SOVIET ATOMIC ENERGY VOLUME 14, NO. 5

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• Document Page Count: 100
• Document Creation Date: January 4, 2017
• Document Release Date: September 25, 2013
• Sequence Number: 4
• Publication Date: March 1, 1964
• Content Type: REPORT

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Volume 14, No. 5 ,
?
March, 1964
SOVIET
ATOMIC
ENERGY
? ATOMHAFI 3HEN-1,1R
? (ATOMN4YA gNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
?,
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RELAXATION'B. N. Finkeyhtein ?Preface by A.S. Nowick
Edited by temperatures, Also investigated are the relation-
, -? A Collection of experimental and theoretical in-
- PHENOIVIENA vestigations of relaxation phenomena in metals and
alloys; the'first to be published iranglish devoted
to this field. All the articles in the collection con-
I
? RI cern themselves with some aspect of internal fric-
tion while investigating the Phenomenon in a wide
variety of metal types. The volume contains several
METALS commercial alloys: -
as a large fraction dealing with the properties of
papers of a-general and fundamental nature as well
,
AND Among some 'measurements
meof the effects studied are: The appli:
of internal friction' to the,
study of the decomposition of super-saturated solid
- ALLOYS smoaltuitoionn;sc;redeepfe; cainsdofthcerybsetahla'vla.ottricoe.sm; pelts a
aas.ticdefor- ,
1 t 1 t high
?
ship between internal friction and brittleness, the
possibility of applying the method of internal fric-
tion to the study of sintered materials, and the
mechanism of- impact fatigue. Considerable' atten-
tion is paid to the effects of cold working and
annealing; of alloy transformations, and of grain.
boundaries'on internal friction and anelastic be:
havior. Of particular interest is evidence of the
-wide use of the low frequency torsion pendulum for
such studies. In addition, the damping characteris-
tics of metals and a new method of defectoscopy
are also discussed. '
The book includes extensive references taken from
a wide range of-publications including those of East-
ern Europe and China.
252 pages Translated from Russian $40.00
CONSULTANTS BUREAU 227 West 17 St., New York 11, N.Y.
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ATOMNAYA NERGIYA
EDITORIAL BOARD
A. I. Alikhanov A. I. Leipunskii
A. A. Bochvar M. G. Meshcheryakov
N. A. Dollezhal' M. D. Millionshchikov
K. E. Erglis (Editor-in-Chief)
V. S. Fursov
I. N. Golovin
V. F. Kalinin
N. A. Kolokol'tsov
(Assistant .Editor)
A. K. Krasin
I. F. Kvartskhava
A. V. Lebedinskii
1.1. Novikov
V. B. Shevchenko
A. P. Vinogradov
N. A. Vlasov
(Assistant Editor)
M. V. Yakutovich
A. P. Zefirov
SOVIET ATOMIC
ENERGY
A translation of ATOMNAYA ENERGIYA
A publication of the Academy of Sciences of the USSR
? 1964 CONSULTANTS BUREAU ENTERPRISES, INC.
227 West 17th Street, New York 11, N. Y.
Vol. 14, No. 5
March, 1964
CONTENTS
PA
ENG.
GE
RUSS.
Lenin Prize Winner B. M. Pontecorvo ?N. N. Bogolyubov
457
441
An Adiabatic Trap with Combined Magnetic Field ?Yu. T. Baiborodov, M. S. Ioffe,
V. M. Petrov, and R. I. Sobolev
459
443
Injecting the Ion Beam into the "Ogra? Magnetic Mirror Machine?A. L. Bezbatchenko,
V. V. Kuznetsov, N. P. Malakhov, and N. N. Semashko
462
446
Theory of the Passage of y -Quanta through Matter?V. S. Galishev
469
453
The Differential Equation for the Thermalization of Neutrons in Infinite Homogeneous
Media ?N. I. Laletin
474
458
Study of Spent Fuel Elements from the First Atomic Electric Station? Sh. Sh. Ibragimov,
L. A. Syshchikov, I. M. Voronin, and V. G. Kudryashov
482
465
Note on Determining Irradiation Costs in a Research Reactor ?V. A. Tsykanov-
486
469
Some Laws of the Formation of Epigenetic Uranium Ores in Sandstones, Derived from
Experimental and Radiochemical Data ? L.'S. Evseeva, K. E. Ivanov,
and V. I. Kochetkov
492
474
LETTERS TO THE EDITOR
Elastic and Inelastic Scattering of a-Particles on Alzi? K. P. Artemov, V. Z. Gol'dberg,
and V. P. Rudakov
499
482
Formation Cross Sections of Krypton and Xenon Isotopes in the Fission of Uranium
by 680 MeV Protons
502
484
Note on the Effect of Neutron Polarization on Neutron Transmission in Media?
P. S. Ot-stavnov.
506
487
Angular Energy Distribution of Neutrons at an Interface?V. A. Dulin, Yu. A. Kazanskii,
and I. V. Shugar
508
488
Slow-Neutron Spectrum in the Horizontal Channel of the VVR-S Reactor?R. V. Begzhanov,
D. A. Gladyshev, S.V. Starodubtsev, and T. Khaidarov
511
490
Study of the Sorption Properties of Silica Gel Irradiated with Neutrons? V. V. Gromov
and Vikt. I. Spitsyn
513
491
Investigation of Ion Exchange in Hydrofluoric Acid Solutions? Separation of RaD, RaE,
and Polonium ?M. K. Nikitin and G. S. Katykhin
516
493
The Separation of Oxygen Isotopes by Thermal Diffusion? E. P. Ageev
and G. M. Panchenkov
518
494
(continued)
Annual Subscription: $95
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)
Gamma Radiation Spectra of Radioactive Ores in their Natural Strata, Determined
PAGE
RUSS.
PAGE
by Proportional Counters?B. M. Kolesov, Yu. P. Lyubavin, and A. K. Ovchinnikov. . . . .
521
496
Gamma Radiation of Elements of the Uranium and Thorium Series in the Low-Energy Range ?
B. I. Khazanov
525
499
NEWS OF SCIENCE AND TECHNOLOGY
XIII Session of the Learned Council of the Joint Institute for Nuclear Research?V. Biryukov
and R. Lebedev
528
502
Conference on Nuclear Reactions on Light Nuclei?I, V. Sizov
534
505
Conference on Heavy Water Reactors
535
506
Symposium on Neutron Recording, Dosimetry, and Standardization? V. I. Ivanov
536
506
[Powerful Reactor Station in Midtown New York
Source: Nucleonics, Jan.-Feb. (1962)
508]
BRIEF COMMUNICATIONS
539
509
Synthesis Of a New Isotope of Element 102
540
510
BIBLIOGRAPHY
New Literature
541
511
NOTE
The Table of Contents lists all materials that appear in Atomnaya tnergiya.
English language are not included in the translation and are shown enclosed
English-language source containing the omitted reports will be given.
Those items that originated in the
in brackets. Whenever possible, the
Consultants Bureau Enterprises, Inc.
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LENIN PRIZE WINNER B. M. PONTECORVO
N. N. Bogolyubov
Translated from Atornnaya griergiya, Vol. 14, No. 5,
pp. 441-442, May, 1963
The committee on Lenin Prizes in science and technology in the Council of Ministers of the USSR has
awarded the Lenin prize for 1963 to Corresponding Member of the Academy of Sciences of the USSR
B. M. Pontecorvo.
Pontecorvo has been awarded the Lenin prize for work in one of the most interesting fields of modern science ?
the problem of weak interactions of elementary particles and neutrino physics. These branches of physics have played
an exceptionally important part in the past and they will no doubt be equally important in the future.
,
The term "weak interaction" is naturally very arbitrary. These interactions are in fact weaker than electro-
magnetic interactions connected with light radiation, but are much stronger, for example, than gravitational inter-
actions governing the motion of the planets.
The history of the physics of weak interactions involves primarily the investigation of properties of probably the
most enigmatic of elementary particles?muons and neutrinos. Bruno Pontecorvo was the first to draw attention to
the considerable similarity between the muon and the well-known electron. This idea made it possible to forecast a
whole number of properties of elementary particles. Pontecorvo himself established experimentally such fundamental
properties as spontaneous decomposition of a muon into three particles, one of which is the ordinary electron, the other
two being neutrinos. Pontecorvo found that the mass of the neutrino is very small, at least 500 times less than the mass
of the electron which until then had been the lightest particle known.
Experiments also confirmed Pontecorvo's suggestion that the muon and electron have the same values charac-
terizing the natural rotation of these particles. Finally, using an atomic reactor arrangement which he proposed, ex-
periments were conducted in which scientists proved the difference. between the neutrino and its antiparticle?the
antineutrino.
The extension of the Pontecorvo idea was the initial point in the theory of universal weak interaction. At the
Joint Institute of Nuclear studies he conducted a brilliant experiment on the capture of muons by He3 nuclei; this
experiment not only qualitatively confirmed the analogy between the electron and the muon, forming the basis of the
idea of universality of weak interactions, but also gave quantitative agreement with the theoretical forecast.
His experiments on the decay of muons confirmed such detail in the theory of the neutrino as the parallelism of
the direction of natural rotation of the neutrino to its direction of motion.
B. M. Pontecorvo's work has made a tremendous contribution in converting a comparatively modest branch of
physics?the physics of weak interactions and the neutrino?to one of the most interesting and important fields of
science, currently engaging the attention of scientists throughout the world. The rapid development of this field of
science has meant that physicists have not only thought about the similarity between the electron and the muon, but
also about the difference between these "similar" particles. This has led to an interesting discovery. It has been
found that there are two kinds of neutrino: muon and electron neutrinos. Each of them interacts in a pair only with
a muon or only with an electron. An extremely bold and clever experiment to check this fact using modern experi-
mental techniques?powerful accelerators of elementary particles?was also suggested by Professor B. M. Pontecorvo.
A study of the role of the neutrino in the evolution of the stars has led B. M. Pontecorvo to the conclusion that
the neutrino is very important at certain stages of evolution. His work in this field has considerably helped the develop-
ment of a new branch of science?neutrino astrophysics.
Ideas on the universality of weak interactions obtained yet another confirmation when physicists discovered a
number of new, so-called strange particles. It was found that weak interactions are also characteristic for them.
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Using the features of these particles, Pontecorvo forecast and then checked experimentally the law of paired genera-
tion of strange particles. These conclusions later became a fundamental part of the systematics of strange particles.
The brilliant experimenter Pontecorvo also has a fine understanding of theoretical matters. These qualities
combined with considerable organizational talent have enabled him to develop a fine group of talented physicists.
The outstanding achievements of Bruno Pontecorvo in the physics of weak interactions and neutrino physics have
rightly earned him the highest award?the Lenin prize.
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AN ADIABATIC TRAP WITH COMBINED MAGNETIC FIELD
Yu. T. Baiborodov, M. S. Ioffe, V. M. Petrov, and R. I. Sobolev
Translated from Atomnaya Energiya, Vol. 14, No. 5,
pp. 443-445, May, 1963
Original article submitted April 11, 1963
We present the results of the first experiments conducted with the PR-5 apparatus?an adiabatic trap
with magnetic field increasing in the longitudinal and radial directions. We have shown that in such
a trap magetohydrodynamic instability of the plasma is absent; the lifetime of the plasma is limited
by the recharging of the fast ions on the neutral gas. The maximum times of decay of the plasma ob-
served in these experiments reach 10-15 msec.
At the International Conference on Plasma Physics and Controlled Thermonuclear Synthesis (Salzburg, 1961)
results were presented of preliminary experiments on the retention of the plasma in an adiabatic trap with plugs in
which the magnetic field increases in the radial as well as the longitudinal direction [1].
The idea of such a trap is based on the fact that the increase in field in the radial direction should prevent the
development of convective instability in the plasma, causing leakage of the plasma across the magnetic field in an
ordinary trap with plugs [2-5]. To set up a field increasing along the radius, the coils of the longitudinal field were
supplemented by a stabilizing winding. ? The latter is a system of linear conductors parallel to the axis of the trap and
placed symmetrically over the azimuth near the side wall of the vacuum chamber; the current passes through neigh-
boring conductors in mutually opposite directions.
The main conclusion to be drawn from the above experiments was the fact that at a fairly high field intensity
of the stabilizing winding the lifetime of the plasma in the trap increases considerably (approximately fivefold: from
100 to 450-500 ?sec). There was also reason to believe that under the stabilized conditions the lifetime is deter-
mined mainly by losses of fast ions of the plasma due to charge-exchange and not to any instabilities. However, due
to imperfections in the vacuum conditions in the apparatus (the minimum hydrogen pressure in the presence of plasma
was 1.10-6 mm Hg) this conclusion could not be drawn with sufficient reliability.
The new PR-5 apparatus was built in 1962?an adiabatic trap with combined magnetic field of the type men-
tioned above and with better vacuum conditions. We present the results of the first experiments carried out with this
apparatus.
A diagram of the apparatus is given in Fig. 1. A longitudinal magnetic field with intensity up to 5000 Oe in
the central part of the trap and with a mirror ratio of 1.7 is set up by coils which are fed from a dc generator. The
stabilizing winding is placed in the gap between the vacuum chamber and the coils of the longitudinal field; the in-
tensity of the field of the stabilizing winding at the wall of the vacuum chamber is up to 4500 Oe. The winding is
fed from a capacitor battery; the half-period of the current is 55 msec. The vacuum chamber, 40 cm in diameter
and 400 cm in length, is made of stainless steel; the chamber is first evacuated to a pressure of 10-6 mm Hg by two
vapor pumps fitted with nitrogen traps. Diaphragms separate the chamber into a number of sections, in each of which
there are titanium evaporators; the titanium is sprayed directly onto the inside surface of the chamber. The differen-
tial system of evacuation by titanium ensures the maintenance of a pressure in the central part of the chamber of
5.10-8 mm Hg with the stationary admission of hydrogen into the plasma source of 500 cm3/h.
