SOVIET ATOMIC ENERGY VOL. 42, NO. 2

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• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 106
• Document Creation Date: December 23, 2016
• Document Release Date: April 1, 2013
• Sequence Number: 2
• Publication Date: August 1, 1977
• Content Type: REPORT

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,
. Russian Original? Vol. 42; No: 2; February, 1977'
August, 1977
SATEAZ 42(2) 91-190 (1977)
SOVIET
ATOMIC
ENERGY
ATOMHAfl 3HEMIR
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
) CONSULTANTS BUREAU, NEW YORK
q?
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physics Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: O. D. Kazachkovskii
Associate Editor: N. A. Vlasov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov
I. N. Golovin
V. F. Kalinin
A. K. Krasin
V. V. Matveev
M. G. Meshcheryakov
V. B. Shevchenko
V. I. Smirnov
A. P. Zefirov
Copyright C) 1977 Plenum Publishing Corporation, 227 West 17th Street, New York,
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
August, 1977
Volume 42, Number 2 February, 1977
ARTICLES
CONTENTS
Engl./Russ.
Thirtieth Anniversary of the First Soviet Nuclear Reactor ? V. V. Goncharov
91
83
Difference-Scheme Solution of Heterogeneous-Reactor Equations
? B. P. Kochurov and V. M. Malofeev
95,16
87
Gas-Thermal Treatment of Nuclear Power-Station Fuel Elements to Separate
the Core from the Can ? G. P. Martynovskikh, A. T. Ageenkov,
M. M. Arduanov, A. F. Bogatov, E. M. Valuev, V. F. Savel'ev,
V. A. Chemezov, G. I. Chechetin, and Yu. V. Yastrebov
100.0-
91
Behavior of Highly Active Waste Products Obtained when Regenerating the Fuel
Elements of Fast Reactors by the Gas-Fluoride Method
? A. P. Kirillovich, Yu. G. Lavrinovich, 0. V. Skiba, M. P. Vorobei,
and D. I. Starozhukov
103 ?
94
Physicochemical Properties of Melts Comprising Mixtures of Uranium Tetrachloride
with the Chlorides of Alkali Metals ? V. N. Desyatnik, S. F. Katyshev,
and S. P. Raspopin
108?
99
Peculiarities of the Chemical Etching of Polyethylene Terephthalate, Irradiated with
Radiations with Various Linear Energy Losses ? N. S. Moshkovskii,
L. N. Gaichenko, and Ya. I. Lavrentovich
112
104
Calculation of the Characteristics of a Tokamak Reactor with Injection of Deuterium
and Tritium Ions ? V. S. Galishev
116
108
The High-Current Electron Accelerator Impul's ? L. N. Kazanskii,
A. A. Kolomenskii, G. 0, Meskhi, and B. N. Yablokov
122
113
Information for the Authors
129
119
Establishing Permissible Doses on the Basis of Biological Risk
? V. G. Denisenko, U. Ya. Margulis, and A. I. Klemin
130
120
DEPOSITED ARTICLES
Effect of Insulator Space Charge on Direct-Charge-Detector Current
? A. A, Kostritsa and L. V. Chekushina.
134
123
Calculation of the Energy Spectra of y Quanta by the Yvon?Merten Method
? V. S. Galishev
134
123
Propagation of y Rays in System of Plane Infinite Layers. I. Space-Energy
Distribution of Secondary Electrons ? I. R. Entinzon, 0. P. Verkhgradskii,
and A. M. Kabakchi
135
124
Potentiostatic and Pulsed-Potentiostatic Electrodeposition of Uranium on Liquid
Zinc with an Anode Layer ? S. L. Gol'dshtein, S. M. Zakhar'yash,
D. F. Rakipov, and S. P. Raspopin
136
125
Optimization of Shielding Containers for Isotropic Neutron Sources
? Yu. N. Kazachenkov, A. P. Suvorov, and R. P. Fedorenko
137
125
Optimal Operation for Research Reactors ? A. S. Gerasimov
138
126
Conditions of Electronic Equilibrium During In-Pile Irradiation of Heterogeneous
Objects ? B. A. Briskman, V. P. Savina, L. V. Popova, and V. D. Bondarev
138
126
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CONTENTS
LETTERS
Conditions for Producing Nonuniform Fields in Nuclear Reactors
(continued)
Engl./Russ.
- A. M. Zagrebaev and V. I. Naumov
140
128
Statistical Regularization Method for Establishing Fast-Neutron Energy Spectra
According to Readingsof Activation Threshold Detectors - V. E. A leinikov,
V. P. Bamblevskii, and M. M. Komochkov
142
129
Electrochemic'al Preparation of Single Crystals of 236UO2 - V. 0. Kordyukevich,
V. I. Kuznetsov, Yu. D. Otstavnov, and N. N. Smirnov
145
131
Precipitation of Molybdenum during Evaporation of Nitrate Solutions
- Yu. P. Zhirnov, E. P. Efremov, M. I. Zhikharev, and A. N. Efimov
148
133
Behavior of Europium Oxide Irradiated in a Fast Reactor - T. M. Guseva,
V. R. Zolotukhin, V. K. Nevorotin, S. A. Kuznetsov, and V. V. ChEsanov
150
135
Determination of the 66Fe(n, p)66 Mn Cross Section at 14.8 MeV
- Z. A. Ramendik, G. M. Stukov, and V. T. Shchebolev
152
136
Bounded Estimate of Absorbed Dose Using Linear Programming
- N. G. Volkov, V. K. Lyapidevskii, and Yu. J. Malakhov
154
138
Thermal-Neutron Transfer from Pulse Source in Moderator with Large Cylindrical
Cavity - Zh. M. Dzhilkibaev and M. V. Kazarnovskii
156
139
Cross Sections for (n, a0), (n, a1), (n, a2), (n, a3), (n, a4) Reactions in 28Si and (n. act),
(n, al) Reactions in 28Si at a Neutron Energy of 14.1 MeV - L. I. Klochkova
and B. S. Kovrigin
158
141
Accelerating Convergence in Perturbed Problems for Nuclear Reactors
- E. G. Sakhnovskii
159
141
Optimal Operating Conditions for Atomic Power Plant Reactors
- A. S. Gerasimov and A. F. Rudik . . . .
162
143
85Kr Concentration in the Atmosphere over, the USSR Territory in 1971-1975
- E. G. Tertyshnik, A. A. Siverin, and V. G. Baranov
164
145
Neutron Leakage from a Manganese Bath - E. A. Zhagrov, Yu. A. Nemilov,
A. V. Platonov, and V. I. Forninykh
166
146
Yields of 121mTe, ingTe, and 123mTe in the Bombardment of Antimony by Protons
and Deuterons - P. P. Dmitriev, M. V. Panarin, Z. P. Dmitrieva,
and G. A. Molin
168
148
INFORMATION: CONFERENCES AND MEETINGS
The First Minergomash Technological Conference - A. I. merenkov
171
150
Soviet-British Seminar on Fast Reactors - Yu. V. Markov
172
150
Meeting of International Working Group on Future Accelerators and on the Development
of High-Energy Physics - A. Vasiltev
174
152
Second Symposium on Collective Methods of Acceleration - V. P. Sarantsev
176
153
Fourth International IAEA Conference on Plasma Physics and Controlled
Thermonuclear Fusion - E. I. Kuznetsov
178
155
European Nuclear Physics Conference on Heavy Ions - V. V. Volkov
180
157
The 58th Session of the UN Scientific Committee on the Effect of Atomic Radiation
- R. M. Aleksakhin
183
158
Powerful Sources of Ionizing Radiation in Radiation Technique - S. M. Terent'ev
185
160
BOOK REVIEWS
A. K. Sledzyuk, N. S. Khlopkin, B. G. Pologikh, A. M. Goloviznin, and V. A. Kuznetsov.
Marine Nuclear Power Plants -Reviewed by V. S. Aleshin
187
161
B. A. Briskman. Components of Absorbed Energy of Reactor Radiation
- Reviewed by Yu. I. Bregadze
188
161
I. V. Goryachev, V. I. Kukhtevich, and L. A. Trykov - Design and Testing of Shielding
against Radiation from Nuclear Explosion - Reviewed by S. G. Tsypin
189
162
The Russian press date (podpisano k pechati) of this issue was 1/24/1977.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
THIRTIETH ANNIVERSARY OF THE FIRST SOVIET
NUCLEAR REACTOR
V. V. Goncharov UDC 621.039.5
In 1943, by the decision of the Party and the Government in Moscow, in order to solve the nuclear prob-
lem, a special scientific establishment was set up ? Laboratory No. 2 of the Academy of Sciences of the USSR,
(now, the I. V. Kurchatov Institute of Atomic Energy). I. V. Kurchatov was appointed its scientific director.
The main task of Laboratory No. 2 was to carry out research which would permit a chain reaction in a nuclear
reactor to be achieved. The reactor would have to be a system of uranium and graphite, moderating the neu-
trons, in which the release of nuclear energytookplace spontaneously. It was postulated that the graphite would
make possible the use of natural uranium (with a content of fissile U-235 to a total of 0.7%)?
Even in 1940, I. V. Kurchatov produced a report at the All-Union Conference on the Physics of the Atomic
Nucleus and published the paper "Fission of Heavy Nuclei." He arrived at the optimistic conclusion that a chain
reaction by slow neutrons was entirely feasible. It might have been assumed to be practicable after the dis-
covery in 1939 of the fission reaction of uranium by the action of neutrons. However, in 1941, after the start of
the Great Fatherland War (Second World War), work in this direction completely ceased in the Soviet Union and
was renewed only in 1943.
A grandiose program for constructing a reactor and for achieving a controlled chain reaction could be
carried out only by solving three basic problems: 1) to develop a detailed reactor theory with subsequent ex-
perimental verification of the theoretical data; 2) to produce graphite of a high degree of purity to the amount
of hundreds of tons and 3) to produce tens of tons of pure metallic uranium. Such graphite and uranium had
never been produced in the Soviet Union.
In Laboratory No. 2, theoretical and experimental investigations of the physical constants were developed,
especially the cross sections of capture by poisons of thermal (moderated) neutrons in graphite. A method of
measuring the absorption cross section for neutrons was found as a result of theoretical work by Ya. B. Zel'do-
vich, I. Ya. Pomeranchuk and I. I. Gurevich, and experimental investigations carried out by I. V. Kurchatov
jointly with I. S. Panasyuk, on the moderation and diffusion of neutrons in graphite. After the development of a
method of measuring such small cross sections, physical tests were started on the absorption of neutrons in
prisms of mass up to 5 tons, in different batches of graphite (graphitized electrodes), developed by industry.
The first results proved to be one hundred times worse than expected, and caused a great disappoint-
ment. Then better batches of graphite were chosen for the tests but they also proved to be unsuitable. The
graphite absorbed so many neutrons that it was impossible to achieve a chain reaction. The presence in the
graphite of impurities was then established, which were poison-absorbers of neutrons. The impurity content,
determined by the amount of ash which remained after ignition of the samples, amounted to 1%.
Kurchatov himself, together with colleagues from Laboratory No. 2, left for the factory and endeavored
under his direction to produce the purest graphite. The workers of the factory consideredthis a completely
unachievable desire of the scientists. They maintained that it was not possible to manufacture graphite blocks
whose purity must be significantly higher than for diamond (also carbon). Kurchatov and his assistants did not
lose faith in their ability to produce graphite of the required purity. But to accomplish this, the technological
process for the manufacture of the graphite blocks would have to be improved considerably.
As a result of physical investigations in Laboratory No. 2, in November 1944 the first stringent require-
ments for reactor graphite were compiled? the content of impurities, i.e., boron, must be not more than a few
parts per million.
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 83-86, February, 1977. Original article sub-
mitted December 13, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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After a detailed analysis of the existing production technology of graphitized electrodes in the factory,
and familiarization with the technical literature, in February 1945 the technical conditions were formulated
and measures were developed, recommended by Laboratory No. 2, for solving this difficult and important
problem. From March 1945, jointly with Laboratory No. 2, scientific-research and pilot-plant projects were
developed in the factory for the purpose of a test production of six experimental batches of pure graphite
blocks of 5 tons. The complexity of the problem was aggravated by the fact that the graphitization process
lasted about two weeks and the duration of the whole technological cycle was approximately two months. On
the first occasion the physical tests of the graphite blocks (measurement of the neutron absorption cross
section) were carried out in Laboratory No. 2 and then they were carried out in the factory.
As a result of intensive and self-consolidated work by the factory, jointly with Laboratory No. 2 with the
support of the National Committee for Nonferrous Metals of the USSR, by August 1945 a special technological
process had been developed successfully and in October the industrial startup of production of the necessary
quality was started. Thus, the critical assignment of the State Committee for Defense of the USSR was ac-
complished ahead of schedule. At the same time, the planning of a new factory was started. Thus, for the
first time in the USSR, a method for the production of graphite blocks for reactors had been developed in an
exceptionally short period; the basic principle was the use of low-ash raw material and pure materials in elec-
tric graphitized furnaces and the achievement of improved processes of thermal and gas refining in graphite
furnaces of the normal type, reequipped for this purpose.
It can be seen from the American official report published in 1945, that the production of pure graphite
in the USA was considered to be one of the most important and difficult problems, as before 1940 carbon
(graphite) had never been produced in such quantity and with such a degree of purity as were required for the
moderator in a reactor. At the beginning of summer 1940, there was no guarantee that it was possible for
graphite to have such purity and in the required quantity. At the beginning of 1942, the position was still un-
satisfactory, and only by the middle of 1942 was the problem mainly resolved. By the autumn of 1942 in Chicago
sufficient graphite was produced to make an attempt to construct a reactor. Thus, in the USA, the development
of a method to produce pure graphite required more than two years (from the beginning of summer 1940 to the
middle of 1942), and only after this was it possible to start the production of graphite for the first reactor, CP-
1.
In the Soviet Union, the problem posed was solved successfully in an extremely short time ? in all, six
months (from March to August 1945), which permitted the industrial production of high-grade graphite blocks
to be organized, for the F-1 reactor.
In the reports presented by the USA at the International Conference on the Peaceful Uses of Atomic En-
ergy in Geneva (1955), data were given about the quality of the American graphite. It was found that the im-
purity content (ash) in the best kind of nuclear graphite, AGOT, was greater by a factor of 3.7 than in the
Soviet graphite. The content and cross section of thermal neutron poison-absorbers in this graphite was also
found to be higher than in the Soviet graphite. Thus, the quality of the American graphite was significantly
less than that of the Soviet Union.
