.25 MeV (the average energy of the Co 60 y -ray spectrum). The scattering of quanta with energies less than 0.01
MeV was not considered since the probability of their absorption greatly exceeds the probabilities for all the other
processes. In the range 1.25-0.01 MeV, only Compton scattering and photo-absorption play an important role. The
mathematical simulation of a y -quantum history was carried out in three steps:
1) the simulation of the creation of a quantum, which occurred uniformly over the entire volume of the source
with uniform distribution in direction;
2) simulation of the quantum trajectory, which was in the form of a broken line within the finite heterogeneous
system;
3) simulation of Compton scattering, which corresponded to the deflection points in the trajectory, and of
photo-absorption which corresponded to the end of the trajectory.
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Fig. 1. Diagrams of models (dimensions
given in mm): 1) source; 2) irradiator;
3) irradiated liquid; 4) model walls.
The amount of energy transferred to matter by the quanta
was summed separately for each material in the system and ob-
tained from the machine in relative units (Tables 1, 2).
The problem of y -ray penetration was solved similarly [4].
The entire volume of the "heat exchanger" was subdivided
into a number of regions occupied by different materials. We in-
dicate the cylindrical regions occupied by the source material by
P o k. In this notation, m1 is the source number in the inner row
(m1 = 1,2,..., M1), and m2 is the source number in the outer row
(m2 = 1,2,..., M2). In our case, M1 = 7 and M2 = 13.
Let bo be the radius of the cylindrical regions. The annular
coaxial cylinders which surround a source are indicated by Pmk
(i = 1,2;..., I-1) and their outer radii by bi.
We consider ak to be the distance from the axis of a source
in the kth row to the central z axis. The external walls of the
heat exchanger, which are also in the form of cylindrical layers,
are indicated by Qj, and their outer radii by cj (j = 3,4,..., J-1).
The remaining volume, which is occupied by the irradiated
liquid, is subdivided into three additional regions: the cylinder
Qo of radius co which contains no sources the axis of this cylinder
coincides with the z axis (cos a1-bl-1), the annular cylinders
Qk (k = 1, 2) from which are removed the regions consisting of the
sources in the kth row together with their surrounding materials,
the outer radius cl of region Ql satisfying the condition a1 + bl-1
cl < a2-b1 _1, and the outer radius c2 of region Q2 equaling
the distance from the z axis to the outer wall of the heat exchanger.
Thus, we have to do with two types of regions (see Tables 1,
2): the regions P 1.11k), where i = 0, 1, 2,..., I-1, and the regions Qj
where j = 0,1,...,J-1.
The height of the heat exchanger is indicated by 2h. The probabilities of Compton. scattering wt and photo-
absorption w2 equal
W1=a?-1; W2=tr 1 (wl-1-w2= 1),
where a and r are the y -ray linear attenuation coefficients for Compton scattering and photo-absorption, respec-
tively. Moreover, in the expressions for o and r, the values which they took at the ends of the straight-line sec-
tions of the trajectory were used. The value of r (in cm-1) was approximated for each material by the formula
ti = Ras+ T,
where a = E/mc2, which holds for a range of E from 0.02 to 2 MeV according to tests that were made. The values
of the constants R, S, T are given in Table 1. The method of calculation of the quantity a and of the quantum
energy loss through scattering did not differ from that described in [4].
The program was constructed so that it could be used for apparatus of arbitrary dimensions having a similar
type of configuration. In particular, the same program was used in this work for the calculation of the distribution
of absorbed energy in the heat exchanger and in the still. In addition, the values of I and J are limited by the re-
quirements I s 9, J `nergiya, 8, 441 (1960).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to.
cover English translations appears at the back of this issue.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP1O-02196ROO0600110003-4
MEASUREMENT OF NEUTRON TISSUE DOSE OUTSIDE
REACTOR SHIELDING
I. B. Keirim-Markus, V. T. Korneev, V. V. Markelov,
and L. N. Uspenskii
Translated from Atomnaya Energiya, Vol. 15, No. 5,
pp. 386-393, November, 1963
Original article submitted January 12, 1963
RUS instruments, developed by the authors, are described that enable one to measure the flux and
tissue dose rate of intermediate neutrons, which make a significant contribution to neutron tissue
dose outside reactor shielding. The neutron dose composition was investigated in experiments at
the IRT-1000 reactor, and it was shown that it depends essentially on shielding composition. It
was established that the neutron tissue dose computed from readings taken with the RPN-1 instru-
ment were actually too low by a factor amounting to one and one half outside water shielding and
to five outside concrete shielding.