The trap was filled with plasma by the "magnetotron" injection described in detail in [6]. In the described ex-
periments n "=-1 109 cm-3; Ti 'A.:: 5 keV; Te R--: 20 eV. The effect of the field of the stabilizing winding Hi on the re-
taining properties of the trap was determined from the change in decay time of the plasma 1- as a function of H.
The value of T was measured by the same method as in [6], based on the recording of the flux of fast neutral charge-
exchange atoms.
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.X:Cr3f/G.
ICSISCIDGle
ONSGall.
>-<
%MI=
8
to pump
(5000 liter/sec)
to pump
(5000 Liter/sec)
Fig. 1. Diagram of apparatus: 1) plasma source; 2) longitudinal field coils; 3) stabilizing winding;
4) protective cylinders; 5) diaphragms; 6) vacuum chamber; 7) titanium evaporators; 8) pickup
electrode.
? r. msec
10,0
1,0
0 0,9 1,8 2,7 HI, kOe
1,00 1,04 1,14 1,30 cri
Fig. 2. Dependence of decay time of the plasma
r on the field intensity of the stabilizing winding
(Hc,? = 3.3 k0e; p = 1.5.10-7 mm Hg).
Fig. 3. Current oscillograms on probe for various values
of the stabilizing field (H011= 3300 0e; p = 1.51.0-7 mm
Hg): 1) H1 = 0, cci = 1.00; 2) H1 = 900 0e, cu. = 1.04;
3) H1 = 1400 0e, al = 1.09; 4) H1 = 2400 0e, al = 1.21.
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Figure 2 gives the dependence of T on I-11, obtained with a longitudinal field at the center of the trap H011
equal to 3300 Oe, and a hydrogen pressure of 1.5.10-7 mm Hg. In addition to HI, the quantity ocl is also plotted
-111-41-1-H
along the abscissa axis; this quantity is equal toHo and characterizes the so-called wall-mirror ratio,
II
i.e., the ratio of the intensity of total magnetic field at the wall of the vacuum chamber to the intensity of the field
at the center of the trap. The curve of Fig. 2 shows that the field of the stabilizing winding acts very effectively on
the plasma: for I-11 = 1500 Oe (cci = 1.1) the plasma decays 35 times more slowly than for H1 = 0. In this experi-
ment the absolute value of the decay time under stabilized conditions (cti a 1.1) was 3.5 msec, as opposed to 0.5
msec in [1]. This difference is due to the different pressure of the neutral gas in the chamber (1.510-7 mm Hg with
the new apparatus and 1.2.10-6 mm Hg previously). This shows that the decay is determined by the charge exchange.
The maximum decay times observed with the new apparatus at still lower pressures reach 10-15 msec.
An illustration of the effectiveness of the stabilizing field in suppressing the plasma instability is provided by
the current oscillograms on a Langmuir probe placed inside the trap. Figure 3 shows these oscillograms for a spheri-
cal 4-mm dia. probe placed at a distance of 50 mm from the side wall in the central cross section of the chamber.
The probe was at a potential of -40 V relative to the walls and measured the ionic saturation current, i.e., the value
proportional to the plasma density in the neighborhood of the probe. It can be seen that the deep density pulsations
due to the plasma instability in the "barrel-shaped" field of an ordinary trap completely disappear as the stabilizing
field is increased. It is an interesting fact that a probe of even such relatively small dimensions considerably reduces
the lifetime of the plasma under stabilized conditions. This fact also points to the prolonged existence of plasma in
a trap in the presence of a stabilizing field.
The new data obtained with the PR-5 apparatus therefore completely confirm the results of the preliminary ex-
n(TWT)e
periments described in [1]. They show quite clearly that at least for a low-density plasma (p---H2/81(
an adiabatic trap with combined magnetic field ensures stable retention of the plasma, undisturbed by magnetohydro-
dynamic instabilities.
The authors would like to thank L. A. Artsimovich for his constant interest in the work, for helping with it and
for very valuable discussions of the results.
LITERATURE CITED
1. Yu. V. Gott, M. S. Ioffe, and V. G. Tel'kovskii, Report CN 10/262 to the International Conference on Plasma
Physics and Controlled Thermonuclear Synthesis, Salzburg, IAEA (1961).
2. M. Rosenbluth and C. Longmire, Ann. Phys., 1, 120 (1957).
3. B. B. Kadomtsev, "Zh. eksperim. i teor. fiz.", 40, 328 (1961). ,
4. M. S. Ioffe, R. I. Sobolev, V. G. Tel'kovskii, and E. E. Yushmanov, *Zh. eksperim. i teor. fiz.", 40, 40 (1961),
5. M. S. Ioffe and E. E. Yushmanov, Nucl. Fusion, Suppl., part 1, 177 (1962).
6. M. S. Ioffe, R. I. Sobolev, V. G. Tel'kovskii, and E. E. Yushmanov, "Zh. eksperim. i teor. fiz.", 39, 1602 (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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INJECTING THE ION BEAM INTO THE "OGRA"
MAGNETIC MIRROR MACHINE
A. L. Bezbatchenko, V. V. Kuznetsov, N. P. Malakhov,
and N. N. Semashko
Translated from Atomnaya triergiya, Vol. 14, No. 5,
pp. 446-452, May, 1963
Original article submitted July 5, 1962
This paper gives results of experiments on producing and focusing beams of molecular hydrogen ions
with energies up to 180 keV, and injecting them into the magnetic field of the "Ogra". The ion cur-
rent injected into the machine is ?450 mA. It is shown that in the operating range, the perturbation
produced in the "Ogra" magnetic field by the injector channel is not more than a few percent.
The idea that forms the basis of the "Ogra" design is that it is possible to accumulate plasma in a magnetic
mirror machine as a result of dissociation by the residual gas of molecular ions injected into the machine. It has
been shown in [1-3] that assuming stable plasma containment, the injection current required to get to a high density
plasma drops off sharply with increase in the energy and mean free path of the molecular ions in the machine be-
fore they are lost at the injector. The ion source developed by P. M. Morozov [4] made it possible, when the "Ogre'
was first built, to get a current of Hi molecular ions of about 400 mA with energies up to 50 keV. Further improve-
ment in the source should increase the energy of the ions to 200 keV. With these injected beam parameters, a mo-
lecular ion free path length of 105 cm before being lost at the channel must be provided in order to pass to a state
where a dense plasma is being built up. It is practically impossible to get such a path length during the time the
ion is moving from the injector to the mirror and back. In the "Ogra," as a result of the finite angular divergence
of the beam, this length is only 30-40 m for a distance between the mirrors of m.
Accordingly, the point and the method chosen for injection into the machine must provide for ten or twenty or
more oscillations of the ions between the mirrors before they are lost in the channel. This means, first, that as a re-
sult of azimuthal drift, the ions must get out of contact with the channel as quickly as possible, which is achieved by
proper choice of configuration of the magnetic field, and second, that the beam losses must be as small as possible at
each contact with the channel. The fraction of the beam incident on the channel at each contact is equal to the ra-
tio of the width of the channel to the pitch of the spiral. Accordingly, in a machine in which particle capture occurs
through dissociation of molecular hydrogen by the residual gas, injection in the vicinity of the mirrors (as in the
DSKh-II equipment) is not so good, although here it is able to produce an almost perpendicular magnetic field, which
greatly simplifies the injector construction.
The center part of the apparatus was chosen for injecting particles into the "Ogra." The magnetic field has an
opening in the injector region, produced by a break in the solenoid, as required to introduce the beam. Inside the
magnetic channel, the beam is bent and injected into the machine at an angle of 20? to a plane perpendicular to the
magnetic field. This gives a large pitch to the spiral in the injector region. After getting out onto the plateau of
the magnetic field, the pitch of the spiral decreases, which increases the mean path length of the particles before
they are lost in the injector.
Three methods have been discussed for injecting particles into the magnetic field:
1) Giving the ions additional acceleration as they enter the magnetic field, and retarding them to their initial
energy as they leave the channel,
2) Balancing out the deflection produced by the Magnetic field by means of a transverse electric field,
3) Injection through the magnetic channel, namely, through an iron screen with a compensating current winding
to reduce the field inside the channel. Both electrostatic methods lead to complete decompensation of the beam so
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300
200
100
0,23
ME10,2
/ ......-
0,15
..--
023
(I
PPP:
0 2
--
...- .---
---
0,15.
2 3
?
Fig. 2.
}H;
5 Id, A
Fig. 1. Diagram of ion source with ferromagnetic electron avalanche trap (magnetic field perpendicular to
plane of the figure): 1) point where electron avalanches strike without being caught; 2) plate of ferromagnetic trap;
3) trapping electrode with bar of Armco iron (point where electron avalanches strike); 4) gas discharge head at a
postive potential of up to 200 kV; 5) intermediate electrode at a negative potential of 15 kV; 6) grounded electrode;
7) supporting post for source; 8) edge of magnet pole.
Fig. 2. Components of the ion current Ii taken from the source as a function of the discharge current Id for
different amounts of gas in the gas discharge chamber of the source.
that it is dispersed by its own space charge in a length much less than the length of the channel. The magnetic
screen does not produce decompensation of the beam. The authors have used the last method of injecting particles
into the magnetic field, namely, through a magnetic channel, the detailed construction of which is described below.
1. Ion Source
The beam of molecular hydrogen ions was produced with the ion source developed by P. M. Morozov, which
has an arc discharge taking place along the magnetic field. The hot cathode and the cold anticathode are at the
same potential, which is negative with respect to the walls of the gas discharge chamber. The ions are pulled out of
the gas discharge chamber across the magnetic field, through a 4x40 mm slit. Between the gas discharge chamber,
which is at a high positive potential, and the grounded pull-out electrode, there is an intermediate electrode at a
negative potential with respect to ground (Fig. 1).
In a source of this type, it is impossible to raise the voltage above 75 kV (for an accelerating space 8 mm long)
without special measures to prevent breakdowns. If a vacuum treatment is used, breakdowns start up again after a
while, i.e., the electrode surfaces do not get "treated out." Increasing the length of the accelerating space makes
breakdown less frequent, but here the breakdowns tend to develop into avalanches, which melt the parts that are at a
positive potential.
Whether or not breakdowns develop with the material used depends essentially on the planeness of the electrodes
and the size of the microprojections on the surface. In order to increase the high voltage strength, the parts were giv-
en an electrochemical degreasing in an alkali bath and an electrochemical polishing to dissolve off the microprojec-
tions. Further, the parts of the source subjected to negative poteniia' 1 were baked in vacuum at a pressure of 5.10-5
mm Hg at temperatures of 600-950?C, depending on the material. These operations greatly increased the high vol-
tage strength of the source. The number of breakdowns was greatly reduced, and when the discharge is going, the
voltage on the source may be raised to 200 kV, with a field strength of ^1.00 kV/cm in the accelerating gap.
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Fig. 3. Schematic diagram of "Ogra" injector: 1)
source magnet; 2) quadrupole magnetic lenses; 3)
magnetic screening channel.
1
ax
-100
0
distance from center of beam, Iran
_
Fig. 4. Relative distribution of current density in the
beam, horizontally, in the image plane: 1) curve
plotted by adding the current distributions in the sepa-
rate ion rays for best focusing (the experimental curve
for the current distribution in a 0.5 mA ion beam is
the same as curve 1); 2, 3) beam currents of 20 and
150 mA respectively (curves taken when the distribu-
tion in the separate ion rays was as given in curve 1);
4) distribution for a beam current of 150 mA, with
the separate ion rays refocused.
qo
20
2
1
2 4
p, 10-4 mm Hg
8
10
Fig, 5. Beam half width A in the image plane, as a
function of the pressure p in the ion conductor for dif-
ferent beam currents, mA: 1) 0.5; 2) 20; 3) 150.
464
However, it is impossible to work with the ion
beam with this voltage on the source, since breakdown
leads to the development of avalanches which melt the
parts in the source. Stable operation of the source is
possible with a voltage up to 100 kV and an accelerating
gap length of ?8 mm, while at higher voltages measures
must be taken to prevent the development of avalanches.
Where the electron avalanches come from and how
they develop may be explained in the following way. A
breakdown in the accelerating gap develops into an arc
between the electrodes which vaporizes the anode and
sets free the occluded gases. The electrons formed in
the arc are drifting in the crossed electric and magnetic
fields in the gap. The height of the electron trochoid is
E
h = 1,240'5 ?1-12 cm,
where E is in V/cm, and H is in kG. For E 100 kv/cm,
and H = 1.4 kG, the height of the trochoid is 0.6 cm,
i.e., for a gap length of 8 mm, the greater part of the
electrons formed in the accelerating gap are lost at the
anode.
Raising the energy of the ions any further means
increasing the length of the accelerating gap, since it is
difficult to raise the electric field strength above 100-
120 kV/cm because of the electrical strength of the gap.
Here, to maintain the angle of rotation of the ion beam,
the magnetic field intensity must be increased in propor-
tion to the square root of the energy, i.e., h is' inversely
proportional to the energy. For an ion energy of 200 keV,
and keeping the electric field at 100 kV/cm, the height
of the electron trochoid is 3 mm, while the length of the
gap is 20 mm. The electrons formed in the accelerating
gap are able to get out of the gap and move along the
equipotentials in the electric field.
If breakdown develops as a result of evaporating the
metal in the electrodes and setting free the occluded gas,
there is a sudden increase in pressure with electron multi-
plication, which ends in an avalanche, increasing expo-
nentially with the distance the avalanche drifts in the
crossed fields. The avalanche that has developed, mov-
ing along the exponentials, circles around the gas dis-
charge head in the direction in which the ion beam is de-
flected in the magnetic field, and drops into the region
of weak magnetic field.
At the point where the height of the trochoid is
equal to the width of the high voltage gap, the electrons
are incident on the supporting rod of the source, which is
at a positive potential (see Fig. 1). As a rule, the ava -
lanche always strikes at the same place, and it has enough
power to melt the supporting rod, in spite of a large
amount of cooling from the water flowing through. Break-
downs occurring between the source head and the wall of
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Fig. 6. Diagram of magnetic channel: 1) iron core; 2)
compensating winding; 3) deflecting winding; 4) receiv-
ing electrode.
