SOVIET ATOMIC ENERGY VOLUME 19, NUMBER 4

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000700020004-2
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 122
• Document Creation Date: December 23, 2016
• Document Release Date: March 15, 2013
• Sequence Number: 4
• Publication Date: October 1, 1965
• Content Type: REPORT

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Volume 19, Number 4
October, 1965
SOVIET
ATOMIC
ENERGY
,
? ATOMHAII 3HEPrlifi
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
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CPYSTALLOGRAPHY
THE GROWTH OF CRYSTALS
A. V: Shuhnikov and N. N. Sheftal', Series Editors ?
This continuing series 9n crystal growth 'represents the
work of Soviet scientists-for the moit originally pre-
sented at the All-Union Conferences on Crystal Growth
held at the Institute of Crystallography in Moscow.
Volume 4
These 42 papers deal with experimental studies on growth -
( iif part, nucleation) of 'crystals and monocrystalline films,.
liquid ct'ystals, the production of monocrystals of various
materials, the search for ways of growing new crAtals,
? important aspects of crystal growth, and surveys for ferro-
electric crystals:Ihcludes two papers on crystal symmetry
by Sheftal' especially eipinded and revised for this edition.
Translated froM,Russian.
CONTENTS: Experimental Studies: Productioh of crystallization
nuclei iii the presence of a seed crystal ? Relation of impurity effects
in crystal growth to pH of solution ?? Growth of epitaxial germanium
films from supercooled droplets ? Effect; of pH on?ilie shape of
ammonium dihydrogen phosphate tryst* ? Production of crystalli-
zation/nuclei at the surface of an aqueous solution by a spark dis-
charge Equilibrium shape offs crystal in relation to the bulk free
energy ? The effects of borax bn the rate of growth of alum crystals
froth solution ? Transfer of defect's in a deformed seed to the grown
crystal ? Anisbtropy in the -melting of o-nitroplienol crystals in the
saturated vapor of camphor ? Formation of skeletal ,cavities in
lithium fluoride crystals ? Conical structures on crystal i ? Frost
patterns on windowsi?,Growth form and properties of liquid crystals
of thiazine -dyes ? Vitrified liquid-crystal films ? GrOwth of. mono-
crystalline neinatic? films ? Growth of Monocrystals and Auxiliary
Studies: Growth arid piezoelectric properties of crystals of acenaph- ?
thene ? 'Aspects of the growth ,of monocrystals of potasSidm dihy-
drogen phosphate ? Some changes in a method of growing crystals
from melts ? Growth of calcite, Monotrystals under hydrothermal
conditions ? Crystallization of a film betWeen parallel growing
germanium dendrites ? Growth of lead sulfide monoeryttals by,
Tamman's method ? Twin structure of germanium dendritic strips ?
Growth Of crYstals of silicon carbide from ths vapor state ? Growth
fcirmS of crystals, of germanium and silicon 'grown from gaseous
,
? solution ? Morphology or needle, whisker, and strip crystals of
silicon ? Oxidation of crystals of ferrites with the spinet structure
during growth by Verneuits method' ? Growth' of crystals during ??
reciprocating motion in .a solution ? Growth-of potassium niobate
crystals on seeds from a potash melt,. Zinc sulfide c6/stsis 'grown
from melt ? Growth of Cr203 monocrystale by Verneuil's method ?
Survey Work and Growth'Methods: Crystallization of zincite under
hydrothermal conditions ? Crystallization of cadmium sulfide from
solutions in catImium halides ? 'Possibility of production of crystals
of montroydite (Hg0) under hydrothermal conditions,* Crystalliza-
tion of alkaline-earth: molybdates under hydrothermal conditions ? ?
Hydrothermal synthesis of trigonal silicates and germanates of
.^zinc ? Reviews: The search for new terroelectrics and`antiferroelec-,
:trios not belonging to the oXide group ? Production of monocryetals'"
of gallium arsenide ? Isomorphism and ferrbelettric properties ?
Oriented overgrowth (epitaxiS) of crystalline materials ? Miscel-
leneous:'N. N. Sheftal: The determination orsymmetry ? The physical
meaning of symmetry ? Diary: N; N. Shelter and E. N. Slavnova:
Exchange of experience in studies on crystal growth.
206 pages ? " ,
Also available: ,
1966
(
$20.00
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368 pages
1962
'$2500
Volume 2
178 pages
1960
- , $16.00,
Volume
295 pages
1958
, $15.00
?CONSULTANTS BUREAU 227 West 17th Street New York, New York 10011
,
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ATOMNAYA E. NERGIYA
EDITORIAL BOARD SOVIET ATOMIC
A. I. Alikhanov M. G. Meshcheryakov
A. A. Bochvar M. D. Millionshchikov
N. A. Dollezhal' (Editor-in-Chief)
V. S. Fursov P. N. Palei ENERGY
I. N. Golovin V. B. Shevchenko
V. F. Kalinin D. L. Simonenko
N. A. Kolokol'tsov V. I. Smirnov
(Assistant Editor) A. P. Vinogradov A translation of ATOMNAYA ENERGIYA,
A. K. Krasin N. A. Vlasov
A. I. Leipunskii (Assistant Editor) a publication of the Academy of Sciences of the USSR
V. V. Matveev
? 1966 CONSULTANTS BUREAU, A DIVISION OF PLENUM PUBLISHING
CORPORATION, 227 West 17th Street, New York, N. Y. 10011
Volume 19, Number 4
October, 1965
CONTENTS
RUSS.
PAGE PAGE
Plasma Jet Deflection in Magnetic Fields?V. F. Demichev, V. D. Matyukhin,
A. V. Nikologorskii, and V. M. Strunnikov
1253
329
The Interaction of a Modulated Flow With Plasma?Ya. B. Fainberg, and V. D. Shapiro
1260
336
The Use of An Integrating Coincidence y-Spectrometer for Analyzing a Mixture of Radioactive
Isotopes?V. A. Blinov, V. N. Dmitriev, and M. I. Kuznetsov
1268
342
The Use of the Pn -Approximation in the Description of the Distribution of Neutrons
in an Absorbing Rod?I. V. Sergeev
1272
346
Electrophoretic Filter Cleans Up Reactor Water?V. D. Ganzha, A. I. Egorov, D. M. Kaminker,
A. B. Kolyadin, K. A. Konoplev, Yu. P. Saikov, and V. T. Sharov
1277
350
Attenuation of Pile Radiations in Serpentinite Sand?G. A. Vasirev, A. P. Veselkin,
Yu. A. Egorov, G. G. Moiseev, and Yu. V. Pankrattev
1283
354
Theory of Cascades for Separating Multi-component Isotope Mixtures
?R. Ya. Kucherov and V. P. Minenko
1290
360
A Study of the Dose-Rate Field in an Irradiator with y-Ray Source Consisting of Spent
Reactor Fuel Elements?V. E. Drozdov, I. M. Zakharova, and S. P. Dobrovol'skii
1301
367
Effect of Temperature and Neutron Irradiation on the Plastic Deformation of a-Uranium
Single Crystals?F. P. Butra, Z. F. Evkina, 0. L. Fufaeva, I. A. Korobeinikov,
and L. M. Lebedev
1307
372
ABSTRACTS
Dissociation of Fast Ions of Molecular Hydrogen and Charge Exchange of Fast Protons
in a Lithium Arc?G. F. Bogdanov, A. N. Karkhov and Yu. A. Kucheryaev
1316
381
Ages and Migration Areas of Neutrons from Polyenergetic Sources in Organic
and Metal?Hydrogen-Containing Moderators?D. A. Kozhevnikov
1318
382
Reducing Capture y-Radiation and Radiative Heat Emission in a Reactor Vessel
by Blocking and Boronizing the Thermal Shield?E. N. Goryanina, K. K. Popkov,
S. M. Rubanov, and S. A. Tsvetkova
1320
383
Method for Calculating the Fuel Depletion in a Cylindrical Reactor With a Mobile
Compensating System?G. V. Mukhina, A. N. Protsenko, and N. M. Trukhachev
1321
383
Choice of the Boundary Conditions in Using the Method of Spherical Harmonics
?V. S. Shulepin
1323
385
Annual Subscription: $95
Single Issue: $30
Single Art de: $15
All rights reserved. No article contained herein may be reproduced for any purpose whatsoever
without permission of the publisher. Permission may be obtained from Consultants Bureau, A
Division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011, U.S.A.
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CONTENTS (continued)
LETTERS TO THE EDITOR
Leakage of Particles from the Accumulator Caused by Amplitude and Frequency
RUSS.