Together with the graphite researchers, a study of the physical characteristics of the small quantity of
available uranium was started. The investigations showed that in order to achieve a chain reaction, pure
uranium is required in which the content of impurities (boron, cadmium, rare-earth elements) amounted to
only negligible fractions. Physicotechnical requirements were formulated for the production of uranium, de-
signed to ensure a high chemical purity and density, and a requirement was established for the capture cross
section, taking into account the neutron absorption in the uranium itself and in all impurities. Consequently,
the immediate problem was the development of a technology for the manufacture of blocks of uranium metal
which did not contain strongly neutron-absorbing poison-impurities.
The problem of uranium p oduction was solved in many establishments; in the scientific-research in-
stitutes, in the mines, concentration plants, chemical production plants and factories.
At first, experimental work on the production of uranium was undertaken by Giredmet Narkomtsvetmet
SSSR* under the direction of Prof. N. P. Sazhina. I. V. Kurchatov was moved for a short time to Giredmet to
offer assistance and to accelerate the accomplishment of the work. At the end of 1945, the decision was taken
to organize the production of uranium metal at one of the factories, but by another technology. Thanks to
strenuous measures and after overcoming many difficulties, the production of uranium steel metal blocks was
successfully started primarily for the F-1 reactor.
*State Rare Metals Research Institute of the National Committee for Nonferrous Metals of the USSR.
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When carrying out in Laboratory No. 2 a series of experiments in prisms with different uranium?graph-
ite lattices, it was discovered that certain batches of uranium blocks which were completely acceptable ac-
cording to the results of chemical and spectroscopic analyses, gave an unsatisfactory neutron multiplication
factor. Because of this, a physical quality control was set up in Laboratory No. 2 for all batches of uranium
blocks issued by industry. The very great importance of the development of a procedure for the chemical
analysis of impurities in the uranium should be mentioned. These procedures did not exist for the majority
of elements and their development represented a difficult problem, due to the insignificantly small quantity of
impurities which it was required to determine. These analytical methods were developed under the direction
of Academician A. P. Vinogradov.
After the arrival of the graphite and uranium blocks in Laboratory No. 2, the conduct of the physical ex-
periments was extended sharply. Day and night in tents and dug-outs, the graphite prisms were assembled with
the uranium and then they were disassembled and reassembled. Tens of experiments were carried out, and
according to the accumulation of experimental data the physical parameters were refined and reactor theory
was improved. The most exact thermal neutron capture cross sections were determined for graphite and ura-
nium. Certain physical characteristics of the uranium blocks were studied also, the optimum parameters were
chosen, and the pitch of their arrangement in the space lattice in the graphite. By means of these numerous
experiments, after the production of a large amount of graphite and uranium, and the study of their properties,
four subcritical models of the reactor were chosen, investigated and dismantled. The calculations permitted
the approximate critical dimensions of the reactor to be estimated and the required number of uranium (up to
50 tons) and graphite blocks (approximately 500 tons) to be estimated for its construction.
A special building with a concrete foundation pit 7 m deep and an underground laboratory with a control
desk for remote control were designed and constructed. When a sufficient number of uranium and graphite
blocks were produced, the quality of which was controlled by physical methods, assembly was started. The ac-
tive zone of the F-1 reactor was a sphere with a diameter of 6 m, built of graphite blocks with dimensions
100 x 100 x 600 mm. It was surrounded by a reflector, 800 mm thick, also made of graphite blocks. In the
graphite blocks about 30,000 openings for the uranium were drilled, forming a space lattice with a defined pitch.
Three vertical channels were provided in the reactor, for the rods of the safety and control system, and also
six horizontal experimental channels.
The F-1 reactor was started up on December 25, 1946. It startup was conducted by I. V. Kurchatov him-
self with the participation of assistants. Thus, it was 30 years ago that a controlled fission chain reaction in
uranium was accomplished. In 1958, Kurchatov wrote: "I recall the emotion with which, for the first time on
the continent of Europe, myself and a group of co-workers successfully achieved a chain fission reaction in the
Soviet Union in a uranium?graphite reactor."
The construction, under the direction of Kurchatov, of the F-i reactor was the greatest achievement of ?
Soviet science and technology, the first stage in the solution of the most complex and difficult of the nuclear
problems. The work was carried out under incredibly difficult conditions by the utmost strenuous efforts and
genuine enthusiasm of all participants. This was an enormous labor feat of Soviet scientists, engineers, and
workers who built the first reactor, and for the uranium and graphite industry.
The startup of the first nuclear reactor in the Soviet Union ensured the feasibility of obtaining many more
important theoretical, experimental and methodological results.
The investigations carried out in the F-1 reactor were of enormous importance. Measurements were
made of the principal nuclear constants, the optimum lattice was determined for the first commercial reactor
and its calculated characteristics were refined, problems of control and safety were studied, and means of
shielding from radiation. The small quantity of plutonium produced in the reactor allowed its chemical proper-
ties to be studied, and a technology to be developed for its extraction from irradiated uranium. The investiga-
tions in the F-1 reactor made possible in every way the further development of reactor theory.
With the aid of the reactor, a method was developed for the quantitative monitoring (by the change of re-
activity) of the physical qualities of uranium, graphite and uranium?graphite lattices. The quality of the uran-
ium, graphite and other industrial articles issued for commercial reactors was checked by this method.
The exceptionally valuable experience obtained on the first reactor, and the investigations undertaken in
it, permitted progress toward the designing and construction of other reactors and, in its turn, toward the construc-
tion of a commercial reactor. Thus, the startup of the first F-i reactor served as the beginning of the birth of the
Soviet nuclear industry.
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In comparing the history of construction of nuclear reactors, it should be noted that in the USA the Ura-
niurnCommittee started operation in October 1939, and the first experiments with carbon (graphite) were com-
menced in April-May 1940, in Columbia University (from this time, all operations on the uranium problem
were classified secret). The chain reaction in the first USA reactor CP-1 was accomplished in December
1942. In the Soviet Union, the first reactor F-1, installed in a special building, was constructed more rapidly
than the American reactor and its experimental capabilities proved to be considerably broader than of the
Amercian reactor. The power of F-1 reached 4000 kW, but the American reactor did not exceed 200 W. It
should be noted that in the Soviet Union, the problem was solved during the war and in the first year of re-
covery of the national economy, which had suffered enormous material and manpower losses. Also, it was
solved only by the efforts of the Russians themselves. In the USA, in a country possessing a highly developed
industry, not having suffered from the war, the investigations and construction of the reactor were accom-
plished with the participation of eminent scientists who had emigrated from Europe.
The F-1 reactor is functioning at the present time in the I. V. Kurchatov Institute of Atomic Energy and
it not only of historical value, but also provides for the carrying out of certain researches which are useful
even at the present time.
As mentioned, in the USA the first reactor, CP-1, was started up in December 1942. Before the startup
of the first production reactor in Hanford, three further research reactors were constructed; at Argonne, with
a power of 20 kW (March 1943), CP-2; Clinton, 1000 kW (November, 1943); and X-10 at Oakridge, 3800 kW
(November 1943).
After the startup of the first Soviet reactor, F-1, the first production reactor was built and brought into
operation in record time in 1948, omitting the construction stage of intermediate expensive facilities.
As the Americans themselves wrote, from the time of the decisive experiments on the chain reaction, the
USA required 3.5 yr to the construction of the plutonium reactor at Hanford. In the Soviet Union, this problem
was solved in 2.5 yr.
The construction of the F-1 reactor served as the start of the general development of work on the peace-
ful use of atomic energy. The world's first nuclear power station was started up in the USSR (in April 1954).
Then reactors were built with a unit power from 240 MW to 1000 MW for nuclear power stations, reactors for
icebreakers, etc. The Soviet Union is operating nuclear power stations and is continuing, withever-increasing
tempo, the construction of new nuclear power stations. Among them are nuclear power stations with high
capacity reactors; Leningrad, Novovoronezh, Kursk, Chernobyl'sk, Smolensk, Ignalinsk, Rovensk, Kol'sk,
Armyansk, etc. With the assistance of the Soviet Union, nuclear power stations have been constructed and
continue to be constructed in the countries of the CMEA countries and in Finland. In the Tenth Five-Year Plan,
the capacities of the nuclear power stations brought into operation in the USSR will be increased by almost a
factor of four, by comparison with the previous five-year plan.
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DIFFERENCE-SCHEME SOLUTION OF
HETEROGENEOUS-REACTOR EQUATIONS
B. P. Kochurov and V. M. Malofeev UDC 539.125.52:621.039.51.12
The equations of a heterogeneous reactor with point sinks and sources were first formulated in [1, 2],
and the literature devoted to heterogeneous methods of calculation is now very extensive. General hetero-
geneous equations, taking into account the finite dimensions of the blocks and including the dipole formulation,
are given in [3, 4]. The equations of heterogeneous theory are in matrix form, so that the calculation time and
the demands on computer storage capacity increase quadratically with the number of blocks, and hence reactors
with more than a few blocks cannot be effectively calculated even using up-to-date computers.
The homogeneous equations have a finite-difference form and so can be applied to large reactors with
several thousand lattice points. In [5, 61, a finite-difference formulation of the sink?source equations was
proposed. The main terms of these equations have the usual finite-difference ',homogeneous form," while the
correction terms depend on more distant points and take into account heterogeneous effects.
Recently, the so-called quasialbedo method was proposed [7]; Elementary solutions are constructed in
each cell and combined so as to give maximum smoothness of the total solution in the reactor. This method
allows heterogeneous reactors with a large number of blocks to be calculated. However, the derivation of
these equations is rather complex, and furthermore their relation to heterogeneous theory is not sufficiently
clear.
The present paper proposes a method for the direct transformation of the heterogeneous equations to
finite-difference form. The approach employed is similar to that of [5, 6], but the formal transformation of the
initial heterogeneous equations considerably simplifies the procedure. The use of difference operators with
free parameters, chosen as so to give the most complete elimination of distant terms, leads at once to differ-
ence equations directly related to the initial heterogeneous equations. These equations are derived without
resorting to concepts such as the mean flux in the reactor cells.
The appropriate difference operator providing sufficient (and in fact very high) accuracy is found to be
broader than the traditional Laplace operator (the difference scheme for a square lattice should include not less
than nine points, which agrees with the results of [7]), so that a member of widely used "horhogeneous" algo-
rithms for the solution are inapplicable. However, the Chebyshev iterational method is completely suitable in
this case, and was successfully used in the present work.
Formulation of Heterogeneous-Reactor Equations
In place of the point theory of sinks and sources, a general formulation of the heterogeneous equations in
the small-group (with a total of G groups) approximation is used (see [3, 4, 8]). The distance between the sur-
faces of the blocks is assumed to be several times larger than the free-path length of the neutrons in the
moderator, while the boundary conditions at the block surfaces are specified in sufficiently general form by
the matrix A
dN = AN; d p (0 lar)Ir=o?
(1)
Here N is the vector of extrapolated values of the neutron flux, of dimensionality G x K; K is the number of
blocks; A is a matrix diagonal ink, consisting of G x G matrices for blocks of each kind; p is the matrix of
block radii. The group fluxes in the moderator satisfy the system of equations
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 87-90, February, 1977. Original article sub-
mitted April 23, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. .4 copy of this article is available from the publisher for $7.50.
95
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TABLE 1. Dependence of Results for Eq. (14)
on z for Nine-Point Scheme in Square Lat-
tice
Z
(Xi
0
Bo
Ri
R2
K0
e
0,1
0,64250,9966--7,730
2,732
0,7614
2,427
1,634-3
0,5
0,64371,020 --2,846
1,706
0,4719
0,924
1,535-3
1,0
0,64771,086 ?1,259
1,283
0,3441
0,421
1,279-3
2,0
0,66241,385 --0,330
0,906
0,2122
0,114
0,667-3
3,0
0,68342,039 ?0,100
0,731
0,1362
0,035
0,259-3
4,0
0,70803,381 ?0,032
0,636
0,0876
0,011
0,081-3
(A-4)n,? g =1, . . . G, (2)
where = 1/7-g; =1/L2; and the parameters ng (g < G) differ from the corresponding moderator densities by
a factor Tg/DG (DG is the diffusion coefficient of the thermal neutrons; 7-g, and L2 are the squares of the decel-
eration and diffusion lengths in the moderator). The general solution of the system in Eq. (2) for a reactor
height H is
N C A, (3)
where the triangular matrix (assuming that energy losses in neutron?moderator collisions are less than the
group width) consists of the elements
C gg = C gg, = VggYC g? I, g,;
(4)
vgg'==tg-Ag--4')(g> g');
A is an arbitrary vector of dimensionality K x G; the matrix of dimensionality (K x G) x (K x G) (diagonal in
g, 1 S g S G) consists of weighting functions depending on the boundary conditions at the external surface of the
reactor. Since the boundary conditions may be formulated using hypothetical sinks and sources situated outside
the reactor in an infinitely extended moderator, while boundary conditions are taken directly into account in the
difference formulation, it is sufficient to take the weighting function in an infinite moderator. In this case the
use of the summation theorem for Bessel functions gives
(5)
where Ko and I are matrices diagonal in k with elements
K0(xgpk), Io(x,pk);
x2 = e 72/H2; and the elements of the matrix F are
g g
Ff,i? Ko(xg I rk? ri I) (1 ? 61,1)?
Applying the boundary conditions in Eq. (1) to Eq. (3), we find
dN=dCS--A? Cd,F A;
d '317-= dKo+ dI04-1- (10F +Ko? Ko) =
= ? dI01-0-1C-iC.F;
dN = ?CI-o-lA+CdIoto-W-1N = AN;
A = yN; v= ?10C-1A?dI0C-1.
Here the expression for the Wrciskian of a Bessel function is used
dK0?d/0/VK0=
Substituting A in Eq. (3) gives
96
N =C,FTN.
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(6)
(7)
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TABLE 2. Basic Reactor Characteristics
Parameter
Reactor
1
2
3
No. of groups
2
3
3
Reactor radius, cm
650
500
105
Spacing, cm
26
20
- 8,5
Growth of neutrons,
cm2
100
40; 80
80; 40
Square diffusion
length, cm2
10000
5000
10000
No. of channels
55; 2
124; 20; 77
124; 97
Fuel-channel radius,
5,7;2.9
5; 3; 5
3; 3
C1/1
Equations of similar structure in which N appears but A does not were formulated in [3, 4] in a rather different
form.
