SOVIET ATOMIC ENERGY VOLUME 21, NUMBER 3

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• Publication Date: September 1, 1966
• Content Type: REPORT

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.ATOMHAH 3HEPfVIH
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
Volume 21., Number 3
SOVIET
ATOMIC
ENERGY
CONSULTANTS BUREAU
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SOVIET
ATOMIC
ENERGY.
Soviet Atomic Energy is a cover-to-cover translation,of Atomnaya
Energiya, a publication-of..the Academy olf Sciences, of the USSR.
An. arrangement with Mezhdunarodnaya Kniga; the Soviet book
export,agency, makes available?'both advance copies of the Rus-
sian journal, and original.~lossy photographs'and'.artwork. This
serves to decrease the necessary time lag between publication
of the original and publication of the translation andhelps?to im
prove the quality,of-the latter.. The translation began with the.first
issue of the Russian journal.
%
Editorial Board of Atomneya'Energiya:
Editor: M. D. Millionshchikov,
Deputy Director, Institute`of Atomic Energy
imeni 1. V. Kurchatov
Academy of Sciences-of the USSR
Moscow, USSR
Associate Editors: N. A. K'olokol'tsov
N. A. Vlasbv
A. I. Alikhanov
.
A. A. Sochvar.
i
N. A. Dollezhal`
V. S. Fursov
I. N. Golovin
V. F.-Kalinin
A.. K. Krasin
A. I. Leipunskii
V. V. Matveev
R. N. lSalei
M. G, Mesh cheryak8v
V. B. Sherchenko
D. L. Simonenko
V: I. Smirnov
A. R. Vinogradov .
A. P.'Zefirov
Copyright ? 1967 Consultants1Bureau, a division of Plenum Publishing Corpora
tion, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. No article
contained herein .may be reproduced for any purpose whatsoever witho6t per-
mission of the publishers.
Subscription Single Issue:.$30
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Volume 21, Number 3 September, 1966
CONTENTS
Engl./Russ.
Analyzing the Oxygen Content of Certain Metals by Recording the Delayed Neutrons
Produced in the 0i8 (y, p) N17 Reaction - M. M. Dorosh, N. P. Mazyukevich and
V. A.Shkoda-U1'yanov .......................................................... 807 163
Acceleration of Electrons in the Annular Phasotron of the P. N. Lebedev Physical
Institute of the Academy of Sciences of the USSR - L. N. Kazanskii, V. N. Kanunnikov,
A. A. Kolmenskii, E. P. Ovchinnikov, V. A. Papadichev, S. S. Semenov, A. P. Fateev,
and B. N. Yablokov .............................................. ........... 811 166
Transverse Coherent Instability of a Charged Particle Bunch - N. S. Dikanskii and
A. N. Skrinskii ................................................................ 821 176
A Criterion for the Efficiency of Utilization of Nuclear Fuel - V. V. Batov and Yu.I. Koryakin, 825 179
Activation of Corrosion Products in Nuclear Reactors - A. P. Veselkin and A. V. Nikitin .... 831 184
Thermodynamic Properties of the y-Phase in the Uranium-Zirconium System - G. B.
Fedorov and E. A. Smirnov ...................... 837 189
X-ray Diffraction Study of the Distribution of Texture over the Cross Section of Uranium
Bars Worked in the a- and y-Phases and Subjected to Quenching - V. F. Zelenskii,
V. V. Kunchenko, N. M. Roenko, L. D. Kolomiets, and A. I. Stukalov ................ 841 192
Sr90 and Cs137 Content in Agricultural Products of Western Slovakia, 1963-1964 - S. Cupka,
M. Petrasova, and J. Carach ................................................... 846 197
ABSTRACTS
On the Analysis of Transitional Processes in a Reactor Close to Prompt Criticality -
Yu. P. Milovanov .............................................................. 850 202
Dose Build-Up Factors for Low-Energy -y Rays in Homogeneous and Heterogeneous
Barriers - D. B. Pozdneev ,, .................... 851 203
Albedo of a Homogeneous Barrier of Finite Thickness for Low-Energy y Rays -
D. B. Pozdneev ................................................................ 852 203
LETTERS TO THE EDITOR
Two-Channel System for Synchronous Registration of Fission Fragments from a Standard
and a Specimen Undergoing Analysis - E. M. Labonov, P. I. Chalov, and U. Mamyrov . 853 204
Absorption of the Energy of -y-Radiation from a Unidirectional Point Source of -Y-Quanta,
in Plane Geometry - F. A. Makhlis, L. A. Sugak, E. A. Plandin, and I. K. Shmyrev ... 855 205
A Source of Lithium Ions for an Electrostatic Generator - V. M. Korol' and V. S. Siksin . . . . 858 .208
A Method for Solving the Diffusion Equation - V. S. Shulepin ............................. 860 209
Use of General-Purpose Electronic Computers for Complex Evaluation of Uranium Prospec-
ting Studies - I. A. Luchin ...................................................... 862 210
The Activation Method for Determining Fluorite - A. P. Bushkov and V. I. Prokopchik . . . . . . 868 215
A Miniature Device for Measuring the Mean Total Concentration of Radon - V. N. Kirichenko,
B. N. Borisov, B. I. Ogorodnikov, V. I. Kachikin, and P. I. Basmanov . . . . . . . . . . .. . . . 871 217
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CONTENTS
Use of SGD-8 Glasses for Dosimetry of y-Radiation from the IGR Pulsed Reactor -
S. A. Sharoiko ...........................................................
SCIENCE AND ENGINEERING NEWS
Scientific Conference of the Moscow Engineering and Physics Institute - V. V. Frolov..
[Meetings of the International Electrotechnical Commission TC-45 (Technical Committee
No. 45) - G. A. Dorefeev, B. G. Egiazarov, and M. L. Raikhman ...............
The First Soviet-Made Industrial Semiconductor Electron-Hole Detector Devices -
V. V.Matveev, Yu. P.Sel'dyakov, and A. D. Sokolov .........................
[Nuclear Research into the Production and Use of Isotopes in Belgium and the
Netherlands - E. Mamonov ................................................
[International Center for Theoretical Physics in Trieste - V. G. Solov'ev ............
Ten Years of the "Atoms for Peace" Exposition - V. Mikhailin .............. :......
Canadian Scientists Visit the USSR ,, ..........................
BIBLIOGRAPHY ........................ ....................
The Table of Contents lists all material that appeared in the original Russian journal. Items origi-
nally published in Englishor generally available in the West are not included in the translation and
are shown in brackets, Whenever possible, the English-language source containing the omitted items
is given.
The Russian press date (podpisano k pechati) of this issue was 8/29/1966.
Publication therefore did not occur prior to this date, but must be assumed
to have. taken place reasonably soon thereafter.
(continued)
Engl./Russ.
873
218
875
220
222]
879
223
224]
228]
881
229
884
231
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ANALYZING THE OXYGEN CONTENT OF CERTAIN
METALS BY RECORDING THE DELAYED NEUTRONS
PRODUCED IN THE 018 (y, p)N17 REACTION
M.M. Dorosh, N.P. Mazyukevich, UDC 543.53
and V. A. Shkoda-Ul'yanov
This article considers the possibility of utilizing the 018 (y, p)N17 reaction
for determining the concentration of oxygen in metal ingots by recording delayed
neutrons. Calculations are made to determine the yields from oxygen impurities
in thick blocks of Be, Ti, and' Zr. The construction of high-current medium-en-
ergy accelerators makes it possible to work out a continuous analysis of metals
and alloys.
The growing industry of heat-resistant metals and alloys for nuclear power engineering, airplane
and rocket design, and scientific research requires the development of new, sufficiently rapid and accu-
rate methods for determining impurities; of special importance are admixtures of the gases H2, N2, and 02,
whose presence reduces the plasticity of metal parts and structures.
Because of the serious technological difficulties involved in determining the presence of small quan-
tities of oxygen in certain metals (e.g., in Be, Ti, or Zr [1, 2]), the development of new analytical methods
for detecting oxygen and the improvement of the existing methods are becoming particularly urgent pro-
blems. The currently used methods of vacuum melting and large-volume dissolution of metals have a
sensitivity of 10-1-10-2% [1, 3] and, furthermore, are laborious and time-consuming. To determine the
amount of various gases (including oxygen) contained in metals by means of nuclear reactors, we activate
a specimen with a flux of neutrons, gamma quanta, or high-density charged particles, and then measure
the induced (3 or y activity. The average sensitivity obtained for oxygen is 10-3-10-4% [4, 5]. However,
it is not always possible to use this method for rapid analysis under industrial conditions because of the
complicated equipment needed, the long time required for irradiation, and a number of other factors. In
practice it is often necessary to know the average oxygen content in a specific part of. the ingot or in the
ingot as a whole. This problem can be solved by using the photoneutron method, owing to the following
special features of this method. In the first place, in large specimens an electron-photon avalanche is
produced when the incident beam is absorbed; secondly, the neutrons emitted by nuclei on y-ray absorption
have a large average path length and will easily pass through a specimen which is thick enough to absorb
the primary beam completely.
Analysis utilizing methods of nuclear physics, which requires a high-intensity irradiator, may be
introduced into factory practice by using high-current accelerators (microtrons, linear accelerators, high-
current betatrons). Today such accelerators have already been designed and built [6-9]; they are charac-
terized by a relatively high electron-beam current (10-100?A or higher) and small size. The use of such
accelerators provides increased opportunities for analyzing metals and alloys at production sites by re-
cording the products of various nuclear reactions immediately - either during or after the irradiation
period. It therefore seems desirable to develop an analytical method in which delayed-neutron precursors
are produced and the yield of these neutrons is measured.
Reference [10] suggests determining the presence of oxygen by recording the delayed neutrons produced
by the disintegration of the radioactive N17 nucleus formed in the O17(n, p)N17 and O18(n, d)N17 reactions whenthe
specimen is irradiated with a neutron flux from a reactor inthe O17(n, p)N17 and 018(n, d)N17 reactions and in the
018(t, o)N17 reaction caused by tritium from the Li6(n, a)H3 reaction. Such a large number of reactions forming
N17 may often create some inconvenience in analyzing the specimen for oxygen, but this difficulty can be avoided
if an electron or photon beam is used instead of the primary neutron flux. In this case the specimen under
Translated from Atomnaya Energiya, Vol. 21, No. 3, pp. 163-166, September, 1966. Original article
submitted April 24, 1964; revised May 16, 1966.
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Maximum Delayed-Neutron Yield Q(E) for investigation (e.g., a metal ingot) must at the same time
10-4% Oxygen in Various Metals (neutrons/ be part of a Faraday cup used to measure the incident
100 ?A ? sec) radiation flux precisely [11] (which is much easier than
E, MeV I QBe(E) QTi(E) I QZn(E)
18
10
20
30
19
40
60
80
211
130
240 140
270
22
200
370
400
23
300
540
590
24
480
780
830
precisely measuring the neutron flux by using the neutrons
as primary radiation sources), and a source of delayed
neutrons produced by the 018(y, p)N17 reaction. As was
shown in [12], the contribution of the 017(n,p)N17 reaction
is negligible in comparison with that of the 018(y, p)N17
reaction. It should be noted that the specimen dimensions
for which the electron or photon radiation effective for
the 018(y, p)N17 reaction is almost completely absorbed
are small in comparison with the path length of the neu-
trons formed in the photo-nuclear reactions. This makes
it possible to minimize the contribution of all the reac-
tions produced by neutrons and yielding the isotope N17.
Thus, suppose that a specimen containing oxygen is irradiated with a beam of electrons or gamma
quanta and that an electron-photon avalanche is produced in the specimen for a specified beam energy and
sufficiently large specimen dimensions. In 018 nuclei, gamma quanta with an energy above the threshold
energy (E = 16.4 MeV) give rise to a (y, p) reactions, forming the beta-active isotope N17 with a half-life of
T1/2 = 4.15 sec. Each N17 nucleus undergoes beta disintegration and is converted into the stable isotope 016
and a neutron. Schematically the reaction may be represented as follows:
Each disintegration is accompanied by the emission of one neutron, and therefore the resulting neutron
"activity" may also be characterized by a half-life of 4.15 sec. Irradiation for about 20 sec saturates
the specimen with the active isotope N17. When saturation is achieved in the activation process, the number
of nuclei formed per second is equal to the number of delayed neutrons emitted by the specimen per sec-
ond. The recording can be carried out either during the intervals between accelerator pulses or after the
irradiation has stopped and saturation has been achieved. In either case, however, the counting apparatus
should be turned on some time after (about 1000 ?sec after) the accelerator pulse. During this time the
prompt neutrons formed in the photonuclear reactions are slowed down to thermal energies and are ab-
sorbed, so that there is virtually no error introduced into the delayed-neutron counting by the contribution
of the prompt neutrons.