PAGE PAGE
Instability of the Compensating Field?A. S. Bakai
1324
386
Limitations of the Densities of Interacting Currents in Opposed
Ultrarelativistic Beams?M. I. Kheifets and V. D. Shapiro
1329
388
Xenon Oscillations in Reactors?I. P. Bacherikov
1331
389
Relation Between Thermal Conductivity and Oxide Concentrations in Sodium
?F. A. Kozlov and I. N. Antonov
1333
391
Back-Scattering of 7-Rays from a Spherical Surface?N. F. Andryushin and B. P. Bulatov
1335
392
Angular Distribution of the Intensity of y-Radiation Scattered by Lead and Water
?L. M. Shirkin
1338
394
Angular Distribution of 7-Rays from a Point Source, Scattered in Shielding
?A. V. Larichev
1340
395
Angular Distribution of Neutron Dose Close to the Air?Ground Boundary
?I. V. Goryachev
1342
396
Spectral Distribution in the Surface Atmosphere of 7-Rays from a Point Source of Co6?
Shielded by Aluminum?V. A. Ionov
1344
397
Light Pencil?A. A. Kurashov, and V. V. Paramonov
1348
400
Human Biological Dose from Internal Radiation Produced by Sr90?V. M. Malykhin,
A. A. Moiseev, and V. P. Shamov
1350
401
SCIENCE AND ENGINEERING NEWS
XVIII Session of the Learned Council of the Joint Institute for Nuclear Research
?V. Biryukov and Yu. Ryabov
1353
406
International Symposium on Electron and Photon Interactions at High Energies
?V. S. Barashenkov
1357
406
Pulsed Neutron Research?M. V. Kazarnovskii, Yu. P. Popov, and I. P. Sadikov
1360
408
Seminar on Applications of Isotopes and Radiations in Industry and in Medicine
?V. Sinitsyn
1363
410
A Conference on Nomography?M. V. Filippov
1366
412
The Russian press date (podpisano k pechati) of this issue was 10/9/1965.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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PLASMA JET DEFLECTION IN MAGNETIC FIELDS
(UDC 533.9)
V. F. Demichev, V. D. Matyukhin, A. V. Nikologorskii,
and V. M. Strunnikov
Translated from Atomnaya nergiya, Vol. 19, No. 4,
pp. 329-335, October, 1965
Original article submitted February 20, 1965
We investigated the motion of plasma jets in a quadripole magnetic field produced by four current
conductors whose axial lines were bent through 90.? (the curvature radius was 30 cm). The maxi-
mum strength of the magnetic field in the "slit" between the current conductors was 6 k0e. The
plasma jet, which was produced by means of a coaxial gun, was injected along the axis of the mag-
netic system. The magnetic system was adequate for deflecting the plasma jet, which had an ini-
tial velocity of 8 x 106 cm/sec and a maximum concentration before deflection of 2 x 1016 cm-3.
The jet velocity was equal to 7 x 106 cm /sec. In spite of the considerable loss of particles (due to
the presence of slits in the magnetic system), the ion concentration in the jet beyond the turn at-
tained 2 x 1014 cm-3, while the over-all number of particles was as large as ?1017.
As a result of deflection, it was possible to eliminate completely the neutral gas accompany-
ing the, jet and to obtain virtually totally ionized plasma. The optimum value of the magnetic
field's strength was ?3 k0e.
The method of injection of plasma blobs into magnetic traps is widely used in investigations in the field of
high-temperature plasma physics. The blobs that can presently be obtained by means of certain types of plasma
injectors may have very high directional velocities (up to 108 mm/sec) and considerable densities 1012? 1016 cm-3.
However, direct utilization of these blobs in traps is very complicated due to the incomplete ionization of plasma
in the blob, the presence of impurities of extraneous elements, and the flonmonochromaticity of the directional vel-
ocities of blob particles. In connection with this, attempts are being made at eliminating neutral atoms and impu-
rities from blobs by means of external magnetic fields. In particular, deflection of the plasma jet in a curvilinear
magnetic field can be used for this purpose. The motion of plasma jets in curvilinear fields is also interesting in it-
self, since jet deflection may be found necessary for filling traps with a complex magnetic field geometry.
Magnetic fields produced by means of a bent solenoid were used in [1-5] for deflecting plasma jets. The re-
sults obtained in these experiments indicate that, under certain conditions, the hydrogen component of plasma can
propagate with a concentration of up to 1013 cm-3 along a curved magnetic field with a strength of 1-2 k0e. It was
found in this case that the heavy-ion impurities were eliminated from the plasma. The-purification is apparently
connected with polarizing electric fields [6], which arise in plasma as a result of the centrifugal and the gradient
drifts. However, the presence of such fields limits the concentration of the plasma as it propagates along the curved
field. The fact that the authors of [1-5] succeeded in deflecting plasma with a comparatively high concentration
was a consequence of the partial neutralization of polarizing fields by the currents flowing over the plasma jet and
closing the circuits either through the source or the metallic diaphragms or the plasma duct walls which were in con-
tact with the plasma.
In order to transmit plasma with higher concentration and velocity values through a bent solenoid (which is of
practical interest), it is necessary to increase the strength of the magnetic field and to neutralize to a greater extent
the polarizing fields. However, this greatly reduces the purification effect, i.e., the plasma retains a large amount
of impurities, the mass composition of which is completed with heavy and slow ions [3].
For plasma jet deflection, L. A. Artsimovich has suggested the use of magnetic fields produced by a system of
conductors in which the current directions alternate. The present article provides the results of an experimental in-
vestigation of the motion of dense plasma jets in a magnetic field produced by a system of four current conductors
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Fig. 1. Conductor system used for producing the
magnetic field (the arrow indicates the direction
of plasma jet injection).
move along a curvilinear path near the AB axis. As
(Fig. 1)., The middle sections of the conductors were bent
through 900. The field strength in such a system is equal to
zero along the axial line AB; * with increasing distance from
this line, the field increases in correspondence with the ex-
pression:
H= '
0 2k1 (r
a 1 -I- (r/a)1, '
where k is the number of conductors, I is the current intensity,
and a is the distance between the axial line of the system
and the conductont
As it is deflected from the axis, the plasma jet expe-
riences the force of excess magnetic pressure in a direction ,
opposite to the deflection. If the gradient of the magnetic
field is sufficiently large for the excess pressure to compen-
sate the centrifugal force, the plasma jet will be able to
a rough approximation, this condition can be expressed thus:
ev2 1 dH
11 4g, dr '
where p = E Mini is the density of plasma, v is the velocity of directional motion of a volume element of the
plasma jet, aind R is the turning radius. Estimates made on the basis of this expression indicate that the chosen con-
figuration of the magnetic field could secure the deflection of plasma jets with very high velocity and plasma con-
centration values. For instance, in a field with a gradient of ?103 0e/cm, a jet moving at a velocity of 107cm/sec
shoula be deflected with a concentration of 1016 cm-3. However, due to the field's diffusion in plasma and the
presence of slits in the magnetic system, the thus obtained plasma densities would actually have much lower values.
EXPERIMENTAL DEVICE AND INVESTIGATIVE METHOD
The schematic diagram of the device used in our experiments is shown in Fig. 2. The hydrogen plasma jet
from the coaxial injector 1 passes through the porcelain cylinder 2 and the quartz cylinder 4 and enters the .space
between the bent current conductors 11, where it is deflected 90? from its initial direction. In order to eliminate
the effect of the plasma duct walls, the curvilinear section of the current conductors is enclosed in a large vacuum
volume 6. In the deflection zone, the current conductors are insulated from the plasma; they pass through Dural
tube sections with vacuum sealing at the ends. Besides the bent section, the current conductors have two rectilinear
sections, one ahead and one beyond the turn (both sections have a length of 30 cm). The curvature radius of the
axial line is also equal to 30 cm. The spacing between adjacent current conductors is 9.2 cm. Each current conduc-
tor consists of two insulator-separated coaxial copper tubes, which are connected in such a manner that the current
passes twice through the entire system. A capacitor battery C3, which has a capacitance of 1500 ? F, serves as the
current source for the magnetic system. The battery is switched on by means of the vacuum discharger D3.
The maximum strength of the magnetic field in the slit between the conductors was 6 k0e. (The value H of
the magnetic field's strength that figures in the text and in the drawings pertains to this location.) The maximum
value of the magnetic field's gradient near the axis attained 1.6 k0e/cm. The period of field change was equal to
0.82 msec; the jet was injected in the field at the instant of time corresponding to the maximum of the field, so
that its strength remained virtually constant during the process.