If we separate out from y a part yi proportional to the source of fission neutrons and divide it by the
eigennumber, the effective multiplication factor A. making the reactor critical (i.e., if we make the substitution
y y ? y2), the equation for N takes the form
(8)
Note that the matrix y is related to the matrix A by the simple transformation in Eq. (7), affecting each
type of block individually.
Transformation of Heterogeneous-Reactor Equations
to Difference Equations
We now pass to a difference formulation of Eq. (8). Introducing an arbitrary (diagonal in k and g) matrix
D* and bearing in mind Eq. (5), Eq. (8) may he transformed to give
UN = (IVK + F) (Ti/k)AT?(F-1- D) 72N; (.7 ? V2.
For the variable SI = UN, we obtain the equation
/V.= (411C0+F) ? (F D) y-21\7;
171,2=
(9)
(10).
(11)
The matrices '71,2 are related to y1,2 by simple transformations individually for each type of block and serve as
effective characteristics for N. Note that Eq. (10) has the structure of the equation for point blocks, although
this was not assumed in the initial theory; characteristics associated with finite blocks are included in 71,2.
The aim of the transformation leading to Eq. (10) is to obtain the matrix F in Eq. (6) as the first operator
in the left-hand side.
Replacing rk by an arbitrary vector r in the elements F leads to the condition (if r r1)
(A,? Fg(r, 11)=0.
This equation will be approximately satisfied if a difference operator which contains the operator al acts on
the variables rk. The operator Ai replaces the Laplacian in the grid of lattice points (a is the lattice spacing)
(A1-4a2) F( r, 1.1) ^.-2, 0; 1k1? 1I> 1;
?>- (Ea fic-FQei 41k) !t et 12,
(12)
*The matrix D is introduced so as to preserve the structure of the equation, but may affect the rate of conver-
gence of the iterative process; so far it has been assumed that D = 0.
97
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where el = (1. 0), while Q specifies rotation of the vector by 0, 90, 180, and 2700.
We now drop the requirement that the operator in Eq. (12) be exactly the Laplace operator on the grid,
and demand simply that it be constructed "locally," i.e., relate only a few adjacent points. In addition, of
course, it is required to be symmetric with respect to rotations around lattice points k on the grid that return
it to its original position. For a square lattice, we may take an operator P (diagonal in g, with elements Pg)
relating to values of the functions on adjacent blocks
g k Ct2A2.--- ? ? ? ? ?a1+
-F6xg2e)fk;
ai =1; a(a1,
i=1
-1)?
(13)
The operator a2 differs from al in the replacement of el = (1,0) by e2 = (1, 1), i.e., ,a2 includes the series of
blocks immediately following k, etc. For example, in the case of a nine-point scheme, Pg contains only A1, A2,
and a2 = 1 ? ai. We denote by Uk the set of adjacent indexes covered by the operator Pg.
The parameters a and g in Eq. (13) are required to provide the most complete elimination of the elements
Fki outside Uk. Since Fki is invariant with respect to shifts of the lattice, to find a and g it is sufficient to con-
sider the case k = 0. It is possible to adopt various criteria, but previously two have been used in the metrics
Lc? and L2
max I P g (a, 13) pg, min, 1 q yo;
E [Pg (a, is) FL 112 ??- Dahl, I quo,
(14)
(15)
where 1 runs through a sufficiently large set of points, including the point 0. If the operator P(a, 6) obtained
from Eqs. (14) and (15) operates from the left on both sides of Eq. (10) then, for each k, it results in approxi-
mately complete elimination of all the elements of the matrix in Eq. (10) outside the region Uk. On the other
hand, the elements of Fkpl E Uk, are not eliminated. We denote by R the result obtained when P (a, 6) operates
on Fkpl E Uk
R P (cc, 6) (F + D).
In place of Eq. (10) we obtain
(16)
(P+ [P D) + 13] ()A) K r (17)
neglecting the results obtained when P operates on Fki, 1 E U.
The structure of Eq. (17) is that of a difference equation: for each k, the effect of the operators P and R
is concentrated in the region Uk, and the other matrices ? j72, (I-01K0 ? D) ? are diagonal in k. Note that
the structure of the matrix By2 is triangular in g.
By extending the region Uk, i.e., adding new series of blocks and correspondingly enlarging the set a,
6 with new parameters, it is possible in principle, to eliminate the operator F ever more precisely outside Uk.
If F is a short-range operator (i.e., in epithermal groups), it may be left in the initial form, as in Eq. (10).
Although the given theory was developed in a monopole approximation, it may also be used for hetero-
geneous equations in a dipole formulation. Symbolically, Eqs. (8) and (10) are unchanged, but the matrix F
must be extended by elements of the form
K,, (xg Frk ? I) exp (in Ipki); n --= ? 1, (18)
where ipk1 may be taken to be the angle between some fixed direction and the vector (1 ? k); it is again possible
to apply a procedure of the form of Eq. (14) or (15), leading to a difference equation similar to Eq. (17). Evi-
dently the theory is also applicable to reactors with blocks at the points of a triangular or hexagonal lattice.
The solution of Eq. (14) or (15) depends only on a single parameter z ==- xga. Table 1 gives solutions of
Eq. (14) (the parameters al and /3; the elements of the operator R at the points 0, el. and e2; values of the Bes-
sel function Ko(z); the maximum error E =max IPFI, 1 E Uk forvarious values of z, for a nine-point scheme in
a square lattice. The difference of 6 from 1 characterizes the extent to which the operator P differs from the
operator al ? z2; the value of Ko(z) shows how far the effect of the initial operator F extends. Note that the
elements of the operator Rare of opposite sign to the elements of P and on the whole, as is clear from a com-
parison with the homogeneous equations, Ry2 characterizes the mean-square migration length of the neutrons
in the reactor lattice (and not purely in the moderator).
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Method of Solving Difference Equation
The solution of Eq. (17) was programmed in a monopole, small-group approximation for a square lattice
using nine- and five-point schemes. Iteration of sources was used, with acceleration by the Chebyshev method
in conjunction with the Chebyshev method for internal iteration [9]. The set of Chebyshev parameters for inter-
nal iteration was determined after a preliminary estimate of the limits of the operator spectrum
Ag Pg+Rgy,, gg.
(19)
As shown by trial calculations, the limits of the operator spectrum Ag always lie on the real axis of the com-
plex plane and are positive, which is necessary for convergence of the internal iteration. Adding the operator
RgrY.-2 gg to Pg leads to narrowing of the limits of the spectrum and improved convergence.
Numerical Comparison with the Direct Method
The solution of Eq. (17) was compared numerically with results obtained by direct solution of Eq. (8) by
a modification of the DIGGER program [8] for a BESM-6 computer and FORTRANfor acylindricalreactor of
radius Rr with correspondingly altered weighting functions.
For a five-point scheme, the error a is large ? two orders of magnitude higher than the corresponding
figures in Table 1 for the nine-point scheme. This leads to considerable disagreement with the direct method
? usually up to a few percent in the neutron flux, and an order of magnitude higher in the eigennumber.
However, the accuracy obtained using the nine-point scheme is good: As a rule, the differences in the
group fluxes of neutrons (thermal and epithermal) do not exceed a few tenths of a percent, and those in the
effective multiplication factor for the neutrons amount to a few hundredths of a percent. Table 2 gives basic
characteristics for three reactors. The differences in the multiplication factor and the maximum difference
in the neutron flux by Eq. (8) (the direct method) and Eq. (17) (the difference method) are as follows: for the
first and second reactors, less than 10-4 and less than 10-3; for the third reactor, 2.5 ?10-4 and 1.4 ? 10-3, re-
spectively. In the first reactor, the active zone had channels typical for a heavy-water reactor using natural
uranium with gas cooling [10] and two asymmetrically positioned regulators; the reflector was taken to be
large enough to exclude small differences in the description of conditions at the external reactor boundary in
the direct and difference methods (in the latter case, the circular boundary was approximated by a discon-
tinuous line). In the active zone of the second reactor, blocks with a moderator and a certain number of light
absorbing rods and hollow tubes were used. The third reactor was small, and contained blocks with a modera-
tor and some heaVy regulators.
Thus, by means of the proposed difference method, it is possible to obtain the solution of heterogeneous-
reactor equations (for a square lattice, a scheme with no less than nine points should be used) with an accuracy
that is entirely satisfactory in practice.
LITERATURE CITED
1. A. D. Galanin, in: Proc. International Conference on the Global Use of Atomic Energy (Geneva, 1955)
[Russian translation], Vol. 5, Izd. AN SSSR, Moscow (1958), p. 571.
2. S. M. Feinberg, ibid., p. 578.
3. T. Auerbach, EIR-200, Eidg. Inst. f. Reaktorforschung, Wiirenlingen, Switzerland (1970).
4. A. D. Galanin, Theory of Heterogeneous Reactors [in Russian], Atomizdat, Moscow (1971).
5. D. Blackburn, in: Proc. EAES Symposium on Advances in Reactory Theory, Vol. 2, Karlsruhe (1963).
6. D. Blackburn and C. Griggs, in: Proc. Conference on Applications of Computing Methods to Reactor
Problems, ANL-7050, Illinois, May 17-19 (1965), p. 231.
7. S. S. Gorodkov, Preprints lAt- 2251 and IAE-2296 [in Russian], Moscow (1973); Preprint IAE-2502 [in
Russian], Moscow (1975)?
8. B. P. Kochurov, Preprint ITEF- 2 [in Russian], Moscow (1974).
9. V. I. Lebedev and S. A. Finogenov, Zh. Vychisl. Mat. Fiz., 13, No. 1, 18 (1973).
10. V. M. Abramov et al., At. Energ., 36, No. 2, 113 (1974).
99
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GAS-THERMAL TREATMENT OF NUCLEAR POWER-STATION
FUEL ELEMENTS TO SEPARATE THE CORE FROM
THE CAN
G. P. Martynovskikh, A. T. Ageenkov,
M. M. Arduanov, A. F. Bogatov,
E.M. Valuev, V. F. Savel'ev,
V. A. Chemezov, G. I. Chechetin,
and Yu. V. Yastrebov
UDC 621.039.546.3:66.094.16.0015
The removal of irradiated fuel-element cans has been considered in a large number of investigations, and
a great deal of laboratory and experimental equipment for mechanical, chemical, electrochemical, pyrochemi-
cal, pyrometallurgical, and combined test methods has been developed [1].
In order to remove the cans of nonirradiated, unconditioned fuel elements, mechanical cutting is usually
employed [2]. Such methods fracture a considerable number of the fuel briquets, which become unfit for a sec-
ond charging; this seriously harms the technological-economic indices of fuel-element production.
The aim of the present investigation is to study methods of processing unconditioned fuel elements of the
VVER and RBMK types so as to be able to extract the fuel briquets from the cans without damage.
As a means to this end we took the method of hydrogen treatment (hydrogenation of the fuel elements) [3-
51, which produces considerable changes in the physicochemical and mechanical properties of cans made from
the zirconium alloy Zr-1% Nb f6, 71 and at the same time creates favorable conditions for freely emptying the
fuel briquets by enlarging the annular gap between the core (oxide fuel briquets) and the hydrogenated can.
0 15 50
Time, min
Fig. 1
45
60
2,
5 1,
a)
'a 40
0
0
(50 0,5 1,0 1,5 230 215
? Length of can, m
Fig. 2
Fig. 1. Kinetics of the absorption of hydrogen by the Zr-1% Nb alloy can;
1, 2) at 770? and 700?C for a hydrogen pressure in the apparatus of 200-
500 and 10-30 mm Hg, respectively.
Fig. 2. Hydrogen distribution in a Zr-1% Nb alloy can after saturation for
60 min. Notation as in Fig. 1; arrow indicates point of hydrogen supply.
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 91-93, February, 1977. Original article sub-
mitted June 21, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West-1-7th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
100
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60
40
to 0
2
0
-
? 3
.
. ?
?
ab
.
Ad
7100
0 ?
B
o
0
_
q5 1,0 1,5
Hz content, wt. 10
Fig. 3
20
10
Ad
?d 100%
4,0
2,0
0 0
20
Fig. 4
Fig. 3. Effect of hydrogen content on the tensile strength ab and relative elongation (5 of the
alloy Zr-1% Nb and increment in the can diameter (ad/d)?100.
Fig. 4. Mechanism for removing the end sections from the fuel elements after hydrogen satu-
ration of their cans.
TABLE 1. Final Hydrogen Content of Can
Material after Thermal Degassing at Rare-
faction of 5 .10'2 mm Hg
Exptl. conditions
Hydrogen content
temp.
duration,
h
of can, wt.%
600
1,0
0,90
600
3,0
0,29
800
1,0
0,03
800
3,0
0.01
900
1,0
,
60 0 30
60 ;min
Fig. 2. Thermographs of highly active waste products: a) chemical
absorbent, dry; b) chemical absorbent, moist; c) sorbent, dry; d) sor-
bent, moist; e) ash, dry; f) ash, moist.
Thus the rate of volatilization was either much smaller than or close to 10-6 g/(cm2 -day). A study of the
extraction of the radionuclides (with water) from the solid waste products showed that a considerable propor-
tion of the activity of the fission products passed into the water even after a brief contact period. The extrac-
tion rate of 137Cs reached 3.8 '10-1-8.0 ? 10-1 g/(cm2- day).
The foregoing results enable us to determine the conditions relating to the storage of waste products
arising from the reprocessing of fast-reactor fuel elements by the gas-fluoride method.
When such waste products (especially the ashes) are to be stored for a long time without preliminary re-
processing, it is essential to allow for rapid evolution of radionuclides from the ashes, as well for their hygro-
scopic properties and inadequate thermal stability and the existence of fluorine-containing gases over the ash.
All this makes it a vital matter to hermetize the vessels used for storing the waste products, to select corro-
sion-resistant materials for the vessels, and to provide for their hydraulic insulation and heat release.
The foregoing experimental data regarding the properties and behavior of the waste products may also
be useful in preparing waste for prolonged burial.
LITERATURE CITED
1. L. J. Anasatia et al., US Patent No. 3753920 (1973).
2. J. Peka, in: Third COMECON Symposium on the Reprocessing on Irradiated Fuel, Marianske Lazne (April
22-26, 1974), Paper No. ML 74/2.