9-0*
350'r
340? 10?
320 OtAveler*
310? $10.41
is 4 41 ft* ? 4A
300? w
290?
I?t?ore? ot
pow I/ VA ill
11
20?
30?
40'
SO?
the vacuum chamber along the magnetic field never
produce avalanches, since the electrons are immedi-
ately lost at the positive electrode.
The electron flux powers for different ways of
operating the source may conveniently be compared
from the X-ray intensity given off by the source. A
microroentgenometer is set up near the source with an
indicating instrument and a recorder. X rays are
formed when the high voltage is applied to the source
even when the discharge is off. When the source is
being given a treatment, it can be seen how the X
rays first slowly increase with time, then breakdown
occurs, and after restoring the operation of the source,
the radiation becomes somewhat less than it was to
start with, then increases again, and another break-
down occurs. The mean radiation level drops after a
series of breakdowns, while the high voltage strength
of the source increases. When the discharge is on, the
CO? radiation intensity increases with increase in the ion
70?
current taken out. This is apparently due to secondary
electron emission from the surface of the intermediate
280? Ill 80 electrode (see Fig. 1, D due to a small part of the ion
II ? ?
270? - 90?' beam being incident on it.
The struggle with avalanches must be conducted
along two lines: disconnecting the high voltage from
the source when breakdown occurs, and catching the
avalanche as close as possible to the place where it
starts. The existing maximum current protective re-
lay in the rectifier is too slow to act when an ava-
lanche develops. The voltage is taken off the source
in ?2 sec, i.e., long after the avalanche has hit the
supporting rod.
Several methods have been tried for catching
the avalanches close to the place where they start.
One of the methods consists in using a special elec-
trode configuration so that as the electrons move along
the magnetic field they will hit an electrode that is
at the same potential as the source. So far however
this method has not given any positive results. The
electrons went between the electrodes and landed on
the support rod, which they melted.
A more successful method of catching the ava-
lanches was to produce local weakening of the mag-
netic field along the path followed by the electrons.
In this method the region where the electrons multiply is reduced by putting a grounded plate a distance of 15-20 mm
from the gas discharge head (see Fig. 1, 2). A block of Armco iron (see Fig. 1, 3) is placed on the positive electrode
to produce local weakening of the magnetic field, so that the height of the trochoid increases, and the avalanche hits
principally this electrode. Since the length of the path followed by the avalanche is reduced by a factor of about 3,
the power in the avalanche is comparatively small, and so does not melt the ferromagnetic trap. If the ion source
operates for a long time with a beam a large amount of heat is generated in both the ferromagnetic trap and the sup-
porting rod. As a result of this, the trap, which is not water cooled, gets heated to ?300?C and the supporting rod to
,-,100?C. There are some breakdowns in which the electron avalanche starts to melt the ferromagnetic trap. Drops of
Z=15
r, cm
50 40 30 20 10 0 -10 -20 -30 Z, cm
Fig. 7. Perturbation of "Ogra" magnetic field, produced
by the magnetic channel, with the optimum current in the
compensating winding: a) in the plane Z = 15 cm; b) in
the vertical plane, co = 0?. (The departure of the curves
from the grid lines is proportional to the magnetic field
perturbation at the point. A 1 cm displacement of the
curve in the r. direction means ro perturbation.)
465
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molten metal fall onto the grounded plate, thus forming a new flux of electrons which hits the supporting rod and
produces extensive evaporation of the metal along with breakdown at the rod.
Breakdown between the gas discharge head and the intermediate electrode at negative potential, for the case
of low power in the rectifier supplying voltage to the intermediate electrode, reverses the sign of the potential on
the electrode and all the secondary emission electrons help to multiply the avalanche. The magnitude of the nega-
tive potential on the intermediate electrode has a substantial effect on avalanche formation. This may be seen from
the X-ray intensity present during steady state operation of the source. For example, with a total current of 300 mA
from the source, the X-ray intensity is 50 mai/sec at -5 kV, 20 mCu/sec at -10 kV, and 10 mCu/sec at -20 kV.
Putting a negative voltage (-15 kV) on the intermediate electrode from a power supply with small enough internal
resistance that the voltage on the electrode remains almost constant when breakdown occurs greatly reduces the
power in the avalanche, and prevents melting of the ferromagnetic trap.
Thus, degreasing and electropolishing of the surfaces, baking the various parts in a vacuum furnace, and high
voltage treatment of the source, as well as using ferromagnetic traps and a high power rectifier to supply the inter-
mediate electrode provides stable operation of the source at voltages up to 180 kV, and with total ion currents taken
out up to 0.7 A.
If the voltage is raised to 200 kV, the source operates stably only if the current is less than 100 mA. Further in-
crease in the total current taken out again caused powerful avalanches to develop on breakdown, together with melt-
ing of the source support rod. The relation between the various components of the current from the source and the
discharge current for different gas flows into the gas discharge chamber (0.23, 0.2, and 0.15 cc/sec) is shown in Fig. 2.
The data in the figure were taken at discharge voltages of 250-300 V, and an ion energy of 180 keV.
2. Ion Optics of the Injector
The ion optics of the injector is to a considerable extent determined by the type of molecular hydrogen ion
source used.
The "Ogra" injection system consists of the rectangular magnet in which the source is located, two magnetic
quadrupole lenses, and an iron-current screening channel (Fig. 3).
In the uniform field of the rectangular source magnet with 1100x 600 mm poles and a 400 mm gap, the ion
beam is sorted according to masses, and the molecular component is sorted out and rotated through 90?. The angular
divergence of the beam leaving the source is 2a =25? in the plane of symmetry of the magnetic field. After being
rotated in the source magnet, the angle of divergence decreases to 1.5?, but aberrations occur in the plane of rotation.
The beam width at this point is "450 mm. The beam height (dimension along the lines of magnetic force) on leav-
ing the source is 40 mm. For the arc running properly, the beam leaving the source is almost parallel to the plane of
symmetry of the magnetic field. When it leaves the magnet, the height is not more than 60 mm. In this case, the
angular deviation of the ion rays from the plane of symmetry turned out to be approximately proportional to the dis-
tance from the plane of symmetry, i.e., the beam is optical in this direction, and there is no need for special correc-
tion of the angles. Shimming of the edge of the magnet was used to reduce the aberration in the plane of rotation.
Correcting the field reduced the angular divergence to 1? and greatly reduced the aberration. However, this had no
effect on the beam focusing.
After leaving the source magnet, the molecular beam goes into a horizontal ion conductor ?8 m long, with
two quadrupole lenses around it, each with an aperture of diameter 2d = 600 mm and 1 m long. The lenses consist
of quadrupole magnets with cylindrical pole faces having the radius 1.15 d. The lenses are located approximately
half way between the source magnet and the magnetic channel, 200 mm from one another. The astigmatism of the
system is achieved by adjusting the currents in each of the lenses independently, which focuses the ion beam into the
60X 60 mm output aperture of the magnetic channel, with an angular beam convergence of not more than 5?.
An investigation of the optical properties of the injection system without the magnetic channel was made on
another injector, just like the "Ogra" injector. At the output from the source magnet, separate 5 mm diameter ion
beams may be taken out of the ion flux as a whole, at any point over the cross-section of the beam. In the image
plane, i.e., the plane where the output aperture of the magnetic channel is located, two probes were set up which
were used to measure the coordinates of the arriving rays, and take the current density distribution over the cross-
section of the incident total ion beam.
466
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A focusing calculation made for the sytem of two quadrupole lenses has shown that with the existing input
beam angles it is possible to get an image in the plane of the end of the magnetic channel consisting of a 30x 20 mm
ellipse with the long axis horizontal. Actually, these dimensions are for small beam currents (--,0.5 mA), or for com-
bining the currents from separate ion rays. As the current is increased, the dimensions of the image increase rapidly
in the horizontal direction, although the distribution of the elementary ion rays remains constant (Fig. 4, curve 1).
The beam width may be reduced by refocusing the ion rays (see Fig. 4, curve 4). The beam blow-up apparently
comes from an increase in the space charge produced by modulation of the ion current. Oscillographs taken of the
ion current have shown that it is always amplitude modulated. If enough gas is. put into the gas discharge chamber
of the source, the depth of modulation can reach 10010. By regulating the amount of gas, the depth of modulation
may be reduced to 15-2010. The modulation spectrum occupies a band from ten or twenty or more cycles per second,
without emphasizing any particular frequencies.
The dimensions of the image are only slightly dependent on the energy of the ions, since, although the volume
density of particles in the beam drops with increase in energy, there is at the same time a reduction in the ionization
cross-section of the residual gas. As a result, the unneutralized charge density changes very little. If the energy of
the ions is increased from 100 to 200 keV, the change in width of the beam image is 1510.
The dimensions of the image depend substantially on the pressure in the ion conductor. The compensation of
the beam improves with increase in pressure, but the scattering by the residual gas becomes appreciable, with the
result that the beam dimensions first decrease, reaching a minimum, and then increase (Fig. 5). As the beam cur-
rent is increased, compensation is reached at a higher pressure, so that the minimum moves to the right. At a cur-
rent of 10-200 mA, the minimum beam dimensions occur at a pressure of from 1.5 to 4.5.10-5 mm Hg.
The area of the 60x 60 mm output aperture of the magnetic channel accommodates ?7010 of the incident beam.
Here, the beam losses over the path from dissociation and charge change at optimum pressure are ^,3010 of the molec-
ular current from the source at an ion energy of 200 keV, or 4510 at an ion energy of 100 keV.
3. The Magnetic Channel
The magnetic channel is a continuation of the ion conductor of the injector, and stops at the vertical diameter
of the "pgra" chamber. It is intended to inject the ion beam inside the magnetic field of the machine, and rotate it ?
through an angle of 20? to the plane perpendicular to the magnetic field. In doing this, the channel must produce the
minimum amount of perturbation in the axial symmetry of the magnetic field in the machine.
The method used to compensate for the perturbation produced by the iron was proposed by G. I. Budker in 1950
and was investigated experimentally by A. A. Arzumanov et al. [5]. Constructionally, the channel is a curved thin-
walled tube of rectangular cross-section made of Armco iron with two windings, a deflecting winding and a compen-
sating winding (Fig. 6).
The deflecting winding consists of a single turn carrying current, placed inside the channel. The shaped wind-
ing and internal walls of the channel produce a magnetic field which deflects the beam 20? and compresses it some-
what horizontally. The compensating winding consists of four current-carrying turns, connected in parallel, and placed
outside the channel, to produce a horizontal magnetic field bucking the main field of the machine inside the winding.
The purpose of this winding is to balance out the perturbation of the '"Ogra" magnetic field produced by introducing
the iron in the channel, and to weaken the field inside the channel.
Figure 7 shows the measured field perturbations produced by the magnetic channel for optimum current in the
compensating winding. The largest field perturbation reaches 2010 at Z = 15 cm, r = 50 cm, and 0;
N (a, it,, = 0 for ux < 0.
(2)
[-Jere N(x, ux, X) is the flux density of photons with wavelength X at the distance x from the source, forming the
angle cos-lux with the normal to the slab (x axis), ?(X) is the total attenuation coefficient of the medium for y -
luanta with wavelength X; K (X', X) is the Klein-Nishina coefficient for Compton scattering with a wavelength
change from X' to X, and 6(x) is Dirac's 6-function. Of the two boundary conditions (2), the first reflects the fact
that the y -quanta only enter the slab normal to the surface (x = 0), while the second corresponds to the assumption
that none of the y-quanta were turned back from the exit surface (x = a).
In considering the possibility of applying Mertens' method to the theory of multiple y scattering in a finite
medium, we shall look for a sOlution of the original Eq. (1) with the boundary conditions (2) in the form
N (x, ux, X).= 6 (1 ? /06(X_X,0) e-40.0)x ?N' (x, ux,
(3)
where the first term is for unscattered radiation, while the second is for radiation that has undergone scattering. If
we further substitute Eq. (3) for the total photon flux density, in Eq. (1), and use the Legendre polynomial representa-
tion of the 6-function, it is not difficult to show that the scattered photon flux density satisfies the equation
ux aN' (x, ux' X) d + II (X) N' (x, ux, X)=
2 )
X S du'xP (4) N' (x, i4, X) ? e?g(40)xK (0,X) X (21+1) P1 " 11 ? + X,') P (ux)
_
with the boundary conditions
N' (0 , ux, k) = 0 for ux > 0;
N' (a, ux, ?)=0 for ux < 0.
(4)
(5)
Let N+(x, ux, X) and N_(x, ux, X) be the scattered photon flux densities of wavelength X at distance x from the
source for ux > 0 and ux < 0 respectively, and expand these functions in Legendre polynomial series in the ranges
0 to 1 and -1 to 0. This gives
CO
N ?(x, u 20= 2, (2i + 1) NP (x, X) P i (2u., T. 1),
(6)
where Pi(x) is a Legendre polynomial of the ith degree. Then, the system of integro-differential equations for the
expansion coefficients Nt(x, X) takes the form
a/VP 1 (x, X) ONpdx (x, X) a N (x, X)
1+1 ?
i ? (2i +1) + (i + 1) + 2 (2i + 1) tx (X) N i (x, k)
dx dx
(2i + 1) (X,', k)
xo t=i ? r=o
(+1 (2r + 1) PN (x, V)} + (2i +1) e? 21+g(2,0>xK (Xo, X) x j ) P 1(1 ? P (7)
with the boundary conditions
NI- (0 , k) = 0, A T.T (a ,?)=0 (8)
and
(? 1)1+iPri = P1 (x) P (2x? 1) dx. (9)
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In order to get a solution in the nth approximation, we retain the system formed by the first n equations of
(7): in the nth equation we take /41-(x, X) = Nn-(x, X) = 0, and, in addition, we shall everywhere assume
P11(1-X+X1) = pn+1(1-X+X') = . . = 0 (this actually corresponds with replacing the 6-function in Eq. (1) by a finite
segment of its Fourier series in Legendre polynomials). Thus, we get a system of 2n linear integro-differential equa-
tions in partial derivatives of the first order, which makes it possible to calculate the two unknown functions, Nt(x,X)
= 0, 1, 2, (n-1)]. The values of the 2n arbitrary constants are completely determined by the condition (8).