*In fact, the zero field line does not coincide with the axial line on the system due to the curvature of the conduc-
tors. However, the shift of these lines is small (-3 mm), and we shall, therefore, neglect it.
f The minus sign in this expression corresponds to a change of the field in the x direction, while the plus sign corre-
sponds to a change in the y direction (see Fig. 1).
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4 D3 1 c3=i5oc jiF
7
5<
or
To pump
D/ C,=5OgiF
" _L
T T
2
C2=-10 p F
D4
Fig. 2. Schematic diagram of the experimental device; 1) injector; 2) porcelain plasma duct
(diameter: 120 mm); 3) measuring magnetic field coils; 4) quartz plasma duct (diameter: 90 mm);
5) UHF antennas; 6) vacuum volume (50 x 50 x 70 cm3); 7) location at which the electric probes,
calorimeters, and thermoprobes are installed; 8) observation window; 9) stainless-steel diaphragms
(thickness, 0.1 mm; opening diameter, 60 mm); 10) plastic insulators; 11) current conductors for pro-
ducing the magnetic field.
i/ni (H=0)
A coaxial electrodynamic injector was used as the
plasma source [7]. The operating conditions chosen for the
2,0 injector ensured the following plasma jet parameters: The
maximum directional velocity (the front velocity) was
vfr = 107 cm/sec; the velocity of the central jet portion,
which had the highest density, was v = 8 ? 106 cm/sec; the
maximum plasma density was (1.5? 2) ? 1015 cm-3; the elec-
tron temperature at the concentration maximum was Te 5 eV;
the length of the jet at the time of entrance into the magnetic
field was L 50 cm. Besides the hydrogen lines, the plasma
spectrum also contained the lines of carbon, copper, and other
elements. The intensities of the carbon line C II 4276 A and
-3 -2 -1 0 the copper line Cu I 5218 A were comparable to the intensity
of H6, which indicate that the hydrogen plasma contained a
considerable percentage of impurities.
Various experimental methods were used in the measure-
.-nents. The high-speed photographing of the process was per-
formed by means of an SFR camera. The velocity of the plas-
ma jet and its density and temperature were measured by
means of double electric and diamagnetic probes. The plasma energy was determined by using the calorimetric
method and a thermoprobe [8]. The light radiation of the plasma jet was investigated by means of a spectrograph
and a UM-2 monochromator with a photomultiplier adapter. Microwave diagnostics (X = 4 mm and X = 8 mm)
was used for measuring the electron concentration and calibrating the electric probes.
2 3 r, cm
Fig. 3. Distribution of the ion concentration over
the transverse cross section of the plasma jet in a
field with H = 3 k0e: ? .and 0) ni distributions
along the x and y axes, respectively.
EXPERIMENTAL RESULTS
The passage of plasma through the magnetic field created by the rectilinear current conductor sections was
inVestigated in the preliminary experiments. The aim of this investigation was to ascertain the efficiency of the
chosen magnetic field configuration for the transportation of dense plasma jets. The results of the experiments per-
formed can be briefly summarized as follows.
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-15
4N40
-17 cm3
to C-3
111
10
5
0 0 20 4,0 6.0 H kOe
1,5
,o
17 i
I-
?
KT?
\
Nin
Fig. 4. Dependences of ni and Nin before deflection
on H (x is the point at which the nm value
measured).
x to-11/cm
3,0
2,0
1,0
was
.
,
45?
1 II
?
.
2,0 4,0
6,0 H, kOe
Fig. 5. Dependence of ni at different points of the
system on H: x) position of the electric probes:
probe 1 is located on the axis of the system; probe 2
is located in the magnetic slit at the middle between
the current conductors.
43`,c
0,5
0
1,5
3,0
4,5 H, kOe
Fig. 6. Dependence of 6 on the H value of the mag-
netic field. The measurements were performed at the
point 2 (see Fig. 5).
cause the deflection of the plasma jet. All the experiments, the results of which are given below,
As it becomes concentrated at the axis of the system,
where H = 0, the plasma jet overcomes the rectilinear sec-
tion of the field, whose length is 40 cm. For a field strength
of 4.5 kOe, no changes in the velocity of the plasma jet's
forward front are observed in this section. In this, the vel-
ocity of the region with the maximum concentration drops
by 10-15/0. The plasma density at the entrance to the field
near the system's axis increases approximately by a factor
of 2, after which it slowly decreases due to the leakage of
plasma through the slits during its motion. The plasma
cross section assumes the shape of a cross whose prongs are
oriented along the magnetic field's lines of force. The ef-
fective diameter of the jet's central portion is approximate-
ly equal to 2.5 cm. It decreases with an increase in the
field; the width of the prongs also decreases. The over-all
number of particles in the jet that have traversed the rec-
tilinear field section is much smaller than the number of
particles in the incident jet. This can be explained mainly
by the fact that the magnetic field configuration under in-
vestigation cuts out of the plasma jet, as it were, only its
central region near the axis, where pv2/2 > H2 / 87r , while
the peripheral regions of the jet are slowed down to a great
extent in interaction with the transverse field, due to which
their velocity drops. The leakage of plasma through the
slits of the magnetic system also contributes to the reduc-
tion in the number of particles.
The ion density distribution over the transverse cross
section of the plasma jet in the field is shown in Fig. 3.
The density maximum is located at the axis of the system.
The distribution is smoother along the magnetic field's lines
of force than across the field. The results of the prelimi-
nary experiments have shown that the magnetic system un-
der investigation can be considered as a satisfactory plasma
duct for dense plasma jets.
G. A. Delone and M. M. Savchenko [9] also investi-
gated the motion of plasma blobs in a quadripole magnetic
field. They have shown that the rectilinear section of the
quadripole field possesses good channeling properties for
plasma with a density of ?1012 cm-3.
The experiments on deflecting plasma jets in a quadri-
pole field were first performed by using a stainless-steel
plasma duct, which was placed inside the magnetic system.
However, the reflection of plasma from the duct walls was '
so intensive that it was impossible to separate the effect of
plasma deflection by the magnetic field from the deflec-
tion effect due to reflection from the walls. In order to
eliminate the effect of the walls, the curvilinear section
of the magnetic system was enclosed in a large vacuum
volume (see Fig. 2). Since, in this case, there were no
walls in the deflection zone, only the magnetic field could
were performed
under these conditions.
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025 0 0,25 0,5 0,75 1,0 r, cm
Fig. 7. Distribution of ni across the magnetic slit
for H = 3 kOe
Fig. 8. Dependence of ni in the jet after deflection
on H (the probe is located at the system's axis at the
point marked by the cross).
No ut /Nin
0,15
0,10
10,05
17
2 4 6 H,
kOe
Fig. 9. Dependence of Nout/Nin on H.
Before reaching the deflection zone, the plasma jet
passed through the rectilinear section of the field. With an
increase in the field strength, the ion concentration in the jet
near the system's axis increased before deflection. For
H = 3 kOe, the concentration ni attained 2 ? 1014 cm-3, and
it remained virtually unchanged with an additional increase
in the field (Fig. 4). The total number Nin of ions entering
the deflection zone was determined with respect to the mea-
sured transversecross section of the plasma jet and its lengths
and concentration. Figure 4 also shows the dependence of Nin
on the magnetic field's strength. In spite of the increase in the
concentration of ions in the jet, the Nin value decreases with
an increase in the field; in this, an especially rapid decrease
is observed in the case of relatively weak fields. This is
mainly due to a sharp reduction in the cross-sectional area of
the jet with an increase in the field strength.
High-speed photographing of the plasma passage through
the curvilinear section of the magnetic field has shown that
plasma overcomes this section in the form of a relatively fine
jet without visible deviation from the system's axial line.
, The curves (Fig. 5) showing the ion density variation at
two different points of the magnetic system in dependence on
the field strength make it possible to estimate the effect of the
magnetic field on the deflection of plasma. The ion concen-
tration at the magnetic system's axis monotonically increases
with an increase in the field strength. The rate of this increase
gradually diminishes and becomes insignificant for 3 kOe.
A sharp increase in the ion concentration, which is connected
with plasma pinching, is observed initially with an increase in
the field strength in the slit of the magnetic system (see curve 2
in Fig. 5), after which (for H > 1 kOe) the concentration de-
creases rather rapidly. For 1.5 kOe, the ion concentration
in the slit and at the system's axis are equal. With a further
increase in the field strength, the ion concentration in the ex-
ternal slit continues to decrease, but it remains fairly high
(ni r:-.1 10" cm-3) even at maximum strength(H = 6 kOe), which
leads to considerable plasma losses due to leakage through the
slit.
