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SOVIET ATOMIC ENERGY VOLUME 18, NUMBER 1

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Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 4t) Volume 18, Number 1 January, 1965 SOVIET ATOMIC ENERGY ATOMHAFI 3HEPrl1fl (ATOMNAYA iNERGIYA) TRANSLATED FROM RUSSIAN CONSULTANTS BUREAU Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 NEW BOOKS I CONSULTANTS BUREAO/T PLENUM PRESS REVIEWS OF PLASMA PHYSICS A systematic, multi-volume review of the present status of plasma theory, serving.both as an introduction for students and for re- searchers entering the field, and _a's a convenient, 'authoritative, up-to-date presentation. of current knowledge for workers in plasma physics. This continuing series, prepared by interna- tionally known Soviet experts in specific, fields, is under the editorship of Academician M. A. Leontovich, of the Xurchatovin stitute of Atomic,Energy. Each volume contains a number of integrated tutorial reviews, covering in depth' and in breadth specific aspects of ithe theory of the given field of plasma physics. In many cases, new material is presented. Transfaled by Herbert Lashinsky, University of Maryland. Volume 1: A comprehensive introduction ?to "classical" Flama physics, contains authoritative papers on: Orbit Theory, by D. V. Sivukhin; Collisions in Fully Ionized Plasma, by B.A. Trubnikov; Plasma Transport- Phenomena, by, S. I. Braginskii; and Plasma Thermodynamics, by A. A. Vedenov. Much of the material in the first two papers is presented here for the first time. Although the theoretical analyses are quite advanced, the experimental aspects of the subject are kept firpily in view throughout. This is especially .true of ? the article on transport phenomena; in which the kinetic approach is developed in derallel with qualita- tive physical descriptions of transport phenomena, including some of the less familiar "transverse" thermal transport effects plasma in magnetic .fields. Many physical examples' and'ap- plications of the theory are given. _ 336 pages ' ($12.50 Volume 2: Contains four review papers concerned primarily with the problem of /plasma confinement: Magnetic Field .Ge,, ometries; Plasma Equilibrium in Magnetic Fields; liydromagnetic Plasma Stability; and Motion of Charged Particles in Electro- ' manetic Fields.. ' Approx. ,300 pages $12.50 Volume 3: Devoted to plasma waves, includes: Electromagnetic Waves in a Plasma; Oscillations of an Inhomogeneous Plasma Introduction to the Theory of a Weakly Turbulent Plasma; and Symmetric Magnetohydromagnetic Flow and'Helical Waves in a Circular Plasma Cylinder. ' Approx. 300 pages ? $12.50 Volume 4: Contains, three papers: Hydrodynamic Descriptions of a Highly Rarefield Plasma; Collective Phedomena in Collision- less Plasma Shock Waves, and Coulomb Collisions in Fully loniied Plasma. The latter paper contains new material on the relevance of this topic in mirror machines, provided 'by the author (D. B. Sivukhin) for the English edition. Approx. 290 pages '$12.50 Volume 5: To be published late in 1965 in the Soviet Union is to comprise a comprehensive review of radiation phenomena in plasma. An English translation will be published promptly. LEBEDEV PHYSICS SERIES Complete English translations of the Proceedings'("Trudy") of the 'ferried Lebedev Physics Institute of the USSR Academy of Sciences published as Consultants Bureiu Special Research Re'- pits. Series edited by D. V. Skobel'tsyn. The fi6t three 'volumes in this distinguished series of ten Special Research Reports in translation, beginning with Volume 25, are: ? ' ? OPTICAL METHODS,' - OF INVESTIGATING SOLID BODIES "Trudy" Volume 25 Includes papers by N. D. Zhevandrpv (on polarized luminescence', of crystals), V. P. Cheremisinov (on vibrational spectra and struc- ture Of oxides in the Crystalline and glassy states) and L. A. Vainshtein on calculation of cross sections for excitation of .atoms and ions 'by electron impact). ' 194 pages 1965 '$22.50 COSMIC RAYS "Trudy" Volume 26 Contains an account of experimental investigations into nuclear , and 'electromagnetic interactions at high and ultra-high energies. Theoretical 'articles on problems of The passage' of high-energy ' ? ,electrons and photons through matter are included, as well as ,some results of the investigations into cosmic rays by means of artificel earth satellites. ? 