3. V. V. Kulichenko, N. V. Krylova, and Yu. P. Martynov, in: COMECON Symposium onthe Reprocessing of
Irradiated Fuel, Vol. 1, Atomic-Energy Commission, Czechoslovakian SSR, Prague (1972), p. 60.
4. A. P. Kirillovich, P. S. Gordienko, and V. P. Buntushkin, At. Energ., 40, No. 5, 427 (1976).
5. L. G. Berg, Introduction to Thermography [in Russian], Nauka, Moscow (1969).
6. Yu. G. Lavrinovich et al., Zh. Prikl. Khim., No. 12, 2083 (1975). ?
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PHYSICOCHEMICAL PROPERTIES OF MELTS
COMPRISING MIXTURES OF URANIUM
TETRACHLORIDE WITH THE CHLORIDES
OF ALKALI METALS
V. N. Desyatnik, S. F. Katyshev, UDC 532.148.608
and S. P. Raspopin
The density and surface tension of molten mixtures of uranium tetrachloride with chlorides of
the alkali metals were measured by the "maximum gas-bubble pressure" method over the whole
range of uranium tetrachloride concentrations.
It is well known that molten halides of the alkali metals form typically ionic liquids; their structure may
be represented as a mixture of complex ions of the MeXr type (Me = cation of an alkali metal, X = halide F,
Cl, Br, or I), "free" Me cations, and vacancies, the mutual disposition of which obeys no special order but is
governed by the laws of statistical distribution [1, 2].
The intrinsic complex structure may also be extended to the molten chlorides of polyvalent metals. How-
ever, in contrast to the halides of monovalent metals, the existence of "free" cations, U(IV) in particular, is
improbable because of their high polarizing capacity. It is more likely that in this case the melt will consist
of complex anions, complex cations, and vacancies.
When uranium tetrachloride is mixed with the chlorides of alkali metals there should be a considerable
redistribution of the bonds in the complex groupings. This in turn should reflect on the physicochemical prop-
erties of the mixtures. Thus the melting diagrams of mixtures of uranium tetrachloride with the chlorides of
the alkali metals are characterized by both congruently (Me2UC16) and incongruently (Me3UC14, MeUC15) melting
compounds [3-5].
The density and surface tension are important physicochemical characteristics, a knowledge of which is
essential in the solution of both practical and theoretical questions; in particular they enable us to establish the
manner in which uranium tetrachloride interacts in the molten mixtures and to assess the most probable form
of existence of the complex uranium ions in these melts.
The density of mixtures of uranium tetrachloride with the chlorides of alkali metals was earlier studied
by the method of hydrostatic weighing [6]. The density of pure uranium tetrachloride was measured by means
of a quartz pycnometer [7] and also by measuring the maximum pressure in a gas bubble [8].
TABLE 1. Density of the Molten Chlorides TABLE 2. Density of Uranium Tetrachlo-
ride, g/cm3
Molten
p = a ? bT, g/cm3
Temp.
saltrange,
a
b.103
1 8.104
I<
L1C1
1,8337
0,4317
11
888--1102
NaCI
2,1332
0,5405
10
1076--1273
K.C1
2,1751
06030
9
1050-1240
RbC1
3,1069
0,8799
13
1012--1142
CsCI
3,7776
1,0716
11
922--1125
Temp., ?C
Expt.
[6]
[7]
590
3,647
3,571
3,50
600
3,624
3,552
3,48
650
3,509
3,454
3,40
700
3,394
3,357
3,30
750
3,280
3,260
3,20
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 99-103, February, 1977. Original article sub-
mitted March 29, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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TABLE 3. Density and Surface Tension of Molten Mixtures of Uranium Tetrachloride
with Chlorides of the Alkali Metals
Conon. of HC14,
mole
p=a-bT?S. g/cm3
= ao - cT?S. mJ/m2
Temp, range,
?K
a
b.103
System LiC1-UC14
0,0
1,8807
0,4317
0,0011
888-1082
0,0
185,64
0,06309
0,04
902-1075
5,0
2,3445
0,5692
0,0012
132,53
0,04473
0,04
885-985
11,8
2,9844
0,8920
0,0015
113,43
0,04230
0,08
845-937
20,8
3,3512
0,9437
0,0014
102,37
0,03469
0,03
812-908
24,3
3,9846
0,9846
0,0021
101,15
0,03492
0,05
787-926
33,2
3,8140
1,1146
0,0012
96,14
0,03513
0,05
748-871
42,8
4,0705
1,2063
0,0014
86,43
0,03008
0,04
773-920
54,7
4,3478
1,3966
0,0030
83,27
0,03419
0,03
785-905
63,0
4,4816
1,4555
0,0014
86,51
0,04165
0,06
778-904
69,0
4,6067
1,5373
0,0016
86,79
0,04664
0,09
806-926
82,0
5,0017
1,8313
0,0011
100,17
0,06338
0,08
829-941
100,0
5,6251
2,2924
0,0021
105,94
0,07567
0,10
891-998
SystemJNaC1-1.1C14
0,0
2,1332
0,5405
0,0010
-
1076-1273
0,0
--
193,63
0,07403
0,02
1090-1242
3,0
2,4533
0,7141
0,0009
169,74
0,06191
0,05
1086-1176
10,0
2,9055
0,8700
0,0012
138,92
0,05481
0,04
1062-1165
20,0
3,2593
0,9002
0,0023
116,26
0,04180
0,05
995-1104
30,0
3,6016
1,0076
0,0013
107,17
0,03878
0,03
826-950
33,3
3,6492
1,0020
0,0012
100,87
0,03474
0,04
772-926
40,1
3,9074
4,1469
0,0008
100,78
0,04005
0,04
741-904
50,0
4,0630
1,1922
0,0024
89,75
0,03594
0,02
793-893
60,1
4,1815
1,2188
0,0017
88,06
0,04030
0,04
762-917
69,1
4,3855
1,3380
0,0018
89,44
0,04479
0,04
773-898
70,1
4,4030
1,3384
0,0021
__
814-898
80,6
5,0030
1,8630
0,0015
94,72
0,05771
0,05
811-899
90,0
5,1948
1,9930
0,0017
99,70
0,06596
0,05
843-948
System KCl--U[C14
0,0
2,1751
0,6060
0,0009
170,61
0,06922
0,05
1050-1240.
5,0
2,4133
0,6467
0,0018
140,40
0,05408
0,06
1041-1160
16,0
2,9156
0,7978
0,0005
124,18
0,04886
0,04
987-1087
25,0
3,1907
0,8607
0,0015
112,78
0,04110
0,05
843-994
33,3
3,3889
0,8917
0,0015
105,41
0,03982
0,03
925--1054
39,7
40,0
3,5880
3,5373
0,9879
0,9260
0,0016
0,0006
-
96,44
0,03715
0,01
823-947
827-946
47,5
3,7947
1,0816
0,0018
-
657-909
50,0
3,8454
1,1017
0,0012
96,76
0,04424
0,04
688-917
57,0
4,1073
1,2821
0,0020
95,23
0,04770
0,03
758-887
60,0
4,1743
1,3098
0,0010
96,96
0,05050
0,02
744-933
71,0
4,5403
1,5502
0,0024
94,92
0,05339
0,02
808-919
75,6
4,7108
1,6705
0,0014
98,55
0,05830
0,04
816-933
89,0
5,2549
2,0808
0,0019
101,70
0,06610
0,05
867-960
System RbC1-1JC14
0,0
3,1069
0,8799
0,0013
155,59
0,06434
0,07
1012-1141
11,6
3,3316
0,8589
0,0013
131,36
0,05733
0,07
957-1079
19,9
3,4593
0,8559
0,0014
119,79
0,04821
0,03
859-989
24,3
3,5412
0,8804
0,0015
-
835-991
25,0
3,5449
0,8759
0,0010
109,56
0,04177
0,06
872-1020
33,3
3,7453
0,9834
0,0011
106,37
0,04120
0,07
914-1018
36,5
3,7730
0,9800
0,0015
-
40,0
3,7992
0,9820
0,0016
1110,33
0,03900
0,06
823-940
48,3
50,0
4,0739
4,0464
1,2061
1,1597
0,0020
0,0021
-
90,30
0,03539
0,07
678-828
700-909
59,8
4,3307
1,3808
0,0019
85,43
0,03718
0,05
680-921
64,4
4,4903
1,5080
0,0028
88,67
0,04217
0,07
729-897
82,9
5,0041
1.8418
0,0016
94,38
0,05670
0,07
800-918
System CsC1-IJC14
0,0
3,7776
1,0716
0,0013
155,50
0,07208
0,06
922 --1125
9,7
3,9260
1,1237
0,0014
141,70
0,06707
0,06
898-1049
15,2
3,9739
1,1288
0,0015
133,42
0,06344
0,03
849-937
17,1
3,9961
1,1328
0,0017
-
813-933
20,7
4,0390
1,1549
0,0033
119,32
0,05351
0,06
837-938
27,8
4,0940
1,1554
0,0020
120,46
0,05536
0,07
883-978
33,2
4,0992
1,1519
0,0021
117,62
0,05523
0,02
941-1041
38.0
4,2199
1,2576
0,0020
110,61
0,05060
0,03
889-980
45,1
4,3147
1,3206
0,0027
96,73
0,03982
0,06
853-937
50,0
4,3038
1,2881
0,0019
97,17
0,04362
0,08
804--916
56,6
4,3872
1,3380
0,0012
92,32
0,04090
0,07
768-922
60,3
4,4550
1,3972
0,0010
88,28
0,04025
0,06
729-912
67,2
4,8184
1,-7390
0,0041 -
86,69
0,04147
0,09
816-895
77,0
5,0408
1,9083
0,0013
95,87
0,05648
0,09
837-898
85,3
5,3414
2,1268
0,0033
99,14
0.06255
0,09
854-916
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In this paper we shall present the results of our own measurements of the density and surface tension of
binary mixtures of uranium tetrachloride with the chlorides of the alkali metals over the whole range of UC14
concentrations. For these experiments we first prepared the alkali metal chlorides and uranium tetrachloride
in pure form. The melting points of these original samples agreed closely with published data [9]; to an error
of ?2?C they were equal to 610, 800, 770, 715, 645, and 590?C for LiC1, NaC1, KCI, RbC1, CsC1 and UC14 respec-
tively.
The density and surface tension of the molten mixtures were studied by a method based on the maximum
pressure in a gas bubble. The working gas was argon, carefully purified from any traces of moisture or oxy-
gen by passing over titanium and zirconium sponge at 800-900?C and over metallic calcium heated to 600-650?C.
The height of the liquid column in the manometer was measured with a KM-8 cathetometer to an error of
-?0.015 mm. As capillaries we used beryllium oxide tube with an internal diameter of 1.5-2.0 mm. The depth
of vertical immersion of the capillary into the melt was regulated with a micrometer screw having a scale
division of 0.01 mm. The vertical positioning of the capillary was verified before each experiment. Before
the beginning of the experiment the capillary walls were sharpened to form a knife-edge no thicker than 0.1
mm. The time required for the formation of a bubble was 40-60 sec.
The density was calculated from the well-known equation
p = (6.1//ah) P., (1)
where AH is the difference between the maximum pressure in the bubble of manometric liquid at different
levels (cm); ah is the difference between the capillary immersion levels at which the maximum bubble pres-
sure was measured (cm); pm is the density of the manometric liquid (g/cm3).
The surface tension was calculated from the Schrodinger equation
rpmhg 2 rg
2
(2)
where r is the radius of the capillary (cm); h is the rise height of the manometric liquid (cm); p is the density
of the melt (g/cm3); g is the gravitational acceleration (cm/sec2).
In calculating the density we introduced corrections for the thermal expansion of the capillary and for
the change in the level of melt in the crucible on immersing the capillary [10], while in calculating the surface
tension we also made a correction for the depth of immersion of the capillary in the melt. The maximum rela-
tive error of the density measurement was 1.0% and of the surface of erosion measurement 1.5%.
The temperature range of the measurements was limited by the high vapor tension of the tetrachloride
at relatively high temperatures, which naturally led to a considerable change in its composition during the
measurement. The composition of the mixtures was determined by chemical analysis after the experiment.
Within the limits of experimental error, the temperature dependence of the density of the chlorides and
chloride mixtures may be described by the equation p = a?bT. The numerical values of the coefficients deter-
mined from the experimental data by the method of least squares are given in Tables 1 and 2. The values ob-
tained for the pure chlorides (Table 1) agree closely with the results of other authors [9].
The standard deviations were calculated for all the salts and mixtures studied from the equation
S = I (Xexpt? Xcalc)2/(n ? P), (3)
where IC
?expt and Xcale are the experimental and calculated densities at each temperature; n is the number of
experimental points; p is the number of coefficients in the equation.
The values obtained for the density of molten uranium tetrachloride agree most closely with those given
in [6] (Table 2).
The results of our measurements of the density and surface tension are presented in Table 3. If we con-
struct the density isotherms for the systems in question, we find that the density of the mixtures increases
monotonically as the concentration of uranium tetrachloride in the melt increases; the experimental values
deviate from the additive law in the sense of greater values for the systems incorporating LiC1, NaC1, and
KCI, while the density isotherms of the RbC1?UC14 and CsCl?UC14 systems have an S configuration.
On analyzing the molar volumes we find a relative deviation from the linear relationship in the direction
of higher values; the maximum deviation occurs at about 60 mole% UC14 in each system. The similar behavior
of the isotherms representing the deviations from additivity in clearly implies monotypic structural changes in
all these systems.
110
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It is quite evident that on mixing melts containing different cations there is a preferential formation of
complex groupings based on the cation with the greater polarizing capacity. In this case the positive devia-
tions of the molar volumes from additivity are associated with the formation of complex uranium ions of the
UC1(x-4)- type. The formation of complex uranium ions in molten uranium chloride mixtures with the chlo-
rides of the alkali metals is confirmed by the results of a study of other physicochemical properties and also by
theoretical calculations [3, 5-7, 11-151. Thus when studying the absorption spectra of mixtures of the alkali
metal chlorides with uranium tetrachloride at least two forms of complex uranium ions were encountered;
UC1r, UC1(xx-4/- (x = 0-4) [11, 131.
The maximum deviation of the molar volumes from additivity increases linearly with increasing radius
of the alkali metal cation. The negative deviations of the thermodynamic properties [3, 12] and the equivalent
electrical conductivity [6] are augmented with increasing radius of the alkali metal cation, while the diffusion
coefficients decline [14]. This indicates that with increasing radius of the alkali metal cation the interaction ,
of uranium tetrachloride with the alkali metal chlorides intensifies. The complex uranium groupings will, in
fact, be more stable if a cation with a smaller ionic moment appears in the second coordination sphere.