The ion concentration distribution along the radius in the
deflection plane is nonsymmetric with respect to the axial line
within the curvilinear section. As was to be expected, the con-
centration near the external slit is much higher than near the internal slit, especially in the case of weak fields. A
reduction in asymmetry is observed with an increase in the field strength. A similar plasma distribution pattern in
the transverse cross section was also observed in measuring the density of plasma energy by means of microcalo -
rimeters.
The width (5 of the slit through which plasma leaves the magnetic system depends on the magnetic field's
strength (this dependence is given in Fig. 6). The 45 value is defined as the half-width of the curve of the plasma
density distribution across the slit (Fig. 7). Starting with H = 3 kOe, 5 changes very little, which is apparently con-
nected with the diffusion of the magnetic field in plasma. Therefore, for the assigned values of the plasma jet's vel-
ocity, density, and temperature at the entrance to the system, increasing the field strength beyond a certain given
value (,-,3 kOe in our case) would be ineffective, since it-would hardly reduce the plasma loss (see Figs. 5 and 6).
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We should mention a peculiarity connected with plasma leakage through the slit. The curve of Fig. 7 repre-
senting the ion density in the slit is asymmetric with respect to the median deflection plane of the magnetic system.
The maximum is shifted to a distance of ?0.3 cm toward the conductor in which the current direction coincides with
the direction of the plasma jet's velocity. This effect is apparently connected with the drift of plasma in the crossed
electric and magnetic fields. The electric polarization of plasma as it moves in a nonuniform transverse magnetic
field [10].
After deflection, the plasma moved, as before deflection, in a field formed by rectilinear current conductors.
The concentration of plasma, its energy, the over-all number of particles and their distribution over the transverse
cross section, and the degree of plasma ionization were measured in this place. After deflection, the velocity of
the densest portion of the jet was equal to 7 x 106 cm/sec.
In the absence of the field, the plasma deflection was not recorded by means of the ordinarily used methods.
However, already for H = 300 0e, the electron concentration in the plasma jet after deflection attained 1.7 x 1013cni 3.
The dependence of the maximum ion concentration in the jet after deflection on the magnetic field's strength is
shown in Fig. 8. The basic increase in concentration occurs as the field changes from 0 to 3 k0e. For H = 3 k0e,
the concentration is equal to 2 x 1014 cm-3, after which it increases very slowly with a further increase in the field
strength, as can be seen from the figure.
The plasma density distribution over the transverse cross section is approximately the same as the distribution
before deflection. However, the distribution in the deflection plane is somewhat asymmetric with respect to the
system's axial line: The ion concentration decreases less sharply toward the external magnetic slit than toward the
internal slit. The distribution of the plasma energy density has a similar shape in this plane. The mean transverse
cross section of the plasma jet only slightly depends on the magnetic field's strength for H > 1 k0e; it is equal to
5-6 cm2.
The over-all number Nout of particles that have been deflected increases with an increase in the field strength
in spite of the fact that Nit" decreases. Here, as in the case of the concentration value, the basic increase in Nout is
observed as the field strength changes from 0 to 3 k0e. The dependence of the Nout /Nin ratio on the magnetic
field's strength is shown in Fig. 9. The over-all number of deflected ions amounted to about 1010 of Nisi; it was
equal to ?5 x 106. In certain experiments, this value attained 1017.
As the plasma jet moves along the curvilinear section of the magnetic system, the effect of elimination of
neutral atoms from the plasma should take place. Neutral atoms, which are retained in the jet only as a result of
charge-exchange collisions, will leave the surface layer of the jet, whose thickness is of the order of the charge-
exchange range X = 1 into , where o is the resonance charge-exchange cross section. The effect of elimination of
neutral atoms from the plasma is considerable when the X value becomes comparable to the transverse dimensions
of the jet as a result of the reduction in the ion concentration.
The checking of the elimination of neutral atoms from the plasma consists in determining the degree of ioni-
zation. One of the indirect methods used for rough estimates of the degree of ionization consisted in comparing the
plasma energy measured by means of a thermoprobe or a calorimeter with the energy carried only by the ions. The
ion energy was determined with respect to the measured distribution of the ion concentration along the jet and with
respect to the ion velocities. According to this estimate, the degree of ionization amounted to ,400/0, while the
measurement error was 201o. More accurate results were obtained by using the optical method. Since the ion
concentration had been measured, the problem consisted in determining the concentration of neutral hydrogen atoms.
The method which we used made it possible to determine the upper limit of the neutral atom concentration
no with respect to the absolute intensity of the Ha line. This method consisted in the following. According to cal-
culations, the distribution of the population of levels with principal quantum numbers n a? 3 should obey the Boltz-
mann law in hydrogen plasma with an electron concentration ne 1014 cm-3 and a temperature Te = 5 eV. Conse-
quently, the over-all concentration of excited atoms with n 3 can be related to the intensity of the Ha line
(n = 4) by means of the expression:
1258
N=
A42hv42
n* _
Igie Te
AE34 ?
Te
go
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Here, 18 is the intensity of the H8 radiation per unit volume of plasma, A42 is the Einstein coefficient of spontaneous
radiation of the H8 line, if 421.s the frequency, g? is the statistical weight of the level, n = j, and ,LE3i is the differ-
ence between the energies of levels with n = 3 and n = j. The summation is performed up to the maximum principal
quantum number no corresponding to the maximum atomic radius 'max in the plasma, which, according to [11, 12],
can be considered to be close to the Debye radius RD. In our calculations, Rmax was assumed to be equal to 0.7 RD.
The thus determined concentration N of excited atoms differed only slightly from no, since, according to calculations,
more than 96/0 of all the neutral atoms were in the excited state with n a 3 in our case.
The concentration of neutral atoms, determined with respect to the absolute intensity of H8 was equal to
(1 ? 0.7) ? 1012 cm-3, which was less than one-hundredth of the ion concentration in the jet after deflection. Thus,
it can be assumed that, after deflection, neutral hydrogen atoms are virtually completely eliminated from the plasma.
The presence of the small number of neutral atoms in the jet is largely due to their entering the jet from the dia-
phragm and the quartz tube's walls as a result of interaction between them and the plasma flowing out the slits. A
small percentage of the neutral atoms in the jet may also be the result of volume recombination.
A complete elimination of the neutral atoms of impurities should also take place in plasma deflection. More-
over, it seems that ionized impurity atoms are also eliminated to a certain extent from plasma after it has been de-
flected. This conclusion is reached, for instance, on the basis of the behavior of the C II 4267 A line intensity; after
deflection, the intensity of C II is reduced by a factor of 500-1000.
Thus, the chosen configuration of the magnetic field proved to be a sufficiently effective system for deflecting
plasma jets with a mean initial velocity of 8 106 cm /sec and a maximum initial density of 2 ? 1016 cm-3. The
plasma passed through the magnetic system near its axial line. The effective diameter of the plasma jet in the mag-
netic field was equal to ,?,2.5 cm, while its length was ?50 cm. The velocity of the jet's densest portion at the exit
from the magnetic system was 7 ? 106 cm/sec. In spite of the fact that the particle losses in plasma jet deflection
were considerable due to the presence of slits, the magnetic system used made it possible to secure a plasma jet with
a considerable concentration after deflection(ni = 2 ? 1014 cm-3), while the over-all number of particles was ?
As a result of deflection, it was possible to eliminate the neutral gas accompanying the plasma jet and to obtain
completely ionized plasma. The optimum value of the magnetic field's strength was 3 k0e.
The authors are deeply grateful to Academician L. A. Artsimovich for the suggested idea of the experiment
his continued assistance during the work, and the discussion of the results. The authors are indebted to A. M.
Andrianov for his continued interest in this project.
LITERATURE CITED
1. B. G. Safronov, V. S. Voitsenya, and I. I. Konovalov, ZhTF, 32, 678 (1962).
2. H. Eubank and T. Wilkerson, Phys. Fluids, 4, 1407 (1961).
3. H. Eubank and T. Wilkerson, Phys. Fluids, 6, 914 (1963).
4. V. S. Voitsenya et al., ZhTF, 34, 280 (1964).
5. G. M. Batanov et al., ZhETF, 46, 1915 (1964).
6. G. Schmidt, Phys. Fluids, 3. 961 (1960).
7. V. F. Demichev and V. D7Matyukhin, Dokl. AN SSSR, 150, 279 (1963).
8. Yu. G. Prokhorov et al., In the Collection: Plasma Diagnostics [in Russian], Moscow, Gosatomizdat (1963),
p. 274.