Thus, we have a new method for measuring the concentration of oxygen in metals and alloys. This
conclusion is supported by numerical calculations.
The total number of (y, p) reactions involving 018 (or the maximum number of delayed neutrons) can
be found by calculation according to the Belen'kii-Tamm theory [13]. We used the value for the cross
section for the 018 (y, p) reaction given in [12], and the critical energies given in [14]; the concentration of
018 in natural oxygen was assumed to be 0.2%, and the concentration of oxygen in the metal was taken to
be 10-4%.
The maximum yields Q(E) were calculated for an electron current of 100 ?A from the accelerator
(see table and Fig). By using these data, we can estimate the time needed for recording the neutrons with
a given statistical accuracy, and we can also determine the N17 saturation level of the specimen.
Let us assume that the counting rate is constant; this is entirely possible if the recording is carried
out during the short time intervals between the accelerator pulses. Let the efficiency of the counting
apparatus be k = 1%, the given statistical accuracy of the recording be 6 = f5%, and the duration of the
transmission-system pulse be T = 10,000 psec, for a frequency of f = 50 cps. As can be seen from the
table, for an accelerator current of 100 pA and an electron energy of about 25 MeV the number of active
N17 nuclei (or delayed neutrons) produced per second in a titanium specimen is Q(25) - 1000 nuclei/?A? sec.
Then the counting rate is kfTQ = 5 neutrons/sec. From the formula for the statistical accuracy,
1
k/ 1.5 min.
zQ82
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Number of delayed neutrons ver-
sus energy of electron beam (for
oxygen concentration of 10-4 %
in metals).
i.e., a value convenient for use in analysis . From the graph
showing the yields (see Fig), we see that this value also holds in the
case of zirconium, but in the case of beryllium the measurement
time required when other conditions remain the same is approxi-
mately twice as long. It should be noted that we can reduce the
value of t somewhat for the constant value of 6 by increasing the
neutron-counting efficiency k and increasing rr.
An apparatus for recording after saturation can be set up
without any technical difficulty. This procedure is preferable in
the cases when the irradiation is carried out with an accelerator
which has a high beam current (of the order of 1 mA or more) or
when the specimen.contains more than 10-4% oxygen.
tIn2
Qn(E)=Q(E)T{l-e 1112)
In 2
we find that the delayed-neutron yield Qn(E) obtained after irradia-
tion for t = 5-Ti/2 (energy 25 MeV, accelerator current 100 ?A,
oxygen content of the titanium 10-4%0) is about 6000 neutrons. Indus-
trial titaniums usually contain more than 0.01% oxygen [15], and for these the total number of delayed
neutrons at saturation should be no less than 6. 105 for. the experimental condition under consideration.
This yield can be recorded with sufficient accuracy in a short time ( the measurement time will be no more
than 1 min), and this is a considerable advantage of the proposed analytical method.
In our calculations we used an electron-current value of 100 ?A, which can be achieved even today in
some types of accelerator, and we considered data obtained for just this magnitude of current. From these
data we can also decide how suitable this type of analysis would be for other conditions (different current
values, oxygen concentrations, etca. In particular, if we consider that the oxygen contamination in indus-
trially produced ingots is about 100 times as high as the values used in our calculations, we see that the
results will not change when the accelerator current is 1/100 of our value, i.e., 1 ?A. This current can
be achieved today without any practical difficulty. In view of what we have said concerning the purity of
industrially produced metal and present-day possibilities of accelerator technology, we may conclude that
the idea described here is worth testing experimentally.
In conclusion, it should be noted that in the proposed method for determining the oxygen content of
metals (or other substances), the isotope composition of oxygen in the specimen (i.e., the percentage of
the isotope 018 in the oxygen impurities) is assumed to be known precisely. Where there is reason to
suppose that the isotope distribution of oxygen in the specimen will be different from the natural distribu-
tion, the actual distribution should be determined once for the particular industrial scheme used in produc-
ing the metal (or other substance) involved.
J. Darwin and J. Baddery, Beryllium [Russian translation]. Moscow, Izd-vo inostr. lit. (1962).
N. F. Litvinova and Z. M. Turovtseva, Methods of Determining Impurities in Pure Metals [in Russ-
ian]. In: "Proceedings of the Commission on Analytical. Chemistry," Vol. XII. Moscow, Izd-vo AN
SSSR (1960).
* Preliminary experimental results were obtained while this article was being prepared for publication.
The delayed-neutron yield of Cu + CuO specimens with different amounts of CuO (specimen weight, 1.5 kg)
was measured with BF3 when these specimens were irradiated to the point of saturation with the brems-
strahlung spectrum of a betatron with an upper limit of 25 MeV (intensity of 25-30 R/min at a distance of
1 m from the target). The sensitivity of the method was about 1% of oxygen in copper (error of the results
?10%, analysis time 10 min). By using high-intensity irradiating apparatus [9-16] (e.g., the betatron [8]
and the microtron [16] developed at the Tomsk Polytechnic Institute and the Institute of Physical Problems
of the Academy of Sciences of the USSR are capable of producing more than 1000 R/min, and 3000 R/min,
respectively, at a distance of i m from the target) and a more efficient counting apparatus, we can in-
crease the sensitivity of this method by several orders of magnitude.
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3. I. A. Berezin and V. I. Malyshev, Zh. analit. khim., 17, 1101 (1962).
4. I. A. Maslov, Zavodsk. laboratoriya, 1, 51(1964).
5. L. Bate, Nucleonics, 21, 72 (1963).
6. Atomnaya Energiya, 5, 589 (1958).
7. S. P. Kapitsa, V. N. Bykov, and V. P. Melekhin, ZhETF, 41, 368 (1961).
8. V. A. Moskalev et` al., "Summaries of Report Delivered at the Fourth Inter-Universities Scientific
Conference on Electron Accelerators, Feb. 13-17 (1962) [in Russian]. Tomsk, Tomsk University
Press, p. 41(1962).
9. 0. A. Val'dner, A. A. Glazkov, and A. N. Finogenov, Pribory i tekhnika eksperimenta, 3, 29 (1963).
10. S. Amiel and M. Peisakh, Atomnaya Energiya, 14, 535 (1963).
11. V. A. Shkoda-Ulyanov et al., Author's Certificate No. 163782.
12. W. Stephens, J. Halpern, and R. Sher. Phys. Rev., 82, 511 (1951).
13. S. Z. Belen'kii, Avalanche Processes in Cosmic Rays [in Russian]. Moscow-Leningrad, Gostekh-
teorizdat (1948).
14. 0. I. Dovzhenko and A. A. Pomanskii, ZhETF, 45, 268 (1963).
15. Nonferrous Metals and Alloys. Testing Methods [in Russian]. Part 2. Moscow, Izd-vo standartov
(1964).
16. S. P. Kapitsa, Atomnaya Energiya, 18, 203 (1965).
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translationsappears at the back of the first issue of this year..
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ACCELERATION OF ELECTRONS IN THE ANNULAR PHASOTRON
OF THE P . N. LEBEDEV PHYSICAL INSTITUTE OF THE ACADEMY
OF SCIENCES OF THE USSR
L.N.
Kazanskii, V.N.
Kanunnikov,
A. A.
Kolmenskii,
E. P.
Ovchinnikov,
V. A.
Papadichev,
S. S.
Semenov,
A. P.
Fateev, and
B. N.
Yablokov
The physical bases for the selection of parameters in the phasotron
of the Lebedev Physical Institute ("FIAN") and details of its construction are
considered. The start-up procedure for the accelerator is described. Results
obtained on working with a beam are discussed.
A new accelerator was started in the Lebedev Physical Institute in October 1965; this was an-elec-
tron radial-sector annular phasotron (the KF) [1]. The annular magnet of the accelerator consists of 40
similar units. Strong focusing is ensured by the fact that the field in neighboring units varies on the same
radial law but in opposite directions [2, 3]. The constancy of the field in time enables a high-intensity
particle beam to be achieved and permits storage of the particles. The construction of the magnet makes
it possible to realize the so-called symmetry, (or two-beam) condition [4, 5], enabling acceleration, storage,
and collision, of beams simultaneously rotating in opposite directions to be carried out. The KF provides
for the use of inductive and resonance (phasotron) acceleration of the electrons and also the study of spe-
cial acceleration conditions (stochastic, "phase-shift," etc.).
Fig. 1. General view of the apparatus.
Translated from Atomnaya.Energiya, Vol. 21', No. 3, pp. 166-176, September, 1966. Original article
submitted March 5, 1966.
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A,
Fig. 2. Stability diagram of the
KF (figures near the circles
show the corresponding values
of the constant component fo).
Fig. 3. Phase diagram describing the ra-
dial motion of particles in the ideal field
of the KF; a) In the middle of the positive
units;. b) in the middle of the negative units.
TABLE 1. Tolerances for the Deviation of the Magnetic
Field in the KF from the Calculated Value (n=16, fo='0:09)
Ideal field
Au (over the r'adius, identical for all azimuths) .... 0.06
Afo ......... .... ................ 10-1
Distortion of median plane, mm:
"resonance" harmonic ........ 0.1
nearest 'neigboring harmonics ............ 0.2
higherharmonics .... . . . .. . ...... . . . . 0.3
Azimuthal asymmetry, %:
"resonance" harmonic ................. 0.1
neighboring and higher harmonics ......... 0.2 to 0.3
An'with respect to azimuth, identical in the region
6r sz~ 6 cm ......................... 0.02
Note. It is supposed that the permissible frequency variation
'is Av;~0.1.
The KF was set Lip in order to make an experimental study of the possibilities of accelerators of the
annular-phasotron type in various special conditions of acceleration and particle storage.
The general form of the apparatus is shown in Fig. 1, in which we see the electromagnet units, the
injection pulse generator, the betatron cores, and "the resonator. The principal parameters of the acceler-
ator are as follows:
Number of elements of periodicity N ....... 20
Field index n ........................ 16
Number of betatron oscillations per turn
(fo = 0.09):
radial ........................... 5.79
vertical ......................... 2.38
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Extent of working region of the field.......... 117 to 160 cm
Working field strength' ................... 27 to 42000e
Origin of profiled pole ................... 150 cm
Vertical gap at radius 120 cm .............. 7 cm
Azimuthal dimension of unit ............... 50
Total weight of magnet ................... 15 ton
Magnet power supply .................... 75 kW
Frequency of rotation of particles:
initial ............................ 19.7 Me/ sec
at critical energy .................... 33.9 Mc/sec
final ............................. 29.5 Me/ sec
Power of hf system ..................... 17 kW
Injection energy ........................ 80 keV
Critical energy ........................ 2.11 Mev
Final energy .......................... 30 MeV
Working Point and Tolerances for the Deviation of the Magnetic Field from the Calculated Value
The ideal magnetic field of the radial-sector annular phasotron, ensuring geometric similarity of the
orbits, may be written in general form [6, 8] as
H=I:=o=Ho(r )n(fo cos N0 fa cos 3.1'0 +f;,cos5N0-
-I...);
Hr =1101__0 = 0,
where N is the number of elements of periodicity, and n the magnetic-field index.
In the KF the higher harmonics fs, f5, etc. make up no more than 6 to 7% of the fundamental harmonic.
The position of the working point on the stability diagram (Fig. 2) depends mainly on n, N, and the
constant component fo; in selecting it and determining the magnet parameters, nonlinear effects have to be
taken into account.
In contrast to ordinary focusing accelerators, tolerances in the annular phasotron, with its consider-
able n value, are established principally on the basis of the limiting amplitudes of the betatron oscilla-
tions. This is because of the severe non-linearity of the magnetic field, leading to the appearance of non-
linear resonances. Especially dangerous are the "ideal" nonlinear resonances, in particular the vi =N/3.
yr = N/4, yr + 2vr = N, 2vr - 2vZ = 0 and 2vr + 2vZ =N, present in the ideal field. (In Fig. 2 these resonances
are shown by thick lines.). If the working point of the accelerator is placed close to one of the resonances
indicated, pulsations of betatron oscillations take place, the value of these depending on the initial ampli-
tude of the oscillations. For a certain "limiting" amplitude, the pulsations lead to the loss of particles in
the injector or on the chamber walls.