The results show that the surface tension falls sharply with increasing proportion of UC14 in the mix-
tures. We may conclude from the character of the surface-tension isotherms that UC14 is a surface-active
substance in all the systems studied. There is a slight bend on the surface-tension isotherms corresponding
to the chemical compound Me2UC16 on the phase diagrams. This is evidently associated with the formation of
complex UCli- ions in the melt, these being surface-active with respect to the chlorides of the alkali metals
but being surface-active with respect to the chlorides of the alkali metals but inactive with respect to uranium
tetrachloride. The surface-tension values close to the bend differ very little from one another, which indi-
cates the concentration of monotypic complex uranium ions in the surface layer.
On the basis of the foregoing experimental data we determined the adsorption of uranium tetrachloride
in the surface layer from the well-known equation
r
N (1? N) da
?
RT dN '
(4) '
where N is the molar proportion of the surface-active component in the volume; a is the surface tension. The
adsorption curves for the melts of all the systems have two considerably differing maxima. As the ionic mo-
ment of the alkali metal cation increases from Cs+ to Li+, the maximum adsorption of uranium ions in the
range 0-20 mole % UC14 increases from 1.26 to 2.99 -10-6 mole/m, the maximum being displaced in the direc-
tion of smaller UC14 concentrations. This agrees closely with V. K. Semenchenko's conclusions [16] to the
effect that the surface activity of the components is determined by the ratio of their generalized moments.
The cations with a large ionic moment have a greater "displacing" power with respect to the uranium ions,
and saturation of the surface layer with the surface-active component takes place at smaller concentrations
of the latter in the interior of the melt.
The second maximum on the adsorption isotherms corresponds to the adsorption of more complex uran-
ium groupings of the UClr type.
Thus we have demonstrated on the basis of density and surface-tension measurements carried out on
molten mixtures of uranium tetrachloride with the chlorides of the alkali metals, together with computed data,
that complex uranium groupings of the UC1(xx-4)- type are formed in the molten mixtures, their stability in-
creasing with increasing radius of the alkali metal cation; the grouping with the greatest stability is UC126-.
LITERATURE CITED
1. M. V. Smirnov, 0. M. Shabanov, and A. P. Khaimenov, Elektrokhimiya, 2, No. 11, 1240 (1966).
2. M. V. Smirnov, Electrode Potentials in Molten Chlorides [in Russian], ffauka, Moscow (1973).
3. A. Bogacz and W. Trzebiatowski, Rocz. Chem., 38, No. 5, 729 (1964).
4. V. N. Desyatnik et al., Zh. Fiz. Khim., 46, No. 8, 2159 (1972).
5. T. Kuroda and T. Suzuki, J. Electrochem. Soc. Jpn., 26, Nos. 7-9, 140 (1958).
6. A. Bogacz and B. Ziolek, Rocz. Chem., 44, No. 3, 665 (1970).
7. T. Kuroda and T. Suzuki, J. Electrochem. Soc. Jpn., 29, No. 4, 215 (1961).
8. V. N. Desyatnik, S. P. Raspopin, and I. F. Nichkov, Izv. Vyssh. Ucheb. Zaved., Tsvet. Metal., No. 5, 95
(1969).
9. A. G. Morachevskii (editor), Reference Book on Molten Salts, Vol. 1 [Russian translation], Khimiya,
Leningrad (1971).
10. B. N. Linchevskii, Technique of Metallurgical Experiments [in Russian], Metallurgizdat, Moscow (1967).
111
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11. J. Morrey, Inorg. Chem., 2, No. 1, 163 (1963).
12. A. Kisza, Bull. Acad. Poln. Sci., Ser. Sci. Chem., 12, No. 3, 177 (1964).
13. 0. V. Skiba, V. V. Gushchin, and A. N. Korzh, in: Physical Chemistry and Electrochemistry of Molten
Salts and Slags, Part I [in Russian], Naukova Dumka, Kiev (1969), p. 49.
14. M. V. Smirnov, Elektrokhimiya, 10, No. 5, 770 (1974).
15. V. N. Desyatnik, S. P. Raspopin, and K. I. Trifonov, Zh. Fiz. Khim., 48, No. 3, 776 (1974).
16. V. K. Semenchenko, Surface Phenomena in Metals and Alloys [in Russian], Gostekhteorizdat, Moscow
(1957).
PECULIARITIES IN THE CHEMICAL ETCHING OF
POLYETHYLENE TEREPHTHALATE,
IRRADIATED WITH RADIATIONS WITH VARIOUS
LINEAR ENERGY LOSSES
N. S. Moshkovskii, L. N. Gaichenko, UDC 541.64+678
and Ya. I. Lavrentovich
Polyethylene terephthalate (PETP) is one of the polymers widely used in various fields of technology. In
certain cases materials based on PETP may be subjected to the influence of intense fluxes of ionizing radiation
with various linear energy losses (LEL) and may be in contact with aggressive media during use. Therefore,
the study of processes of interaction of the irradiated polymer with such media is of substantial interest. The
literature contains information concerning nonirradiated PETP. Thus, e.g., the mechanism of hydrolysis of
PETP by solutions of alkali has been studied in the greatest detail [1]; the mechanism of the action of solutions
of sulfuric acid on the polymer has been investigated [2]. There is practically no information on the chemical
influence of aggressive media on PETP preliminarily irradiated with various types of ionizing radiation.
In this work we investigated the peculiarities of chemical etching of PETP irradiated with radiations with
various LEL, in solutions of potassium hydroxide.
Experimental Method. Industrially produced PETP (MAT = 27,000, d = 1.38 gicm3) was used for the inves-
tigation in the form of films 12, 50, and 125 ? thick. The molecular mass MV was determined according to the
formula log Mv = 1.176 log [q] + 3.036 on the basis of data on the viscosity (7j) of solutions of PETP in a mixture
of phenol and dichloroethane (40 : 60) at 20?C [3]. The samples were irradiated under vacuum (10-4-10-5 atm)
at room temperature. For the irradiation we used the y radiation of 60Co, deuterons (13 MeV), and y particles
(23 MeV), which permitted variation of the LEL within broad limits (0.2-50 keV/?).
The absorbed dose in' irradiation was determined with dosimeters of cellulose diacetate and colored
cellophane [4, 51. In the irradiation of PETP with heavy charged particles, the absorbed dose was calculated
on the basis of data on the linear energy losses by the particles in the polymer and the value of their integral
flux [5].
After the irradiation of the film, the PETP was subjected to chemical treatment in aqueous solutions of
potassium hydroxide of various concentrations at the temperatures 20-95?C. In this case samples of the same
size (circles 38 mm in diameter) were loaded into a thermostatically controlled glass flask with the solution
(300 ml), equipped with a reflux condenser. The substantial excess of the alkali solution and mixing ensured
constancy of the alkali concentration near the surface of the sample. After definite time intervals, the samples
were removed from the solution, washed thoroughly in distilled water, dried to constant mass at 60?C, and
weighed with an error of 4 -10'5 g.
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 104-107, February, 1977. Original article sub-
mitted January 7, 1976.
112
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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1,2
46
200 240 280 A, nm 0 40 80 120
retch* min
Fig. 1. Absorption spectrum of hydrolysis products of PETP (a) after etching in
3 N KOH solution with an addition of ethanol; variation of the optical density (b)
at 240 nm with the time of etching for solutions in which irradiated (?) and non-
irradiated (0) polymers were exposed.
160
8
6
6
retch* h
Fig. 2
10
12
3
0 20 40 60 80 100 120
Dose, Mrad
Fig. 3
Fig. 2. Change in the mass of samples of PETP irradiated with the y radiation
of 60Co during hydrolysis in 3 N KOH solution at 85?C. 1, 2, 3) PETP irradiated
with a dose of 20, 50, and 100 Mrad, respectively; 4) nonirradiated.
Fig. 3. Dependence of the rate of etching of -y irradiated PETP on the absorbed
dose (3 N solution of KOH at 85?C).
We also investigated the products of etching of PE TP that passed-into solution. For this purpose, in
several experiments we collected samples of the solution and determined their UV absorption spectra on a
Specord spectrophotometer. The change in the surface of the samples during etching was observed visually
with an MBI-8m microscope in transmitted light.
Results and Discussion. The experiments showed that after chemical etching of irradiated and non-
irradiated samples of PETP in KOH solution, products are detected that absorb light in the UV region of the
spectrum (Fig. la). The concentration of these products increases with increasing time of contact of PETP
with the KOH solution (Fig. lb). According to the literature data [1,6], it can be assumed that a salt of tere-
phthalic acid, which is formed in the hydrolysis of the polymer macromolecules, is accumulated in the solu-
tion. It must be noted that the nature of the UV spectra is the same for solutions in which the PETP samples
irradiated with radiations with various LEL were treated. Evidently the LEL of the radiation does not affect
the composition of the water-soluble products.
The surface of nonirradiated samples and those irradiated with the y rays of 60Co remains practically the
same throughout the entire period of etching. In the case of etching of samples irradiated with heavy charged
particles, in the initial period the formation of a microcontour is observed on the surface, and it subsequently
remains-unchanged. In this case, the surface of the samples becomes dull, since the heavy charged particles
create regions of especially strong radiation damage in the polymer along their track, and these regions are
etched at a higher rate than the remainder of the surface.
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20 40 60 80 100 120 0 20 40 60 80 100 120
Dose, Mrad Dose, Mrad
Fig. 4. Dependence of the rate of etching on the absorbed dose for PETP
irradiated with deuterons (a) and a particles (b) (3 N solution of KOH at
85?C).
TABLE 1. Influence of Temperature on the
Rate of Etching of PETP by a 3 N Solution
Temp., ?C
Dose,
Mrad
Wt. rate of
etching2
mg/cm` ?h
Ratio of rates of
irrad. and initial
samples
65
65
75
75
85
85
95
95
0
5
0
5
0
5
0
5
0,09
0,16
0,23
0,46
0,38
0,78
0,76
1,83
1,83
1,96
2,05
2,40
Figure 2 presents the kinetic data on the change in the mass of samples of PETP irradiated with the y
radiation of 60Co, and kinetic data for a nonirradiated sample, from which it can be seen that the change in the
mass of the samples during etching is directly proportional to the time of contact. Analogous data were also
obtained for samples irradiated with deuterons and a particles, according to which the weight rate of etching
V was calculated.
From Fig. 3 it can be seen that the rate of etching of the samples increases with increasing absorbed
dose of the y radiation of 60Co; moreover, a linear relationship is observed in the region of 1-100 Mrad.
Figure 4 presents the dose dependence of the rate of etching of samples irradiated with heavy charged
particles, which differs substantially from the dependence obtained for y irradiated samples. In the region of
low absorbed doses, the rate of etching increases very sharply, reaching a maximum value in the interval 5-15
Mrad, but then gradually decreases with increasing dose. A comparison of the curves of the dependence of the
rate of etching on the absorbed dose for samples irradiated with deuterons and a particles shows that in the re-
gion of the maximum, the rate of etching of a-irradiated samples is significantly higher than for samples irra-
diated with deuterons. This can be explained by the fact that a particles, possessing a larger LEL than deu-
terons, more substantially disrupt the polymer along their track. The general nature of the change in the rate
of etching as a function of the dose of heavy particles may be due to the fact that in the region of low doses the
polymer is etched, and a microcontour is formed on account of the separated tracks of the particles. In the
case of large absorbed doses, when the track of the particles merge with one another, the rate of etching may
decrease on account of a smoothing out of microinhomogeneities. It is also possible that in the region of large
doses of heavy charged particles, a three-dimensional structure is formed in the PETP on account of cross-
linking of macromolecules; moreover, the effectiveness of this process at the same dose may be substantially
higher in the case of irradiation with heavy charged particles than in the case of y irradiation. The formation
of supplementary cross-links between macromolecules may increase the chemical stability of PETP. A com-
parison of the results shows that the absorbed dose in the track of the heavy charged particle may exceed 100
Mrad (Figs. 3 and 4).
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TABLE 2. Influence of Additives on the
Rate of Etching of PETP
Compos. of
solution
I-)
r
a.
E
0)
E-,
Dose,
Mrad
Wt.
rate of
etching,
mg/
cm2 ?Ii
Ratio of wt.
rates of
etching for
trtai;l. and
Initial sam-
pies
3 N solution of
KOH
3 N Solution of
KOH + 1% sodi-
Lim dodecylsul-
tate
C2H5OH +3 N
KOH (2 : 3)
85
85
65
0
5
0
5
0
5
0,38
0,78
0,21
0,45
0,46
0,80
2,05
2,13
1,74
12
10
6 8 10 12
retch' h
Fig. 5. Change in the mass of PETP sam-
ples irradiated with a particles (*) and non-
irradiated (0), in the process of etching in
KOH solution at 85?C: 1) 1 N; 2) 2 N; 3) 6 N
solution.
Table 1 presents the results for samples of PETP irradiated with a particles with a dose of 5 Mrad and
generalizes the data on the influence of temperature on the process of etching of PETP.
From Table 1 it can be seen that with increasing temperature, the rate of etching of nonirradiated and
irradiated samples of PETP increases substantially, and their ratio increases. On the basis of data on the
dependence of the rate of etching on the temperature, we calculated the effective activation energies [71; they
proved equal to 17.0 and 19.7 kcal/mole for the initial PETP and a sample irradiated with a particles with a
dose of 5 Mrad, respectively.
Figure 5 presents the kinetic curves of the change in the mass of PETP samples treated in aqueous solu-
tions of KOH of various concentrations, from which it can be seen that an increase in the concentration of the
solution increases the rate of etching and the ratio of the rates of etching of irradiated and nonirradiated sam-
ples.
In an investigation of the influence of additives on the rate of etching of PETP in KOH solution, surface-
active substances were introduced, e.g., sodium dodecylsulfate or sodium stearate, and ethanol was also added.
Data on the influence of these additives are cited in Table 2, from which it follows that additions of surface-
active substances to the solution decrease the rate of etching of the initial and irradiated PETP. But these ad-
ditives negligibly increase the ratio of the rates Virr/Vinit. Ethanol increases the rate of etching of the initial
and irradiated samples; however, in this case the Virr/Vinit ratio changes negligibly. The increase in the rate
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of etching by a solution with ethanol may be a consequence of dissolution of hydrolysis products of the polymer
macromolecules by the alcohol and their more rapid passage from the surface into the solution.