9. G. A. Delone and M. M. Savchenko, ZhTF, 34, 1409 (1964).
10. I. I. Demidenko et al., ZhTF, 34, p. 1183.
11. H. Margenau and M. Lewis, Rev. Mod. Phys., 31, 595 (1959).
12. Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena
[in Russian], Moscow, Fizmatgiz (1963).
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THE INTERACTION OF A MODULATED FLOW WITH PLASMA
(UDC 533.9)
Ya. B. Fainberg and V. D. Shapiro
Translated from Atomnaya nergiya, Vol. 19, No. 4,
pp. 336-342, October, 1965
Original article submitted December 28, 1964; revised May 4, 1965
The disturbance of longitudinal waves by the interaction of a modulated flow of electrons with plasma
is investigated. Conditions are found for the generation of instabilities, and the frequency spectrum
and increment of growth of the oscillations are calculated.
The majority of papers published on the theory of bunch instabilities deal mainly with the interaction of origi-
nally unmodulated beams of charged particles with plasma (see the literature cited in [1]). It is plain, however,
that the modulation of a beam must essentially change the frequency spectrum and the growth increment of the os-
cillations generated, and also the effective beam and plasma temperature due to the oscillations. Preliminary mo-
dulation will destroy the particle phasing, necessary for the development of instabilities, for those oscillations with
frequency and wavelength different from the modulation, and so this modulation will lead to the disruption of cer-
tain instabilities. At the same time the modulation aids in the development of instabilities with frequencies and,
wavelengths coinciding with those of the modulated frequency, since in this part of the spectrum the initial ampli-
tude of the oscillations considerably exceed the fluctuation amplitude.
When an originally unmodulated beam interacts with plasma a wide wave packet with a relatively low field
strength of the wave vector k in each harmonic is generated, but if the beam is modulated there will be strong reso-
lution of the spectrum. We also note that, because of the phase grouping of the particles, caused by the modulation,
the energy scattering due to the excitation may be considerably reduced, i.e., there will be a decrease in the effec-
tive temperature of the beam and the plasma. In addition to the change in the frequency spectrum and in the growth
increments of the bunch instabilities, there will also be new instabilities connected with parametric resonance. The
width of parametric resonance is small, however, and so the inhomogeneities and collisions in real systems will weaken
these instabilities and sometimes eliminate them entirely. The above qualitative conclusions concerning the inter-
action of modulated beams with plasma (see also the paper [1] by one of the authors) are confirmed by the experi-
mental results described in [2, 3].
Theoretical studies of the interaction of modulated beams with plasma have up to the present been limited to
the consideration of the generation of oscillations in the approximations obtained with the assumption of a given cur-
rent [4, 5]. In [6-8], parametric instabilities of a modulated electron beam without plasma were investigated by
using a self-consistent approximation. To investigate parametric and bunch instabilities caused by the interaction
of a modulated beam with plasma, we must consider the generation of oscillations in a self-consistent approximation.
In the present article, this problem is solved for the case when the beam is a periodic sequence of compensated
bunches moving through plasma with a constant velocity U. All calculations were performed in a reference system
related to the bunches. In such a system the density of a bunch when there are no oscillations varies according to
the law
1260
where
Nb= NI E (z ? 1n)--cr(z?ln?a)
n=-00
ATI at 71
1,6.1016
300
28
3,0
114
1,6.1016
--
11
5,8
.113
5,5.1017
300
3
13,5
>71
1,6.1016
--
14
503
113
5,5.1017
300
5
9,2
>71
5,5.1017
--
7
21,3
>71
5,5.1017
300
9
11,2
>71
5,5.1017
--
8
22,1 '
>74
1,6.1016
450
13
1,2
109
1,6.1016
200
18
3,7
106
1,6.1016
450
16
2,2
120
1,6.1016
200
20
4,2
120
1,6.1016
450
17
1,4
110
1,6.1016
200
22
6,6
118
5,5.1017
450
1
6,2
>71
5,5.1017
200
4
11,6
>71
5,5.1017
450
9
4,8
>71
5,5.1017
200
6
15,9.
>71
--
--
?
?
--
5,5.1017
200
10
13,2
>71
--
--
--
?
--
P, kg coi
Sc
20
10
20
JO
20
(0
010
2
b
87
a
0 10 20 30 40 50 60 ,%
Fig. 12. Orientation of strain axes and strain curves
of single crystals annealed for 2 h after irradiation
with a flux of 5.5 ? 1013 neutrons/cm2; a) without
annealing; b) annealing at 200?C; c) annealing at
450?C.
S, kg/mm2
7
6
5
4
3
?
17
55.10 neutrons/cm2
16./O'ffneutro
5/cm2
0 100 200 300 400 500 t,t
Fig. 13. Effect of the annealing temperature of
the irradiated single crystals on the critical shear-
ing stress of the (010)? [100] system.
DISCUSSION OF RESULTS AND SUMMARY
The study of strain in single Crystals of a-uranium
from +20 to has shown that the plastic deformation
of both perfect single crystals obtained by recrystallization
in the a-region and imperfect ones obtained by the 0.-+
transformation takes place by way of the same slip and
twinning systems. The perfection of the structure, however,
affects such mechanical characteristics as the critical shear-
ing stress for slip. In samples with block disorientations of
2 to 3? the value of S for the (010)? [100] system at room
temperature equals 0.6 ? kg/mm2.
Our experiments have shown that for appropriate
orientation of the strain axes the single crystals undergo
slip deformation in the (010)? [100] system with little hardening up to comparatively large elongations (4010). This
kind of deformation is called easy slip. Slip in the (010) plane also occurs at ?196?C (see Fig. 3 and 4); however,
the 10 to 12-times increase in the critical shearing stress for certain orientations of the strain axes impedes the re-,,
laxation of local overstresses on twinning, and this leads to rupture of the samples for slight elongations.
1313
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Fig. 14. Microphotographs of the surface of single crystals
after slight deformations (x 120): a) nonirradiated single
crystals; b) single crystal irradiated with a flux of
1.6 ? 1036 neutrons/cm2; c) single crystal annealed at 450?C
for 2 h after irradiation.
Slip is the simplest form of plastic deformation, and the most sensitive to disruption of the crystal lattice.
Hence the effect of neutron irradiation on plastic deformation appears most markedly in single crystals whose strain
axis orientation corresponds to the onset of deformation by slip in the system (010)? [100]. The rise in the yield
stress and the appearance of "yield teeth" in such samples characterizes radiation hardening.
It is suggested in [16, 17] that, as a result of fast-neutron irradiation, "impoverished zones" with high vacancy
concentrations are formed in metals. The radiation hardening is explained by a dispersed distribution of the impo-
verished zones and their interaction with dislocations. Electron-microscope study of uranium irradiated by a flux of
thermal neutrons (1011 neutrons/ cm2) [18] showed damage in the form of a series of fine spots having definite crystal-
lographic orientations and also in the form of dislocation loops.
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We are not quite sure of the nature of the radiation defects in the irradiated a-uranium single crystals, but it
may well be that radiation damage to the lattice after irradiation by fluxes up to 5.5 ? 1017 neutrons/cm2 fixes the
dislocation sources and thus impedes deformation by way of slip. At first, when the radiation dose is still small,
damage to the lattice increases rapidly, but as the total flux rises the part played by radiation annealing becomes
more important, until dynamic equilibrium sets in between the defects being formed and those being annihilated;
this leads to saturation of the critical shearing stress associated with slip. After irradiation by. large fluxes
(4 ? 1020 neutrons/cm2, burnup 0.16%) the single crystals still have considerable ductility, the elongation reaching
4050 for slip in the (010) plane.
Radiation defects are sensitive to annealing. Annealing single crystals irradiated by fluxes up to
5.5 ? 1017 neutrons/cm2 leads to a softening process. After two-hour annealing at 200?C the critical shearing stress
of the (010)- [100] system changes little, but after annealing at 450?C it falls and approaches the value for nonir-
radiated samples. At 450?C the mobility of the atoms is quite considerable, and this leads to the resorption of the
complexes of radiation defects restraining the multiplication and motion of dislocations.