Thermal, intermediate, and fast neutrons each make their contribution to the neutron tissue dose outside reac-
tor shielding. The quality of the shielding is often checked with an RPN -1 instrument which detects only thermal
and fast neutrons, and thereby, the contribution of intermediate neutrons to tissue dose is not taken into account.
This is associated not only with the unsatisfactory development of the intermediate neutron dosimetry problem, but
also with the absence of the necessary instruments [1]. The creation of the RUS? instruments [2, 3] make it possible
to partially eliminate the gap and to evaluate the intermediate neutron contribution to tissue dose outside shielding.
The RUS instruments have two scintillation counters T1 and T mounted on an FEU-35 (Fig. 1) and meant for
the detection of slow neutrons. The zinc sulphide phosphor, 7 cm2 in area and containing natural boron or B10, which
was used in [4] was used as a scintillator. It is also possible to use the T-1 phosphor [5]. The scintillation counter
T is a compressed disk 1.2 mm thick containing 0.5 g ZnS-Ag, B and 1 g of plastic which contains 7 mg/cm2 of
boron, and which is approximately ten times more efficient than T1. Depending on the discrimination level, one
pulse from the counter T corresponds to 0.3-1.5 thermal neut/cm2. This counter is practically. insensitive to y-radia-
tion (Co60) up to 0.1 r/sec. By means of a Pu239 check source mounted in the rotating cover of the counter, the cali-
bration of the instrument is checked at the time of measurement.
In the main, the detection of intermediate neutrons by the RUS instruments is based on two well known princi-
ples [ 1, 6], one of which consists of shielding the scintillator by a cadmium layer 0.3-0.5 mm thick as a result of
which the detector T becomes insensitive to thermal neutrons but detects neutrons of intermediate energies (above
0.4-0.5 eV). For Fermi spectrum neutrons ( ^-Ent), the efficiency of a thin boron detector covered by a cadmium
filter is 25 times lower than the efficiency of the unfiltered detector for thermal neutron detection [1] in calcula-
tions based on unit flux. Actually, the ratio of the average efficiencies of such a detector for detecting the inter-
mediate neutrons of a Fermi spectrum (E i) and for detecting thermal neutrons (CT) is
5-1O5
1.128 dE
1
0
dE
6T
U,4
? RUS-2 (USD), RUS-3, RUS-4, and RUS-5 instruments were exhibited at the Exhibition of the Achievements of the
National Economy of the USSR in 1957.
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Mixture of paraffin
and boron carbide
Fig. 1. Neutron detectors of the RUS-5 instrument: T)
slow neutron scintillation counter; K) cadmium cover;
R) moderator for measuring intermediate and fast neu-
tron flux; D) moderator for measuring intermediate and
fast neutron dose.
since the integral in the denominator equals 14, and the ratio of the magnitude of the resonance integral to the mag-
nitude of the thermal neutron capture cross section for thin detectors (1/v type) is 0.5.
Thus, by placing the detector T, without the cadmium cover, in a thermal neutron flux of known density
(DT cm-2 ? sec-1, one can calibrate the detector with cadmium cover as an intermediate neutron dosimeter. Since
a flux of 300 Fermi spectrum intermediate neutrons per cm2 produces a maximum tissue dose of 1 prem [1], then
the neutron tissue dose rate measured by the instrument will be defined by the ratio 25 ? T/300 = `FT/12 1rem/sec.
A similar relation is valid for lithium detectors and other detectors which are based on the use of nuclear reaction
r
with a cross section a - En 2 1/v.
If the detector is not thin, i.e., thermal neutron absorption is large, then an intermediate neutron dosimeter
calibrated by the method presented above will overestimate the magnitude of the tissue dose by a factor
aTn(1-e Tn)-1, where n is the number of boron (lithium, etc.) atoms per cm2 for the effective thickness of the
detector. This factor is 1.17 for the detector T. The specified method of calibration is valid under the condition
that the intermediate neutron spectrum actually obeys the - En' law. This condition is fulfilled sufficiently well
in a number of cases [7, 8]. However, if the shielding contains materials with a large slow neutron capture cross
sections, then the Fermi spectrum is depressed in the low -energy region and the calibration factor for the detector
turns out to be too low. The maximum tissue dose per neutron, averaged over the actual spectrum, thereby increases.