In the first approximation (n = 1), we have, to find the two unknown functions N (x, X), the system of two
integro -differential equations
aiq (x a.)
? 'F 2? (X) 11T, (x, X) = K (X0, X
with the boundary conditions
?ii(x.9)x 4_ K (X', X) [N.,1; (x, X') + N; (x, X")] dA,' (10)
N'of (0, X) = 0, i\i; (a , X) = 0. (11)
The approximate analytic expressions for the solution of the system of equations (10) may be found by the
method of successive approximations.
As a "zero" roughest approximation for the desired solution, we take the functions 40(x, X) found from the
two equations
_4_ ON 4(x,
ax 21i ()) N4 (x, = 212?, K (X,, X) e-4(,0)x
with the boundary conditions
N,1-0 (0, X) = 0, N (To (a, X) = O.
Then to find the functions Nh(x, X) for the first approximation, we will have the following two equations
with
(12)
(13)
-I, 21i (k) N (x, A,) ?I- K (X,7 X) e-ai(X0)x + K (V , 11? o+0(x., X') + (x, X')1 d' (14)
dx ?)1E .
ko
N(0, X)=0, N;, (a , X)= O. (15)
Continuing the solution in this way, we obtain the two infinite sequences of functions
N4 (x, X), N (x , X),
A I X), . . . , N (x , X),
satisfying the recursion formulas01
? 211 (X) N (x, X) =K (Xo, X) e-11(4?)s?
K (k', X) [Ni; ,,-1 (x, X') + N ?_i (x, X')I dX'
40
with
If we assume
we have
(16)
(17)
# 7, (0 , X) = 0 , 1?1,? (a X) = 0
(n= 1, 2,3, ...). (18)
N41(x, X)?N(t (x, ?)=1(x, X),
N (x , X) =- (x, X),
v-0
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(20)
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where
and
for
a-Kft (x
+ On
.1\1(x, 1)=N4(s, X)
2? (A) Non (x; X) =? K (k', X) (r, X') -I- NO , (x, X')] dX'
a:0)
N-c;? (0, X) = , Nn (a, X) = 0
(n=1, 2, 3, ... ,). (22)
(21)
The solutions of Eqs. (21) satisfying the boundary conditions (22) are of the form
YoFn (x, X) =dX' K (k', X) dx' e-211(x)(x?x' x (x', X') n_i (X', X')1, (23)
4.0
a
A/5n (X, X) = dX' K (X' , X) c dx'e-211(x)('-x) X EN46,11--i (X', A') +N, n_l (x', X')I. (24)
a
The difference between Eqs. (23) and (24) is that in the first case, S dx' . . . is replaced by dx' . . . , and,
in addition, x and x' exchange places in the exponent. Accordingly, it is entirely sufficient to make the subsequent
transformations, for example, %(x, X). We express the integral in terms of I110-0(x, X). For n = 1, we obtain
KTL(x, X) =
dk1K (kr, c dx0-211(x)(x?x1) x [N-01.? (xi, xi) + er1, ))J.
If, however, n> 1, the appropriate expressions take on more complex form:
n
X .e-211(20(x-xl) X irj2 dXiK (Xi, A-1)
i
N1)-7, (x, X) = (211., A) S '
xj_i a
X [ dxie -2g (Xi-1)(xi-1-xi) + dxie-2g X UV,?0 (X7, , Xn) (xn, An)].
(25)
(26)
It is natural to expect further that the solution of the system of twO integro -differential equations (10) with the
boundary conditions (11) will be in the form of a sum of infinite series
E N gt(x, X), (27)
n=0
where the expressions for ron are given by Eqs. (25) and (26), while the corresponding expressions for i\-101 are ob-
tained formally from these equations in a way similar to that in which (24) is obtained from (23).
Thus, the method of successive approximations actually enables one to make a more general study of the first
approximation to the problem n of the passage of y -quanta through a plain parallel slab.
CONCLUSION
The spectral' distribution of the scattered photon flux density at a distance x from the source is given by the
integral of Nt(x, ux, X) over all possible values of ux. From Eq. (6), this integral is
472
N' (x, ux, X) dux = N; (x, X) + N; (x, X).
--1
(28)
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The values of Nti(x, A) are given approximately by the first approximation discussed in the preceding section.
Accordingly, the calculations given above point to a method for making an approximate calculation of the
spectral distribution of the scattered photon flux density in the problem of the passage of y -quanta through a plain
parallel slab. At the exit surface, because of the boundary conditions (8), No-(a, A) = 0, and the spectral distribution
of the scattered photon flux density is given by means of
Nc+,. (a, ---- N (+), (a , A) + Ni (a, A) + Ar, (a, A) (29)
For 1\--ch-I+ ra, --, X11 we find, from Eq. (12) and the boundary condition (13)
o
1V K e-?(A,o)ct x [i e-{20)3a 1.d0-13 (a' 21t [211 (A)-11 N)1
The expressions for the other terms in (29) are also easily found by using Eqs. (25) and (26). At the input surface of
the slab, the spectral distribution of the scattered photon flux density is found by means of
(30)
where
Arc; (o, X).= AT,To (0, X) + Noi (0, X) +N(-)2 (0,
)+...,
K (A, 2,1
N0 (o, A) s (1
[2? (X)+11 (4)]
(31)
(32)
while the expressions for all the other terms are also easily found from equations similar to (25) and (26).
The application to concrete cases of the above method of calculating the passage of y -quanta through matter
will be discussed in a special paper.
LITERATURE CITED
1. V. S. Galishev, V. I. Ogievetskii, and A. N. Orlov, Usp. fiz. Nauk, 61, 161 (1957).
2. N. F. Nelipa, Introduction to the Theory of Multiple Particle Scattering [in Russian], Atomizdat, Moscow (1960).
3. 0. I. Leipunskii, B. V. Novozhilov, and V. N. Sakharov, Propagation of 7-Quanta in Matter [in Russian],
Fizmatgiz, Moscow (1960).
4. U. Faho, L. Spencer, and M. Berger, Penetration and Diffusion of X Rays, Handbuch der Physik, 38/2, 660 ed.,
Springer, Berlin (1959).
5. L. Spencer and U. Fano, J. Res. Nat. Bur. Standards, 46, 446 (1951).
6. H. Goldstein and j. Wilkins, Calculations of the Penetration of Gamma Rays, NYO-3075 (1954).
7. R. Mertens, Compt. rend., 236, 1753 (1953); 237, 1644 (1953); 238, 53 (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-
cover English translations appears at the back of this issue.
473
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THE DIFFERENTIAL EQUATION FOR THE THERMALIZATION
OF NEUTRONS IN INFINITE HOMOGENEOUS MEDIA
N. I. Laletin
Translated from' Atomnaya tnergiya, Vol. 14, No. 5,
pp. 458-464, May, 1963
Original article submitted July 18, 1962
We consider the problem of the calculation of the spectrum of slow neutrons in an infinite, homoge-
neous medium with constant sources. From the investigation of solutions for cases when absorption is
absent and the medium is a gas of heavy atoms (m ? 1) and atoms of hydrogen (m = 1), a differen-
tial equation of the second order is obtained for the asymptotic solution of the problem for a mona-
tomic gas with arbitrary atomic weight m; this solution is then generalized to apply to a medium
with absorption. For m >> 1 and m = 1, this equation is converted into known differential equations,
and can thus be applied in the case of a monatomic gas with nuclei of arbitrary mass.
INTRODUCTION
The neutron density in an infinite, homogeneous medium with constant temperature T and constant sources
satisfies the differential equation
[Ga. (z) G (z)] N (z) = G (z' --> z) N (z') dz' S (z),
(1)
where z is the energy E of a neutron in kT units, i.e., z = EAT (k is the Boltzmann constant); N(z) the density
of neutrons with energy in the interval (z, z+ dz); S(z) the density of sources of neutrons with energy z; Gs(z) the
probability that a neutron with energy z' experiences scattering in unit time; Gs(z'--).z) the probability that a neu-
tron with energy z' is scattered and that its resulting energy is in the interval (z, z+ dz); Ga(z) the probability that
a neutron with energy z is absorbed. It is obvious that, in Eq. (1), Gs(z) and Gs(z'-+z) can cease to be probabilities
only in the case of scattering that is connected with the measurement of neutron energy in a laboratory coordinate
system.
For neutrons with energies z 1, the probabilities Ga(z), Gs(z), and Gs(z' -9-z) must be calculated taking into
account the thermal motion of the nuclei and the interrelations between these motions. This problem is rather com-
plicated, and is of independent interest. But even when the relevant probabilities are known, the solution of Eq. (1)
is very difficult. We note that the method of solving the equation for the determination of the energy distribution of
the neutrons by dividing up the neutron spectrum into groups relative to their energy (the group method), which is val-
id in a region of moderation (z>> 1), is exceedingly laborious in problems concerning thermalization (z k. 1). To
understand the reason for this, we write Eq. (1) in the form
dQ
where
Q (z) dz" G s (z' z") N (z') dz'
`-6
dz" G (z' z") N (z') dz'
(la)
Here 0a(z) = Ga(z)N(z) is the absorption density. The meaning of Q(z) is clear from the equation: it is the so-
called current along the energy axis. For z >> 1, when neutrons are scattered they can only lose energy, and Q co-
incides with the moderation density. In the moderation region, 0a(z) and S(z) are usually small, and so Q(z) varies
only slightly. Even when the neutrons are divided according to energy into relatively large groups, this fact permits a
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reasonably accurate description of the behavior of the neutrons inside a group, and a resulting good accuracy in the
determination of the group constants.
In a thermalization region, there is not such a small variation in the parameters. The quantities Q(z) and
N(z) vary weakly, and so, to obtain a sufficiently accurate solution of Eq. (1), it is necessary to use a large number
of groups. [The quantity N(z)/M(z), where M(z) is the equilibrium Maxwellian distribution, varies weakly on the
average in the region of thermal neutron energy when the absorption is small, but it increases rapidly with increasing
energy in a region of transition from thermal energy to epithermal energy.]
Moreover, in contrast to the problem of moderation, the neutrons in the thermalization problem can pass from
one group to another as a result of scattering, and they do not necessarily pass into a group with lower energy. These
facts complicate the calculations. It is thus not surprising that a great amount of attention has been paid to the in-
vestigation of the simple cases where the integral equation for N(z) can be reduced to a differential equation. A
differential equation for N(z), equivalent to the integral equation (1), can be obtained when the medium is a mona -
tomic gas consisting of nuclei with mass m = 1 (the neutron mass is taken as the unit) and the scattering cross sec-
tion is independent of the relative velocity of motion of neutrons and nuclei. (This latter condition is reasonably
well-satisfied when the temperature is not too high, because of the behavior of neutron cross-sections at free, quies-
cent nuclei for low neutron energy, which is known from the results of quantum mechanics.) In this case, the differ-
ential probability of scattering Gs(z'->z) is given in the ranges z' z and z' z in the form of a product of func-
tions, one of which depends only on z and the other only on z'.
As a result, Eq. (1) for N(z) can be reduced to the following differential equation, known in the literature as
the Wigner-Wilkins equation (see, for example, [1])?:
where
fr ?-- [AT (,) (G (z) G (z))]} R (z) (G a (z) G (z)) --,_ N (z) = 0 ,
d
d: az z
(z) =
Jr az ez
e?Vzzerf)"z
R (z),.(z)i2 e- 2z .
2e/2 jrn
(2)
If the medium is a monatomic gas with mass m >> 1, then for N(z) we can obtain an approximate differential equa-
tion of the second order, that is to say that this equation is correct to the zeroth and first approximation in the expan-
sion of the probabilities in powers of 1/m
In the zeroth approximation, the equation is
where
zcIr H- zCIY (1) r 1 6', = 0,
= z N (z); A= 2n2aa (kT) . cr /,\ _
s(o9) ") (3)
-
(3)
This equation was first obtained by V. I. Davydov in [2] in the course of an investigation of the motion of elec-
trons in gases. It was introduced into neutron physics by Wilkins in [3], and is known in this type of work as the
Wilkins equation.
The equation of the second order for N(z) in the second approximation was obtained by Corngold in [4], and is
zii)" [ in
( 3z3,2 H- 4-2 )1i H CI) {1 A , 1
-- 1 A
(4)
A
4 V z ; m ?[ z2 1 j_ 223/2
-1--
1 1 i A2
1 ) 31/-A 1 1 _ 0.
z. 12 ji z, i i
In the present problem it is equivalent to an equation of the fourth order obtained for this case by Wilkins [3].
The fact is that the neutron density N(z) satisfies a differential equation of the second order in two limiting
cases; when the mass of the nucleus is m = 1 and the change in the neutron energy due to one collision is large, and
? In [1], Eq. (2) is given in the variables x = Iri and for v (x) =-__ N (x)
JIM (x) ?
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when m >> 1 and the energy variation is small. This points to the conjecture that there is a differential equation for
the asymptotic part of N(z) for a gas of nuclei of arbitrary mass. (Such an equation can evidently not describe the
nonasymptotic part of the solution, such as the irregularities in the solution investigated by Placzek [5] in the theory
of neutron moderation.)
We recall that, in the problem of the space distribution of neutrons in a breeding medium, the asymptotic part
of the solution as satisfies the differential equation of the second order (see [6] for example)
V2(Das (1) ? 7721 alas =
(5)
where L2 is the solution of a certain transcendental equation [for a medium with isotropic scattering it is the solution
of the equation (//L) = tanh(/s/L), where -1 is the total free-path length and /s is the path length relative to the
scattering].