Thus, the stability of irradiated PETP in aqueous solutions of potassium hydroxide depends not only on
the absorbed dose, but also on the type and energy of the exciting radiation. In the case of irradiation of PETP
with radiations with increased LEL, its stability is sharply decreased in the region of low absorbed doses,
while in the case of high doses it is somewhat increased and stabilized.
The influence of temperature and alkali concentration on the rate of etching was determined. The data
obtained must be taken into consideration in the use of materials based on PETP subjected to irradiation and
the influence of aggressive media.
LITERATURE CITED
1. T. E. Rudakova et al., Vysokomol. Soedin., Al2, No. 2, 449 (1972).
2. T. E. Rudakova et al., Vysokomol. Soedin., A16, No. 6, 1356 (1974).
3. A. F. Nikolaev, Synthetic Polymers and Plastics Based on Them [in Russian], Khimiya, Moscow?Lenin-
grad (1966), p. 695.
4. Ya. I. Lavrentovich et al., in: Summaries of Reports at the Fifth All-Union Coordination Conference on
the Dosimetry of Intensive Fluxes of Ionizing Radiation [in Russian], Izd. VNIIFTRI, Moscow (1974),
p.
18.
5. Ya. I. Lavrentovich et al., Khim. Vys. Energ., 3, No. 2, 147 (1969).
6. H. Paretzke, in: Proc. Intern. Conf. on Nuclear Photography and Solid State Track Detectors, Bucharest,
Vol. 1 (1972), p. 322.
7. N. M. Emanuel' and D. G. Knorre, Course in Chemical Kinetics [in Russian], Vysshaya Shkola, Moscow
(1969), p.48.
CALCULATION OF THE CHARACTERISTICS OF A
TOKAMAK REACTOR WITH INJECTION OF
DEUTERIUM AND TRITIUM IONS
N. V. Karetkina UDC 533.992
The authors of [1] described for the first time the possibility of building a thermonuclear reactor in
which nuclei are synthesizedby stopping a beam of fast deuterium ions in a cold tritium plasma. This type of
thermonuclear reactor was termeda two-component scheme. Its efficiency in terms of energy was previously
studied in [2, 3] in which the dependence of the ratio of thermonuclear power to injected power upon the energy
of both the injected particles and the plasma temperature was determined.
A three-component scheme of a thermonuclear reactor was described in [4], according to which beams
of high-energy deuterons and tritons are simultaneously injected into a deuterium?tritium plasma with hot
electrons. The investigations included the relatively low electron temperature [4] at which the change in the
distribution function of the deuterium and tritium ions depends upon the slowing down at electrons; but the colli-
sions of the fast ions among themselves were disregarded.
The problem of plasma heating by a beam of high-energy particles was solved in a linear approximation
[4-6], i.e., the injected ions and the plasma ions were separately described. This is correctwhenthe intensity
of the particles injected is smaller than the plasma density.
We consider in the present article the possibility of building a thermonuclear reactor with intense injec-
tion of deuteron and triton beams at a rather high electron temperature. In this case the ions need not be
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 108-112, February, 1977. Original article sub-
mitted March 3, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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Fig. 1. Dependence of the distribution functions of a) the deuterons
and b) the tritons upon x = v/vod for various y values at Ed = 200,
Et = 40; Te = 15 keV, TN, t = T" = 2 sec; Nd = Nt = 4.1013 cm-3.
TABLE 1. Dependence of the Effective
Cross Section of the Thermonuclear Reac-
tion D + T = 4He + n upon the Deuteron En-
ergy (fixed tritium)
E, keV I
":.
c,
.
-
E, key I
0.1024, Cm2 I
E, keV I
i
.
-
E, keV I
.
0
-
W
..
.
.
-
20
0,05
70
2,60
120
5,00
170
3,50
300
1,30
30
0,20
80
3,50
130
4,90
180
3,20
350
1,00
40
0,60
90
4,30
140
4,50
190
3,00
400
0,85
50
1,00
100
4,80
150
4,20
200
2,80
450
0,70
60
1,80
110
4,90
160
4,00
250
1,80
500
0,60
separated into plasma ions and injected ions, but the collisions of the fast ions among themselves must be
brought into account. One therefore obtains a system of two nonlinear kinetic equations for the distribution
functions of the deuterium and tritium ions.
Let us consider the simplest form of the problem. Assume that both the sources and the losses are
described by isotropic functions of the angle in velocity space and that the distribution functions depend only
upon the absolute value of the velocity. Then the stationary state of the reactor using an intense injection of
deuterium and tritium ions is given by the following system of equations for the distribution functions of parti-
cles of type a (a = d , t) [71:
4a4etLIV0 1 0 2 f Tft ao
(v) d- bpfa(v)} ? v a (v) f (v)? par'oa (v voa)= 0. 00 ao 1 Tap V uV
a Tnfs
0==d,t, e
The notation is interpreted as follows: a denotes deuterons andt, tritons; No and, To denote the density and the
temperature (average kinetic energy) of the corresponding type of particles:
00
N= 4t S fs(v) v2 dv;
TR? 4n ?IP-- fa (v) v4 dv.
? 3 No -
o
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(2)
(3)
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0 1
Fig. 2. Ratio of the distribution functions of deuterons and tritons to
the corresponding Maxwell distributions at equal temperatures and
densities.
X* VIVed .
TABLE 2. Characteristics of the Tokamak
Reactor with Intense Injection of Deuterium
and Tritium*
V
T.E.d
tE, t
Td
Tt
Qde
Qie
sec
keV
0
1 1,2
3
5
0
1 2,0
3
5
1,20
0,96
0,60
0,36
2,00
1,61
0,99
0,59
1,20
0,93
0,62
0,49
2,00
1,57
1,04
0,80
33
31
27
23
26
25
22
19
23
21
18
15
19
18
16
14
0,61
0,56
0,44
0,32
0,40
0,37
0,31
0,23
0,22
0,19
0,13
0,08
0,15
0,14
0,10
0,06
2,0
1,8
1,5
1,1
2,5
2,3
1,9
1,5
* Ed = 200: = 40: Te= 10 keV;Nd---Nt -= 4 ? 1013CM-3.
The coefficients ao and bo are expressed by the distribution functions f(v) as follows;
a5= 421 IsipTa rni3 fa (iv) w4 div +v3 S fp (w) du } ;
3
0
bp-- fp (w) iv2 div.
The summation in Eq. (1) is extended over all types of particles, including the a. The second term on the
right side of each of the equations of system (1) describes the loss of the particles a, whose intensity is given
by the function va(v); the last term on the right side describes the source of the particles a; the source intensity
is pa; the energy distribution is characterized by the function Foa (v - voct), where voa denotes the beam particle
velocity corresponding to the characteristic injection energy Ea = mcoia/2. Thefunction Foa is normalized to
unity;
118
4n Fo?(v-voc,)v2dv = , a=d, t.
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TABLE 3. Characteristics of the Tokamak
Reactor with Intense Injection of Deuterium
and Tritium*
tE d
rE I
Td
Q de
Qte
sec
keV
3
5
3
5
1,2
2,0
1,20
0,93
0,65
0,43
2,00
1,64
1,08
0,70
1,20
0,89
0,59
0,47
2,00
1,50
0,96
0,75
46
42
36
30
36
34
30
25
34
30
25
20
29
27
22
19
0,46
0,40
0,30
0,20
0,32
0,28
0,21
0,15
0,18
0,14
0,08
0.04
0,13
0,11
0,07
0,04
2,7
2,5
2,2
1,6
3,9
3,6
3,0
2,5
* Ed.= 200; Et= 40; Te i5keV ;Nd=-- Nt= 4 ? 1013CM-?
When each of the equations of system (1) is multiplied by 4rrv2 and 27rmav4 and integrated over the veloc-
ity, the following equations are obtained:
(N?ITN,)= 0, a= d, t;
Q,13-(s'TE, ,) = a=d, t.
(4)
(5)
Equation (4) describes the particle balance. with TN,a denoting the lifetime of the particles given by the for-
mula
= d, t. (6)
Equation (5) expresses the energy balance. In Eq. (5), ea = 3/2 NaTa denotes the energy of the particles of type
a; TE oc, denotes the lifetime at that energy; Quo denotes the power of injection into the plasma; and a to parti-
cles ,B:
-1
TE. f f k 2arna
ec,
0
d, t;
ef
Q. = 2Turw,L Focc(v-v0) v4 dv, c = d, t;
Co
Q = 64n3ege k1AL fc,(v)v (iv) w2 dw ) d_L f5(w) w X
MR
o
X f c, (v) v2 dv) du)}.
(7)
(8) ,
(9)
The particle lifetimes TN,a and TN3 characterize the losses of deuterons and tritons by various pro-
cesses, e.g., charge redistribution, instabilities, etc. Therefore TN,d and TN,t can be considered parameters
of the apparatus.
Let us consider the case in which Nd and Nt, TN,d and N3 as well as the temperature of the electrons
in the tokamak reactor, have values corresponding to reactor conditions [8]. The intensity of the sources is
determined from Eq. (4).
It is a well-known fact that the lifetime of the particles with energy is several times smaller than the
corpuscular lifetime (particles with high energies can be retained to a lesser degree). This can be pheno-
menologically brought into account by modeling the losses with the aid of an increasing function of the velocity.
We consider energy losses of the type:
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4
2
200 400 600 Ed, keV
Fig. 3. Dependence of the gain Q of
the reactor upon the energy of the
injected deuterons at a triton injec-
tion energy Et = 40 keV; various y
values. Electron temperature Te =
15 keV.
a = d, t, (10)
where vod, v ot, and Y denote certain numerical parameters. The degree to which the functions of Eq. (10) in-
crease determines y and therefore characterizes the difference between the lifetime of the particles with ener-
gy and the corpuscular lifetime. By appropriate selection of this parameter one can reach the necessary rela-
tion between the lifetime with energy and the corpuscular energy and, in particular, one can obtain the ratio
TN,a/TE,a 3 observed in the majority of experiments on the tokamak reactor. We note that y= 0 corresponds
to the limit at which the lifetime with energy is equal to the corpuscular lifetime; Tma = TE ,a' with a = d, t.
The parameters pod and vot are selected so that the lifetime (6) of the particles in the stationary state assumes
a predetermined value, i.e., so that the following relations are satisfied;
4av0c, c fa, (v) exp {7 v2 du ? , a ? d, t.
voc, Tx, a
'0
Since the relaxation time of the electrons is smaller than that of the ions, a Maxwell distribution is used
for the electrons. Since the plasma is quasi-neutral, the electron density is Ne = Nd + Nt.
Equation system (1) is numerically solved with the method of settling [9]. The efficiency of the thermo-
nuclear reactor depends upon the ratio of the power of thermonuclear reactions to the injected power;
Q = gEthni E P aE
Ct=d, t
where Ethn = 17.6 Mev denotes the energy released in the thermonuclear reaction D + T = 4He + n; the DD
reaction with its small cross section was disregarded; E paEa denotes the injected power;
cg=d,
vci?vt
,.
q = N dN t (ay) = .f dyd .c dvtl v a? Vtla (Illd?Vti) f a (vd) f t (v t) =8m2 ) ft (v s) vt dui .. fd(vd)vddvd a (u)uz du
o o Iva-vtl
denotes the average number of fusion reactions per cm3 of the plasma per second; u = vd?vt denotes the
relative velocity of the deuterons and tritons; a(u) denotes the effective cross section of the DT reaction at
fixed tritium.
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We used in the present work the experimental a(u) values of Table 1 [10].
Results of Calculations. The distribution functions which were obtained by the numerical solution of
Eq. (1) for deuterons and tritons allowed the determination of various characteristics of the thermonuclear
reactor with intense injection of deuterons and tritons. We could determine the temperature of each type of
ions (Eq. (3)), the rate of energy transfer from one type of particles to another (Eq. (9)), the lifetime of the
ions with energy (Eq. (7)), the gain Q of the reactor and its dependence upon the lifetime of the ions (Eq. 6)),
the temperature of the electrons, and the parameter y.
The results of the calculations of various characteristics of the reactor, which correspond to the elec-
tron temperatures 10 and 15 keV for TN,d = TNA = 1.2 and 2 and for y = 0, 1, 3, and 5 are listed in Tables 2
and 3. In these calculations the energy of the injected ions was assumed as 200 key for deuterium and 40 keV
for tritium. The results of the calculations show that when y decreases, i.e., when the lifetime of the parti-
cles with energy increases, Q increases. The efficiency in terms of energy can be increased in the reactor by
increasing the lifetime of the particles or by increasing the temperature of the electrons.
Figures 1 and 2 show the distribution functions of the deuterons and tritons and the ratio of these dis-
tributions to the corresponding Maxwell distributions. The distribution functions were normalized as follows:
OD
4n $ .tc, (x) x2 dx= Na ? 10-13, cc= d, t.
It follows from Fig. 2 that the maximum of each of the ratios fa(x)/(ma(x) is reached at a velocity voa which
corresponds to the injection energy Ea, i.e., for x = 1 in the case of deuterium and for x=4mdEt/mtEd
0.37 in the case of tritium.
Figure 3 shows the dependence of the reactor gain Q upon the energy of the injected deuterons for vari-
ous y values. The maximum of Q is reached at Ed rz 100 keV, which approximately corresponds to the maxi-
mum of the cross section of the DT reaction and which several times exceeds the maximum Q values deter-
mined in [4]. The dashed line of the same figure indicates the dependence of Q upon the energy of the injected
deuterons for the two-component reactor scheme at Te = 15 keV [3]. This curve differs sharply from the cal-
culated curves for the following reasons. It was assumed in [3] that the deuterons participate in the fusion
reactions only during the time in which they are slowed down, whereas, in our model, the hot deuterons and
tritons react during their entire lifetime; therefore the dependence of Q upon the energy resembles the depen-
dence of the cross section of the DT reaction upon the deuteron energy. In [3] we used the well-known approxi-
mation formula of Artsimovich [11] for the cross sections cr(u). At high velocities the cross sections which are
calculated for the DT reaction with this formula are approximately two times greater than the cross section
values used in the present work. Furthermore, Etha = 22.4 MeV [3], i.e., the energy (4.8 MeV) of the capture
by 6Li, which is part of the blanket, was taken into consideration.