Previously, it was difficult to estimate the error which was introduced by the deviation of the actual. neutron
spectrum outside the reactor shielding from the -En-1 spectrum assumed in the calculations. From a comparison of
the readings from this detector with the results of neutron tissue dose measurements made with other instruments in
various radiation fields, it is clear that this error does not exceed 30% (an example of such a comparison is given
below).
The second principle of intermediate neutron detection which was used in the development of the detectors is
based on neutron moderation. One of the moderators is in the form of a cadmium-covered polyethylene sphere 210
mm in diameter into which the detector T is introduced (see Fig. 1). The dimensions of the moderator are so chosen
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13
1.4
12
U 11
N
1.0
t- -0.7
nC
0.3
0
08
"i I ~
0.1
Neutron energy, MeV
Fig. 2. Dependence of detector R efficiency on neutron energy.
that the efficiency of the scintillation counter with moderator (detector R) is independent of neutron energy, at least
within the range from 25 keV to 5 MeV (with an accuracy of ?20%). The detector operates like a "long" counter
of intermediate and fast neutrons with isotropic efficiency.
Curves are given in Fi-g. 2 for the dependence of detector R efficiency on neutron energy which were obtained
in 1958 with photoneutron sources that were compared with the USSR standard, and which were refined in 1959 with
monoenergetic neutrons from a Van de Graaf generator. Detector R exhibits .a lesser dependence of efficiency on
energy as compared with detectors using cylindrical paraffin moderators 62 and 50-75 mm thick [9, 10].
The configuration of the moderator for the fast and intermediate dosimeter of the RUS-3 instrument (detector
D), selected with the help of photoneutron sources, is in the form of a drop-shaped paraffin mass (250 mm in diam-
eter). Within it is a concentrically located paraffin-filled cadmium shell 150 mm in diameter. The variation of
this dosimeter with hardness is shown in Fig. 3.
In 1959, additional measurements were made a Van de Graaf generator which made it possible to select im-
proved moderator configurations. The dimensions of the internal sphere in detector D of the RUS-4 and RUS-5 in-
struments were not changed, but the external absorbing layer was increased to a diameter of 300 mm and it was filled
with a mixture of paraffin and boron carbide (in a ratio of 10:4 by weight).
As can be seen from Fig. 3, the variation with hardness of detector D in the RUS-4 and RUS-5 instruments does
not exceed ?3G o in the energy range 0.1-5 MeV. The dosimeter posesses an increased efficiency for the detection
of neutrons with energies below 0.1 MeV. The mean efficiency for the detection of Fermi spectrum neutrons is over-
estimated by approximately 30%. Such a discrepancy is permissable since 43% of the maximum tissue dose from the
intermediate neutrons in the Fermi spectrum falls in the energy range 0.1-0.5 MeV, and only 20% in the region below
1 keV [11]. The variation with hardness of detector D is considerable better than that for detectors with paraffin cyl-
inders 115 mm thick or with paraffin spheres 255 mm in diameter [9].
Measurements of neutron flux and tissue does outside reactor shielding were made with detector T in conjunc-
tion with moderators and cadmium filters. Thermal neutron flux density (~T was recorded by detector T without
cadmium filter, neglecting possible changes in neutron temperature. The thermal neutron tissue dose rate PT was
determined from the relation 1100 neut/cm2-sec ^- prem/sec [1]. The intermediate neutron tissue dose rate PI
was measured by detector P (counter T with cadmium shield) which was calibrated by the method given above. The
intermediate and fast neutron flux density ((tI + F) was determined from the readings of the detector R. The total
neutron flux density' was determined from the sum of the quantities measured by detectors T and R.
The intermediate and fast neutron tissue dose rate PI + F was measured with detector D which was calibrated
by means of a Po-Be source. Calibration was made on the basis that neut/cm2-sec was equivalent to 1 prem/sec.