Table 1 shows the tolerances for the parameters of the KF magnetic field, obtained by numerical
calculation in an electronic computer. The results were analyzed by means of phase diagrams (Fig. 3),
which enabled the limiting amplitudes and frequencies of the oscillations to be determined quite accurately
from data relating to the initial turns.
Field-Stability Requirements. For the betatron oscillations, practically any perturbation of the mag-
netic field is slow and can only lead to a change in the working point and breadth of the resonance bands.
On the basis of the tolerances indicated in Table 1 we see that the azimuthal distortion of the field
at any moment in time must not exceed 0.1%. Since the field in the KF depends considerably on the radius,
the azimuthal distortions are very sensitive to distortions of n in the units, Hence the tolerance for the
resonance azimuthal harmonic of instability of n is very rigorous.
Table 2 shows the tolerances for the instability of the magnetic field and the value of n, calculated
on the assumption that the total displacement of the working point is no greater than 0.1.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
TABLE 2. Tolerances for the Instability of Magnetic Field with fo = 0.09
Frequency of
perturbation
Change in n, simultaneous for all azimuths
any
0.06
Position of working point
Drift of constant field component f0 ... .
any
10'3
ditto
Azimuthal asymmetry of field (resonance
harmonic)
Change in n with respect to azimuth
(resonance harmonic)
any
0.02 ?
ditto
Resonance perturbations of field,
10 to 150 kc/sec
2'10'3
Amplitude of synchrotron
Slow changes in field,%
150 kchec
5.10-E
ditto
Noise perturbation of field (mean square)
10 to 150 kc/sec
0.02%
ditto
TABLE 3. Current inthe Windings for f0=0.09
206.7
167.1
II
8.516
6.884
III
0.8516
0.6884
On the yoke
8.1
5.8
Accelerator Magnet
The most reasonable way of forming the magnetic
field of the annular phasotron [8-11] is the use of am-
pere-turns distributed over the surface of the magnetic
poles. The shape of the pole surface may in general be
arbitrary, but itmust be remembered that in order to
ensure similarity of the magnetic field it is simplest if
all the dimensions of the magnet determining the shape
of the field are made to increase in proportion to the
radius. In order to make better use of the useful vol-
ume of the gap, the turns of the distributed winding are laid in grooves in the poles. The requirement:
for accuracy in the positioning of the conductors extends to accuracy in the finishing of the grooves. The
characteristic tolerance for the accuracy of finish is ? 0.1 mm.
In the region of high magnetic fields (r = 150 to 160 cm), profiled poles are used instead of distributed
windings, the gap between the poles being reduced by a factor of several times. This is quite permissable
since the amplitude of the betatron oscillations is here considerably reduced.
The KF electromagnet units (see Fig. 1) are set on the circumference of an annular stand welded
from nonmagnetic steel and consisting of two insulated halves. The divisions in the stand coincide with
the insulating divisions of the vacuum chamber. The units are. fixed to the stand by means of supports
adjustable in position for all degrees of freedom. Each unit consists of two identical "beams" (upper and
lower), shaped pole tips, and a stand for the rear yoke. The azimuthal width of a unit (with respect to the
iron) is 5?. The vertical gap, equal to 7 cm at a radius of 120 cm, rises. in proportion to the radius up to
r = 150 cm.
The width of. all the grooves is the same in the radial sense and equals 8 mm; the depth is determined
by the number and cross section of the conductors. The step between the grooves in the radial sense
equals 15 mm, which prevents any magnetic-field distortions due to the discrete nature of the winding [9].
The currents in the distributed windings for fo = 0.09 are given in Table 3. (The primary windings are
made of tubing 6 mm in diameter and are water-cooled).
In order to obtain the required field distribution, a winding on the yoke is necessary in addition to the
distributed windings [8, 11]; this compensates the stray field of the distributed windings in the initial radii
due to the finite magnetic conductivity of the yoke. The yoke winding consists of individual sections, which
enables the necessary number of turns to be selected when correcting the azimuthal distortions of the field
in the initial radii. No precise adjustment was made to the form of the shaped pole. The' shape of the pole
was only maintained with respect to the median line of the unit, so that the pole could subsequently be
finished after connecting up the multiwire. conductors in the region of the distributed turns.
After assembly, the constancy of the field index along the radius, for optimum current in the yoke
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
winding, was verified for all the units. The measurements were made on a testing device equipped with a
system for supplying stabilized current (? 0.05%) to three units [121.
Magnet Supply System. This system has to ensure a high stability of the magnetic field in time (see
Table 2) and reproducibility of its characteristics from one switching-on to another. When the magnet is
switched on or off in an irregular manner, additional distortions of field and field gradient appear. Hence
the following requirements are imposed upon the switching-on and off processes: 1)a matched (accuracy
5.10-4) standard rise of the currents in all the windings at a given velocity; 2) the absence of any surge at
the end of the current rise (accuracy 5.10-4); 3) a standard switch-off procedure (as rapid as possible) for
the currents in the windings. Stabilization of the currents must be no worse than 3.10-4. It should be
noted that, in the absence of a field-stabilization system at small radii, there requirements would be an
order more rigorous [13].
For feeding the windings with a 200-A current, two dc generators of 65 kW each are employed.
Other windings of the magnet and the excitation windings of the two generators are fed from a supplemen-
tary generator of 13 kW dc. Voltage pulses are suppressed and the steady components of current stabil-
ized by tube units connected in parallel to the excitation windings of the generators and each magnet-wind-
ing circuit.
The magnet is switched on by the simultaneous closing of contacts in the circuit of each generator.
The linear current rise is ensured by feeding a negative-feedback voltage signal through a dc amplifier
and Rc circuit to the tube network of the control units. When the magnet is switched off, the contacts open,
and the commutation currents are shunted by the diodes. In this way all switchings-off of the magnet (in-
cluding accidental ones) are made identical.
Arrangement of the Magnet Units. The magnet units have several well-finished surfaces on which
all the attachments for measuring the position of the units are mounted. For measuring the radial and
vertical position of the units, a rotating gage furnished with micrometers is used. The azimuthal position
of the unit is measured with a theodolite. For measuring the slope of the unit relative to the upper beam,
an attachment incorporating two levels is provided.
The deviations of the measured position parameters of the units from the ideal case are converted
into magnetic-field distortion harmonics. The azimuthal asymmetry due to inaccuracy in the positioning
of the units is 0.01 to 0.02%, and the distortion of the median plane 0.01 mm.
Magnetic Measurements. According to the table of tolerances, the dangerous harmonics of the
azimuthal field distortions AHZ, k/HZ, 21 10-3, where k is the number of the harmonic. For this we must
satisfy the following condition for the distortion of the field in each unit (on the assumption of the statis-
tical "independence of the deviations in each unit) ; AHZ AIIZ 3 10-3
. An analogous requirement
is laid on the radial component of the magnetic field II,, k /HZ,20 :~ 10-3. The influence of the azimuthal com-
ponent H0 on the z motion is six or seven times weaker than the corresponding influence of Hr. Dangerous
harmonics of H0 are the supplementary harmonics He, 20?k, which, combining with the 20-th harmonic of
the orbit ripple, give low harmonics in the distortion of the median plane.
Measurement of all three components of magnetic field Hr., H0, Hz in the injection region (r = 120 cm)
is effected by a compensation method, using a magnetometer [13]. For moving the pickup, the same rod
that was used for gaging the positions of the magnet units is employed. Before installing the chamber in
the magnet, the rod is rotated by a small motor and the measured data are fed to an automatic record.
In the presence of the chamber, the tube carrying the pickup is passed through openings in the chamber
opposite each of the units. This system enables the pickup to be set at the same radius in different units
to an accuracy of ? 0.01 mm and displacements along the radius to be made to an accuracy of ? 0.03 mm.
The constancy of coordinate z on displacing the pickup along the radius is ensured to an accuracy of not
worse than 0.1 mm. The azimuthal displacements can be fixed to an accuracy of 10" with the theodolite.
The results of measuring Hz, Hr, and Hg, after correction, are shown in Fig. 4, from which we see
that the values of the harmonics lie within the tolerances laid down.
The ratio of the constant component of magnetic field to the fundamental harmonic was measured to
an accuracy of 1.5%, which for fo = 0.9 corresponded to Av. ti 0.04 and Av, 0.015.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
1 2 3 4 5 6 7 8 9 1011 12 1314 1516 1718 19 20 K
a
1234 567 $ 9 10 11 17 13 14 15 15 17 /5 19 2021 27K
b
Fig. 5. Block diagram of the hf system; 1)
Resonator; 2) power amplifier, 29 to 35 Mc/
sec; 3) amplitude modulator; 4) comparison
system; 5) unit for measuring the amplitude
program; 6) amplitude modulator; 7) phase
reverser; 8) phase shifter; 9) generator; 10)
automatic adjustment for initial frequency;
11) frequency modulator; 12) frequency pro-
grammer; 13) synchronizer; 14) key delay
unit; 15) amplitude programmer; 16) key; 17)
frequency monitor.
9101 1 Control system. For controlling the field
stability, a system for measuring the field at small
radii is employed; this is based on measuring the
2101 magnetic potential difference between the upper and
lower beams. Magnetically-conducting frameworks
101 are fixed to the upper and lower beams, on their
end surfaces. In the gap between these conductors
is a magnetic-field pickup on the same type as that
used for the magnetic measurements. The signals
1 2 3 4 5 6 7 8 9 10 111713 /4 15 16111819 Z0~1277324252521K
C from the pickup: pass through a step selector to an automatic recorder. The system "runs around" the
Fig. 4. Results of measuring a) Hz, b) Hr, and ring in 15 min and records any changes of field
H0 after correction (r = 120 cm). associated with irregular connection, short-cir-
cuiting of the turns in the windings, displacement
of the units, and so forth.
Accelerating System of the KF
Acceleration of particles in the KF is effected at the beginning of the cycle by the eddy field of two
betatron cores and later by means of the hf voltage.
The betatron condition is used for the rapid extraction of particles from the injector and their accel-
erationto about350 keV, on reaching which the particles are drawn into the phasotron condition of accel-
eration. Use of preliminary betatron acceleration considerably narrows the range of frequency modula-
tion, increasing the initial frequency from 19 to some 29 Mc/sec.. Acceleration is effected during the
growth of the magnetic flux; the fall in flux is retarded by the inclusion of a damper [141. The two beta-
tron cores can accelerate the particles up to 4.5 MeV.
The hf acceleration system incorporates a frequency-modulated generator with a range of 15 to 35
Mc/sec, units for forming the frequency and amplitude programs, delay systems, and a system for tying
to the selected frequency values (Fig. 5). For the critical energy Ecr = V1 n Eo = 2.1 MeV the auto-
matic phasing in the KF vanishes, and special measures have to be employed for further hf acceleration.
In order to carry the electrons through the critical energy, a phase shifter and electronic switch are em-
ployed; by this means a phase jump in the hf voltage is introduced at the moment at which the critical en-
ergy is reached. The phase jump may be regulated between 10 and 180? by including sections of coaxial
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Fig."7. Pulse to the injector cathode (1);
pulse to the inflector (2); current from the
infector (3). Multiturn injection; time
base 2.5 psec/cm.
Fig. 6. Arrangement of vacuum chamber;
1) Pump No. 1; 2) mirror; 3) pump No. 2;
4) measuring unit; 5) pump No. 3; 6) Fara-
day cylinder No. 2; 7) Faraday cylinder
No. 1; 8) pump No. 4; 9) pump No. 5; 10)
photomultiplier; 11) Faraday cylinder No.3;
12) diffusion pump; 13) grid; 14) induction
electrode; 15) screen; 16) injectors.
cable of various lengths. The particles may also be car-
ried through the critical energy without any phase throw
by rapidly switching the accelerating voltage off and on.
The voltage from the output of the frequency-
modul'ated generator falls on to a power amplifier, the
load of which is a resonator shunted with a resistance
of 50 Sl. The equivalent capacity of the resonator is
800 pF, and the power of the amplifier is 15 M.
The frequency programs are formed in constant
R, L, and C elements by means of electronic switches.
The amplitude program is formed in diodes. The prin-
cipal parameters of the hf system are the following:
Multiplicity ....................... 1
Initial frequency...... ............ 29 Me/sec
Frequency at critical energy ........... 33.5 to 34.5 Mc/sec.
Maximum amplitude of accelerating
voltage ........................
Rate of frequency modulation:
at beginning of cycle ...............
at end of cycle ...................
Permissible rate of frequency change:
on approaching critical energy ........
at the instant of phase shift ..........