LITERATURE CITED
1. R. Cahn, Acta metallurgica, 1. 49 (1953).
2. L. Lloyd and H. Chiswik, Trans. AIME, 203, 1209 (1955).
3. P. Lacombe, D. Calais, and N. Simenel, J. Nucl. Materials, 4, 325 (1959).
4. R. Teeg and R. Ogilve, J. Nucl. Materials, 3, 81 (1961).
5. L. Lloyd et al., J. Nucl. Materials, 4, 231 (1961).
6. P. Lacombe and D. Calais, In the book, "Transactions of the Second International Conference for the Peaceful
Uses of Atomic Energy," Collection of papers by foreign scientists [Russian translation], Vol. 6, Moscow,
Atomizdat (1959), p. 126.
7. A. Lemogne and P. Lacombe, J. Nucl. Materials, 2, 203 (1959).
8. S. T. Konobeevskii et al., "Atomnaya gnergiya," 4, 34 (1958).
9. G. Quere and F. Nakache, J. Nucl. Materials, 2, 203 (1959).
10. S. Billington and J. Crawford, Radiation Damage Solids, New York (1961).
11. In the Book "Transactions of the International Conference on the Peaceful Uses of Atomic Energy, Geneva
(1955), Metallurgy of Nuclear Energy and Effect of Irradiation on Materials " [in Russian], Moscow, Metal-
lurgizdat (1956), p. 642.
12. F. P. Sutra, E. F. Evkina, and 0. P. Fufaeva, "Fizika metallov i metallovedenie," .15, 873 (1963).
13. E. Shmidt and V. Boas, Ductility of Crystals (Especially Metals) [in Russian], Moscow, GONTI (1938).
15. V. I. Rozhanskii, "Dokl. AN SSSR," 123, 648 (1958).
16. A. Seeger, Radiation Damage Solids, Vol. 1, Vienna IAEA (1962), p. 101.
17. J. Diehl et al., Phys. Letters, 4, 236 (1963).
18. E. Ruede and S. Amelinckx, J. Nucl. Materials, 9, 116 (1963).
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions 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 2013/03/15: CIA-RDP10-02196R000700020004-2
ABSTRACTS
DISSOCIATION OF FAST IONS OF MOLECULAR HYDROGEN
AND CHARGE EXCHANGE OF FAST PROTONS IN A LITHIUM ARC
(UDC 621.039.6)
G. F. Bogdanov, A. N. Karkhov, and Yu. A. Kucheryaev
Translated from Atomnaya gnergiya, Vol. 19, No. 4,
p. 381, October, 1965
Original article submitted May 26, 1965
The dissociation of fast H2 ions in a high-vacuum lithium arc is used to accumulate high-temperature plasma
in the DSKh-2 apparatus [11. Similar experiments were performed with the "Ogra" equipment in 1963 [2]. To select
optimum accumulation conditions, we need to know the principal parameters of the arc, namely its density and elec-
tron temperature, the cross-section for the formation of protons by the dissociation of fast HI ions on Li+ ions, and
the effective cross-section for charge exchange by fast protons in the lithium arc. Our article described the measure-
ment of all these quantities except the electron temperature. The electron density was measured with a radio-inter-
ferometer working at 8 mm wavelength. To separate the products of the elementary processes occurring during single
passage of a beam of HiF or Hi ions of energies 40-160 keV through the lithium arc, we used the magnetic field of
"Orga."
To record fast neutral atoms from dissociation and charge exchange, we used a thin nickel foil. The yield of
protons from the foil in the above energy range was measured in two different ways.
It was found that the density of the arc increases with the amount of lithium vapor fed to the anode, but is al-
most independent of the voltage applied to the arc. During the cross-section measurements, the density of the arc
was varied in the range (0.5-4) ? 1012 cm-3.
The cross-section for proton formation by dissociation of H2+ ions with energy 160 keV on Li+ ions is ??1.0
? 10-15 cm2, about 1.5 protons being formed for each molecular ion lost. When the energy of the H2+ ions is decreased
to 40 keV, the cross-section for proton formation remains unchanged, but the cross-section for formation of fast neu-
tral atoms of hydrogen increases by a factor of ?2.5. The dissociation cross-section is independent of the condition
of the arc.
...
-
-
/
/1
/
,
',.
,
...
....
....
/
.... ... ..?
.
...........j
cr
_
."---...?.........,.....i
60 80 100 120
Proton energy, keV
140
16
Cross-section of capture of electron by proton in the arc, plotted
versus proton energy: 0-0.04 mg/cm2 foil; ?-0.2mg/cm2 foil.
1316
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The study of charge exchange by fast protons in the lithium arc is complicated by a number of interfering.
factors (charge exchange with the residual gas in the "Ogra" chamber, scattering of protons by the beam receiver,
and presence in the proton beam of HiE ions with energies equal to half of those of the protons). The diagram shows
the effective cross-section for charge exchange in the lithium arc, plotted versus the proton energy. The solid curve
was measured with a 0.2 mg/cm2 foil. The dashed curve, which was measured with a 0.04 mg/cm2 foil, illustrates
the influence of H+ ions present in the proton beam. The charge-exchange cross-section was not found to vary with
the arc conditions outside the scatter limits (shown as vertical lines on the graph).
To check the method, separate measurements were made of the dissociation cross-section of fast H2+ ions and
of the charge-exchange cross-section of fast protons in nitrogen.
The measured values of the cross-section for formation and loss of protons yield an explanation in general
terms of the results of experiments on hot plasma accumulation in the "Ogra" apparatus with lithium arc.
LITERATURE CITED
1. Thermonuclear Division Semiannual Progress Report. ORNL-3564 (1963), p. 16; ORNL-3652 (1964), p. 28.
2. N. N. Semashko, Report to Symposium on Magnetic Traps (Paris, 1963) [in Russian], L. A. Artsimovich, Report
No. 297 presented by the USSR to the Third International Conference on the peaceful Uses of Atomic Energy,
Geneva (1964).
1317
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Declassified and Approved For Release 2013/03/15: CIA-RDP10-02196R000700020004-2
AGES AND MIGRATION AREAS OF NEUTRONS
FROM POLYENERGETIC SOURCES IN ORGANIC
AND METAL-HYDROGEN-CONTAINING COMPOUNDS
(UDC 621.039.532)
D. A. Kozhevnikov
Translated from Atomnaya Energiya, Vol. 19, No. 4,
p. 382, October, 1965
Original article submitted February 23, 1965. Note submitted May 24, 1965
For physical calculations on nuclear reactors and shielding, we need to know the ages and migration areas of
fission-spectrum neutrons in moderators; such data have been found experimentally only with ampoule sources, while
theoretical calculations are difficult because of our lack of knowledge of neutrons characteristics and the difficulty
of allowing for certain specific effects (heterogeneity). The energy spectra of neutrons from ampoule sources are
quite different from the fission spectrum, so that the experimental curves cannot be used without some corrections.
In our paper, we solve the problem of determining the age and migration areas of neutrons from a polyenergetic
source by means of the experimental values of these parameters for neutrons from sources with different spectra
(in the same media).
The age 7* (e) of neutrons with energy & from a polyenergetic source with spectrum A is equal to
A
(e) = [113 (0-13 (8)1 KAB+ t?21 (8),
where 7; (e) is the age of neutrons from a polyenergetic source with spectrum B; r A? (&) and r ?B (e) are the mono-
energetic ages for the lower limits of spectra A and B, respectively; and KAB is the modulus of spectrum A relative
to spectrum B, equal to
?60, A, B? gA:B (eo) ee deo,
KAB-- (6?)A <
(60)13
(80)
where g(80) is the weight function of the spectrum. The monoenergetic ages T1, B (&) can be calculated accurately,
because inelastic scattering and diffraction of neutrons do not occur at energies e & Tin. Furthermore, in this
energy range the scattering cross-sections for neutrons of the nuclei of many elements are either constant or vary
only slightly with the neutron energies. The migration area of thermal' neutrons is calculated similarly to the age:
(m2B MtB) KAB+ mt/A.
Our article gives the ages of indium neutrons in various moderators (H2O, D20, Cl2H10, C51-46, Ci2H/000.735,
CH2, C12, Be9, Be0) for the sources U235, Po? Be, Ra ? Be, Pu? Be, Po ? B. The table gives the quantitative char-
acteristics of the energy spectra of these sources (< & 0 >
= mean energy, D[e 01 = spectral dispersion).