The desired differential equation for the energy distribution of neutrons in a homogeneous medium must evi-
dently be sought as having the same relation to Eq.. (1) as Eq. (5) has relative to the kinetic equation for cl)(i).
If we succeeded in finding the differential equation for N(z) in the Case when the medium is a monatomic gas,
then by ascribing a definite physical sense to the coefficients of this equation we could try to extend it to be appli-
cable to other media. An advantage of such an equation, in addition to the fact that it can be much more easily
solved numerically than the integral equation, would be that, instead of a complete knowledge of the scattering in-
dicatrix Gs(zt?-,?z) which is a function of two variables and a knowledge of which is consequently equivalent to a
knowledge of an infinite number of functions of one variable, a knowledge of a bounded number of functions of a
single variable (in our case not more than three) is all that would be needed. In the present article, an attempt will
be made to find the differential equation for the asymptotic part of the solution of Eq. (1). In view of the fact that
the equation proposed in this work was obtained from the integral equation in a not completely rigorous way, and that
our results are based on an investigation of known limiting cases (a monatomic gas with m = 1 and m ? 1), its range
of applicability is not completely clear. However, using the fact that even calculations using a rough model of a
heavy, monatomic gas yield satisfactory results in many interesting cases and need only small correction, we can
hope that our differential equation will be useful.
A Homogeneous Medium without Absorption
In order to obtain the differential equation for the asymptotic solution of Eq. (1), we turn at once to the inves-
tigation of the homogeneous integral equation
CO
[G (z) + G s (z)] N (z) G (z' z) N (z') dz' (6)
0
We start by considering a medium without absorption, i.e., with Ga(z) = 0. In this case, the solution is the Maxwell
distribution: M(z) = e-z. This is however not the only solution of Eq. (6). In fact this equation can be written
in the form dQ/dz = 0, where Q is obtained from (la). The solution is obviously Q = const. But the Maxwell distri-
bution corresponds to a zero current along the energy axis Q = 0. There must therefore be one or several solutions
for a constant current along the energy axis. The objection might be raised that, in an infinite medium without
sources or absorption, there can be no current along the energy axis, and because of the existence of such a current
our solution has no physical meaning. This, of course, is true, but the consideration of this case is nevertheless
of value.
To clarify the position, we again turn to the problem of the propagation of monoenergetic neutrons in an in-
finite medium. In such a medium with no absorption, the general solution of the kinetic equation for 4)(i) is a linear
function. If the medium is infinite, then only the constant component of the solution has any physical sense. The
variable component due to the constant propagation of the current must be discarded. But if the medium is finite but
large, i.e., its dimensions are much greater than the length of the mean free path of a neutron in matter and at its
boundary there are neutron sources on one side and neutron sinks at the other, then in the whole region, except for
small neighborhoods of the sources and sinks (of the order of the free-path length), the solution will coincide with the
general solution of the equation for an infinite medium, i.e? it will be a linear function.
In our case we can similarly assume that there is a source emitting neutrons with a finite but very large energy
z1? 1, and that neutrons are being absorbed in regions of very low energy z zs, where zs ? 1. Then for the en-
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ergy range z2 < z < z1 we should expect that N(z) would give a good description of the general solution of Eq. (6)
everywhere except in the immediate neighborhood of the energy boundaries z1 and z2.
We rewrite (6) for Ga = 0 in the form
G (z z?) N (z') N M (z) dz' =0.
, (e) (z).
Here the detailed-balance principle
(7)
G (z' z) M (z') G (z ---> z') :M. (z).
is used. We will assume that, in addition to the obvious solution N(z)/M(z) = const, there is a further solution
N(z)/M(z) = f(z).
The function f(z) cannot have a largest or smallest value for any z in the range 0 < z < co. In fact if the in-
equality f(z) f(z0) were satisfied for all z zo, then the integrand in (7) would have a constant sign at the point
zo because of the definiteness of Gs(z->z'), and the integral could not be zero. Since Eq. (7) must also hold at the
ends of the z range, then f(z) can increase indefinitely at only one end of the interval and must decrease indefi-
nitely at the other.
We thus assume that the asymptotic solution of (7)- has the form
-14 (f) = Ci+ C 2f
where C1 and C2 are arbitrary constants. Since there are only two constants, the function N/M, and thus N, can
satisfy a differential equation of only the second order.
We write this equation as two linear equations of the first order:
dQ =0;
dz
d d
d; ? dz 1-VN ) ? j
(8)
Up to this stage, our investigation has proceeded without the use of any concrete model of the medium. To ob-
tain a definite form for the function f(z) we must now consider known, simple cases: monatomic gases with m = 1
and in >> 1.
The solutions of the Wigner-Wilkins, Corngold, and Wilkins equations for Ga = 0 can be obtained simply. We
write them in succession, and also the expression for the probability of neutron scattering in a gas with mass m:
for m=1,
(z) ez' dz' ez
X [c
za
0 (z'H-72-1 )erf ' ?e - (z erf1/72-i- V ,7-7 e-4
for in >> 1,
N (z)
C C, [
m (z) )
dz'
I 9m
M
r C ez?dz' 1*
1 N (z) = 4- C2 L (z)
9,n
-00
(9)
? The integral in the Wilkins solution must be taken from -Go, since the integral from 0 to z diverges. A comparison
of the expressions in (9) clearly shows that the equations obtained by expanding the probabilities in powers of 1/m is
not applicable for z ? 1/m.
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e-niz
G s (z) --= 2nii erf
y
It is obvious from a comparison fo the formulas in (9) and (10) that, for a gas with arbitrary mass m, the solution
for N(z)/M(z) can naturally be expressed in the form
(10)
N (z)
M(z) (z) = C1+ C 2(S d: 10
Vs s
0
where les = Gs(z)M(z) is the equilibrium scattering density. It is not hard to see that all the formulas in (9) can be
pbtained from this expression.
Thus the second equation of the sytem (8) can be written as
Q = const d (
dz
dz
where Os = Gs(z)N(z) is the scattering density. The constant is easily obtained by using the fact that, for z ? 1,
we must obtaine the known solution of the neutron-moderation problem at motionless nuclei
vs.(z 1) .
" d o
?Tzi's a
Noting that
d Ors-1 Z for z>> 1, we obtain const = = 1 +1a In a as the mean logarithmic loss of
1:1)-E Tz Vs
energy when a neutron is scattered at a motionless nucleus
(a = (m+1)
m-1 2
We finally wirte the equations for a monatomic-gas medium without absorption
dQ A.
dz
Q = (W)2 d
0 , d dz kl)! ) ?
Ws-1- (B>s)
Two functions Gs(z) and t characterize the scattering properties of the medium in Eq. (11). The second of
these functions is constant in the case of a monatomic gas. For an arbitrary medium, it is natural to assume that the
form of the equations remains unaltered, and that the functions Gs(z) and t(z) occur in them. In the general case,
the quantity t(z) naturally does not have to be constant. Only for z>> 1 will it tend to a constant value, which will
be characteristic of scattering at motionless, free nuclei.
A Homogeneous Medium with Absorption
We will try to extend the differential equations to be applicable to media with absorption. The first of the
Eqs. (11) will now be
(7Q
= a (Z)
where Oa(z) = Ga(z)N(z) is the neutron-absorption density. To find out how to change the second equation, we argue
as follows. In a medium without absorption, the current along the energy axis depends only on the scattering density.
When there is absorption, the current must also depend on the absorption density. It is natural to expect that the ab-
sorption and scattering densities will occur in the expression for the current along the energy axis in the dame way.
We again turn to the consideration of the relation between the current in the direction of the energy axis and the neu-
tron density for high energies. For neutron moderation, we have the following relation at free, motionless nuclei:
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- z y 1
Em ; )2 [ 1? a + a ln a --1 a (In a)2 (1 ?
( " a)
E' )2
1 n --
. (1 ?a+a In a)2
E
Thus, in a medium with absorption, the scattering and absorption densities occur in the combination
the expression for the current along the energy axis for z ? 1.
Assuming that these densities occur for other energies in the same combination, we obtain
;
(-1Q
)
I
Q = ( 1. W)2 ( ( *3 -11-1 Va dz 1 ) }
4 I
? in
(12)
For t = y = 1 and values of Gs(z) given by the formula (10), Eq. (12) for N(z) with m = 1 yields the Wigner-Wilkins
equation (2). On the other hand, taking m ? 1 and rnz ? 1 and expanding in (12) in powers of 1/rn arid 1/mz, we
obtain the Wilkins equation (3) for a zeroth approximation, i.e., when we have discarded all terms of the order of
1/m and limz (here we must assume that ma a (RT) (z) = v Ga (z) X S (io (e)2
1+ Cs (2) ?
For Ga = const with m = 1 and m 1, the last formula gives the expressions in [6].
? This is the exact expression for hydrogen moderation. For moderation at other nuclei, the validity of the expression
requires that the scattering and absorption cross sections have only a small variation in a lethargy region of order E
(see [7] for example).
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0(Z)
0,
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0'
i,.
1 1
\
?\
?
1 i .1
S.?
?????
,
It
- ?
i.
i r
. //.
/ ./
/Ai . 1 , .
''3.-
/
?
iI
10
Fig. 1. The relation between the neutron flux and
the energy: the upper group of curves are for 6 = 0.1;
the middle group for 6 = 0.5; the lower group for 6 =
= 1.5;
O Ila(hT) .
- ; in= 1; - ? - m _2;
--- ? -- - ? ? -- m= 12; - - --m= co:
Integral Characteristics of Neutron Spectra
m
Values of 6
0.1
0,5
1,5
Red
a
Red
a
Red
a
1
19,3
1,620
1,93
4,63
2,48
3,80
2,10
3,80
6,23
2
18,9
1,650
1,96
4,49
2,62
3,92
1,99
4,21
6,40
4
18,8
1,653
1,97
4,41
2,69
3,98
1,92
4,54
6,57
12
18,7
1,665
1,98
4,34
2,79
4,04
1,88
4,81
6,68
.4-co
18;6
1,670_1,98
,431-2,72
4,07
1,84
4,96
6,77
Notes.
? /Pu PdE = S a au(E)
E ;
0 .
0,4 ev
1. Rcd
co
= 03 ,
S N(E)dE 5. /u .=.? 5 o'1(E) -v-.
0,4 ev 0,4 ev
0,4 ev
2. a =
S craPu(E)a)(E)dE
o
0,4 ev ,
5 ccau (E)(D(E)dE
0
0,4 ev
o
3.
13 0,4 ev ;
S crua (E)a)(E)dE+ /u
o
480
012
0,8
04
0,4
0,
00,1
.,
',..
;
,
...?... ,
I
I I
I I
lit
10
Fig. 2. The relation between the neutron flux for the
energy axis and the energy: the upper group of curves is
for 6 = 0.1; the middle group for 6 = 0.5; the lower for
6=1,5; --m=i; -?-- m= 2 - - - m
The relation (13) is also useful for numerical cal-
culations. Figure 1 shows curves for the neutron flux
4)(z) = liN(z) as a function of the energy z for three
values of the parameter
tY(co)
of the nuclear mass m. The curves are normalized to
the same behavior for z ?.
It can be seen from the graphs that, for fixed values
of ?Oa) , the curves for different values of m are not
cri(gb)
greatly different. The difference is apparent only for the
curves corresponding to a sufficiently strong absorption
aa (kT) 1.5. (Here approximately one-half the neutrons
tas(co)
are absorbed above the "cadmium limit" of 0.4 eV.) Fig-
ure 2 shows the corresponding curves for the relation be-
tween the energy of the flux along the energy axis (the
curves are normalized to a unit neutron source of infinite
energy).
and for various values
*Here the asymptotic representation for the functions
N(z) and Q(z) have been used:
4 ?4
anz.-n/2
3/2 a1z; (z) z1/2
n=0 ii==0
where
1 Gi
ao; a2= (2+ 3v-i- 112) ao;
11
_Ga ( 19 8 3y 00;
3 3m Y 21 7 2 }
(t4=
( 55 31 _L2 2 10 65v 2
+26 3v V -3m 12m m )
3 3
+6---m-+?v1 anT 0.
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cra--(1CT)
The accompanying table gives some integral characteristics of neutron spectra for various values of
(00)
and m. For the integral characteristics we have taken quantities that can be relatively easily obtained experimen-
tally. Here Rcd is the cadmium ratio for an absorber with absorption cross-section cra ?'?v , and also the ratio of
the integral absorption cross sections for U235 and Pu239 averaged over the relevant spectra. The characteristic 3 is
defined as follows: to the calculated values of the integrals are added the corresponding, experimentally' determined
resonance integrals. Their values are taken from the results in [8]. It is assumed here that the dependence of the
form of the spectrum in the energy range above 0.4 eV on m and the parameter Q is weak, and that the vari-
4:1i (co)
ation in the resonance integrals due to this dependence can be neglected. The temperature of the medium is as-
sumed to be 300?K, and the absorption cross sections for U235 and Pu239 are taken from [9].
We stated above that Eqs. (12) could be tested for applicability to an arbitrary medium. For this we must un-
derstand the physical meaning of the functions E(z) and y(z) that characterize the scattering. It is clear that, in
contrast to the quantity Gs(z) which gives information only on the probability of scattering, the functions t(z) and
y(z) must characterize, so to speak, the quality of the scattering. For a monatomic gas, these functions are constants,
i.e., the "quality" of the scattering is the same for all neutron energies. When it is necessary to take into account
the relations between the nuclei, the functions E(z) and y(z) must obviously depend on the energy.
In conclusion I must thank P. E. Stepanov, Ya. V. Shevelev, and L. V. Maiorov for many valuable discussions
of the work.
LITERATURE CITED
1. E. Kogen, in the book: "Experimental Reactors and the Physics of Reactors" [in Russian], Reports of Foreign
Scientists at the International Conference on the Peaceful Uses of Atomic Energy (Geneva, 1955), Gostekh-
teorizdat, Moscow (1956), p. 257.