The total neutron tissue dose rate P was determined from the sum of the measurements with detectors T and D. The
fast neutron tissue dose rate PF (neutrons with energies En > 1.5 MeV) was estimated with the RPN -1 instrument
1
I
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10- 10-3 10-2 10-1 1.0 10
Neutron energy, MeV
Fig. 3. Dependence of detector D efficiency on neutron energy: 1) maximum tissue dose per unit neu-
tron flux, x 0.72 ? 10-8 rem/neut-cm-2 [1, 2]; 2) neutron detection efficiency of detector D in RUS-4
and RUS-5 instruments; 3) neutron detection efficiency of detector D for the RUS-3; 4); 4) variation
with hardness of detector D in the RUS-4 and RUS-5 instruments; 5) variation with hardness of detector
D for the RUS-3.
which was calibrated simultaneously with detector D and which discriminated against as much as 50 pc /sec of Co60
y -radiation. It was assumed that 25 neut/cm2-sec corresponded to 1 prem/sec for flux densities measured with the
RPN -1.
Besides neutron flux density > 1, R > Rk? (31)
In conclusion, we turn our attention to the fact that coalescence of gas pores is usually accompanied by an in-
crease in volume of the whole sample. This is due to the fact that the flow into the pores of vacancies occurring in
the lattice, which tends to remove the local stresses around the pores, is made up for by the same amount of vacan-
cies coming inside the material from the surface. Assuming that the change in volume of the material is exactly
equal to the change in volume of the gas pores, we obtain for large times (r 00)
AV _ 2a T ,2 R3 v3 (X) X dX - S v3
0 0
where VO is the original volume of the sample.
For coalescence when particles are being born continuously, we have qo # 0 in Eq. (12). In proceeding to a
discussion of the pore distribution mechanism under conditions where particles are being born continuously in the
lattice, we assume, as in the preceding section, that the function 8(y) approaches a constant limit S ,, as y increases
without limit, which cannot be less than 80, since otherwise the law of conservation of matter [Eq. (12)] would be
violated.
Taking 8 = R in Eq. (17), we find that the concentration of gas particles in the lattice varies with time as
according to the law
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We use this result to find the unknown quantity D,o. Substituting (33) in the law of conservation of matter gives the
asymptotic equation
4u = `)2 p (v, . y) dv.
(34)
Equation (34) may be used to find the value of a.. It is very complicated, and it is impossible to make an
exact solution without knowing the initial distribution function. Nevertheless, a number of conclusions may be
drawn regarding coalescence under conditions where gas atoms are being continuously produced in the lattice. A
detailed study shows that b w >
50.
This fact is responsible for the peculiar nature of the coalescence under the
conditions being discussed (qo ~
0).
Note first of all that in this case, at some instant of time r 0, a range 6 v (which
increases with. time to the value
ii
) occurs in the values of v, in which the rate of change of the pore
00
dimensions in v-space is positive. This means that as r -* oo, a finite number of grains of the new phase will re-
main undissolved in the solid solution, i.e., gas pores having the asymptotic dimension v2(g0). It follows from this
that
qoP. vv2 N (90).
The value of r 0(q0) is found from the condition
P ('0) =
We find from Eq. (35) that
Il 90Y
vN (90)
q0
v1V (q0)
(37)
It appears at first glance that if q0 - 0, S oo, and thus, the agreement between the results of the present
and the preceding section no longer exists. However, this contradiction may easily be got rid of if it is borne in
mind that S ,o is only reached asymptotically.
Reducing q0 increases the time interval To required for the curve showing the function dv2/dy = 4(v, y) to
touch the v axis at the point vo = 2 as it moves in the direction of positive values of dv2/dy. Here, the number of
points that have been able to cross the vicinity of the point vo = 2, and, in the final count, disappear at the origin
of coordinates, increases, while the number of points N(qo) "captured" asymptotically at the point v2 decreases
correspondingly. In the limit, when q0 --' 0, we have v2 v1 vo, and contact at the point vo = 2 only occurs
asymptotically, i.e., N(q0) -* 0, qo -> 0, r -. On the other hand, an increase in q0 is accompanied by a decrease
in ro, and, hence, by an increase in N(qo). Since the value of N(q0) cannot be greater than the original number of
pores, we have N(q) -> N0q0/ v for large values of q0.