Reproducibility of maximum frequency
from cycle to cycle ...............
Total acceleration time .............. .
104 Mc/sect
3 Mc/sect
104 Mc/sect
103 Me/sect
10-4
5.5 msec
Vacuum Chamber
The vacuum chamber of the KF has the form of a torus, the cross section of which largely repro-
duces the form of the gap in the electromagnet. The chamber is made of nonmagnetic steel sheet 4 mm
thick; in the gaps between the magnet units, 40 fins 10 mm thick are welded for the sake of rigidity. The
camera is divided into two parts insulated by polystyrene and rubber seals; in order to prevent the direct
incidence of the beam these are covered with metal screens. The chamber has 26 tubes leading off from
the outer side of the ring and 19 from the inner (Fig. 6). To some of the outer tubes are connected titan-
ium pumps each rated at 100 liter/sec; the working vacuum is 2.10-6 mm Hg. The other outer tubes and
those of the inner set which are not occupied by injectors are used for siting recording apparatus.
In the inner wall of the chamber are 21 additional openings through which instruments may be in-
serted for measuring the magnetic field within each unit, just as in the case of the inner tubes.
Injection System
The injector is a Pierce electron gun designed for a working voltage of up to 100 kV and furnished
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Fig. 8. Spontaneous breakaway of the beam
from the injector in the constant magnetic
field of an annular phasotron; a) Pulse from
signal electrode, beam rapidly debunches;
b) pulse from accelerated particles (beta-
tron) to the photomultiplier (betatron pulse
switched on 12 ?sec after injection, set in
the center of the frame; scan velocity 2.5
?sec/cm); c) multiturn injection, signal
from electrostatic signal electrode (beam
bunched and debunched several times); d)
multiturn injection, pulse from accelerated
particles to photomultiplier ( lifetime of
broken-off beam 150 ?sec, scan velocity 20
?sec/cm, pulse of betatron core shifted 100
y from'injection).
short positive voltage pulses (25 nsec, 3.5 kV)
Starting the Annular Phasotron
Fig. 9. Spontaneous bunching and debunch-
ing of the beam; a) Bunching and debunch-
ing for multiturn injection without acceler-
ation, with a period of about 25 psec, scan
velocity 60 psec/cm; b) bunching and de-
bunching for multiturn injection after beta-
tron acceleration, betatron pulse switched
on 25 ?sec after injection, bunching-de-
bunching period about 50 ?sec; c) initial
section of oscillograms, scan velocity 0.5
?sec/cm.
with an electrostatic inflector for rotating the beam
through 90?. The voltage to the inflector plate is
supplied through a separate insulated lead. The
current at the output from the injector reaches 0.4 A;
the dimensions of the beam are no greater than 2 mm
in the horizontal direction and 10 mm in the vertical
(divergence of f 1.5 and t 0.5? respectively). The
injection angle is controlled within ? 3.5? by the
inflector voltage.
The injector is fed from a. negative-pulse
generator supplying an extracting voltage to the
cathode of the electron gun (3 ?sec, 20 to 100 kV), a
positive-pulse generator for the inflector (2.5 ?sec,
0 to 25 kV), and a generator for supplying additional
to the inflector for single-turn injection (Fig. 7).
The KF incorporates units with magnetic fields of different sign; hence injection may take place
either in a positive (focusing in the radial direction) or negative unit. Each has advantages and disadvant-
ages. According to linear theory, the envelope of the radial betatron oscillations has a maximum in a
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Fig. 10. Oscillograms of the first turns of
the beam (without acceleration); signal from
electrostatic signal electrode scan velo-
city 0.1 ?sec/cm.
positive unit and a minimum in the negative. Since the
vertical aperture is much smaller than the radial in an-
nular phasotrons, injection would be more advantageously
carried out in a negative unit, the vertical motion in which
is favorably conditioned. In starting the accelerator it
turned out, however, that injection in either positive or
negative unit was about equally favorable.
Since the tolerances relating to the perturbation
harmonics were satisfied, no field correction was made
during the start-up process. An exception was the fine
adjustment of fo at small radii, effected by shifting the
reference level of the field-stabilization monitors. This
correction was made after obtaining a circulating beam
and betatron acceleration. The correction facilitated
adjustment of the various particle-capture conditions and
also improved the stability of the beam.
For observing the first turns, grids covered with
a luminophore of about 0.5 "transparency" were used;
these enabled the position of the beam to be recorded to
about 1.5 mm. For measuring the beam current in the
first turn and calibrating the recording equipment,
Faraday cylinders were employed.
The circulating beam is indicated by means of inductive electrodes 4 cm wide covering a range of
116 to 147 cm over the radius. The use of inductive electrodes for recording the beam proved to be
feasible, not only for single-turn injection and in the hf-acceleration condition, but also for multiturn in-
jection and in the inductive-acceleration condition, thanks to the "self-bunching" of the beam. The use of
inductive electrodes enabled such interesting. effects as the spontaneous "breakaway" of the beam from the
injector to be observed.
For recording the accelerated beam, a scintillator movable over the whole working region is used.
The starting of the accelerator takes place in several stages: first, the initial turn is obtained (in-
jection energy varied between 70 and 90 keV), then several turns are obtained (capture), then comes
betatron acceleration, and finally the phasotron condition.
After finishing the magnetic measurements, the first turn (for injection in a focusing unit) was
studied; this confirmed the good quality of the magnetic field. After adjusting the position of the injector
by means of the grids and Faraday cylinders, the "broken-off" circulating beam could be recorded on the
signal electrode, both for single-turn and multiturn injection. Then the condition of inductive acceleration
was obtained,.first. for injection in a focusing unit, and later for injection in a defocusing unit. At this
stage the constant component of the magnetic field at small radii was adjusted with respect to the maxi-
mum of the accelerating current. As a result of this, the intensity of the accelerated beam was increased
by approximately an order.
For optimum field adjustment and a current of about 50 mA in the first turn, the actual beam "broke
off" from the injector and circulated in the chamber for some tens of microseconds. The life-time of the
"broken-off" beam was measured by throwing it on to the target by means of a betatron pulse delayed
relative to the injection pulse. The life-time of the beam was greater than the bunching-de bunching period,
as may be seen by comparing the oscillograms of signals from the inductive electrodes and the photo-
multiplier (Fig. 8).
The effect of the beam breakaway from the injector was observed for both single-turn and multiturn
injection ( in the latter case the effect occurs over a wider range of injection angles). For multiturn in-
jection, the beam spontaneously bunches itself, as may be seen with the inductive electrodes. This phe-
nomenon of bunching and debunching of the beam may take place both before acceleration and during beta-
tron acceleration (Fig. 9). By adjusting the constant field component at the injection radius (by displacing
the working point on the stability diagran- and the inflector voltage (initial conditions), we can set up
different particle-capture conditions for the first turns (Fig. 10). The upper oscillogram of Fig. 10 shows
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Fig. 11. Transition through
the critical energy by switch-
ing off the amplitude of the
accelerating voltage in the
neighborhood of the critical
energy; a) Signal from induc-
tive electrodes; b) envelope
of accelerating-voltage amp-
litude; c) change in the fre-
quency of the accelerating
voltage with time.
the case in which the intensity of the initial turns falls off smoothly and
the intensity of the broken-off circulating beam is small. In the oscillo-
gram of Fig. 10b (after an adjustment of some 3% with respect to the con-
stant component and 1? in angle), we see a sharp fall in current after the
fourth turn; the intensity of the broken-off beam, however, is an order
greater.
Thanks to the bunching of the particles in the course of betatron
acceleration, it was possible to make exact measurements of the particle-
rotation frequency at the critical energy, using the beat signal of the sig-
nal-electrode voltage mixed with the voltage from a standard-signal
generator.
Inclusion of the accelerating hf voltage enabled phasotron accelera-
tion up to the critical energy (2.1 MeV) to be obtained almost immediately
after selecting the optimum frequency and the right instant for switching
on the accelerating field. The particles were drawn into the phasotron
accelerating condition, both for a slow rise in the amplitude of the hf
voltage (in 100 gsec, equal to approximately 10 to 15 periods of the syn-
chrotron oscillations) and also for an "instantaneous" rise in amplitude.
The transition through the critical energy was effected .either by
adjusting the amplitude or shifting the phase. The efficiency of the trans-
ition was about the same in both cases. Fig. 11 shows oscillograms of the
voltage from the signal electrodes and photomultiplier, together with the
envelope of the hf voltage and the frequency-modulation program.
Measurement of the betatron-oscillation frequency by a hf method
showed that the actual working point differed very little from the calcul-
ated value yr = 5.82; vZ = 2.40).
In the phasotron condition, the electrons are accelerated to 10 MeV, which corresponds to the end
of the region of the distributed windings. The intensity is about 2.109 electrons/pulse (1011 electrons/sec).
The following took part in the work associated with the starting of the accelerator: V. S. Voronin,
D. D. Krasil'nikov, A. N. Lebedev, O. A. Smirnov, V. G. Gapanovich, N. V. Platonov, G. T. Ponomarev,
V. A. Ryabov, N. A. Skalkina, E. F. Troyanov, G. I. Kharlamova, L. N. Chekanova, and also a number of
technicians and mechanics, to whom the authors express their sincere thanks.
Members of various other organizations took part in developing the FIAN annular phasotron; among
these special mention must be made of NIIE FA colleagues N. A. Monoszon, B. V. Rozhdestvenskii,
K. M. Kozlov, A. M. Stolov, V. A. Titov, V. B. Zalmanzon, and E. A. Dmitriev.
LITERATURE CITED
1.
A. A. Kolomenskii et al., "Atomnaya Energiya", 20, 513 (1966).
2.
A. A. Kolomenskii, V. A. Petukhov, and M. S. Rabinovich, in "Some Questions in the Theory of
Cyclic Accelerators" [in Russian], Moscow, Izd. AN SSSR, p.7 (1955); "Pribory i tekhnika eksperi-
menta", No.2, 26 (1956).
3.
K. Symon, Phys. Rev., 98, 1152 (1955).
4.
A. A. Kolomenskii, ZhETF, 33, 298 (1957).
5.
T. Ohlawa, Rev. Scient. Instrum., 29, 108 (1958).
6.
A. A. Kolomenskii, "Atomnaya Energiya", 3, 492 (1957).
7.
A. P. Fateev, ZhTF, 31, 238 (1961).
8.
V. N. Kanunnikov and A. P. Fateev, ZhTF, 29, 1228 (1959).
9.
V. N. Kanunnikov, Pribory i tekhnika eksperimenta, No.2, 136 (1960).
10.
V. N. Kanunnikov et al., Proc. of the Intern. Conf. on High Energy Accelerators and Instrumenta-
tions, CERN, p.89 (1959).
11.
V. N. Kanunnikov, ZhTF, 33, 592 (1963).
12.
V. S. Voronin and V. N. Kanunnikov, Pribory i tekhnika eksperimenta, No.1, 143
(1966).
13.
V. S. Voronin and V. N. Kanunnikov, Ibid., No.2, 160 (1965).
14.
L. N. Kazanskii and V. N. Kanunnikov, Ibid., No.4, 217 (1965).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
OF A CHARGED PARTICLE BUNCH
The instability condition of a bunch of charged particles (instability due
to finite conductivity of the accelerator chamber walls) is derived.
The finite conductivity of vacuum chamber walls is responsible for a coherent transverse instability
in a beam of particles rotating in the accelerator magnetic track. This phenomenon has been discussed
[1, 2] with reference to a continuous beam. This article discusses the effect in a short bunch oscillating
as a single entity. The treatment is also applied to a continuous beam.
The curvature of the beam trajectory, and wave effects, are neglected when we find electromagnetic
fields in the interior of the vacuum chamber. We shall treat the chamber as a uniform toroid,with highly
conducting walls and with no additional elements in its interior, In such a case the electric field inside
the chamber can be given by
E? _ Eb.-'?- E,C, (1)
where Eb is the beam free-space electric field, and Eic is the electric field associated with charges in-
duced on the conducting walls of the chamber.
For the magnetic field, similarly,
where Hb is the beam free-space magnetic field and Hi, is the magnetic field associated with current in-
duced in the conducting walls of the chamber.
We assume for simplicity that the linear density (p) of beam particles varies slightly in azimuth at
distances commensurate with the transverse dimensions of the chamber shortened y times. Using the
tp H
notation of Fig. 1, we can state this condition as P/ ly >' - (it can be shown that this restriction is not essential
to find the growth rate). Moreover, l = " = 1 (where this is possible).