Characteristics of Energy Spectra of Various Sources
1318
Source
CEO,
MeV-
D [F0],
MeV2
U235
2,03
2,50
Po?Be
4,35
5,70
Ra?Be
3,63
8,17
Po?B
3,07
1,00
Pu?Be
4,07
6,92
In determining the age and migration areas of neu-
trons in heterogeneous metal-water mixtures by the method
described above, we are confronted with the problem of
estimating theerrors caused by ignoring the heterogeneity
in calculating 7?A,B(e). It is shown that the maximum
error in 7 ? and M2 for the fission spectrum is less than half
of the error in 7? and M. Graphs are given of the calcu-
lated ages of indium neutrons from the fission spectrum in
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zirconium-water, bismuth-water, iron-water and aluminum-water mixtures, plotted versus the volume ratio of metal
to water for various degrees of heterogeneity. For some mixtures, in addition to the experimental results obtai-ned
with ampoule types sources, we give results of measurements of the fission spectrum; these agree with the theory.
The ages and migration areas of fission-spectrum neutrons in complex media can thus be calculated from laboratory
measurements with ampoule type sources, without the need for experiments with reactors or critical assemblies.
?
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REDUCING CAPTURE y -RADIATION AND RADIATIVE HEAT EMISSION.
IN A REACTOR VESSEL BY BLOCKING AND BORONIZING
THE THERMAL SHIELD
(UDC 539.121.73 : 539.122)
E. N Goryanina, K. K. Popkov, S. M. Rubanov, and S. A. Tsvetkova
Translated from Atomnaya nergiya, Vol. 19, No. 4,
p. 383, October, 1965
Original article submitted May 22, 1964; revised June 15, 1965
This paper is a theoretical study of the effects of boronizing the iron-water thermal shield of a water-mo-
derated water-cooled reactor, and also of various types of blocking of the reactor vessel, on radiative heat emission,
and on the y-ray dose due to radiative capture of neutrons in the thermal shield and reactor vessel.
The authors study iron-water thermal shields with homogeneous and heterogeneous compositions, with iron
concentration ?70 vol. %.
The spatio-energetic distributions of the neutron fluxes were calculated with an M-20 computer, in plane
geometry, with the semi-grouped scheme suggested in [1].
The homogeneous type of thermal shielding was an iron-water mixture of thickness 25 cm. An estimate was
made of the compositions, varying with thickness of the thermal shielding layer, to which was added boron. In the
heterogeneous types, the thermal shielding was boronized by successive replacement of the steel screens by screens
of boron steel (0.5 and 1 wt. %boron); the thermal shielding was 28 cm thick.
The paper also discusses compositions in which the boron concentration in the thermal shielding screen nearest
to the reactor vessel was varied. To study the efficiency of blocking the outer surface of the vessel, the blocking
materials used were boron steel (with up to 5 wt. ?Jo boron), boron carbide, lead and lead boride. Layers of various
thicknesses were used: for boron steel, lead and lead boride they were up to 10 cm, for boron carbide up to 3 cm.
Compositions were also studied in which various boron concentrations were used in the primary shielding water. The
methods of calculation used were those given in [2, 3, 4].
The paper shows (1) that addition of boron to the thermal shielding screens reduces radiative thermal emission
in the reactor vessel, (2) that it is not desirable to use boron steel screens with > 250 boron in the thermal shielding,
and (3) that the use of boron-containing materials and lead for blocking the outer surface of the reactor vessel can
markedly reduce the capture 7 -ray fluxes from the thermal shielding and vessel (by a fact& of three to five).
The most effective material is lead; however, increase of blocking layer thickness db leads to increased yield
of capture y -radiation from lead, and this becomes predominant at db > 6 cm. Lead boride is free from this defect,
and its use shows some promise.
LITERATURE CITED
1. D. L. Broder et al.,Atomnaya nergiya, 12, 129 (1962).
2. D. L. Broder and K. K. Popkov, Atomnaya nergiya, 15, 370 (1963).
3. L. P. Bokacheva et al., Inzh.-fiz. zh., VI, 47 (1963).
4. D. L. Broder, K. K. Popkov, and S. M. Rubanov, Biological Shielding of Marine Reactors [in Russian], Leningrad
Sudostroenie (1964).
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METHOD FOR CALCULATING THE FUEL DEPLETION
IN A CYLINDRICAL REACTOR WITH A MOBILE COMPENSATING SYSTEM
(UDC 621.039.51)
G. V. Mukhina, A N. Protsenko, and N. M Trukhachev
Translated from Atomnaya gnergiya, Vol. 19, No. 4,
pp. 383-384, October, 1965
Original article submitted May 26, 1965
The changes in reactivity and the run duration of a reactor basically depend on the distribution of neutron
fluxes, which vary during the depletion process. Most of the planned and operating reactors are maintained in the
critical state by means of a compensating system (CS) of control elements which are arranged in a certain manner
in the core. Figure 1 shows one of the possible CS positions in themost general case: Here, the core without CS has
3 x 3 = 9 zones. The introduction of compensating elements in this case resulted in two new zones: ABCD and BEFC.
The boundaries AE, EF, FD, and DA are mobile. As the CS shifts, certain zones may disappear, and others may appear.
In certain cases there may be 15 zones.
rf :DAM
mplegift,
SEEM ''' WEE
Fig. 1. One of the possible CS posi-
tions in the reactor.
bO
900
800
a.)
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numerical solution of such a problem is rendered complicated by the fact that the coefficients entering the equations
and the boundary conditions depend on the coordinates and the time, while the method for calculating these coeffi-
cients and the depletion equation are rather cumbersome for most reactors. Therefore, we used a method for deter-
mining all the parameters which made it possible to reduce the computer time by a factor of several tens. These
parameters are represented by polynomials, the argument of which is a quantity proportional to the integral heat
release:
where
(r, z, t)=ei (r, z, (r, 2, 1),
(I)? 11) (r, z, t) Ep (r, z, t)dt.
Here t2? t1 is the time interval during whichCS is present (absent) at a certain given point of the core; 4, is the
thermal neutron flux, normalized with respect to power.
The two-dimensional boundary problem was solved by using the grid method; the "continuous count" method
was used for solving the finite-difference equations [3].
Figure 2 shows the results obtained in calculating the variation of the CS position during the depletion process
for the atomic icebreaker Lenin (solid curve). The points refer to experimental data [4]. The agreement between
the theoretical and experimental results is entirely satisfactory.
LITERATURE CITED
1. A. D. Galanin, Theory of Thermal Nuclear Reactors [in Russian], MOscow, Atomizdat (1959).
2. G. I. M'archuk, Methods for Calculating Nuclear Reactors [in Russian], Moscow, Gosatomizdat (1961).
3. A. N. Tikhonov and A. A. Samarskii, Dokl. AN SSSR, 108, 393 (1956).
I. I. Afrikantov et al., Report No: 313, submitted-by the USSR at the Third International Conference on the
Peaceful Uses of Atomic Energy, Geneva (1964).
1322
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions 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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CHOICE OF THE BOUNDARY CONDITIONS
IN USING THE METHOD OF SPHERICAL HARMONICS
(UDC 621:039.51:12)
V S. Shulepin
Translated from Atornnaya gnergiya, Vol. 19, No. 4,
p. 385, October, 1965
Original article submitted April 20, 1965. Abstract submitted June 21, 1965
This article is devoted to the application of the variational principles presentedin [1, 2] for determining the
conditions at the boundary between two media in solving the single-velocity kinetic equation in the Pn-approxima-
tion of the method of spherical harmonics. In seeking the conditions at the boundary between two media, the use of
the variational method [1] provides one half of the number of boundary conditions that iS required for solving the
kinetic equation in the even or the odd Pa-approximation. The necessary number of boundary conditions can be ob-
tained by using the variational principles [2]. The present article describes the use of the method [1] for determin-
ing the conditions at the boundary between two media on the basis of variational principles [2].
The boundary conditions found as a result of using the variational principles are in complete agreement with
the corresponding conditions given in [3]. However, the variational boundary conditions cannot be considered as the
best. For instance, in the case of the P2-approximation, numerical calculations show that the conditions of conti-
nuity of unidirectional neutron fluxes at the boundary between two media are better than the variational boundary
conditions. The expansion of the solution of the kinetic equation ?z, 1.1) in a series with respect to Legendre poly-
nomials in the P2-approximation is given by
(I) (z, 7 [To (z) + 3qi (z) Pi (11)+59)2(z) P2 (11)1,
(1)
where z is the space coordinate (two-dimensional geometry), p is the cosine of the angle between the direction in ?
which the neutrons move and the z axis, and p are Legendre polynomials. When the solution is written in the form
given by (1), the condition for the continuity of unidirectional fluxes is equivalent to the condition for the conti-
nuity of
, 5
wi and To -I" (P2, (2)
while the variational conditions imply the conditions for the continuity of (pi and vo + 22.