In a way similar to what was done in the preceding section, we now find the change in volume of the material
as a function of time for large times:
AV =BLa2-4n
v3fo(v)dv.
V0 3
Comparing this expression with the corresponding formulas of [7], we see that taking account of coalescence does
not change the asymptotic character of the relation between the volume change and the time. It follows from the
arguments given above that the role of coalescence when particles are being born continuously is simply that of re-
distributing the pores in dimensions, with the result that the pores having an original dimension less than some criti-
cal value are dissolved, while the pores remaining in the solution equalize their dimensions asymptotically. In this
case, the total number of pores decreases, which, however, has no effect on the relation- between the volume change
and the time.
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Note that for the conditions under discussion, the mean pore dimension in v-space for qo o 0 is asymptotically
equal to
qu ?1
-l\1+ (q0)
(39)
In conclusion, the author expresses his gratitude to V. M. Agranovich for discussion of the results of the work
and valuable comments, as well as to 9. Ya. Mikhlin and Yu. V. Konobeev for useful discussions.
LITERATURE CITED
1. 0. M. Todes, Zh. fiz. khim., 20, 630 (1946).
2. 0. M. Todes and V. V. Khrushchev, Zh. fiz. khim., 21, 302 (1947).
3. I. M: Lifshits and V. V. Slezov, Zh. eksperim. i teor. fiz. 35, 479 (1958).
4. C. Wagner, Z. Elektrochem., 65, 581 (1961).
5. Berns, In the book: Transactions of the Second International Conference on the Peaceful Uses of Atomic Energy
[in Russian], selected papers by foreign scientists, Vol. 6, Moscow, Atomizdat (1959), p. 325.
6. S. Pugh, J. Nucl. Mat., 4, 177 (1961).
7. V. M. Agranovich, f. Ya. Mikhlin, and L. P. Semenov, Atomnaya 6nergiya, 15, 393 (1963).
8. G. Greenwood and A. Boltax, J. Nucl. Mat., 5, 234 (1962).
9. G. Greenwood, A. Foreman, and 0. Rimmer, J. Nucl. Mat., 1, 305 (1959).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-,
cover English translations appears at the back of this issue.
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
LETTERS TO THE EDITOR
THE MOTION OF ISOLATED CHARGED PARTICLES
IN A MAGNETIC FIELD WITH HELICAL SYMMETRY
V . M. Balebanov, V . I Volkov, V. B. Glasko, A. L. Groshev,
V. V. Kuznetsov, A. G. Sveshnikov, and N. N. Se-mashko
Translated from Atomnaya L`nergiya, Vol. 15, No. 5,
pp. 409-410, November, 1963
Original article submitted March 13, 1963
In this paper we consider the possibility of stabilizing a plasma in a magnetic mirror trap with the help of
helical stellarator windings. In contrast to the case of a toroidal stellarator, in which changing deflection and the
radius-dependence of the spacing between lines of force produces stabilization, in the case of an open-ended mag-
netic mirror trap stabilization can only occur as a result of the drift of the particles. We shall call the particle
drift "useful" [1] if it leads to stabilization. (The direction of drift in this connection is opposite to the direction of
particle rotation).
Let us consider the motion of particles in a magnetic field produced by current I passing through a triple spiral
winding with radius a and pitch L. In addition to this let there be a homogeneous longitudinal field of intensity Ho.
We shall neglect the effect of the mirrors, assuming that the trap can be made sufficiently long. It may be ex-
pected that particles injected in such a field inside the separatrix [2] will not come out at the side walls along the
lines of force. In what follows we shall consider predominantly particles injected inside the separatrix.
Study of the equations of motion in the drift approximation shows that actually in the central region the parti-
cles move on surfaces which for small values of the Larmor radius RL almost coincide with the magnetic surfaces
encircling the axis. For large values of RL the surfaces in which motion takes place are turned through 60? with
respect to the magnetic surfaces, but they remain closed.
Fig. 1. Regions in which the plasma can be absolutely contained
(shaded region forbidden); 6 = w - az; u = cos 6.