The total fields are determined, in our approximation, at each azimuthal value of the local instant-
aneous particle beam density, when the walls are ideally conducting, and the fields vanish as the beam is
removed. If the wall conductivity o- is not infinite, then Eb and Hb continue to
"track" the instantaneous beam density. But the transverse components of
Eic vanish rapidly as the beam departs (in a time on the order of the charge
relaxation time), while the magnetic field associated with the induced cur-
rents flowing in a layer of finite thickness still persist for quite a while
in the chamber interior. The coherent transverse instability is in fact re-
lated to the slow pace at which this residual field disappears.
We now find the magnetic field remaining inside a tube after a single
pass (parallel to the tube axis) of a short bunch (with geometry and notation as
in Fig.1). First consider a subsidiary problem (with the provisional assum-
ption , Oz A0 and A > co. The role
of sources A) and C) may be quite arbitrary; for equilibrium activity of Co60 the contribution of source A)
increases. In general none of the three sources of activation can be neglected.
4. The part played by the purification of the reactor water in reducing the contamination of the sur-
faces is mainly determined by competition between impurity removal by the purification system and de-
position of particles on the walls, as may be seen from the relation
Al :AZ :A4 NC,. ?' ,Q' :1
For long-lived activity the role of the purification system becomes more important.
5. Solution of the problem for long-lived activity (? ai > a2, for short-lived isotopes this in-
equality intensified.
8. The accumulation of activity in the primary circuit of the reactor containing water under pres-
sure is a particular case of the problem in question for G5 = 0.
Solution of the Nonstationary Problem
Since the characteristic equation of system (1) to (3) is at least cubic, it is difficult to solve without
making substantial simplifying assumptions. The solution given below is principally valid for the accumu-
lation of isotope Co60 on nonirradiated surfaces. This solution is obtained on the following assumptions:
1) Equilibrium is attained with respect to the mass transfer of the target nuclei, i. e., A0t>> 1, wt>> 1, yt>> 1;
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
TABLE 1. Mass-Transfer Constants of the TABLE 2. Relative Mass-Transfer
Corrosion Products of Various Nuclear Velocity for Various Oxides in the
Reactors Dresden APS
sotope
sec-1
,sec-1
2,0,sec-
OI/y
~
I
wl era-
t
u
Fe69
3,5.10-5
5.10-8
10-5
700
[6]
Fe59
-
-
-
720
[1]
Fe59
6.10-2
2.6.10-7
2.3.105
C066
7.10-2
2.3.10-7
3.105
Cu64
9,4.10-6
2,8.10-6
1,9.10-5
3,4
Cr51
1.3.10-4
4.10-9
3,2.104
[7]
Sb122
4.5.10-3
1.5.10-5
300
Sb124
4,5.10-3
small
lar e
g
-
5.8.10
4.4.10
1.3
-
40-6
5.40-6
} 5,7.10-5
0.2
} 181
Fe203
Cr2O3
NiO
CU 0
~v);Fezo3
1.0
0.76
0.88
0.34
2) activation source B) is not taken into account (see
above analysis); 3) the radioactivity of the impurities
in the reactor water is independent of time.
A2 (t)=AZ (1-a-Pt),
where Az is found from expression (7) without the term corresponding to activation source B) and
A=(Y-f- _0 (Y+_)+6A (23)
Xo (Y+X)+s CY s, + x)
For preferential accumulation of activity on the reactor surfaces p A S1//S2, and for accumulation of ac-
tivity in the filter p y + A . The accumulation of activity on the surfaces washed by the condensate is
analogous to expression (22).
Analysis of Experimental Data
Since the nuclear-physics constants and circuit parameters required for the calculation are usually
known, computing errors are mainly determined by the accuracy of the mass-transfer coefficients (espec-
ially the deposition and erosion rates); information regarding these constants is very meager, however,
and quite contradictory (Table 1) [7, 8]. We may suppose thatw>> y, and it follows, from the time for
establishing equilibrium activity of the reactor water [1], that in order of magnitude y _ 10-7 sec-.
Information regarding the growth of oxide films was obtained by means of a radioactive indicator,
Fe59, in the SM-1 reactor [6]. Analysis of existing data with respect to the relations derived above showed
that for samples with various holding periods the quantities w and y lay within the limits-of w= (0.9- 5) ?10-5
sec-1 and y=(3-7)'10-8 sec-1. For samples with holding periods of more than 1000 h the best agreement
was obtained for w = 3.5.10-5 sec-1 and y = 5.10-8 sec-1.
It is known that the water of the Dresden Atomic-Power Station contains 70g of corrosion products
and the surface of the circuit 50kg [1]. Hence in view of relation (14)w/y=720, which agrees closely
with the data of [6]. From chemical analysis of the corrosion film and impurities in the water [1] we may
draw certain conclusions regarding the relative velocity of mass transfer for various oxides (Table 2).
It follows from the tabulated data that the values of w/y are of the same order for the oxides of Fe, Cr,
and Ni, i.e., they are carried around the circuit mainly in the form of particles. On analyzing other
data with respect to water-cooled, water-moderated reactors, a value of w/y = 440 to 1000 with respect
to iron was obtained.
The values of mass-transfer constants obtained in the, DIDO circuit differ considerably from data
relating to other reactor systems (see Table 1); the thickness of the superficial oxide film is about 200 ?
the relative efficiency of the purification system in comparison with the deposition on the reactor surfaces
equals 0.2% for Fe59, 5% for Co60, and so on. In view of the unusual conditions in the system (material
carbon steel, water pH 10.5, corrosion products in the dissolved state), the use of constants taken from [7]
when analyzing other reactor systems demands caution.
The mass-transfer coefficients recommended in [8] do not agree with experimental data obtained with
other reactors.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
The data available in the literature are insufficient to enable final conclusions to be drawn regarding
the deposition and erosion coefficients. We can only recommend a ratio of around 700 for these coeffi-
cients. The values of coefficients given in this paper should be considered approximate. It is felt that
the true values will be rather higher than those recommended, although the authors have no concrete evi-
dence tosupport.this as yet.
The authors have been greatly aided by discussions with M. A. Styrikovich and his colleagues and
also with V. V. Gerasimov et al. The authors are grateful to B. A. Alekseev and O. Ya. Shakh for a useful
exchange of views,
t
N1
Al
al
Ql
ql
Vl
m
S
Si
m
Cl
G1
operating time of the reactor;
total amount of the i-th element in the 1-th medium (index i usually omitted);
total activity of i-th isotope in 1-th medium;
specific activity of i-th isotope per unit weight of impurity in 1-th medium;
rate of access of the i-th element into the reactor water from the 1-th medium;
rate of access.of the activity of the i-th isotope from the 1-th medium into the reactor water;
weight of heat carrier in the 1-th medium;
surface of the m-th construction material in the 1-th medium;
effective corrosion rate (emission rate) of the m-th construction material in the 1-th medium;
flow of heat carrier in the 1-th medium;
e4, e9 efficiency of purifying filters for the reactor and supply water;
cx proportion of activity deposited from the vapor into the turbine;
time constant for purification of the reactor water;
p effective time constant for the accumulation of activity on the wall;
k apparent distribution coefficient of the impurities between the saturated vapor and boiling
water.
The rest of the notation is taken from [8].
LITERATURE CITED
1. F. Brutschy et al., Corrosion of Reactor Materials, Vol. 1, Vienna, IAEA, p. 133 (1962).
2. E. U. Kramer, Boiling-Water Nuclear Reactors [Russian translation]. Moscow, IL (1960).
3. V. Hall et al., Nucleonics, 19, No. 3, 80 (1961).
4. Power Reactor Technology, 4, No. 3, 56 (1961).
5. C.Breden et al., AEG-Euratom Conference on Aqueous Corrosion of Reactor Materials, Brussels,
TID-7587, p. 48 (1959).
6. C. Bergen, Nucleonics, 20, No. 6, 70 (1962).
7. G. Walton and E. Hesford, Corrosion of Reactor Materials, Vol. 2. Vienna, IAEA, p. 547 (1962).
8. Protection of Nuclear Reactors, Edited by T. Rockwell [Russian translation]. Moscow, IL(1958).
9. D. L. Broder, K. K. Popkov, and S. M. Rubanov, Biological Protection of Naval Reactors [in
Russian]. Leningrad, "Sudostronenie, " (1964).
10. S: Yerazunis et al., KAPL-M-SMB-98. May 27 (1959).
11. Corrosion and Wear in Water-Cooled Reactors. Edited by De Pol [Russian translation]. Leningrad
(1958).
12. P. A. Akol'zin and V. V. Gerasimov, Corrosion of Construction Materials in Nuclear and Thermal
Power Stations [in Russian]. Moscow, "Vysshaya shkola" (1963).
13. M. A. Styrikovich, Processes in Boilers [in Russian]. Moscow-Leningrad, Gosenergoizdat (1954).
14. 0. 1. Martynova, Doctor's Dissentation [in Russian]. Moscow(1963).
15. M. A. Styrikovich, "Atomnaya Energiya, " 15, 214 (1963).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
THERMODYNAMIC PROPERTIES OF THE y -PHASE
IN THE URANIUM-ZIRCONIUM SYSTEM
G, B. Fedorov and E, A, Smirnov UDC 621.039,542.32;536.77
Alloying with zirconium has a beneficial effect on uranium fuel; the corrosion
resistance, dimensional stability, and some physicomechanical properties are all
improved [1-5].
It is therefore of interest to study the thermodynamic and diffusion properties of
uranium-zirconium alloys at temperatures above 750?C, for which unlimited solubility
exists between these metals.
The thermodynamic properties of the uranium-zirconium system were studied by measuring the
emf of the electrochemical cell
U (solid) I U+3 +(KC1-NaC1)I U-Zr (alloy).
In setting up the cell we used data relating to the equilibrium potentials of uranium and zirconium
in molten NaCl and KC1, the oxidation-reduction potentials of these metals relative to the chlorine
comparison electrode, the polarization of uranium and zirconium anodes during electrolysis, and the
measured heats of formation of uranium and zirconium chlorides [6-8]. Comparison of existing
information shows that in the uranium-zirconium pair the more electropositive element is uranium and
that the stable valence of uranium in the temperature range studied equals +3. The experimental
electrochemical cell is shown in Fig. 1. After assembly it is placed in a furnace evacuated to a residual
pressure of 10-2mm Hg and held for 2h at 500?C in order to remove traces of moisture from the
electrolytes. After several flushings, the cell is filled with purified argon and heated to 800?C.
Tervalent uranium ions were introduced into the electrolyte by anodic dissolution, for which a
double-walled alundum cylinder was used. Inside the cylinder was a uranium anode and between the
Fig. 1. Arrangement of electromechanical
cell: 1) Steel roof with rubber gasket;
2) leads; 3) port for evacuating and
:admitting argon; 4) copper tube for water
cooling; 5) stainless-steel cylinder;
6) molybdenum screens; 7) alundum tubes
for introducing Chromel-Alumel thermo-
couples and tungsten leads for the
electrodes; 8) three metal holders;
9) alundum cylinder containing electrolyte;
10) base plate.
Translated from Atomnaya Energiya, Vol, 21, No. 3, pp. 189-192, September, 1966. Original
article submitted February 1, 1966. V. G. Bukatov and V. Ya. Vodyanoi took part in this work.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
walls a tungsten-wire cathode. The inner wall served
as a semipermeable membrane, letting sodium and
TABLE 1, EMF Values for Uranium- potassium ions through to the cathode and holding up
Zirconium Alloys the uranium ions. Thus uranium trichloride was
Uranium
Temper-
Coefficients of equation
Ernf,
E=AT+B
content,
ature,
?K
mV
A, mV/deg
B, mV
14,1
1030
125.47
1068
125.78
0111
0
114.1
1124
126.53
,
1160
126.80
27.6
1097
94,64
1097
95.50
0141
0
12
80
1138
95,94
.
.
1182
96.70
41.5
1045
20.11
1039
29.80
0158
0
12
43
1132
30.50
,
.
1184
31,35
so,s
1048
18.02
1
082
18.65
0179
0
81
-0
1121
19,40
.
.
1178
20.40
75
.1030
14.00
1063
14,48
0168
0
3.
504
1120
15,52
.
,
.1175
16.45
89
1036
8.62
1075
1
9.21
.980
0,0147
-6.590
1172
10.70.