2. V. I..Davydov, "Zh. eksperim. i teor. fiz.", 7, 9-10, 1069 (1937).
3. J. Wilkins, Ann. Math., 49, 189 (1948).
4. N. Corngold, Ann. Phys., 6, 368 (1959).
5. G. Placzek, Phys. Rev., 69, 423 (1946).
6. A. D. Galanin, The Theory of Nuclear Reactors with Thermal Neutrons [in Russian], Atomizdat, Moscow (1957).
7. S. Gleston and M. tdlund, The Elements of Nuclear-Reactor Theory [in Russian], Izd-vo most, lit., Moscow
(1954).
8. R.-Stoughton and J. Halperin, Nucl. Sci. Engng, 6, No. 2, 100 (1959).
9. D. Huges and R. Schwartz, BNL-325, Neutron Cross Section, II ed. US AEC, New York (1958).
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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STUDY OF SPENT FUEL ELEMEN:TS FROM THE FIRST ATOMIC
ELECTRIC STA TION
Sh. Sh. Ibragimov, L. A. Syshchikov, I. M. Voronin,
and V. G. Kudryashov
Translated from Atomnaya Energiya, Vol. 14, No. 5,
pp. 465-468, May, 1963
Original article submitted June 21, 1962
Data are given from a metallurgical study of three fuel elements from the First Atomic Electric Sta-
tion, which had operated in the reactor for 111, 324.5, and 557 effective days. The results may be of
use in designing reactors of the same type as the First Atomic Electric Station.
The length of operation of nuclear power plants is determined principally by the behavior of the fuel elements
in use. During use, the fuel elements operate under very complex conditions (compound stressed state, neutron field,
elevated temperature, contact with a different medium, etc.). Investigating the changes in properties of the fuel el-
ements after a definite period of service makes it possible to judge whether or not the design is reliable, and whether
or not it should be used in further operation.
The present paper gives the results of a study made on fuel elements that had operated in the reactor of the
Atomic Electric Station for 111, 324.5, and 557 effective days to mean burnouts (of U235 atoms) of 11.81, 28%, and
59% respectively.
The total length of the ring type fuel elements in the Atomic Electric Station is 1700 mm, and they consist of
two Steel tubes, the, inner of which is the main element, while the outer is principally a cladding to catch fission
fragments. The angular space (between the tubes) is filled with fuel (grains of a uranium-molybdenum alloy con-
taining 90/0 molybd num, held together by metallic magnesium). The U235 enrichment for two of the fuel elements
(the ones that had operated 111 and 557 days) is 5%, while that of the third is 6%. During operation, coolant flows
through the inner tube, consisting of water at an input temperature of 1752190?C and an output temperature of 260-
280?C for nominal reactor power. Here, the maximum temperature of the outer surface of the fuel element is not
greater than 360-370?C. The outer surface is in contact with a gas mixture of the following composition [1]: 02
(0.21o); H2 (0.2/o); CO2 (0.5%); and the rest N2.
After the fuel elements had operated for the above lengths of time, they were discharged until the shortlived
fission products had decayed, and then taken to the "hot" laboratory for tests, where they were subjected to the fol-
lowing operations:
1) external inspection and diameter measurement,
2) mechanical disassembly and cutting of samples,
3) metallographic tests, and
4) mechanical tests of the tube material.
External Examination and Diameter Measurement of Fuel Elements
The external observation of the fuel elements, made visually through the viewing window of the "hot" chamber
using binoculars with a magnification of 10, did not show any defects on the outer surface, except for a thin (about
1 p) oxide film of various colors (from light brown to dark gray).
The diameter measurement, made with a remote-controlled micrometer in two perpendicular directions along
the length, indicated swelling, the amount of which varies along the fuel element, and is determined by the degree
of burnout (Fig. 1). The maximum increase in diameter was observed approximately in the center of the fuel ele-
ment, and was 0.10, 0.15, and 0.20 mm for fuel elements that had operated 111, 324.5, and 557 effective days
respectively.
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14,20
14,16'
14,08
?-
14,0
2
ks
-
x
x
/
x
?
x
1
x
"
Top
Bottom
20 40 60 80 100 120 140 16'0
Length, cm
Fig. 1. Diameter change of fuel elements along the
length (1, 2, 3--fuel elements that have operated
111, 324.5, and 557 effective days respectively).
14,20
p 14,16
14,12
14,0
0
8 16'
24
38 40 48
56'
6'4
72
80
?
Burnout, 0/0
Fig. 2.
Fuel element diameter change as a function of
U235 burnout.
Fig. 2 gives the curves showing the change in fuel element diameter as a function of U235 burnout* (in terms
of atoms of the U235 isotope). It may be seen that the diameter change has a tendency to saturation, which is appar-
ently reached at burnouts of about 800/o. The diameter change in the fuel elements is probably due to swelling of the
uranium-molybdenum fuel at the operating temperature. A simple calculation shows that the change in volume of a
fuel element for 10/o U235 burnout (of all the atoms in the uranium-molybdenum alloy) is about 10/o, while for 1510 U235
burnout, the swelling will be approximately 3% from the formation of solid fragments alone. Accordingly, swelling
of the uranium-molybdenum alloy during irradiation is to a considerable degree held down by the magnesium filling
and the material in the cladding.
Mechanical Disassembly of Fuel Elements and Cutting of Samples
Mechanical disassembly of the fuel elements and cutting of samples was done on a special remote-controlled
milling machine and lathe. Samples for mechanical tests and microstructure study were cut out at 4 places on the
length of the tube in the form of toroids (rings) 4 mm high. The uranium-molybdenum alloy held together with mag-
nesium was got out of the rings by dissolving the magnesium chemically in aqueous NH4NO3 solution at a tempera-
ture 70-80?C.
Metallographic Study
The samples were polished and examined by remote control in two hot chambers. The microstructure of the
samples was observed under a remote-controlled MIM-14 optical microscope at magnifications of from 100 to 1000.
The microhardness of the material in the tubes was also determined by remote control on a PMT-4 apparatus at loads
of 50 and 100 g. Before measurement, the samples were subjected to electropolishing. Not less than 10 impressions
were made in each sample to determine the mean value of the microhardness.
TABLE 1. Mechanical Properties of Tube Material
Place cut out
Fuel element operating time, effective days
lit 324,5 557
Position of tube
inner
outer
inner
outer
inner
outer
1751^" 6, %
ghrirn2
6w,
kg/mm2
6, .%
6, %
kg/mm2.
aw
kg/mm 2
6, cyo
crW
kg/nun'.
%
H
kg/mmlkg/mm
W
6, %
Top
375 mm from top. . .
850 mm from top (center
1375 mm from top . . .
64,0
69,0
72,0
68,0
21,5
21,0
18,5
19,0
75,5
76,0
78,0
21,5
90,5
15,0
66,0
70,0
75,0
28,0
23,5
20,0
18,0
77,5
82,0
80,5
83,0
11,5
15,5
6,5
72,0
77,0
79,0
72,0
14,5
11,5
16,0
17,0
310
313
300
290
81,0
89,5
86,5
80,0
8,5
5?5
3,0
11,0
*The values for U235 burnout are calculated, and, as is shown in [2, 3], are in satisfactory agreement with the
experimental data.
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Fig. 3. Microstructure of the material in the
outside fuel element cladding (middle part),
after operating 557 effective days.
80
Bottom
20 40 60 80 100 120 140
Length, cm
Fig. 4. Variation of the ultimate strength of the
material in the inner tube of the fuel element
along the length (1, 2?fuel elements that had op-
erated 111 and 557 effective days respectively).
A study of the microstructure of the samples cut from four different parts of the fuel elements shows no appre-
ciable changes in the microstructure of the material in the tubes and the samples from fuel elements that had oper-
ated 111 and 324.5 effective days, nor is there any interaction between the steel and the magnesium or between the
fuel and the surrounding medium. There is practically no deposit from the cooling medium on the outer tube surface,
but visual observation shows a uniform light brown film, 1-2 ? thick.
The outer cladding of the samples cut from the fuel element that had operated 557 effective days shows micro-
scopic cracks (Fig. 3) running axially, which start on the outside of the cladding, and, propagating from grain bound-
ary to grain boundary, reach depths of 100 i. Further, there is an increase in etching of the outer surface of the steel
samples of thickness up to 30 ? . The formation of microscopic cracks is probably due to the constantly acting radial
stresses (from flowing of the uranium-molybdenum alloy, and to radiatio'n brittleness of the 1Kh18N9T steel.
Determination of Mechanical Properties of Tube Material
The ring samples were tensile tested at room temperature on a remote-controlled UMD-5 machine. All the
measurements of the ultimate strength au and the relative elongation 6 were made on no less than five samples.
Although the tests on the rings are nonstandard, and do not show the true mechanical characteristics of the material,
they nevertheless give quite satisfactory results in comparative studies of the properties of the material before and
after irradiation.
30
25
20
15
0 10 20 30 40 50 60 70
Integrated flux, nen/cm2
Fig. 5. Mechanical properties of the mateiial in the
inner tube of a fuel element as a function of integral
radiation dose.
340
320 1
300 q
ecs
280 cl
tb
260
80x1019 cf)
.484
TABLE 2. Mechanical Properties of Tube Material after
Annealing at 650?C*
Fuel
element
operating
tune,
effective
days
Position of tube
inner
outer
OW
kg/mm2
6, %
4'
kg/mm2
crw
%
kg/mm2
111
324,5.
557
58,5
59,0
55,0
27,5
40,5
32,0
190,0
205,0
200,0
63,5
67,5
64,0
33,0
36,0
30,0
? Samples from middle of fuel elements.
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Mechanical properties of the samples cut from different parts of fuel elements before and after heat treatment
(annealing' at 650?C for 0.5 h), are given in Tables 1 and 2. It may be seen from the Tables that as a result of oper-
ating the fuel elements in the reactor, au and the microhardness of the material in the tubes (cladding) increase,
while 6 decreases, i.e., hardening and brittleness of the steel is observed with the properties in the material of the
outer cladding changing considerably more than the inner, and depending on the place the samples were cut out. A
curve showing the change in au of the tube material as a function of length, as well as the curve of fuel element
diameter change, is similar to the burnout distribtuion curve (Fig. 4). With increase in burnout, and hence in inte-
grated neutron flux, the degree of hardening and brittleness of the material in the tubes becomes greater.
The greatest change in mechanical properties is observed in the material of the tubes in the fuel elements that
had operated 557 effective dayst. Figure 5 gives curves of au, the microhardness, and 6 of the material in the in-
ner tube as a function of the integrated fast neutron flux (a.- 1 MeV). It may be seen that for fluxes of about 5'1020
neutrons/cm2, the curves for these properties reach saturation. Note that for practical purposes, saturation from neu-
tron irradiation of small size samples at 220-255?C occurs at doses of about 3.1020 neutrons/cm2 (mean neutron energy
36 keV, neutrons with energies > 1 MeV amount to 1059). Here, the maximum changes in au and 6 are 10 kg/mm2
and 400/0 respectively [5]. When using ring samples cut from fuel elements, the increase in au at saturation doses is
20-22 kg/mm2. The relative elongation reduces by a factor of almost 2.5. This probably comes from the compound
stressed state of the material in the tube during irradiation.
The effect of heat treating the samples at temperatures of 650?C for 30 min is to remove the hardening and
brittleness of the material almost completely, i.e., the radiation defects which produce the change in the mechanical
properties of the material are annealed. After such an annealing, the properties of the material in the fuel element
tubes are very nearly the same as the properties of nonirradiated 1Kh18N9T steel (see Table 2).
LITERATURE CITED
1. N. A. Dollezhal' et al. in the book: "Transactions of the second International Conference on the Peaceful
Uses of Atomic Energy"(Geneva, 1958), Papers by Soviet Scientists, Vol. 2 [in Russian], Atomizdat, Moscow
(1959), page 15.
2. A. P. Smirnov-Averin et al., "Atomnaya Energiya," 8, No. 5, 446 (1960).
3. A. P. Smirnov-Averin et al., "Atomnaya Energiya," 11, No. 2, 122 (1961).
4. Sh. Sh. Ibragimov, V. S. Lyashenko, and A. I. Zav'yalov, "Atomnaya Energiya," 8, No. 5, 413 (1960).
5. Sh. Sh. Ibragimov, I. M. Voronin, and A. S. Kruglov, "Atomnaya Energiya" (in press).
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.
? It is known from [4] that in austenite steels irradiated at temperatures below 400?C, the radiation hardening defects
anneal out almost completely at 650?C.
f Note that part of the samples?the rings cut from the outer cladding of the fuel element that had operated 557
effective days?showed zero elongation in tests, and 'failed at low stresses, which is due to the presence of the micro-
scopic cracks observed in the metallographic study.
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NOTE ON DETERMINING IRRADIATION COSTS
IN A RESEARCH REACTOR
V. A. Tsykanov
Translated from Atomnaya Energiya, Vol. 14, No. 5,
pp, 469-473, May, 1963
Original article submitted October 11, 1962
A method is presented for determining expenses in operating a research reactor and calculating exper-
imental research costs, with allowance for the effectiveness of channels used, and such factors as reac-
tor contamination, effect of research specimen on reactivity, compatibility of experiments, and speci-
men cooling time.
From a costs standpoint, the research reactor may be approached as a plant designed to produce neutrons. As
in the case of any other operating plant, materials and means are consumed in operating a research reactor, and its
output?neutrons?has a certain cost.
Since most of the neutrons produced in a reactor are used to sustain reactor operation, and a fraction of the re-
maining neutrons is unavailable for use because of leakage and useless absorption, it is only natural that reactor oper-
ation losses must be scaled to those neutrons actually used in experiments.
Neutrons are consumed when a particular experiment is carried out, and the cost of a given experiment may be
determined, therefore, if the relative fraction-of neutrons used is known. The problem lies in correctly assessing this
relative fraction. .