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Vi, degrees
Fig. 2. Drift angle corresponding to the pitch
of the helical winding as a function of the in -
jection angle 0i for y = 0.5, ro = 0.2 (a) RL
=0.2;b)RL=0.1):1)a=2;2)a=1.3;3)
a = 1.
given
Fig. 3. Drift angle as a function
of the injection angle of particles
bi for large RL near the separa-
trix (to.= 0.7, RL = 0.2, (x = 1,
y = 0.08; arrow shows emergence
from wall): ? wo = 0; 0 - rpo
= 30?; x - coo = 60?.
The exact eouations of motion also give regions in
which a particle may be found [3]. In the case of helical
symmetry it may be shown that these regions may have
radial gaps, or, alternatively, may be closed around the
axis, depending on the initial conditions (Fig. 1).
The sign of the azimuthal drift of the particles may
be determined if the magnetic field is known as a func-
term in the series of Bessel functions, then in a cylindrical system of coordinates the square of the field may be
2,ta _ 21
where a= L , Y- jlod
H =Ho [1+6,1, (r )3 cos 3 (T-az) -;-36y2 (r)4]
a / a
From this equation it is clear that for small radii the field increases with radius in some azimuths and falls in
others. Hence particles moving inside the separatrix and going around the axis of the system must experience a
change in the sign of the azimuthal drift. The sign of the total drift may be determined on solving the equations
.of motion of the particles in such a field.
The motion of the particles was investigated both in the drift approximation, where an analytical relation be-
tween the drift of the particles and the field parameters is obtained, and by way of numerical integration of the
exact equations of motion. The solution of the drift equations shows that the relations between the angle of drift of
the particles and the injection angle 0 i (Fig. 2) is analogous to the relation in [4] for a corrugated field. However,
in the case of .a helical field the positions of the transition points between "useful" and "harmful" drift depends on
the pitch of the spiral winding. With increasing pitch these points move to the left (see Fig. 2a). The shift to the
left also takes place on reducing the Larmor radius (see Fig. 2b). On increasing the current I or the injection radius
ro the transition point does not move, but the steepness of the curves increases sharply. The left-hand boundary of
the region of "useful" drift is determined by reflection from the field maximum. (It must be noted that the curves
of Fig. 2 are constructed for injection at the field minimum.) The left-hand boundary moves to the right with in-
crease of y, to and a.
Calculations of particle motion on a high-speed digital computer showed that the drift theory gives the correct
form of the relation between total drift and the field parameters and injection conditions. However the numerical
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value of the drift given by the computer differs somewhat from the value obtained in the drift approximation. This
is apparently linked with the fact that for the values of Larmor radius considered (RL/a = 0.2) the drift equations are
insufficiently accurate.
Numerical integration of the equations of motion was also carried out in a series of cases in which reflections
of particles take place from the field maximum. The injection points were chosen close to the separatrix, both in-
side and outside. The total drift in the majority of cases had negative sign. In certain variants particles were ob-
served to leave at the side walls (Fig. 3).
The calculation shows that in a field with helical symmetry inside the separatrix "useful' drift only takes
place for particles with large Larmor orbits in a narrow range of injection angles. On going across to smaller Larmor
orbits (RL/a < 0.1) the region of "useful" drift vanishes. This shows that for small Larmor orbits the stabilization
effect cannot exist. -
1. V. Balebanov et al., J. Nucl. Energy, 5, 205 (1963).
2. A. I. Morozov and L. S. Solov'ev, Zh. tekh. fiz., 30, 271 (1960).
3. V. M. Balebanov et al., Report No. 10/211 presented to the International Conference on. Plasma Physics and
Control of Thermonuclear Synthesis, Salzburg, MAGAT9 (1961).
4. A. I. Morozov and L. S. Solov'ev, Zh. tekh. fiz., 30, 261 (1960).
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
INELASTIC SCATTERING OF 14-MeV NEUTRONS BY LIGHT NUCLEI
E. M. Oparin, A. I. Saukov, and R. S. Shuvalov
Translated from Atomnaya Energiya, Vol. 15, No. 5,
pp. 411 -413, November, 1963
Original article submitted March 25, 1963
Calculations of the passage of neutrons through thick layers of various materials are made more difficult by
the lack of necessary data on the spectra of fast neutrons inelastically scattered by light nuclei with atomic weights
ranging from 6 to 16. Some information of the spectra obtained when neutrons are scattered by beryllium and carbon
is given in [1-3]. It is impossible to base the calculations on the temperatures of scattered neutrons for energies of
0.5-4.0 MeV, measured in [4], since in the scattering of neutrons with energies higher than 10 MeV a considerable
role is played by the processes of direct interaction of neutrons with the individual nucleons of the nucleus. This
leads to a substantial increase in the average energy of the inelastically scattered neutrons.