94
1039
4.43
1123
5.61
0.0116
-7.568
1165
5.98
formed in the inner space and sodium and potassium
ions were deposited on the cathode. The current
density at the anode during electrolysis was 30 mA/cm2,
The equimolar mixture of sodium and potassium
chlorides used contained 0.5 wt,% uranium trichloride.
The alloys were prepared from iodide-type
zirconium and electrolytic uranium in an arc furnace
with a cooled copper hearth, in an atmosphere of pure
argon. The samples for thermodynamic study, 2.2 to
2.4 mm long and about 0,7 cm2 in cross section, were
preliminarily homogenized at 900?C for 100h, after
which they were water-quenched. The samples for
2
diffusion measurements, 6 to 8 mm long and 1 cm in
cross section, were subjected to five-fold phase
recrystallization (heating to 1000?C and cooling in air)
with a subsequent homogenizing anneal for 2h at 1000?C.
The annealing and quenching were carried out in sealed
quartz ampoules under continuous evacuation.
The emf were measured over 100 to 200h by a
compensation method for a temperature range of 750
to 910?C. The cell temperature was maintained to an
accuracy of ?2?C. At each. temperature the emf was
measured to an accuracy of ?0.05 mV; the values during
heating and cooling agreed to within 0,5 mV. .For
TABLE 2. Principal Partial Thermodynamic Functions of the Uranium-Zirconium
System at 800?C
ca
ezU,
l/g-at.
ZZZr? Zr'
OHcal/g-at.
cal/g-at. ~a1/g-at.deg I cal/g-at.
Zr'
Ascal/g-at. deg
0.141
0,017
0,83
-8730
-7900
0,769
-400
-456
-0,052
0.276
0.045
0,60
-6600
-5555
0,975
-1060
-1167
-0,1
0.415
0.385
0,20
-1980
-810
1,094
-3420
-3580
-0.15
0,605
0.55
0,15
-1280
50
1.239
-4120
-4390
-0.25
0.75
0,62
0.12
-1030
220
1,163
-4770
-4767
0.028
0.89
0,74
0.032
-640
450
1,018
-7360
-4730
2.45
0.94
0.85
0.0036
-340
530
0.806
-12000
-5870
5,7
0
-1000
-2000
-3000
4nnn
AZideal
Fig. 2. Integral molar free Fig. 3. Integral molar en-
energy of the uranium-zir- thalpy of the uranium-zir-
conium system at 800?C. conium system at 800?C.
Fig. 4. Integral molar en-
tropy of the uranium-zir-
conium system at 800?C.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Fig. 5. Coefficients of hetero-diffusion
in the uranium-zirconium system as
functions of concentration: 1) 800?C;
2) 900?C; 3) 950?C [11]; 4) 1000?C [11].
TABLE 3. Diffusion Coefficients of Urani-
um and Zirconium in Uranium-Zirconium
Alloys (D x 1010 cm2/sec)
(Zircon -
rum con-
tent o
element
Soo
900
940
1000
1050
1056
1065
1065
0
Zirconium 0.79
1.5
-
2.7
3.3
i -
35
Uranium
-
2;1
-
8,1
-
18
Zirconium
-
1.2
2.0
4.0
-
7.2
50
ranium - 2.6
4.3
8.9 --
20
Zirconium - 0.93
-
4.2
10.5
70
Uranium
3.5
-
12
-
21
Zirconium
_
0.79
1.4
5.0
11
100
ranium
-
5.6
8 17
-
26
uranium-rich alloys the constancy of the emf was attained more rapidly and the data reproduced to a
greater accuracy.
The diffusion of the components in the uranium-zirconium system was studied by means of
radioactive isotopes U235 and Zr95, which were vacuum-deposited on to the prepared sample surfaces.
Diffusion annealing 2 to 10h in duration was carried out over the temperature range 800 to 1065?:C in
quartz ampules under continuous evacuation. The temperature was kept constant to ?5?C. The diffusion
coefficients were determined by the layer-removal method, the total radioactivity of the remaining part
of the sample being determined [9].
The radioactivity was recorded by means of scintillation counters; for recording the a-radiation
of U235 we used zinc sulfide and for the y-radiation of 'Zr95 sodium iodide activated by thallium. The
emission from the radioactive zirconium was separated from the background of y-radiation from the
uranium samples by means of a differential discriminator.
The averaged results of the emf measurements are shown in Table 1. The coefficients of the
analytical equation E=AT+B for the temperature dependence of the emf were found by the method of
least squares.
The thermodynamic activity of uranium in the alloys was calculated from the formula
log au = 2.ZUEF3RT = -15120 TE
and the activity of zirconium by graphical integration of the Gibbs-Duhame equation
NU
Ig au vu
log azr = - N2 dNU - -logau.
0 r Zr
The resultant values are shown in Table 2. The values of emf were also used for calculating the partial
and integral molar thermodynamic functions of uranium and zirconium (see Table 2 and Fig. 2 to 4).
The partial molar entropy of zirconium was calculated by graphical integration of the Gibbs-Duhame
equation and the remaining thermodynamic functions by means of the ordinary thermodynamic
relationships. The measured diffusion coefficients in the uranium-zirconium system are shown in
Table 3.
Diffusing Temperature, ?C
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
The resultant thermodynamic and diffusion characteristics of the uranium-zirconium alloys
enabled us to calculate the heterodiffusion coefficient [10] from the Darken formula for 800 and 900?C.
D = (NUDZr+NzrD*U) C 1+ 81n fu
a1nNU
where D*Zr and D*U are the diffusion coefficients of the components, fU is the coefficient of activity
of uranium, NU and NZr are the atomic proportions of the components.
The calculated concentration/heterodiffusion-coefficient relationships are shown in Fig. 5 together
with the data of [11] obtained for higher temperatures by the Matano method.
In the temperature and concentration ranges studied there was a negative deviation of the
activities of the two components from Raoult's law. This indicates an intensification of the binding
forces between the uranium and zirconium atoms in solid solution as compared with the corresponding
forces between atoms of similar types.
We see from Figs. 2-4 that the maximum deviation of the integral thermodynamic functions from
the ideal state occurs in the concentration range 30 to 35 at.% uranium, which at lower temperatures
corresponds to the range of existence of the 6-phase.
It is well known that the coefficients of heterodiffusion calculated from the Darken formula (using
data relating to the diffusion of radioactive isotopes and the concentration dependence of the
thermodynamic factor) are more reliable than measurements by the Matano method [12, 13]. However,
despite the difference in the methods, the resulting concentration dependence of the coefficients of
heterodiffusion agrees with the results of [11, 14]. At high temperatures the concentration dependence
of the coefficients of heterodiffusion has a sharp minimum in the range of concentrations corresponding
to extremal values of the excess integral thermodynamic function (see Fig. 5); on lowering the temperature
temperature this minimum becomes smoother.
1. V. S. Emel'yanov, and A. I. Evstyukhin, Metallurgy of Nuclear Fuel [in Russian]. Moscow,
Atomizdat (1964).
2. A. S. Zaimovskii, V. V. Kalashnikov, and I. S. Golovin, Heat-Evolving Elements of Atomic
Reactors [in Russian]. Moscow, Gosatomizdat (1962).
3. G. Ya. Sergeev, V. V. Titova, and K. A. Borisov, Metallurgy of Uranium and Other Reactor
Materials [in Russian]. Moscow, Gosatomizdat (1960).
4. Physical Metallurgy of Reactor Materials, Vol. 1. Nuclear-Fuel Materials. Edited by D. M. Skorov
[Russian translation]. Moscow, Gosatomizdat (1961).
5. V. V. Gerasimov, Corrosion of Uranium and Its Alloys [in Russian]. Moscow, Atomizdat (1965).
6. M. V. Smirnov, and 0. V. Skiba, "Dokl. AN SSSR", 141, 4 (1961) .
7. V. E. Komarov, M. V. Smirov, and A. N. Baraboshkin, In the collection"Electrochemistry of.
Molten-Salt and Solid Electrolytes" [in Russian]. Sverdlovsk, Izd. Instituta elektrokhimiya
Ural'skogo filiala AN SSSR, p.3 (1960); O.V. Skiba, and M.V. Smirnov. Ibid., p.3 (1961);
V. E. Komarov, M. V. Smirnov, and A. N. Baraboshkin. Ibid. , p. 25 (1962); O.V. Skiba,
M. V. Smirnov, and O.'A. Ryzhik. Ibid., p. 41 (1962).
8. Physical Chemistry of Molten Salts and Slags [in Russian]. Moscow, Metallurgizdat (1962).
9. P. L. Gruzin, "Izv. AN SSSR. Otd. tekhn. n. ", No. 3, 383 (1963).
10. L. Darken, Trans. AIME, 175, 184 (1948).
11. Y.Adda, and J. Philibert, Compt. rend., 242, 3081 (1965); 243, 1316 (1965).
12. S. D. Gertsriken, and I. Ya. Dekhtyar. Diffusion in Metals and Alloys in the Solid Phase
[in Russian]. Moscow, Fizmatgiz (1960).
13. R. L. Fogel'son. "Fiz, metallov i metallovedenie", 19, 212 (1965).
14. N. Muller, Z. Metallkunde, 50, 562 (1959).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
X-RAY DIFFRACTION STUDY OF THE DISTRIBUTION OF TEXTURE
OVER THE CROSS SECTION OF URANIUM BARS WORKED IN THE
a- AND y-PHASES AND SUBJECTED TO QUENCHING
V.F. Zelenskii, V.V. Kunchenko,
N.M. Roenko, L. D. Kolomiets,
and A. I. Stukalov
This article contains the results of an x- ray diffraction study of texture distribution over
the cross section of a uranium rod worked in the a- and y-phases and subjected to /3- and y-
heat treatment. The pole-density distribution P(hkl) and growth index Gx depend on the con-
ditions of mechanical and heat treatment; this enables the possible nature of dimensional
changes taking place over the cross section of the rod in the course of radiation growth to
be determined.
(114)
0.12 0
000(223)0 02
O.D7 (112) 0.06o(/)
000(113)000(133) 0
cX
0.05
0
9.05
-0.10
1.58
1.170 1.180
0.760- '00-1--fog
(150)
13t 0 0,73
Fig. 1. Reciprocal pole figures for a-worked (A, B) and y-extruded (C) rods
and distribution of growth index Gx over the rod radius.
Translated from Atomnaya nergiya, Vol. 21, No. 3, pp. 192-197, September, 1966. Original
article submitted July 15, 1965; revised February 7, 1966.
0.9.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
When a polycrystalline metal is intensively strained in any one direction, a very considerable
texture develops within it; the character and intensity of this is determined by the conditions of plastic
deformation. Mechanical methods of finishing metals designed to produce conventional profiles (rods
or sheet) produce inhornogenedus distributions of strains and stresses [1, 2]. The strain texture thus
has different values at various points in the cross section of such samples.
For textured polycrystalline metals having noncubic crystal lattice symmetry, an inhomogeneous
distribution of texture may lead to undesirable consequences in use (for example, leading to the develop-
ment of thermal stresses [3] and hence buckling or spontaneous cracking of components).
For uranium blocks and rods used as fuel elements in reactors, an inhomogeneous texture
distribution may cause inhomogeneous radiation growth over the cross section of the rod [4], leading
to breaks in the coating and finally to breakdown of the reactor.
As a rule, the cores of fuel elements are blocks or rods which have been subjected to special
heat treatment (quenching from the )3- or y-phase [5-8]). In some cases nonuniform texture distribu-
tion over the cross section has been observed [4].
In this paper we present some results of an x-ray diffraction study of texture distribution over
the cross section of uranium rods worked in the a- and y-regions and quenched from the /3- and y-phases.
Distribution of Texture in a-Worked Uranium Rods
The texture was studied by plotting reciprocal pole densities [9], and the growth index Gx for the
end sections of the rod [10, 11].
The absolute error in determining P (hkl) and hence Gx is determined primarily by how well the
standard (isotropic) sample is chosen or the intensity values Ji (hkl) for the isotropic state calculated [12].
In our case we used Ji(hkl) values calculated for the isotropic state and corrected from a standard
sample not having texture (the degree of isotropy was checked by measuring the coefficient of linear
thermal expansion in three mutually-perpendicular directions). Instrumental errors were thus ex-
cluded, since all the x-ray pictures, were taken in a single apparatus under constant conditions. This
made it possible to estimate the error in determining P(hkl), which could reach 20% of the measured
value (in the case of a relatively coarse-grained metal structure), being determined by the number of
crystallites taking part in the diffraction of the x-rays [13].