The availability of data from which to estimate the costs of an experiment or pile irradiation program aids not
only in correctly distributing expenses between simultaneous experiments, but also in analyzing the cost factors of
different types of research reactors. The latter point takes on added importance as applications of research reactors
continue to expand.
At the present stage, capital investment and running costs in research reactors vary over quite a wide range, de-
pending on the reactor type and the basic design function. Some experiments can be carried out in principle with
equal chances of success on many different reactor types, although the costs incurred in performing the experiment
will not be the same in every case. A proper costs analysis must therefore take appropriate stock of the particular
experiment geared to a concrete reactor. This in turn will free certain special experimental reactors from experi-
ments which could just as well be performed on other, cheaper reactors.
In the present article, we shall make an attempt to elaborate a useful procedure for assessing irradiation costs
in research reactors.
Running Reactor Costs
The total expenditures in materials in the course of reactor operation may be broken down into amortizable
costs, operating costs, and fuel costs (the fuel component). Capital installation costs ? are known so that, if the useful
reactor operating life is properly determined, amortizable items may be readily spread over the entire period, At the
present time, however, there is no basis for any firm assertions on the useful life of a research reactor, since the per-
formance characteristics and the design of each particular research reactor vary considerably depending on the func-
tion seen for the reactor. Even in standardized research reactors, their individual components are constantly being
? In very-low-power reactors, the fuel load may remain unchanged for several years. In that case, fuel costs should
obviously be accounted as part of the total capital investment and, on that basis we may proceed to determine the
amortizable portion of the expenses. However, in practice, reactors developing appreciable power and in which fuel
reloading is frequent are of greater interest. On that account, fuel costs are accounted for separately in the form of
the fuel contribution to the total costs.
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replaced and improved, and operating experience has yet to be accumulated. Under these conditions, an individual
approach to determining the useful lifetime of each particular reactor is out of the question, and we have to be con-
tent with averages derived from experience. In most cases, it is a reasonable assumption that the lifetime of a re-
search reactor will span 15-odd years.
Operating costs may be broken down into labor costs for the servicing personnel, costs for materials used (in-
cluding electricity, steam, water, etc.), and maintenance costs. All of these entries may be determined with reason-
able accuracy.
We shall deal in somewhat greater detail with the fuel component in the total costs.
The labor costs do not depend on reactor power level, and materials costs, with a certain allowance, may also
be viewed as not dependent on reactor power and on variations in reactor experiment load with time. The fuel com-
ponent, on the other hand, is directly affected by these factors. It is therefore determined as the integrated energy
output of the reactor over a certain time span. If the thermal reactor power is Q(t), in MW, and the reactor has
been in operation for to h, then the integrated energy output during that time will be
' to
Q*-= Q (t) dt MWh. (1)
For each reactor, the amount of nuclear fuel burned up is known (in grams), as the amount required to produce
one MWh energy'. If we denote this quantity as E (in g/MWh), then G'= gQ. grams of nuclear fuel will be burned
up in the reactor over a time to.
We know that nuclear fuel is not completely burned up in a?pile. If the relative and average btirnup is denoted
as yo, then the total expenditure of nuclear fuel will come to
G'
G=--- gQ*
(2)
The nuclear fuel is loaded into the reactor core in the form of fuel elements costing a known amount (Cf el)
with a known fuel content (G1). Dividing the cost per fuel element by the fuel content in an element, then, we may
determine the fuel cost per item
Cf el
uCf = r bles/gram.
Next, we determine with ease the nuclear fuel costs spread over a time to:
cp
Cfuel = GCf ? Cf rubles.
gQ
(3)
(4)
An assumption was made, in performing these calculations, to the effect that the fuel left over in spent fuel
elements is not recovered. When fuel is reprocessed for recovery, the purchase costs of the fuel elements, which de-
pend on the difference in the cost of residual-enrichment uranium and recovery costs, may be partially offset.
We may now proceed to calculate the total reactor operating costs over the time to. In fact, designating the
total sum of annual amortization writeoffs as A, and the annual salary and wage fund for servicing personnel as C.
and the annual running materials costs as Cm, we find that the round-the-clock operating total costs over the time
interval to will be
(5)
Q* r,
---- A?CP+Cm to+ gcp
760
AH-Cp+Cm to+t-fuel -
Ct--= 8760 8
*This amount depends on the pile neutron spectrum and on the type of nuclear fuel used (because of variations in the
of/oa ratio).
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If, in the course of a certain time, the pile thermal power is kept constant at Q (MW), then the costs for 1 h
of reactor performance will be
C r
C A gQ
8760 uf rubles/hour.
Distributing Costs Between Experiments and Determining Irradiation Costs
(6)
The distribution of costs is proportional to channel effectiveness. An experimental reactor is usually provided
with several irradiation channels. These channels differ in size and neutron flux. The larger the volume of the ex-
perimental channel and the greater the neutron flux in the channel, the greater will be the amount of material that
can be placed in the channel for irradiation and the more efficient will be the irradiation process. In simultaneous
exposures involving all the channels, then, costs could not possibly be distributed evenly over all the experiments.
The effectiveness of each particular channel must be taken into proper account.
A measure of channel effectiveness is the product of the effective channel volume Veff (in cm3) by the (vol-
ume) average neutron flux in the channel, -cfk (in neutrons cm/sec). The effectiveness of a particular channel is
EK = Veff.713-K neutrons?cm/sec. (7)
If there are n channels in the reactor and the effectiveness of each of the channels is known, then the irradia-
tion cost in the i-th channel (with full utilization of all the channels) will be
C
C1= n Ei = Vi eff CP!, (8)
E Weft.
5=1
The formula so obtained is valid for the ideal case when the degree of reactor contamination does not vary
with time during the irradiation process, the reactor suffers no shutdown for miscellaneous reasons, and so forth.
Proper corrections must be introduced for all such factors which will affect the result.
:raking into account the effective utilization of the reactor. We come across cases where not all the experi-
mental potentialities of the reactor are being exploited, even though the experiments being performed in the occu-
pied channels require operation of the reactor and of all the associated equipment at the rated conditions. In that
case, the reactor operates solely to provide the exposure in some of the experimental channels, and all the costs fall
on the experiments being conducted in those channels.
If, in carrying out a given series of experiments, k channels (K < n) are occupied, then the irradiation costs
in the i-th channel may be found from formula (8) by replacing the summation limit by K in that formula. The
more K differs from n, the more the experiments will cost.
It is very important, in this context, to plan the reactor operating schedule so that peak loading will be assured.
It is also worthy of note that, if the reactor is being operated not with the rated number of experimental channels
(e.g. when the experimental channels are put into use successively with the reactor already in operation), there will
necessarily result an overexpenditure of means on experiments.
Compatibility of in-pile experiments. In the preceding section, we considered the case of incomplete reactor
loading due to incorrect planning or a limited demand on the experimental channels. We shall now take up the case
of incomplete loading of the reactor due to incompatibility of the experiments. Incompatibility of the experiments
is always possible eventually, since it frequently occurs that some experiments will either require different reactor
power levels, or else the program of reactor work required for one particular experiment will render the simultaneous
conducting of other experiments unfeasible or impossible.
If among K experiments being conducted in a pile, there are K1 (Ki < K) such that experiments cannot be
conducted at a particular moment in K2 = n ? K channels, then the irradiation costs in the K2 channels over the time
in question (the cost of the "nonexistent" experiments) must be added to the cost of just the K1 experiments, with the
supplements proportional to the effectiveness of the channels occupied during these experiments. In that case, the
cost of the compatible (K ? K1) experiments will be determined from Eq. (8), and the cost of the incompatible exper-
iments (K1) from the formula
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C. =
7i
E.
j=1
(9)
The sense of this formula is quite understandable: the first term is the irradiation cost in the i-th channel (i
of the number K1) when the reactor is fully loaded, the second term is the supplement to the cost owing to the fact
that experiments were not carried out in K2 channels. The sum in the numerator of the second term is equal to the
cost of the nonexistent experiments in K2 channels, with Cq determined from Eq. (8). Summing over q is carried
im
out with respect to the channels not occupied during the experiments (K2 channels). The ratio EK/ EK is the
portion of the additional cost falling on the experiment in the i-th channel. Summing over m is carried out with
respect to the number of channels occupied by the incompatible experiments.
By way of elucidation, consider the following example. The reactor has six experimental channels. Their ef-
fectiveness is. reported below (in relative units).
Channel
number
1
2
3
4
5
6
K
2
1
5
,
,_,
10
4
Over a certain time span, the reactor was operating at constant power, with experiments in progress in channels 2, 3,
4, and 5. Channels 1 and 6 remained free, since the experiments in channels 2 and 5 required conditions under which
experiments in channels 1 and 6 would have been impossible.
It is required to determine the costs for experiments when the total reactor operating costs during that time
amounted to C. The value of C is determined here from Eqs. (5) or (6).] In our notation, K = 4 (channels 2, 3, 4,
5); K1 = 2 (channels 2 and 5); K2 = 2 (channels 1 and 6).
c _
=The costs of the compatible experiments are: C3= - .)=0,2C; 'C4= - 3 0,12C. The costs of the incom-
patible experiments are: C?=-- 1? 1 ?0,0iC 16C = 0,04C+ 0,0218C = 0,062C;
- ' 1 -1,- 10 11
C C
- '
C-= ' ' I( 10=0,4C -!-0,218C=0,618C. Now check the total costs:
1- )
HC41,-05=0,062CH-0.2C+0,12C+0,618C=C.
Taking into account the effect of specimens on reactivity. Specimens loaded into experimental channels for
irradiation always exert some effect on the pile reactivity, but the extent of this effect varies and is dependent on
the properties of the specimen and on where the channel is located in the pile. The effect of specimens placed in
channels remote from the core on reactivity may be ignored in actual practice. On the other hand, specimens in
core channels may exert a significant effect on reactivity.
In a research reactor, the output parameter is the amount of neutron flux, which depends, for a-given reactor
design and set of reactor properties, on the power generated per unit core volume. Consequently, at different pile
thermal power levels, if the core varies in volume, a neutron flux of uniform magnitude may be achieved in any
channel. The volume of the core (or the effective loading of the reactor) is related to the change in reactivity, and
therefore depends on the specimens loaded in. A specimen introducing positive reactivity makes it possible to reduce
the effective core volunie, and this leads to a diminished pile thermal power level and, as a consequence, to fuel
savings. On the other hand, a specimen introducing negative reactivity is responsible for fuel penalties. Consequent-
ly, both the savings achieved in the first instance and the additional costs incurred in the second instance must be
ascribed to those experiments which affect the pile reactivity.
Since the reactivity varies as a rule more during the time the reactor is in operation than during loading and
un'eading of specimens, corrections for reactivity in the irradiation costs must be introduced only in the case of speci-
men irradiations which drastically affect the reactivity. A yardstick for the amount of reactivity starting with which
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it becomes necessary to introduce this correction can be arrived at only concretely for each reactor, with the change
in reactivity during operation due to the properties of the reactor itself given due attention. In any case, this correc-
tion would hardly necessitate being introduced in most modern reactors when the specimens bring about a reactivity
change less than 0.5%.
In order to determine the required corrections for irradiation costs necessitated by reactivity changes, we must
have information on the relationship between the amount of fuel loaded into the core and the reactivity, on the one
hand, and on the mean thermal power per unit weight of fuel or per unit core volume, on the other.
Suppose that among n experiments being carried on, there is one which severely affects the reactivity. We
then proceed as follows in order to calculate irradiation costs. The loading and the reactor power are known, and
the change in reactivity brought out by each given specimen is taken into account. We term this power level the
actual power, and designate it by the symbol Qa. In addition we know (or are in a position to determine) the reac-
tor loading, and this means that we also know the reactor power (without taking the reactivity introduced by the
specimen into account). We call this power level the computed power, and designate it by the symbol Qc. Using
Eq. (6), we can determine the following costs in operating the reactor:
The difference in the cost categories
Ca ;.= A+Cp+Cm gQ, Cf
8760'
QCc = A+Cpd-Cm , g Cf
8760 y
gCf
PC = Ca ? Cc = ?(Qa ? Qc)
49
(10)
(12)
(PC < 0 when the reactivity p> 0, PC > 0 at reactivity p< 0).
Calculations for n-1 experiments are carried out with respect to the computed costs, since the specimens used
in this case do not affect the reactivity, and the difference in costs must be laid at the door of an experiment respon-
sible for the change in reactivity. Accordingly, for n-1 experiments, irradiation costs may be determined, depend-
ing on the case involved, from either Eq. (8) or Eq. (9). The cost of an experiment in which reactivity is affected is
also computed using these same formulas (depending again on the case involved), but the quantity AC determined
from Eq. (12) is then added to the result so obtained.
If among ri simultaneous experiments, there are K such that the reactivity is affected, then similar calcula-
tions may be carried out for each such experiment.
Taking the specimen cooling time into account. During the time it takes any given specimen to cool down
before it is withdrawn from the channel, there will be a forced reactor outage, if no measures are taken to provide
for the cooling-down process during reactor operation (e.g. remotely controlled withdrawal of specimens and auto-
matic displacement of the specimens to a cooling-down zone).
Whenever the reactor is shut down, the total costs will be reduced only by the amount of the fuel contribution
to the costs. If the shutdown is not due to cooling (preventive maintenance, fuel reloading, etc.) and the shutdown
time is automatically taken into account in determining costs by Eq. (5), with these costs distributed over all the ex-
periments, then the costs accompanying a cooling shutdown will have to be determined separately, and these costs
will have to be accounted to the experiment which called for the cooling time in the first place. There would be no
point in charging up this downtime to the other experiments.
This points up the striking importance of instrumentation designed to achieve this cooling while the reactor is
in operation, as well as adequate and correct planning ahead of experiments which call for simultaneous cooling-down
of several specimens. Let a specimen be cooled down over a time t in one channel and, simultaneously, let cooling
of a second specimen begin in another channel, where the latter specimen requires a cooling-down time tn. The
total reactor operating costs during that time will be
A?Cp+Cm
ut= t.