The present paper concerns the study of the spectra of neutrons inelastically scattered by lithium, beryllium,
boron, carbon, nitrogen, and oxygen for an incident-neutron energy of 14 MeV. The experimental procedure, based
on measurement of the flight time, is similar to that described in [5]. The geometry of the experiment is shown in
Fig. 1.
0209400 mm
Fig. 1. Geometry of the experiment: 1) Lead shield;
2) neutron detector; 3) specimen under investigation;
4) lead; 5) monitor; 6) collimator; 7) water shield; 8)
tritium target; 9) cast-iron cube; 10) alpha counter.
As the neutron detector we used a plastic scintilla-
tor 100 mm high and 100 mm in diameter, with an FEU-36
photo multiplier. The resolution time of the apparatus
(2 r), determined from the gamma peak, was 3.5 ? 10-9 sec.
When neutrons were recorded, this time was increased to
5.4.10-9 sec. The increase was the finite time of neu-
tron flight through the detector and also to the smaller
number of pulses and their greater amplitude dispersion
in the scintillator used. We used 60 x 100 x 100 mm
specimens made of the following materials: lithium hy-
dride (LiH), beryllium, carbon (graphite), boron carbide
(B4C), melamine (C6H6N6), and water. Since the meas-
urements were made at an angle of 90? to the original
neutron beam, the presence of hydrogen in the compounds
studied left the measurement results unaffected, within
the limits of experimental error. The use of shielding
made it possible to obtain an effect -to -background
of about 3 -4 in the region of the elastic -scattering peak
at a counting rate of 20-25 pulses per minute.
Figure 2 shows the observed dN/ dt spectra of the
scattered neutrons at an energy of 14 MeV. Since the
resolving power of the equipment was insufficient to distinguish the peak of the elastically scattered neutrons from
the spectrum of inelastically scattered neutrons, this distinction was made by using data on the energies of the first
states of the B", C'2, N14 and 016 nuclei given in [6]. For each nucleus the number of neutrons scattered with the
excitation of a specific level of the nucleus was taken to be proportional to a-Ei/6, where Ei is the energy of the
level, and a is an empirical parameter so chosen that the energy of the neutrons, averaged over all possible excited
states of a given nucleus, will be equal to the average neutron energy Eav, found from the experimental spectrum
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0 10 20 30 40 so 60
Time of flight, 10-9 sec
a
30 40 SO 60 70
Time of flight, 10-9 sec
20 30 #0 SO 60
Time of flight, 10-9 sec
d
0 10 20 30 40 50 60
Time of flight, 10-9 sec
e
0 i0 20 30 40 SO 60 70 90 0
Time of flight, 10-9 sec
c
I
20 30 40 30 6'O
70
Time of flight, 10-9 sec
f
Fig. 2. Time spectra of neutrons scattered by lithium (a), beryllium (b), boron (c), carbon (d), nitrogen (e), and
oxygen (f). (The dot-and-dash curves on graphs c and e represent the spectra for boron and nitrogen; the dashed
curves on all the graphs represent the parts of the spectra corresponding to inelastic scattering.)
where Ei is the scattered -neutron energy corresponding to the excitation of the given level. In order to determine
the experimental value of Eav, we first made an approximate distinction between the elastic and inelastic portions
of the spectrum on the assumption that the initial section of the spectrum, corresponding to inelastic scattering, has
the shape of a Gaussian curve with a peak in the region of the first levels. After selecting the value of 0, we con-
structed a time spectrum of the neutrons, taking the resolving power of the apparatus into account. In the final
construction of the spectrum of inelastically scattered neutrons, we used only the initial portion of the calculated
spectrum.