The x-ray diffraction experiments were made in the URS-50I diffractometer, using filtered CuKa
radiation. Subsequent layer removal was effected by electrolytic etching.. Uranium of 99.76 to 99.80%
purity was used for the experiments.
The samples were prepared in the form of rods or thick wires 4.2 to 6.3 mm in diameter, using
the following technology [14]:
A) Extrusion in the a-phase with subsequent rotatory forging and gage drawing at room
temperature;
B) Extrusion in the a -phase at high temperatures and gage drawing at 150 to 200?C;
C) Vacuum extrusion at the temperature of the y-phase.
Figure 1 shows the reciprocal pole figures for metal samples obtained in these ways. The same
figure shows the variation of the Gx growth index over the rod cross section, this characterizing the
ratio of the contributions of poles of the [010] and [100] types in the direction of the rod axis.
It follows from these data that extrusion in the low-temperature region of the a-phase (scheme A)
causes the formation of axial texture of the [010] type along the extrusion direction. In such rods the
texture is distributed nonuniformly over the cross section; the contribution of [010] poles is slightly
increased at the axis of the rod, but the character of the texture is unchanged.
When the conditions of working are changed (scheme B), the texture and the character of its
distribution over the cross section remain practically unaltered. A typical pole figure (see B in Fig. 1)
indicates a certain contribution of (240) poles close to (110) in the direction of the rod axis, this being
a consequence of high-temperature working with a high degree of reduction (about 95%) [15]. However,
we still have a dominating [010] texture in the direction of the rod axis, the character of the texture not
changing over the cross section.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
24049
? 0.79 047
,0.54 ? .025
0,42 -u'0'' 093
15%78 ?0.74.036 ?034
?0,791 .0.64 ?0.90
I
123 0,89 161170 231 18
2,3630~07~f4~0890.~01097
041062 021043 001
114
?152 133 ?113
?fl2
1,, 96 1,10 0.460,730.5'. 1.61010
,0,75 ?0.93 ?0.83
?0
' ?0,81
?0.78 --~ 0,67
? 0.70 1.14
L,,' 09240
Fig. 2. Distribution of pole density P (hkl)
over the cross section of a-worked uran-
ium rods.
P(OkO,
6
4.5
4.0
3,5
3.0
2.5
2.0
1,5
to
050.8 1.2 1,6R,mm
Fig. 3. Fig. 4.
Fig. 3. Reciprocal pole figures for uranium rods
quenched from the 9- and -y-phases,
Fig. 4. Pole-density distribution over the cross
section of a y-quenched rod (1000 sec holding
period at 800?C).
Figure 2 shows the variation in the density of the poles determining the type of texture over the
radius of the rod for cases A and B.
Extrusion from the y: phase leads to a qualitatively different texture. In the section of the rod
perpendicular to the extrusion direction there is a composite texture, in which the poles of the (001)
planes and those close to the (240) and (041) coincide with the axis of the sample.
As the radius diminishes, there is a weak tendency for a relative increase in the contribution
of the poles close to the (240). This explains the negative values of the growth index Gx (see C in Fig. 1).
Thus the character of the texture and its distribution over the section of the rods depends on the
conditions of thermomechanical treatment. Conditions may be chosen in such a way as to lead to a
quasi-homogeneous distribution of texture over the cross section.
It is interesting to consider the texture of rods quenched from the /3- and y-phases of the rods,
since this form of heat treatment is usually used in order to break up the texture of the uranium as much
as possible. The technological methods developed for the treatment of the uranium cores of fuel ele-
ments [6, 11, 14] ensure the production of a quasi-isotropic structure of a-uranium, and hence a satis-
factory radiation resistance of the fuel element. However, quenching from the /3- or y-phases does not
always lead to desirable results. Certain conditions of heat treatment do not ensure complete elimina-
tion of the preferential orientation of crystallites [4, 5]. There is also a nonuniform distribution of the
average coefficient of thermal expansion over the cross section of a quenched uranium core [4, 14].
Distribution of Texture Over the Cross Section of /3- and y-Quenched Rods
We studied the distribution of texture in samples quenched from the /3-phase (rods obtained by the
B method, heated slowly to 740?C in the furnace, held for 35 min, then water-quenched [5, 14] and y-phase
(heated in molten magnesium to 800?C, held 1000 see, and water-quenched [141). This' kind of heat
treatment led to practically the same type of texture (Fig. 3). It was also interesting to trace the dis-
tribution of the texture over the cross section of such samples. Figure 4 presents the distribution of pole
density P(hkl) for samples quenched from the y-phase (holding time 1000 see). The pole-density dis-
tribution curves P(hkl) were obtained by successive x-ray diffraction of the rod cross section after
electrolytic removal of layers from the cylindrical surface. In the surface zone there was a maximum
density of (062) and (041) poles and those close to the [010]..
The character of the texture does not vary over the cross section, although the extent to which
it is expressed is not uniform (Fig. 5).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
1301 ?1.1 .0,6
? 10.0 ,7 .0,3
1 ?0.5
.0.5 04
'0.0 ?0.7 par
42 2,9 1,6 1,2 1. 1.3.
1
3,2 0410011 Q43 U3 00
1,4 3,5/2.01,5 0.8 LO 1.3
015
-0.7.0,4
.0.3 .0.7 --
?0.7 .03 0.9
?0.3,
?0.4 .07 Q8
?0.4 ?1,2
24 0/240
Fig. 5. Reciprocal pole figures for a sample
quenched from the y-phase (800?C,1000sec),
corresponding to various cross sections.
GX
024
0.20
0.16
0.12
0.08
0.04
19 1
rr~ ~ ~z ~, ~ ~V
0X
025
020
0.15
0,10
0.05
Since the texture is uniaxial and the distribution
of the coefficients of thermal expansion of these samples
indicate a monotonic increase in their values as radius
diminishes [14], we may extrapolate the pole-density
distribution curves P(hkl) toward the center of the
sample (see broken curve in Fig, 4). The variation in
the pole density over the cross sections of samples
quenched from the 0-phase has an analogous character.
A more complete picture of the possible variation
in the coefficient of radial growth over the sample cross
section is given by the radial variation of the growth
index Gx rather than the distribution curves for the
density of individual poles. Figure 6 shows the distribution
of growth index Gx over the cross section of a rod
quenched from the /3-phase. The layer-removal scheme
is indicated in the same figure. In Fig. 61 the layers
were taken from the cylindrical surface and the x-ray
diffraction carried out from the remaining (shaded)
circular area. The graph of Fig. 611 is plotted for rings
successively increasing in area (ab, then ad, and so on);
this was achieved by grinding the end surface of a sample
in which conical holes had been drilled, Point b' cor-
responds to averaging over the surface of ring ab, and
the point corresponding to the center of the sample
(radius R = 0) is obtained by x-ray examination of the
whole end section. This made it possible to trace the
qualitative picture of the texture distribution over the
whole cross section, which cannot be done by taking
layers from the outer surface of the sample.
The holding period spent in the 3- and -y-phases
0 0040601,0121.41.618R1nm d 1!c lb'o expansion [14]. This is because of the change in the type
nnn~_~
of texture. Figure 3 shows not only the reciprocal pole
1 figures plotted for samples quenched from the 0- and
y-phases (1000 sec at 800?C), but also that of a sample
Fig. 6. Distribution of growth index Gx over held at 800?C for 10 sec. The texture.of this sample
differs from that of a sample quenched from the -y-phase
with a holding time of 1000 sec, in that the density of
poles close to the [100] and [001] is increased. This kind
of texture is typical of several cases of quenching from the
/3-phase, involving rapid heating of the samples into the
temperature range corresponding to the existence of the /3 -phase and a short holding time at this
temperature [14].
By comparing data relating to the distribution of texture over the cross section of the rod before
and after quenching, we may conclude that the original texture does not have a decisive influence on the
formation of texture in the quenched metal, since samples with the same initial texture have very different
textures after different forms of heat treatment.
Apparently the texture of the quenched uranium in the present case is determined by the distribution
and magnitude of stresses arising in the sample as a result of volume changes during phase transforma-
tions and also thermoelastic stresses.
Annealing the uranium at the temperatures of the /3- and y-phases leads to additional "alloying" as
a result of the dissolution of inclusions, which reduces the temperature of the phase transformation and
thus modifies the effect of stresses on the formation of the texture observed after quenching. This explains
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
the influence of the holding time (in the temperature range corresponding to the existence of the high-
temperature phases) on the.intensity and distribution of texture over the cross section.
1. Ya, S. Umanskii, X-Ray Diffraction of Metals [in Russianl, Moscow, Fizmatgiz, p. 291 (1960)
2. S. I. Gubkin, Plastic Deformation (Working) of Metals [in Russian], Vil. 1, Moscow, Metallur-
gizdat, p? 346 (1960).
3. V. A. Likhachev, "Fiz. metallov i metallovedenie", 2, 792 (1961).
4. J. Gittus et al. , Radiation Damage in Reactor Materials, Venice, 7-11 May, 1962, p. 109. Part
of the Proceeding of the Symposium on Radiation Damage in Solids and Reactor Materials.
5. F. Foote, In: Metallurgy of Nuclear Power and the Effect of Radiation on Materials [Russian
translation]. Contributions of non-Soviet scientists to the International Conference on the Peaceful
Use of Atomic Energy (Geneva, 1955). Moscow, Energoizdat, p. 146 (1956).
6. Metallurgy of Reactor Materials (Reviews of the Battelle Institute), Book I. "Nuclear-Fuel
Material", [Russian translation], Moscow, Gosatomizdat (1961).
7. A. S. Zaimovskii et al. , In: Transactions of the Second International Conference on the Peaceful
Use of Atomic Energy (Geneva, 1958). Contributions of Soviet scientists [in Russian], Moscow,
Atomizdat, p. 573 (1959).
8. B. Kopelman, Materials for Nuclear Reactors [Russian translation], Moscow, Gosatomizdat,
p.328 (1962).
9, G. Slattery and D. Connelly, TRG Report, 360 (S) (1963).
10. E. Sturcken and W. McDonell, J. Nucl. Mat., 7, 85 (1962).
11. V. E. Ivanov et al. , "Atomnaya Energiya", 18, 357 (1965).
12. G. Harris, Philos, Mag., 43, 113 (1952).
13. P. Morris, J. Appl. Phys. , 35. 2553 (1964).
14. V. E. Ivanov et al., "Atomnaya Energiya", 16, 325 (1964).
15. A. N. Holden, Physical Metallurgy of Uranium [Russian translation], Moscow, Metallurgizdat,
p.103 (1962).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Sr90 AND Cs137 CONTENT IN AGRICULTURAL PRODUCTS
OF. WESTERN SLOVAKIA, 1963-1964
S. Cupka, M. Petrasova, UDC 551.577.7:614.776
and J. Carach
The Sr90 and Cs137 levels in agricultural crops grown in Western Slovakia in 1963-
1964 were investigated. Highest content of both isotopes in grains and a relatively low
content in legumes were reported, with the lowest content in row crops. The different
Cs137/Sr90 ratios in the crops studied is accounted for by the sorbing power of the plants
and primarily by the amount of radioactive fallout occurring during the period in question.
The purpose of this article is to describe determinations of levels of the most important radioiso-
topes found in agricultural crops in areas contiguous to nuclear power station sites..
At present, with Sr90 and Cs137 fallout levels gradually declining, there is interest in investigating
migration, extraction of isotopes from the soil by plants, and circulation in the food cycle. Some farm
produce containing radioactive materials enters the human organism directly. Other agricultural
products are utilized as raw material in the food industry or as fodder for livestock. In the latter case,
only a certain fraction of the radioactive materials originally present enter the human organism because
of discriminating effects in the metabolism of the livestock. The radioactivity of agricultural products
of this type, which make a significant contribution to national crop production, was studied to obtain a
quantitative estimate of this effect. Grains, corn, tobacco, and the like were scrutinized (Table 1).
Samples were taken at three sites in Western Slovakia: Bratislava-Raca, Bohunice, and Pesttany. One
kg assorted grains, 2 kg legumes, 4 kg row crops, and 100 g tobacco and 100 g tobacco leaf, unprocessed,
were sampled for analysis. Only the edible portion of potato plants was analyzed. Sugar beet and fodder
beet samples were carefully freed of clinging farm soil before being analyzed.
The authors isolated both radioisotopes radiochemically, employing techniques described in the
literature [2, 3], and then determined the beta-activity of the isotopes.
Average Sr90 and Cs137 specific activities in crops grown in Western Slovakia in 1963-1964 are
listed in Tables 2 and 3.