Thus, the analysis of the efficiency in terms of energy of a thermonuclear reactor with intense injection
of deuterons and tritons indicates that it is possible to obtain a positive yield of energy from such a system.
The author is indebted to I. N. Golovin for formulating the problem and to Yu. N. Dnestrovskii and D. P.
Kostomarov for valuable discussions.
LITERATURE CITED
1. L. A. Artsimovich, Usp. Fiz. Nauk, 91, 365 (1967).
2. J. Dawson, H. Furth, and F. Tenny, Phys. Rev., Lett., 26, 1156 (1971).
3. V. I. Pistunovich, At. Energ., 35, No. 1, 11 (1973).
4. J. Cordy and W. Core, Nucl. Fusion, 15, 710 (1975)?
5. D. Callen et al., in: Proc. IAEA Intern. Conf. on Plasma Physics and Nucl. Fusion Research, Tokyo,
CN-33/A16-3 (1974).
6. J. Cordy and M. Houghton, Nucl. Fusion, 13, 215 (1973).
7. N. V. Grishanov et al., Fiz. Plazmy, 2, 260 (1976).
8. I. N. Golovin, At. Energ., 39, No. 6, 3-79 (1975).
9. A. A. Samarskii, Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow (1971),
p. 450.
10. Report ORNL3113 (1971).
11. L. A. Artsimovich, Controlled Thermonuclear Reactions [in Russian], Fizmatgiz, Moscow (1963), p. 12.
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THE HIGH-CURRENT ELECTRON
ACCELERATOR IMPUL'S
L. N. Kazanskii, A. A. Kolomenskii, UDC 621.384.659
G. 0. Meskhi, and B. N. Yablokov
The accelerator Impul's, which is of the first generation of high-current electron accelerators, was de-
signed and built in the Laboratory of Problems of New Accelerators of the Physics Institute of the Academy of
Sciences in 1969-1971 [1]. In 1973 a second block was added to the accelerator and two-beam operation was
used on it for the first time in the Soviet Union. This made it possible to increase the efficiency of the accele-
rator utilization and to perform in parallel different experiments with two independent beams [2].
At the present time the accelerator Impul's consists of a common pulse-voltage generator in air, the
associated equipment, and two identical cylindrical blocks. Each block comprises a double pulse-shaping line,
a transforming line, and an electron gun (Fig. 1). The transition from one single-beam experiment to another
requires only a few minutes and is reduced to changing the connections between the blocks and the pulse vol-
tage generator. The two blocks are connected to the pulse voltage generator for synchronous generation of two
beams.
The pulse-shaping lines which were used for the first time on the accelerator and increase the voltage,
the glycerin (a = 44) used for the insulation of the system comprising the double pulse-shaping line and the
transforming line, the uncontrolled multi-spark gap, the 30-0 junction between the glycerin and the vacuum,
etc. required trial runs. We describe in the present article the design and its testing in the course of long
accelerator operation.
Selection of the Parameters and Design of the Main
Accelerator Components
The accelerator Impul's was designed for the generation of single electron beam pulses with a duration
of 30-40 nsec and the parameters 1 kJ, 1 MeV, and 35 kA at the smallest possible dimensions of the apparatus.
SF5
DPSL2
TL2 EG2
Sh2
A Drift
chamber
2
G2
1
I Gg Gg G2 G1 Trigger 1
1
F00-I Foo- -0 0-1I-0 040 kw-- I
0 kV
I PVG i
L
IJEG1
Drift
chamber
DPSL1
TL1 EG1 Shl b
Fig. 1. a) Overall view of the accelerator Impul's and b) its structural scheme. PVG)
Pulse voltage generator; EG1, EG2) electron guns; DPSL1,DPSL2)double pulse-shap-
ing lines; G1-G9) gaps; Shl, Sh2) shunts; TL1, TL2) transforming lines. Subscripts: g)
gap; gr) ground.
Translated from Atomnaya Energiya, Vol. 42, No. 2, pp. 113-119, February, 1977. Original article sub-
mitted June 4, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
122
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1 2 3 4
/ / I
a
Fig. 2. a) Spark gap of the double pulse-shaping line; 1) high-voltage elec-
trode; 2) housing; 3,4) grounded electrode and igniting electrode, respec-
tively. b) High-voltage input lead to the double pulse-shaping line; 1) adhe-
sive junctions; 2) sphere; 3) high-voltage rod; 4) insulator; 5) supporting
disk; 6) guard ring in the housing of the double pulse-shaping line.
TABLE 1. Dependence of the Ratio of the
Lengths of the Transforming Line and the
Pulse-Shaping Line upon the Transforma-
tion Coefficient
K Z /Z.
tr out in
1 /I
a d sl
H
tr
Z /7. I /1
out in a dsl
1,2
1,44
0,33
1,8
3,24
3,5
1,3
1,7
0.69
2,0
4,0
4,8
1,4
1,96
1,1
2,5
6.22
8,2
1,6
2,58
2,2
3,0
9,0
12,0
Taking into consideration the volt-second dependency of the electrical breakdown strength of the dielectric
materials (Et1/3 const fort 1?sec), it was decided to increase the voltage in the transfer of energy to the elec -
tron guns; the accelerator circuit comprising the pulse voltage generator, the double pulse-shaping line, the trans-
forming line, and the electron guns were accordingly chosen,
Transforming Line. The transformation coefficient of the transforming line is limited by the tolerable
increase in the length of the apparatus at a given distortion aU/U of the pulse shape. When both the double
pulse-shaping line and the transforming line are made of the same dielectric material and when aU/U = 0.1,
the ratio of the lengths of the lines is given by the tabulated values. We selected lt1 =ldsland Ktr = 1.4 for the
ImpulTs. The transforming line was given the form of a coaxial line with a conical central electrode having a
diameter of 90 mm at the input and of 15 mm at the output. The outer electrode had a diameter of 410 mm, and
the transforming line a length of 850 mm. The wave impedance changes from 14 to 30 O. The measured dis-
tortion of the top of a 35 nsec pulse does not exceed 10%.
Double Pulse-Shaping Line. The total capacity of the double pulse-shaping line with a safety margin of
25% is obtained with the formula Cdsi = 1.25(2W/U2sg)Ktr and is approximately 5 nF, where W denotes the given
energy in the beam and Ueg, the voltage at the gun; the required charging voltage is Lids' = 700 kV. A wave
impedance of 14 12 is obtained (Zdsi= Cdsl/Tp); the best impedance matching is obtained with identical Z values,
with Z = 0.5, Zdsi =7 SI.
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1,6
1,4
1,2
1,0
48
46
44
42
0,1
1,0 2,0 3,0 4,0
Cd/Cl
Fig. 3. Dependence of KW, Ku, and KKw
upon Cd/Ci.
Ku
Ku Kw
The selection of the parameters of the double pulse-shaping line sets rigorous requirements to the switch-
ing time of the spark gap:
ts 2.2 [4? + (igtZ)211/2
where L denotes the inductance of the spark gap and TR denotes the time constant within which the resistance
of the sparks decreases. Assuming that the contributions of the two components are equal, we obtain the fol-
lowing conditions for a current of ?100 kA: Lg 5 20nHand 3 nsec; these values canbe obtained only with
multi-spark operation of the spark gaps.
When the wave impedances Z of the double pulse-shaping lines are fixed, the condition of maximum
energy storage can be used to determine the optimum ratio aopt of the diameters of the electrodes forming the
line and the optimum dielectric constant aopt [3]. It is assumed that the liquid dielectrics with various values
have the same dielectric breakdown strength values;
(1)
60 E2 1n3
?e=4 1n3 a
const a 4 ,
SC Z2
(2)
where V denotes the volume of the double pulse-shaping line and c, the velocity of light. The maximum of the
specific energy capacity is reiched at aopt = 2.12, whereas the dielectric constant which corresponds to cyopt
and Z is eopt = [(60/Z)lnceopt1 = 2000/Z2. For Z = 7 St, we have eopt = 4 2 , and this led to the selection of gly-
cerin (s = 44) as the dielectric.
We also took into consideration that the glycerin does not require a purification system and special ma-
terials and that satisfactory relations are obtained between the lengths and diameters of the double pulse-
shaping line and the transforming line. The maximum field strength in the double pulse-shaping line was as-
sumed as 200 kV/cm in the operation; accordingly, the following diameters of the coaxial electrodes of the
double pulse-shaping line were assumed: central diameter 90 mm, average diameter 190 mm, and external
diameter 410 mm. The length of the double pulse-shaping line was ids' = Tpc/20?5 P.: 850 mm. The central
electrode of the inner line of the double pulse-shaping line was grounded through an inductance Lgr =3.5 1.4H
whose impedance at the discharge frequency is much smaller than the impedance of the pulse voltage genera-
tor and, in the nanosecond range, much greater than the output resistance of the double pulse-shaping line.
The inductance was inserted into the initial portion of the transforming line and was a cylindrical, single-layer
coil with an average diameter of 30 mm, the coil wound from 2 mm copper wire.
Spark Gap of the Double Pulse-Shaping Line (Fig. 2a). The spark gap was inserted into the external line
and upon breakdown automatically cuts off the pulse voltage generator from the double pulse-shaping line. This
position of the spark gap is advantageous also for controlling its ignition. The spark gap was mounted in a
barrel-shaped Plexiglas insulator with a diameter of about 250 mm and a height of about 250 mm and attached
to the face of the double pulse-shaping line. The anode of the spark gap is a truncated sphere (radius and diam-
eter ?180 and 150 mm, respectively); the anode is made from 2-mm-thick aluminum. The grounded cathode
consists of 6 rods with a diameter of 30 mm and hemispherical roundings; the rods are arranged on a circle
with a diameter of 120 mm. The upper rod sections are made from stainless steel. The spark gap was filled
with the inert gas SF6 to a pressure of 150-400 kPa.
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Z 3 4 5 6 7 8
Fig. 4. a) Overall view of the cathodes used and b) schematic sketch of the gun: 1) inter-
nal electrode of the transforming line; 2) ring acted as a diaphragm; 3) jacket; 4) high-
voltage insulator; 5) matching cone; 6) cathode holder; 7) cathode: 8) anode.
Z,
70
60
50
40
30
20400
80
70 -
60
50 -
411
30
20
10
0
500
600
700
U , k V
t, nsee
Fig. 5. Dependence of the impedance of the
gun upon the voltage in the case a) of fixed
anode? cathode distance and b) during .a high-
voltage pulse.
Pulse Voltage Generator. The use of glycerin with the small specific resistivity p 106 ?cm limits the
line's discharge time. The energy losses occurring upon the discharge of the double pulse-shaping line with a
voltage of 0.5Umax(1 ? coswt) and the switching at the maximum of the voltage are aW/W r=, 2.6 ?1013/wep.
When we tolerate an energy loss of at most 10%, we obtain for glycerin with E = 44 and p 2 ? 106 St? cm a
charging time tch = iri.o of less than 1 ?sec for the double pulse-shaping line. The discharge capacity Cd of the
voltage pulse generator should be selected so that the maximum energy is transferred to the pulse-shaping
line. When the losses are disregarded, we have
Wdsl ICdCdsi /(Cd Cdsl )9 Wg = K wWg
(3)
where W denotes the energy stored by the pulse voltage generator. The voltage at the double pulse-shaping
line should be greater than the discharge voltage of the pulse generator voltage. Based on these considerations,
the ratio Cd/Cdal should be selected near the maximum of KwKu , where Ku = UdsliUd (Fig' 3)*
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-41110111110111110.'
--
1/2 10,5 V
A 4,.
T.
IIE
10,5 mT'llir
20 kA.
at EGI
o,5 mv 111
20 kA
!
. AIL
Fig. 6. Oscillograms of the charging voltage, the voltage and
the current of the electron gun in; a) single-beam and b) double-
beam operation of the accelerator; c) oscillograms of the charg-
ing voltages of the two double pulse-shaping lines in the case of
beams shifting in the course of time. Time marks of 200 nsec
at the charging voltages; calibrating sinusoidal voltage of 100
MHz.
We assumed for one double pulse-shaping line Cd = 2Cdsl: the minimum discharge voltage of the pulse
voltage generator is obtained from the relation Ud = Ug/[exp(-1T/2Q)]Ku, where Q f:?-? 15 denotes the Q factor of
the charging circuit (-600 kV). The inductance of the charging circuit must be less than 20 H.
The pulse voltage generator of the accelerator Impul's comprises four standard GIN-400-0.06/5 genera-
tors which are connected in parallel and in series. Identical stages of the two columns (two GIN-400 generators
in each column) are electrically connected to the common lines of the switching spark gaps which are mounted
in a common vinyl plastic tube with a diameter of 110 mm and which are operated in a nitrogen atmosphere un-
der a pressure of 100-500 kPa. By changing the pressure, one can adjust the output voltage of the pulse voltage
generator during operation. The first spark gap of the high-voltage generator is a trigatron with a separately
adjustable nitrogen pressure. The shock-load capacity of the pulse voltage generatoris12 nF, its inductance is
5 ?H, the length of a single-period resonance discharge of the double pulse-shaping line is about 0.65 ?sec, and
the measured Kg value is 1.3. The charging voltage is applied to the double pulse-shaping line through a coni-
cal Plexiglas insulator (see Fig. 2b).
Electron Gun. The dimensions of the guns of the accelerator Impul's were selected so that a convenient
attachment to the drift chamber was possible and that a magnetic field could be applied (length 250 mm, diam-
eter -180 mm for the guns). The dimensions of the electron guns limited their electric breakdown strength
(Ueg max 850 kV), but to date we have not used electron guns of large dimensions. The transition from the
medium with a high e value necessitates the conical shape of the insulator and precludes gradient rings (Fig. 4a)
[4]. The high-voltage pulse which is applied to the electron gun from the transforming line passes through a
three-layer coaxial line with a constant wave impedance; the line is formed by the jacket, the insulator, and the
transition cone. Titanium foil with a thickness of 20-50 ? or a stainless steel net are used as the anode. Dur-
ing operation, the vacuum in the gun is at least (1-2) ?10-5 mm Hg. The cathode holder is designed so that the
anode-cathode gap can be changed between 0.5 and 2.5 cm and that the impedance of the gun can be appropriately
selected.
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60
50
40
30
20
30
Egp
4g
Qgp
_
4/ 43 1 3 10 :10 100
f, MHz
Fig. 7. High-frequency properties of the gly-
cerin; g) 94% glycerin; gp) glycerin of brand
"p" (pure); p = 1.7 ? 106 and 60.106 a ? cm, re-
spectively.