1166
B~ C
oron
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 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
Data on the Spectra of Neutrons Inelastically Scattered
by a Number of Nuclei
Relative number of scattered neutrons, Olo
Energy
c 1.
range,
MeV
>8.5
-
i
17
15 i
19
28
18
8.5-6.0
18
23 1
21.19
21
34
39
24
27
6.0-4.5
24
19 1
17
112
16
16
23
19
20
4.5-3.0
22
16 1
16
;19
13
23
20
15
21
3.0-2.0
21
14
16
119
I1
16
20
16
19
2.0-1.5.
16
11
11
116
10
11
I
1
i
i
I
?3.0!?2.0
1
?3.01 1I ?4.5
Note. Columns 1, 2, 3, and 4 include data from the follow-
lowing studies: present study [7], [9], and [8], respectively..
When neutrons are scattered by beryllium through the (n, 2N) process, the picture is more complicated, and
therefore, when a distinction was made between the elastic and inelastic types of scattering, the dashed curves in
Fig. 2 were so drawn as to make the ratio of the areas under the curves correspond to the known cross sections of
elastic and inelastic scattering by beryllium, on the assumption that there was spherical symmetry in the angular
distribution of the neutrons produced by the (n, 2n) reaction. The first excited level of lithium had a very low ex-
citation energy (470 keV), and it was therefore included in the elastic scattering. This assumption is completely
acceptable for calculations of the passage of neutrons through a substance. In Figs. 2a, b we show by solid curves
(without dots) not only the experimental curves but also the spectra of inelastically scattered neutrons, calculated
on the assumption that the spectrum is Maxwellian at a temperature T = 2Eav. As can be seen from these figures,
the temperature curves corresponding to the statistical model differ considerably from the experimental curves.
The final results of the measurements are shown in the table, which gives the relative number of neutrons in
various energy ranges in comparison with the data of other studies [7-9]. It can be seen that the results of the differ-
ent measurements are in satisfactory agreement..
1. J. Anderson, Phys. Rev., III, 572 (1958).
2. D. Hughes and R. Schwartz, Neutron Cross Sections. Supplement I. (1957).
3. I. V. Gordeev et al., Handbook of Nuclear Physics Constants for Reactor Design [in Russian] (1960).
4. E. Craves and L. Rosen, Phys. Rev., 89, 343 (1953).
5. V. I. Strizhak, V. V. Bobyr', and L. Ya. Grona, Zh. 6ksperim. i teor. fiz., 40, 725 (1961).
6. Nuclear Physics, V, 11 (1959).
7. E. Remy and K. Winter, Nuovo cimento, IX, 664 (1958).
8. J. Singlatary and D. Wood, Phys. Rev., 114, 1595 (1959).
9. L. Rosen and L. Stewart, Phys. Rev., 107, 824 (1957).
All abbreviations of periodicals in the above bibliography are letter-by-letter transliter-
ations of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of this issue.
Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
 Declassified and Approved For Release 2013/02/25: CIA-RDP10-02196R000600110003-4
Yu. V. Taran
Translated from Atomnaya Energiya, Vol. 15, No. 5,
pp. 413 -414, November, 1963
Original article submitted April 3, 1963
In a number of experiments with polarized thermal and resonance neutrons it is required to change the adiaba-
tic direction of the polarization vector of a neutron beam with respect to some given direction (for example, the
nuclear polarization vector). The adiabatic rotation of the neutron polarization vector through a given angle may
be effected by means of a rotating magnetic field. Such a device is called a spin rotator. From the adiabaticity
criterion proposed by Hughes [1] it follows that the frequency of Larmor precession wL = yHo of the magnetic mo-
ment of a neutron must be greater than the frequency of the rotating magnetic field w0, that is, WL = kwo, where
k >> 1. In this case the spin of the neutron will follow the field adiabatically. Obviously, the criterion for non-
adiabaticity will be the inequality wL 8 1,0 i>2
Ta181-100 0.137
0.95?0.10
1.35?0.1 1.45?0.15 1 1.51.) 0.15
1.10?0.1 5
0.303
0
482
0.35?0.05
0.45?0.115 0.50?0.05 0.50?0.05
0.50 0.05
.
-
0.30?0.05 0.504-0.05 0-5-
-)?0.05
0.60 } 0.0(;
an (total)
1.30?0.15 2.10?0.20 2.45?0.20-
I 2.60?0.20 1 2.20?0.20
Ba135 - 7
Ba137-.11.3
0.49
0.66
-
-
-