The maximum calcium content in grain crops is reported in oats-the minimum in millet. Of all the
products studied by the authors, potatoes and corn contain the least calcium, poppy and tobacco the most.
TABLE 1. Contribution of Slovakia and the WesternSlovak. Distrietto the Total
Agricultural Production of the CSSR, 1964
Crop
Slovakia, %
West.Slovak
District, Olo
Crop
Slovakia, %
West.Slovak.
District, ?Jo
Wheat ............
27.6
18.1
Sugar beet ........ .
25.7
20.2
Rye ..............
12.6
4.4
Potatoes ..........
21.0
4.3
Barley .............
35.7
23.6
Corn (silage)........
30.1
16.9
Oats ..............
14.0
4.2
Tobacco ..........
91.2
-
Corn (whole grain) ....
91.0
76.8
Poppy seeds .........
16.7
-
Legumes .. .......
30.4
-
District Public Health and Epidemiological Station, Bratislava, CSSR. Translated from Atomnaya
Energiya, Vol. 21, No. 3, pp. 197-201, September, 1966. Original article submitted November 6,
1965; revised April 12, 1966.
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
TABLE 2. Specific Sr90 Activity in 1963-1964 Crops
Ca 'A .... .. .
Sr , pCi/k
Sr 90 : Ca, p&/ kg* . . . . . .
Cs 137,pCi/kg . . . . . . . . .
Cs 137 : Sr 90 . . . . . . . . . . .
1963
1964
0.51
0.50
1,32
1,14
0.20
0,14
69.0
105,7
15.8
16,6
8.6
8.6
135.3
211.4
12.0
14,.6
43.0
61.4
279.5
265.1
310.9
171,0
68.1
29,4
4,0
2.5
19.7
10.3
7.9
3.4
Crop
No. of
sample
Calcium content,
_ /kg
Sr90 content,
pCi/kg
Sr90/Ca icontent 1963/1964
pCi/g ~Sr90/Ca
sites
1963
1964
1963
1964
1963
1964
I ratio
Grains
Wheat
6
0.45
0.40
108.7
123,8
241.5
309.5
1.3
Rye
4
0.49
0.51
77.3
114.9
157.8
225.7
1.4
Barley
8
0.36
0.43
66.2
162.9
183.9
381,4
2.1
Oats
7
1.06
0.83
62.9
108.1
59,3
130.6
2.2
Millet
2
0.19
0.32
29.7
18.8
156.3
59.4
0.4
Legumes
Peas
4
1.32
0.88
15.8
10.4
12.0
11,7
1.0
Beans
1
-
1.89
-
25.0
-
13.2
-
Lentils
1
-
0
.65
-
14.5
-
22.3
Row crops
Cleaned potatoes
12
0.05
0.05
5.2
2.7
104.0
54.0
0.5
Corn
8
0.05
0.06
3.7
2.1
75.5
35.0
0.5
sugar beet
4
-
0.22
-
22,4
-
101.8
-
Fodder beet
12
0.51
0.20
17.0
7.4
33.3
37_0
1.1
Miscellaneous crops
Poppy
2
-
12.56
-
22.0
-
1.9
-
2
-
34.80
-
350.3
-
10.1
-
Fodder beet foliage
5
6.10
-
494.2
-
81.0
-
-
TABLE 3. Specific Cs137 Activity in 1963-1964 Crops
crops
Wheat ..............
Rye ...............
.............
? ..............
.............
Grains
Peas ..... .........
Beans ..............
Lentils .............
Legumes
Cleaned potatoes ? ......
Corn ..............
Sugar beet ...........
Fodder beet ..........
Miscellaneous crops
Poppy
Tobacco ............
Fodder beet leaves .....
Crop
Number of
sampling
Cs137 content, pCi/kg
Cs131 /Sr90 ratio
1964/1963
137 data
sites
1963
1964
1963
1964
ratio
6
180.0
299.2
1.7
2.4
.7
1.7
4
505.9
344.6
6.5
2.9
0.7
8
.2
197.2
175.5
3.0
1.1
0.9
7
0.1
290.1
268.4
4.6
2.5
0.9
2
224.5
.5
248.0
7.6
13.2
1.1
4
310.9
108.5
19.7
10.5
0.3
1
-
132.7
-
5.3
-
1
-
271.8
-
19.4
-
12
44.0
32.7
8.5
12.1
0.7
8
150.6
58.6
40.7
27.9
0.4
4
24.4
15.2
-
0.7
0.6
12
53.2
11.3
3.1
1.5
0.2
2
-
117.2
-
5.3
-
2
-
647.1
-
1.8
-
5
1266.6
-
2.6
-
-
TABLE 4. Average Specific Activities of Sr90 and Cs137 in 1963-1964 Crops
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
The Sr90/ Ca ratio is lowest in poppy samples (1.9) and tobacco samples (10.1), owing to the relatively
high content of calcium in the product. The Sr90 concentration (in strontium units) is much higher in the
remaining products, on account of the low calcium content.
Maximum Sr90 concentrations were detected in grains (211.4 strontium units) and minimum in
legumes (14.6 Sr units). Concentration in row crops was intermediate (61.4 Sr units). The lowest Sr9o
level in the 1964 crops studies was in the edible part of the potato plant (2.7 pCi/kg) and in corn
(2.1 pCi/kg).
A rise in Sr90 level in almost all crops above the 1963 level was observed in 1964. The highest
increase was observed in barley and oats (the level doubled in these cases). Sr90 activity dropped in
corn and potatoes (by about 50%).
The maximum specific activity of Sr90 and Cs137 was observed in tobacco leaf and beets (Cs137 content
totalled 647.1 pCi/kg, in some cases 1266.6 pCi/kg), followed by grains with an average of 265.1 pCi/
kg for 1964, legumes with 171.0 pCi/kg, and finally row crops with a low of 29.4 pCi/kg (Table; 3 and 4).
The content of Cs137 in agricultural crops was higher than that of Sr90 owing to radioactive fallout,
in which the Cs137 activity is higher than Sr90 activity. The Cs137/Sr90 ratio in atmospheric fallout
usually ranges 1.5 to 2, although it can sometimes surpass that range [4]. The greatest difference in
Cs137 and Sr90 contents is found in corn, where the Cs137/Sr90 ratio is 27.9, and in potatoes (12.1). The
average Cs137/Sr90 ratio for legumes was 10.3 in 1964, and that of the grains millet showed the greatest
difference in Cs137 and Sr90 content.
The 1964 specific activity of Cs137 ran below the 1963 figure in all crops studied. A significant
decrease as much as 80% was recorded in row crops
TABLE 5. Cs137 and Sr90 Content in Atmo- with the smallest decrease in grains, viz. 5% (see
spheric Fallout Over the Territory of Table 4).
Western Slovakia,. 1963-1964 Sr9o and Cs137 specific activity in plants depends
.. ..........:... I primarily on the amount of those isotopes present in
Year pheric LS"' /Jr-- aulnubp1lul i . iaiivuI. I Lv1111./al i~v1i uy Lnu au,.uvi o vi
fallout, CS 137 I Sr 90 ratio Cs137 and Sr90 activities in monthly atmospheric
mm
fallout reports covering 1963-1964 (Table 5) and in
1963 558 29.0 22.5 1.3 crops (see Table 3) show that the slowdown in the rate of
1964 555 15.5 16.9 0.9 137 137
196, : 1963 - 0.53 0.75 - Cs fallout from the atmosphere also affected Cs
content in plants.
TABLE 6. Relative Amounts of Sr90 and Cs137 Present in 1964 Crops
Crops compared
Ca
K
Sr90
Sr90:Ca
Cs137
wheat/peas .........
0.5
0.5
11.9
13.5
2.9
wheat/potatoes .......
4.8
1.0
20.3
2.4
7.0
peas/potatoes ........
9.3
1.7
1.7
0.2
2.4
fodder beet foliage/beet
12.0
0.9
29.1
2.4
23.8
TABLE 7. Distribution of Sr90 and Cs137 Activities in Potato Tubers
weight of wet tuber, g ..
Ca, mg
Sr90 pCi/kg ...... .
Cs137 .pCi/kg ........
Cr": Ca, pCi/kg .... .
Cs 137: Sr90 . .. .. .. . .
1000
662
66.2
1000
798
79.8
82
49
59.8
94'
53
56.4
11.1
5.2
46.8
6.1
2.7
44.3
61.0
44.0
72.1
.44.2
32.7
74.0
135.4
106.1
64.9
50.9
5.5
8.5
7.2
12.1
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
Radioactive materials precipitated to the earth's surface are retained mostly in the topsoil layer.
Cs137 becomes trapped in the top organic layer [5-8], Cs137 is taken up by plants from the soil in amounts
only one-twentieth the amount of Sr90 taken up. The Cs137/Sr9o ratio in plant uptake from the soil is
roughly 0.03 to 0.20 [9]. The rise in Cs137 content in legumes and row crops over the Sr90 content can be
accounted for only by uptake of cesium which had settled out on the surface of the plant foliage, i. e.,
traceable directly to atmospheric fallout. I
Sr90 and Cs137 contents also depend on what part of the plant yields the isotope. As far as Sr90 is
concerned, there are indications that the root system accounts for only 10% of the total amount of this
emitter in the plant, whereas the aerial part of the plant concentrates about 90% of the isotope [5, 10].
The isotope distribution in the aerial part of the part is not the same either. Table 6 lists data on
content of Sr90, Cs137, calcium, and potassium in samples of 1964-harvested wheat, peas, and potatoes.
We see on comparing the data that wheat contains 4.8 times more calcium than potatoes. do. The ratio
of Sr90 present in those products attains the value of 20.3, however. There is no correspondence between
the amounts of potassium and Cs137 either. Fodder beet foliage accounts for about 96% of the total
Sr90 and Cs137 activity. We can state, in general, that there is no direct relationship between potassium
and Sr90 content, nor between potassium and Cs137 content in plants (e.g., poppy and tobacco, for which
see Tables 2 and 3).
The distribution of radioactive materials in the fruits is also nonuniform. Sr90 and Cs137 distribution
in potato tubers was. studied, with the edible portion and the skin scrapings analyzed separately. The,
edible portion of the potato accounts for 45% of the total Sr90 activity and 75% of the Cs137 activity,
whereas the edible portion accounts for 66 to 80% of the total weight of the tubers (Table 7). The amount
of this edible portion depends on storage time, brand, and on the size of the potato tubers.
1. Statisticka rocenka CSSR 1965, [Statistical Almanac of the Czechoslovak Socialist Republic,
1965]. Prague, SNTL-SVTL, (1965).
2. W. Haussermann and W. Morgenstern, Atompraxis, 8, 37 (1962).
3. V. Zboril and T. Trnovec, Chem. zvesti, [Chemical Bulletin], 17, 268 (1963).
4. Report of the UNO Science Committee on Effects of Atomic Radiation (17th session of the UN
General Assembly). Appendix 16, New York (1962).
5. E. Mercer and F. Ellis, Report ARCRL, 12, 49 (1964).
6. E. Niemann, Atompraxis, 7, 370 (1961).
7. V. I. Baranov et al., Atomnaya energiya, 18, 246 (1965).
8. Radioactive Contamination of the Environment. Collection of articles edited by V. P. Shvedov
and S. I. Shirokov. Moscow, State Atom press, [in Russian] (1962).
9. H. Squire and L. Middleton, Report ARCRL, 8, 66 (1962).
10. V. M. Klechkovskii and I. V. Gulyakin, Article in the book: Soviet Scientists Speak on the Dangers
of Nuclear Weapons Testing. Edited by A. V. Lebedinskii. Moscow, Atom press, [in Russian]
p.58 (1959).
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 Declassified and Approved For Release 2013/03/12 : CIA-RDP10-02196R000700040003-1
ON THE ANALYSIS OF TRANSITIONAL PROCESSES IN
A REACTOR CLOSE TO PROMPT CRITICALITY
Yu.P. Milovanov UDC 621.039.512
For the case in which there are no neutrons in a reactor up to the onset of the transitional process,
the kinetic equation with allowance for delay neutrons can be written as follows:
do k 1- ~1 R _ t
dt = 0) - + Z LJ Pikie bit kne4it dt,
i 0
with the usual notation. If we introduce a function
kit
e- ii 1 kne) t
i dt
then (1 j becomes
t
S kit dt
0
~j I'i~i~i (t) t
dnk(1-(3)-1n{ kndi.
alt - l l
The principal properties of cpi (t) are as follows:
Ti (0) =1; (Pi (t)