Various cathode configurations were tested; single-needle cathodes, multi-needle cathodes, and a cathode
with a flat emitting surface and inlaid dielectric (see Fig. 4b). Presently cathodes with a diameter of 44 mm
made from smooth graphite or stainless steel are used; the cathodes have seven concentric grooves with a
spacing of 3 mm. The gun impedance is -30 l at an anode-cathode distance of 10-17 mm and changes approxi-
mately like U-V2 when the voltage is increased (see Fig. 5a). The change of the gun impedance during a high-
voltage pulse is shown in Fig. 5b. At a voltage of 700-800 kV at the gun, the electric field strength on the sur-
face of the cathode holder reaches (3-4)405 V/cm, which causes emission from the lateral surface and subse-
quent breakdown over the surface.
Conditions of Operation of the Accelerator Impul's
Single-Beam Operation. In single-beam operation the accelerator delivers a beam with a maximum
energy of about 800 keV, a current of up to 30 kA, a pulse duration of -40 nsec, and an energy of about 700 J
(Fig. 6). The voltage and current pulses have a leading edge of -18 nsec, which corresponds to the distortion
in the spark gap, in glycerin, and at the input of the electron gun. A sharp cut, which is caused by flashover
of the insulator of the electron gun,, is frequently observed on the top or at the leading edge of the pulse. Us-
ually the accelerator is operated with up to 700 keV and 20 kA; the beam at the anode is relatively homo-
geneous and has a diameter of 3-5 cm. When a truncated Teflon cone (height 12 mm and diameter 5/12 mm)
is placed at the center of the cathode, the beam is reduced to a width of a few millimeters.
Two-Beam Operation. In two-beam operation the two double pulse-shaping lines of the Impul's are
charged in parallel and two beams are generated in synchronism.
We obtain for the amplitude of the charging voltage of each of the n pulse-shaping lines having the capa-
city C1 with an accuracy sufficing for practical applications;
Ung/g (2Cg/(C8 nC 1)] exp ?
(4)
where Ug and Cg denote the voltage and the capacity of the pulse voltage generator; and Q denotes the Q factor
of the charging circuit. In the case of the accelerator Impul's, we have Cdsi = 0.5Cg in single-beam operation
and nCdaj. Cg in double-beam operation, with Q Pe, 15. According to Eq. (4), at these relations of the capaci-
tances, the parameters of each of the two synchronous beams are reduced to -80% of the accelerating voltage
and to -60% of the stored energy of single-beam operation.
In double-beam operation, the switching spark gaps must be simultaneously triggered or the voltage of
one of the spark gaps must be slightly reduced when the other is prematurely triggered. Therefore, each of
the lines is connected to the pulse voltage generator through an additional decoupling inductance Ladd = 2L0,
where Lo denotes the inductance of the pulse voltage generator. The possibility of simultaneously generating
two beams is influenced by the stability of operation of the spark gaps of the double pulse-shaping line. In the
accelerator Impul's, in which uncontrolled spark gaps are used, particular risks were encounteredandexperi-
mentally verified. It turned out that the mean-square spread of the triggering of the spark gaps of the double
pulse-shaping lines does not exceed 10 nsec, provided that the pressure in each of the pulse-shaping lines is in-
dividually adjusted with an accuracy of about 0.02 mm Hg.
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When the two beams are simultaneously generated, the voltage at the guns reaches 700 kV, the current
20 kA, and the energy about 400 J in each beam. Oscillograms, which illustrate the two-beam operation of
the accelerator, are shown in Fig. 6b. The accuracy of the beam synchronization was better than 10 nsec.
In the case of external mismatching of the pressures in the spark gaps, the pulses can appear shifted on the
time scale by about 100 nsec and with a stability of ?12 nsec; it follows from the oscillograms of Fig. 6c that
the triggering of the spark gap of one of the double pulse-shaping lines does not sharply modify the voltage of
the other pulse-shaping line.
Result of Investigations and Experience in
the Operation
The experience gathered in the operation of the accelerators has shown that the voltage pulse generator
provides only a small range of control (15-209). The reason is that there is no light guide between the spark
gaps, that the surge level in the first stages of the GIN-400 generator is low (-40%), and that the design has
shortcomings which preclude the accurate adjustment of the distances between the electrodes of the spark gaps
(spread -?109).
Owing to the internal charging inductance (Lgr) in the double pulse-shaping lines, there exist voltage dif-
ferences between the pulse-shaping lines and the voltage difference is applied to the electron gun. Investiga-
tions of the influence of Lgr upon the amplitude of the voltage before the pulse and upon the energy losses dur-
ing the main pulse have shown that good results obviously cannot be obtained when the inductances are placed
in a medium with a large E value. Acceptable results (amplitude of the voltage before the pulse -10% and
energy losses -201,) can be obtained in our case, because an additional inductance of 12 1.tH was inserted be-,
tween the voltage pulse generator and the double pulse-shaping line.
When the accelerator Impul's was built, the high-voltage and high-frequency properties of glycerin were
investigated (Fig. 7). The drop of a and Q at frequencies exceeding 30 MHz limits the curvature of the pulse
edges to values a-10 nsec. But when pulses with an edge length of 10-15 nsec are shaped, glycerin can be
used. The high-voltage properties of glycerin are appropriately described by the formula
Eacc 0.35telif3fSelifif?(mv/cm), (5)
=
where teff and Seff denote the effective time (?sec) and area (cm2), respectively.
Glycerin proved appropriate as a dielectric but when it was filled in, the lines had to be evacuated and the
glycerin heated to 50-60?C. In our apparatus, the glycerin kept its insulating characteristics and high-frequency
characteristics for two to three years even after several breakdowns had occurred in it.
The form of the electrodes of the switching spark gap of a double pulse-shaping line guarantees that two
or three sparks burn in each discharge without ignition. The accuracy of triggering is ?10 nsec. The over-
voltage reaches 1.6-1.8 in the spark gap at the time of the breakdown. Switching currents up to 100 kA at a
voltage of 700 kV occur within 8-10 nsec in a 2.2-cm gap. These results are in good agreement with the esti-
mated inductance and resistance of the two sparks [5, 6].
The accelerator "Impul's n proved to be suitable for experimental work and was rather reliable even in
prolonged use. The total number of discharges made in the accelerator reaches several ten thousand. Basi-
cally suitable proved the measures taken in building the accelerator, e.g., the selection of the system compris-
ing the pulse voltage generator, the double pulse-shaping line, and the transforming line, the coaxial form of
the lines, the multi-spark gaps, and the use of glycerin in a small, compact apparatus. Particularly important
is the great advantage obtained by using the accelerator in double-beam operation.
The authors thank A. N. Lebedev, D. D. Krasil'nikov, V. B. Sidorov, 0. I. Saksonov, V. T. Eremichev,
S. I. Vlasenko, and A. V. Serov for their great help and support in building the accelerator and in putting it into
operation.
LITERATURE CITED
1. L. N. Kazanskii et al., Preprint JINR D-9-6707 [in Russian], Dubna (1972), p. 161.
2. L. N. Kazanskii, A. A. Kolomenskii, and B. N. Yablokov, in; Trans. Fourth All-Union Conference on
Accelerators of Charged Particles [in Russian], Vol. 1, Nauka, Moscow (1975), p. 310.
3. L. N. Kazanskii and B. N. Yablokov, in; Trans. Second All-Union Conference on Accelerators of Charged
Particles [in Russian], Vol. 1, Nauka, Moscow (1972), p. 98.
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4. G. 0. Meskhi and B. N. Yablokov, in; Trans. Second All-Union Conference on Accelerators of Charged
Particles Vol. 1, Nauka, Moscow (1972), p. 90.
5. S. I. Barannik, S. B. Vasserman, and A. N. Lukin, Zh. Tekh. Fiz., 44, No. 11,2352 (1974).
6. W. Pfeiffer, Elektrotech. Z. A., 95, No. 8, 405 (1974).
INFORMATION FOR THE AUTHORS
The articles submitted to the journal Atomnaya Energiya must be presented in very concise, brief form.
One must avoid repetitions of tabulated data and graphs and omit the simultaneous presentation of numerical
results in the form of tables and graphs.
Reviews normally must not exceed 20-22 pages; original articles, 10-12 pages; abstracts of deposited
articles, 2 pages; and letters to the editors, 5 pages of typed text (including figures with legends, tables, and
reference citations).
In preparing manuscripts, the authors must be guided by the following rules:
1. The texts (which must necessarily comprise the first of the typewritten copies) and the illustrated
papers must be presented in four copies in final form for printing. The text must be written with double spac-
ing and with 28-29 lines per page; the margins must not be narrower than 4 cm; handwritten inserts cannot be
accepted.
2. The text (writing of formulas, Greek and Latin letters, lower-case letters and capital letters, abbre-
viations of words, etc.) must conform to the usual rules adopted in scientific and technical journals. Letters
used for the notation which are hard to discern in manuscripts and corresponding must be explained on the mar-
gins.
3. The units of all physics quantities must be indicated in the International System.
4. Tables appended to the test must be given numbers in the order of their appearance; each table must
have a title.
5. Drawings are to be made with black Indian ink on 15 x 20-cmpaper; photographs must have sufficient
contrast and a size of 12 x 18 cm.
6. Legends to figures must be appended on a separate sheet. The text must refer to the drawings.
7. The cited literature is stated at the end of the paper in an overall list which has to indicate;
a) in the case of journal articles, the name and the initials of the authors, the name of the journal, the
year, and the numbers of the volume, the edition, and the page;
b) in the case of books, the name and the initials of the authors, the full title of the book, the place of its
edition, the editorial, and the year of the edition; in the case of foreign books, also information pertaining to
its Russian translation must be indicated;
c) in the case of articles of a collection, the name and the initials of the authors of the article, the title
of the collection, the initials and names of the compiler or editor of the collection, the portion thereof, the edi-
tion, the place of the edition, the editorial, the year, and the page.
No reference must be made to unpublished work.
8. Articles, reviews, and letters to the editor must be accompanied by abstracts which are to be compiled
according to the rules of the abstracting journals; the goal and the results of the work must be clearly stated.
Furthermore, abstracts of articles and reviews must be translated into English (with the translation strictly
corresponding to the Russian abstract).
Translated from Atomnaya Energiya, Vol. 42, No. 2, p. 119, February, 1977.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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9. The titles of all papers submitted to the editor (articles, reviews, deposited articles, reviews, de-
posited articles, and letters to the editor) must be translated into English and both the name and the initials
of the authors must be transliterated into English.
10. The texts and the figures must be signed by all authors. The exact address, the telephone number,
the name, the full name, and the patronymic of the authors mjst be indicated.
The editorial office sends to the author only one corrected copy which he must return within the shortest
possible time.
Manuscripts which do not satisfy the above requirements will be ignored. Rejected articles will not be
returned.
ESTABLISHING PERMISSIBLE DOSES ON THE
BASIS OF BIOLOGICAL RISK
V. G. Denisenko, U. Ya. Margulis, UDC 539.1.01/539.1.04
and A. I. Klemin
In planning the development of nuclear energy, and in the principal use of radioactive materials and
sources of ionizing radiation, it is important to estimate the possible effect of radiation on the population and
the surrounding environment, in order to produce definite requirements as to the reliability and positioning
of nuclear equipment. In normal use, radiation sources may produce only small doses. To estimate the ef-
fects of such small doses, according to the recommendations of the International Commission on Radiological
Protection (ICRP), data on the long-term effects of comparatively large doses (which can be reliably identi-
fied) can be extrapolated to the region of small doses, assuming a linear relation between the radiation dose
and the biological effect. Extrapolation on the assumption that there is no threshold in the effect of radiation
loads to an overestimate of the probable risk associated with small doses [1-3]. Because of the many im-
ponderables involved in the genesis of long-term effects, it is difficult and sometimes even impossible to re-
late effects to previous irradiation. Therefore, the long-term effects of small doses of radiation can only be
estimated by statistical means, determining the total yield of injuries in a large population.
To ensure radiation safety, it is necessary to create conditions such that the incidence of possible injur-
ies in the population is at a low level, not posing a danger to society. But what number of injuries may be
regarded as justified This problem is not purely scientific but also social. Without doubt, the criteria will
be different at each stage of society. The chosen criterion might be the number of injuries in the safest
branches of industry (e.g., dressmaking or light industry) or due to natural causes (damage by meteorite
shower, lightning, etc.). One proposed approach to establishing such a norm is to make a quantitative com-
parison of the incidence of a certain biological effect in conditions where radiation has been present and ab-
sent (apart from ordinary background radiation). In this case it seems more correct to apply the condition of
no observable effect, according to which the number of injuries resulting from the use of atomic energy must
not exceed the random variations of similar injuries, due to natural causes; in particular, this condition is dis-
cussed in [4].
According to this condition, the "acceptable" level of radiation for any population of N humans is that at
which the number of radiational injuries cannot be isolated by statistical analysis of a sequence of values ob-
tained at different times, characterizing the dynamics of the same kind of natural morbidity. As a rule, the
considered population is part of some larger population (e.g., a whole state), numbering No people. At time t,
the larger population may be represented by some set of No/N population of equal size, and hence it is possible
to consider distributions of two types.
Translated from Atomnaya 1nergiya, Vol. 42, No. 2, pp. 120-122, February, 1977. Original article sub-
mitted October 8,1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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Arem
10
10
4 5 6 7 8 tg
Fig. 1. Dependence of limiting dose
of external y radiation on population
size N.
1. Denoting by i the number of the considered population in the indicated set (i =1, 2, ..., No/N) and by
f(i, N, t) the frequency of morbidity characterizing the i-th population of N people at time t, it is possible to
consider the distribution of the frequency f over the No/N equal-sized populations.
We denote the arithmetic mean of this distribution by cb(N, t) and the standard deviation by ug,(N, t).
2. For each population i, the frequency f may be used to construct a sequence of values obtained at dif-
ferent times characterizing the evolution of morbidity for the given population. Assuming a random variation
of f with time, we obtain some distribution over time; we denote the arithmetic mean of the distribution by
43(i, N) and the standard deviation by cr4,(i, N).
Note that cr4)(i, N) is used to determine the norm. If there is a linear dependence between the radiation
dose D of the critical organ and the effect of the radiation, then the initial condition leads to the requirement
that
CDN