The results of numerical calculations (in the single-velocity approximation) of the cell loss factor and the
critical core dimension in reactors with reflectors indicate that the accuracy of calculations based on conditions (2)
is close to the accuracy of the P3- approximation.
LITERATURE CITED
1. V. S. Vladimirov, Vychislitel'naya Matematika, No. 7, 93 (1961).
2. G. Pomraning and M. Clark, Nucl. Sci. Engng, 16, 155 (1963).
3. G. Ya. Rumyantsev, Atomnaya gnergiya, 10, 26 (1961).
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LETTERS TO THE EDITOR
LEAKAGE OF PARTICLES FROM THE ACCUMULATOR
CAUSED BY AMPLITUDE AND FREQUENCY INSTABILITY
OF THE COMPENSATING FIELD
(UDC 621.384.60)
A. S. Bakai
Translated from Atomnaya gnergiya, Vol. 19, No. 4,
pp. 386-388, October, 1965
Original article submitted January 16, 1965
The total number of particles N(t) in the accumulator is determined by the number of particles n(t) injected
per unit time and the mean lifetime r of a particle in the accumulator:
N(t)_?e?M [N0 + n (s) e?' ds ,
0
where X = hr.
For a constant injection intensity n(t) = n, the accumulation of the necessary number of particles N is com-
pleted during the time
(
?
N
?n
,
n )
while the maximum number of particles stored is Nmax = n/ X. After the end of injection, the accumulated cur-
rent decreases, obeying the e" X t law.
The value of the particle leakage X from the accumulator can be written as a sum of-several terms:
each of which characterizes the magnitude of leakage caused by a certain specific factor. Generally, the X i values
are not independent; however, the effect of any single factor on the lifetime of a particle in the accumulator can
be characterized by the corresponding leakage value X i in the absence of all the other factors.
The magnitude of the particle leakage from the accumulator caused by collisions with the residual gas atoms
and the quantum character of radiation was calculated in [1, 2]. We shall calculate here the amount of leakage due
to the instability of the amplitude and frequency of the potential difference applied to the dees, which compensates
the radiation loss of the particle energy. A similar problem was stated in Blackman's report [3], but, as far as we
know, its solution has not been published.
We shall consider that the amplitude V and the frequency u of the compensating field are random functions,
while
where
1324
(V)=V0; (v)=v0;
/( AV 2\ ? 2 ( Av 2N
170 - El;v0 ) 82,
=
AV= V?V0; Av=v?v0.
(1)
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We shall assume that the disturbances p v and AV constitute fast random processes, while their spectral densities lie
at frequencies which greatly exceed the frequency of synchrotron oscillations, but are much lower than the partiale
revolution frequency. Then, the equations of radial and phase motion of an electron in the accumulator, averaged
with respect to a certain number of revolutions, can be written thus [1];
, AV
1 -r-w 54, ctg cps) A;
-1-4?Vo AT?
Qg ctg cps;
?
Av
where A is the amplitude of radial .oscillations;
E ? Es
e?qa
Es '
(2)
n is the phase shift of the compensating field; q is the frequency multiplicity; a Is the expansion coefficient of the
orbit;
eVo sin cps
02_
27rEs
is the square of the frequency of phase oscillations; and r1 and r are the damping decrements.
The stable motion of particles corresponds to trajectories in a certain limited region of the phase space; the
particles leave the accumulator when the trajectories reach the boundary of this region. The region boundary can
be assigned by the equations;
A=?110; S2S12+ e2=
(3)
The amplitude of radial oscillations decreases in time as ?e-rit, while the random character of changes in
the particle energy inside the dee leads only to insignificant changes in the rate of decrease. On the average, the
amplitude of phase- oscillations decreases as et; however, the diffusion of the particle trajectory in the phase space
occurs due to the random character of the right-hand sides in (2). As a result of this diffusion, the trajectory reaches
the boundary of region (3), and the particle leaves the accumulator. ? If the mean value of the random impulse is
small (e 1.2 ? r), the particle dwells almost all the time in a small region of the phase space in the neighborhood
of the point
while, if it leaves this region, it is highly probable that it will return to it. For determining the lifetime of a par-
ticle, it is sufficient to determine the steady-state distribution of particles in the stability region of the phase space
for the assigned intensity of injection into this region.
It should be noted that the steady-state distribution depends only on the over-all number of injected particles,
since, no matter at what point of the phase space a particle was injected, it is highly probable that it will be found
in the vicinity of the A = = 6 = 0 point shortly after injection.
The distribution density 43 (A, n, E ) of particles in the phase space is determined by the Fokker?Planck
?Kolmogorov equation. This equation can be conveniently written by using the variables
u?(52,3y2+e2)1/2; v=arc tg .
? The method for determining the mean lifetime of the systems described by equations of the type (2) and (3) has
been described in detail in [2]. The fundamentals of this method are briefly set forth in the present article.
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Since it is clear from the physical point of view that the distriblition density does not depend on the phase v, the
averaging can be performed with respect to v. Then, the Fokker?Planck?Kolmogorov equation, averaged with
respect to the variable v, will assume the following form:
all a r a (1)
797- = 57/1 L a 1A2 TA-7r r 1A(D1
ao
+ k [ (13 +Piu2) r, (F42 ?13) (1)? g (4, A),
while
where 52t
(? Ao, u)=--_013 (4, u0):= 0, a1 = 7T- ctg2tp8ei;
1 1
ai .Qt,q2a1; p, = 78- Qsq: ?
(4)
(4')
and g(u, A) is the injection density, averaged with respect to the variable.
Since the steady-state distribution density is independent of the form of g(u, A), the density equation can be
written thus:
a
a A r L atA2
where
a r
L (0 -r Piu2) X (no? 6) (I) ASD ------ 0, (5)
au
Ao uo
S S g(u, A) du dA
-A00
? A0 u0
S S I (A, u) du dA
-A0 0
Thus, the problem has been reduced to the determination of the eigenfunction and the eigenvalue of the operator
(5), (4'). The positive function of this operator is unique, and it corresponds to the smallest eigenvalue. It should
be noted that the variables in Eq. (5) can be separated, while the smallness of the leakage X makes it possible to
seek the solution of this equation as an expansion with respect to powers of X [2].
The solution of Eq. (5) with the boundary conditions 4', which determines the steady-state distribution of par-
ticles in the phase space, is given by
while the leakage value is
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To (A, u)=--15 (A) r+131
(1 -1-13ip u2) 2131
u2 r-01
x 11 + 2 pi) [1_ (1 + 13r_ v) 2131
0
dv
2 (r-1)
I
[ ) 2131 A "1 dv
Tv A v
0
(6)
(7)
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The approximate expressions for X can readily be obtained from Eq. Cl). noting that r>i Thus, for instance,
for 81u/8 ? 1,
while, for
X
(r_0)2 u e 20 uo
r-1-111
F2 ( Pi 213.
1+ T3 Ut
Pt
(9)
As was to be expected, in the case of instability of the compensating field's amplitude and frequency, the leakage
of particles from the aceumulator occurs only as a consequence of the buildup of phase oscillations.
The root-mean-square deviations of the particle parameters from their equilibrium values, calculated by
means of distribution (6),- are determined by the expressions:
213 213 20
(82) -= ; (12) = 92r , (e2) = q2r
where
R--R,
Q ? Bs ?
The dependence of the leakage value on energy can readily be estnblished. For this, we note that
r
; ug c226 ? y2.
Here y = E/ m0c2, where mo is the rest mass of a particle. Assuming that the root-mean-square deviations 6 and
ei are fixed, we shall consider two cases.
1. 0, &? 0. From expressions (7)-(8), we have
2. el = 0, 4 0 0. In this case,
while
y2 e?c2v2,
(12)
cf, c2 >> 1.
The expressions obtained make it possible to determine the degree of accuracy with which the amplitude and fre-
quency of the compensating field must be maintained for the limitation imposed on the leakage value. As an ex-
ample, we shall consider an electron-positron accumulator with strong focusing that is characterized by the follow-
ing parameters:
Es= 2,2-10? eV; r_?_-2,3?10-5;
52g =-- 6.10-7; q=4;
1(2
(13)
Consider that the amplitude V and the frequency ti assume with an equal probability any of the values in the
following intervals:
?An allowance for the nonlinearity of synchrotron oscillations may necessitate some corrections in the expressions
obtained.
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then,
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Vo? AV < V < Vo + AV;
v0--7Av v,,