8760
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During the first half of this time, the costs will be spread over the two experiments, and later the first experiment
will carry the entire cost. Any additional costs for cooling the second specimen down will therefore come to
Ct AH-Cp+C, t
A C 2 -4- -
8760 4
and costs for cooling down the first specimen will be
AC Ct Ct 3 c A+Cp+C?, 3t
4 m 2 4 t 8760 4
Neutron beam experiments. Experiments on neutron beams brought outside the reactor are of a very unique
nature. In the interests of a uniform approach to the problem, the cost of conducting this type of experiment will
be handled in the same way, by reference to effectiveness. In determining the effectiveness of the neutron beam,
we must take the channel volume into account only inside the core and inside the reflector (but not inside the
shielding), as well as the neutron flux in that volume. It should be noted that the channel effectiveness arrived at
in this fashion may not always correctly characterize the value of the channel for beam experiments. However, in-
troduction of further refinements in this application would hardly find justification at the present state of knowledge.
491
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000600100004-4
SOME LAWS OF THE FORMATION OF EPIGENETIC URANIUM ORES
IN SANDSTONES, DERIVED FROM EXPERIMENTAL
AND RADIOCHEMICAL DATA
L. S. Evseeva, K. E. Ivanov, and V. I. Kochetkov
Translated from Atomnaya griergiya, Vol. 14, No. 5,
pp. 474-481, May, 1963
Original article submitted June 21, 1962
The paper gives the results of experiments on the simulation of precipitation of uranium from aqueous
solutions in a sandstone bed enriched with freshly precipitated iron sulfides. An oxidation zone and a
cementation zone enriched with uranium precipitated from aqueous solutions were obtained in the bed
model. Neogeneses of iron sulfides in the form of "rolls," analogous to natural ore beds, were observed
in the cementation zone. It is shown that the formation of ore concentrations of uranium takes place
during the continuous movement of the oxidation zone in the direction of movement of the solutions
and the redistribution of uranium near the boundary between the oxidized and unmodified rocks. The
experimental results are confirmed by the results of an investigation of radioactive equilibrium between
ionium and uranium under natural conditions.
INTRODUCTION
As a result of the increased importance of epigenetic sedimentary deposits in the over-all balance of uranium
reserves there has recently been increasing interest in study of the formation of these deposits.
Deposits in permeable arenaceous-argillaceous rocks with oval and crescentiform ore bodies, known as "rolls,"
are of particular interest. These ore bodies have been described in detail by D. Shaw [1], who indicates that an in-
vestigation and explanation of their structure may help to determine the genesis of a deposit.
A. I. Germanov [2] suggested that bodies of the roll type originated by infiltration and are formed under condi-
tions of descensional pressurized movement of underground waters where the strata are of relatively uniform composi-
tion and permeability.
The rate of movement of water in a uniform permeable bed with impermeable strata above and below decreases
from the center of the bed to the periphery. As a result, the oxidized zones formed in the sandstone beds are in the
form'ciftdfigues extending in-the direction of movement of the water, while the ore bodies, localized near the contact
of the oxidized and unmodified rocks and following the outline of this contact, are crescentiform or roll-shaped.
Deposition of uranium from the waters takes place when oxidizing conditions are replaced by reducing ones, in which
the' migration capacity of uranium is markedly reduced. It is evident that the greater the content of matter in the re-
duced state in the rocks and the more uniform the rate of its oxidation, the greater will be the contrast in the bound-
ary between the different conditions and the more favorable will be the environment for uranium concentration near
this boundary. Substances which are intensively oxidized by the oxygen of waters in sandstone rocks include sulfides,
coalified plant debris, bituminous substances, ferrous compounds, etc.
These theories of the conditions of formation of roll-like ore bodies formed the basis of experiments by L. S.
Evseeva and V. I. Kochetkov on the simulation of uranium precipitation from aqueous solutions in a bed of sand en-
riched with iron sulfides. K. E. Ivanov's radiochemical investigations on a natural ore occurrence confirmed the in-
filtration genesis of such bodies and made it possible to establish the date of their formation.
EXPERIMENTAL PROCEDURE
The bed model (Fig. 1) was a glass-like transparent plastic box (2.0x 0.15 x0.20 m) filled with fine-grained
homogeneous ferruginous quartz sand. Clay was deposited in the floor and roof of the bed. To isolate the bed from
492
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000600100004-4
Fig. 1. Model of a bed of sand.
atmospheric oxygen, it was covered by a close fitting lid with a rubber lining. The model was fixed at a moderate
angle, the rate of movement of solutions through the bed being 5 liters/day, corresponding to a linear filtration ve-
locity of 12.5 n-/day. To convert iron oxide in the sand to sulfides, distilled water saturated with hydrogen sulfide was
passed through the sand before commencing the experiment. When all the sand had turned black, the bed was washed
with distilled water until there was no odor of hydrogen sulfide. Uranium-containing water was then passed through
the bed for a considerable time. In the first experiment, uranium was added to the solutions in the form of sodium
uranyltricarbonate, and in the subsequent experiments, as uranyl nitrate. Solutions with uranium concentrations of
n.10-6-n?10 -5 g/liter and n?10 -3-n.1.0 -2 g/liter were passed through the bed. At the bed outlet the uranium content of
the solutions was (1-4)?10-7 g/liter and (1-4)?10-6 g/liter in the first and second cases respectively.
Solutions with a uranium concentration of 2-10-3 g/liter were used as the working solutions in the experiments;
their pH was 6-7. The uranium content of the solutions at the bed outlet was checked once per day. The analyses
were carried out by the luminescence method.
The Fe203 content of the initial sand was 0.5 and 1.3% in the first and second experiments respectively. The
volume of uranium-containing solution passed through was 75 and 245 liters respectively. The first experiment lasted
20 days and the second about two months. It should be mentioned that during the feed of the solution the hydrostatic
head in the bed varied slightly as the water level in the feed bottle fell (see Fig. 1).
0,009 4004 0,903 0,004 0,00o7 0.005 .4005
0,013 40?0150,000 0,01-40ri02
0,021
0,003
0,003
- - _
Fig. 2. Zonality and distribution of uranium in a sandstone bed (second experiment). Zones:
I) oxidation; II) clarification (transitional); III) roll-like neogeneses; IV) unchanged rocks.
0,001
0,000
ii
Ili ? -
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Declassified and Approved For Release 2013/09/25 : CIA-RDP10-02196R000600100004-4
C:=3 1 1=32 F771.3 Gin 4
Fig. 3. Diagram of the formation of "inverted" rolls:
1) clay; 2) unchanged sand; 3) oxidation zone; 4)
ore roll; the arrow indicates the direction of move-
ment of water.
Eh,
my
+0,6
+0,4
+0,2
0
0,
0,
1
2%,
3 ?:(k
4
N
?
?
\'' \_
\
? 1
? 4 ?
\ I
1%
?
?. ? s
Q1
4I\
\
.
N
b
\
.
2 4 6 8 Pit
Fig. 4. Relation between the redox potential (Eh)
and pH in solutions obtained by oxidation of sulfides:
1, 2) pyrite; 3) pyrite with a chalcopyrite admixture;
4) boundary between the UO2 and UO2(OH)2 stabil-
ity fields.
1
2
3
Fig. 5. Diagram of the location of ore rolls in an
arenaceous -argillaceous formation: 1) crystalline
rocks; 2) clays; 3) sandstones; 4) ore rolls.
494
After the experiments had been completed, the
uranium distribution in the bed was investigated. Sand
samples were taken with a stainless steel tube at 20 cm
intervals over the bed cross section. Nine samples were
taken from each cross section. Where the uranium con-
tent was at least 0.003% it was determined chemically,
the luminescence method being employed for lower ura-
nium contents.
RESULTS OF THE EXPERIMENTS
First experiment. As filtration of solutions con-
taining uranium and atmospheric oxygen proceeded, a
distinct oxidation zone in the form of a tongue, extended
in the direction of movement of the water and advancing
continuously through the bed at a rate of 1-2 cm/day,
was formed in the latter. This rapid advance was due to
the fact that freshly formed iron sulfides are oxidized
very readily. During the advance of the oxidation zone,
unoxidized areas in the form of disconnected lenses en-
closing clay interlayers, remained in the roof and floor
of the bed. The uranium content of these lenses was
0.00950. A uranium content of 0.00859 was observed in
the unoxidized sand near the contact with the oxidized
part of the bed. Further away from the contact, both the
oxidized and unoxidized sand contained 0.002-0.00350
uranium.
Second experiment. As a result of filtration of
uranium-containing solutions, four distinct zones were
formed in the sand bed: I) oxidation; II) clarification
(transitional); III) roll-like neogeneses; IV) unchanged
(unoxidized) rocks (Fig. 2). The formation of a more
complex zonality in the second experiment than in the
first one may be due to the higher sulfide content of the
sand and the greater duration of the experiment. The
transitional, clarified zone was evidently formed as a re-
sult of the non-uniform rate of oxidation of iron sulfides,
due partially to their crystallization in the form of min-
erals oxidized less rapidly than amorphous sulfide. Under
natural conditions, the spotted ore (incomplete oxidation)
zone, formed as a result of the different rates of oxidation
of individual sulfides and the non-uniform permeability
of the strata, may correspond to this zone.
The third zone consists of roll-like accumulations
of black sand alternating with interlayers of light-gray
sand. This is a cementation zone enriched with redepos-
ited iron sulfides. According to analytical data, the iron
content of the rolls, calculated as Fe203, is 1.80-1.855),
whereas in the oxidation zone and unchanged sand it is
< 0.4450 and 1.2050 respectively.
The oxidation and clarification zones were clearly
outlined soon after the commencement of the experiment,
but the third zone was formed only towards the end. All
three zones were mobile, moving slowly in the direction
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Declassified and Approved For Release 2013/09/25 : CIA-RDP10-02196R000600100004-4
10/u, %
700
600
500
400
300
200
100
0 200 400 600 800 1000 1200 1400 1600x
tv.c.:11 r.:3 2
Fig. 6. Change in the ionium/uranium ratio
Io/U for a dip in the bed. Sandstone: 1)
stable; 2) oxidized.
of movement of the water; the number of rolls in the third
zone increased with time.
The formation of series of rolls may presumably be ex-
plained by the non-uniform hydrostatic head during feed of
the solutions to the bed in the course of the experiment. But
such non-uniformity is usual under natural conditions. Re-
plenishing of water-bearing horizons is intensified during per-
iods of rainfall and decreases during the dry season.
After completion of the experiment the following ura-
nium distribution was observed (see Fig. 2): in the unoxi-
dized sand at the contact with the clay the uranium content
at the beginning of the bed was 0.009-0.02110 and 0.007% in
the rolls; in the oxidation zone, in the initial section of the
bed, where uranium was sorbed by limonite, it was 0.0091o.
In the unchanged sand, at a considerable distance from the
rolls, and in the frontal part of the oxidation zone the urani-
urn content was 0.0001-0.00021o.
During the experiments it was found that the boundary between the oxidized and unoxidized rocks has a simple
oval shape only if the bed permeability is uniform. But if a lens of argillaceous rock is placed in the path of the ox-
idation zone, the frontal part of the oxidation zone boundary splits into two tongues which circumvent the lens, as
shown in Fig. 3. As a result of the low permeability, oxidation in the clay is slower than in the sand; this leads to
formation of an "inverted" roll with its convex side facing the direction of movement of the water. A series of rolls
with different orientations and "capricious" shapes, like those described in [3], may evidently be formed in the case
of a variegated alternation of areas with different water permeability in rocks.
According to [4], a relation between the distribution of uranium deposits and the filtration capacity* of rocks is
observed in the Colorado Plateau. These deposits are most frequently found in rocks with a non-uniform filtration
capacity: Morrison sandstones, Shainar conglomerates and Chenelle sandstones. It may be assumed that this law is
due to the non-uniform rate of oxidation of the rocks as a result of their different permeabilities, which establishes
conditions for the formation of numerous ore rolls, as was shown above.
To determine the geochemical nature of the reduction and concentration of uranium by iron sulfides, we inves-
tigated the relation between the redox potential (Eh) and the pH of the medium during oxidation of pyrites. Pyrite
from sedimentary rocks, crushed to 100-200 mesh, was placed in distilled water (2 g per 100 ml of H20) and oxidized
for ten days by atmospheric oxygen. Solutions obtained in this way had a pH of 3.0-4.1, Eh +450 to +550 my, and
contained ferrous and 'ferric iron (more than 10 mg/liter Fe), SO4 (up to 120 mg/liter) and evidently sulfur ions of
lower valence numbers (these were not determined chemically). To obtain the relation between Eh and pH, the so-
lution was titrated in absence of oxygen (in a CO2 current) with a soda solution (0.5-2%) in a glass beaker with a rub-
ber stopper in which the electrodes and CO2 inlet and outlet tubes were fixed. pH and Eh measurements were made
with an LP-5 potentiometer until the last three measurements were identical. The results obtained are given in Fig. 4,
Uranium/Ionium Ratio in Bed Waters Associated with Sandstones
No. Characteristics of the adjoining rocks
Depth,
U cont.
g/liter
io/u, Gio
1 Alternation of limonitized sandstones and clays
2 Same
3 Gray argillaceous sandstone with uranium oxides
4 Brown sandstone, markedly limonitized
5 Brown-yellow sandstone, weakly cemented with ferruginous carbonate cement
6 Brown sandstone, markedly limonitized
7 Contact between unmodified (dark-gray sandstone with uranium oxides) and
oxidized (brown, limonitized sandstone) rocks
11.0
11.0
17.5
60.0
60.0
60.0
60.0
3.25.10-4
7.5.10-3
5.6.10-3
1.1'10-4
2.4.10-4
1.410'4
1.3.10-4