2,62 pages 1965 . ? $27.50 RESEARCH'IN MOLECULAR SPECTROSCOPY - "Trudy" Volume,27 Devoted to spectroscopic' investigations into matter in various [states of aggregation by' the methods of Raman scattering 'and infrared absorption. A special section is devoted to the metho: dological problem of Correcting-'measured quantities forInstrit: mental errors. Great ,attention is' paid to the investigation 'of -- the temperature dependence of sdch spectroscopic quantilie:i as , the profile, width, and integrated intensity of Raman lines and absorption bands. 214 pages 1965 $22.50 CONSULTANTS 'BUREAU! PLENUM PRESS 227 ly.,17th St., New York, N.,Y: 10011 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 ATOMNAYA ikERGIYA EDITORIAL BOARD A. I. Alikhanov A. A. Bochvar N. A. DollezhaP K. E. Erglis V. S. Fursov I. N. Golovin V. F. Kalinin N. A. Kolokol'tsov (Assistant Editor) A. IC Krasin I. F. Kvartskhava A. V. Lebedinskii A. I. Leipunskii M. G. Meshcheryakov M. D. Millionshchikov (Editor-in-Chief) I. I. Novikov V. B. Shevchenko A. P. Vinogradov N. A. Vlasov (Assistant Editor) M. V. Yakutovich A. P. Zefirov SOVIET ATOMIC ENERGY A translation of ATOMNAYA iNERGIYA A publication of the Academy of Sciences of the USSR @ 1966 CONSULTANTS BUREAU ENTERPRISES, INC. 227 West 17th Street, New York, N.Y. 10011 Volume 18, Number 1 January, 1965 CONTENTS PA ENG. I GE RUSS. The Seventieth Birthday of Academician A. L. Mints 1 3 High-Frequency Oscillations Excited on Interaction of an Electron Beam with Plasma ?A. K. Berezin, Ya. B. Fainberg, L. I. Bolotin, and G. P. Berezina Interaction of Plasmoids with an Electromagnetic Wave?V. I. Veksler, I. R. Gekker, E. Ya. Gol'ts, G. A. Delone, B. P. Kononov, 0. V. Kudrevatova, G. S. Luk'yanchikov, M. S. Rabinovich, M. M. Savchenko, K. A. Sarksyan, K. F. Sergeichev, V. A. Silin, and L. E. Tsopp 12 14 Determining the Perturbations of the Parameters in the Magnetic and Accelerating Systems of an Electron Synchrotron on the Basis of an Analysis of Information Regarding the Beam?I. P. Karabekov 17 18 Phase Stability of a System of Particles in Self-Regulated Accelerators? E. A. Zhil'kov and A. N. Lebedev 22 22 Measurement of the Photoneutron Yield from Thick Copper and Water Targets and Determination of the Excitation Function of the (y, n) Reaction for 016 and Cu63 by Means of the Belen'kii-Tamm Equilibrium Photon Spectrum?I. A. Grishaev, D. I. Sikora, V. A. Shkoda-Ul'yanov, and B. I. Shramenko 29 28 Transient Processes and the Measurement of Reactivity of a Reactor Containing Beryllium ?S. S. Lomakin and Yu. A. Nechaev 35 33 ' The Crystal Hydrate UF4.4/3 H2O?Yu. V. Gagarinskii, E. I. Khanaev, N. P. Galkin, L. A. Anan'eva and S. P. Gabuda 43 40 The Relative Volatility of Solutions of HTO in H2O?Ya. D. Zel'venskii, V. A. Shalygin, V. S. Tatarinskii, and D. A. Nikolaev 49 46 Determination of y-Ray and Neutron Absorbed Dose in Polymers?F. A. Makhlis and I. M. Kolpakov 52 48 Increasing the Depth of Prospecting for Concealed Uranium Ore Bodies by Means of the Primary Aureole?S. V. Grigoryan 57 52 LETTERS TO THE EDITOR Phase Stability of Particle Blobs in Accelerators with Automatic Control?E. A. Zhil'kov . . 62 58 Simple Method for Measuring the Frequency of Free Transverse Oscillations in Cyclotrons ?S. A. Kheifets and S. K. Esin 65 60 Nomograms for Determining the Potential Barrier's Height and for the Breit?Wigner Formula ?G. N. Potetyunko 67 61 Annual Subscription: $ 95 Single Issue: $30 Single Article: $15 All rights reserved. No article contained herein may be reproduced for any purpose what- ? soever without permission of the publisher. Permission may be obtained from Consultants Bureau Enterprises, Inc., 227 West 17th Street. New York City, United States of America. Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 CONTENTS (continued) P AGE EN6. I RUSS. Simple Unsteady-State Kinetic Equation?V. G. Morogov and S. A. Kholin 70 62 Angular Distribution of y-Quanta in U233, U235, and PO" Fission on Thermal Neutrons G. A: Petrov, D. M. Kaminker, G. V. Varskii, and L. A. Popeko 72 64 Determination of the Absolute Yield of the 74-keV U239 and 87-keV Th 233 y-Lines N. Yurova and A. V. Bushilev 75 65 Spatial Distribution of Neutrons with Energies of 3 and 15 MeV in Beryllium?S. P. Belov, V. A. Minn, Yu. A. Kazanskii, and S. G. Tsypin 78 67 Reduction of the Capture y-Radiation from the Reactor's Structural Materials by Screening Them with Boron-Containing Screens?B. P, Gromov, D. V. Pankratov, M. A. Solodyankin, and M. M4 Sokolov 80 69 Dependence of the Density of RadiatiOn Damage to the Reactor Vessel on the Composition of the Ferro-Aqueous Thermal Shield?K. K4 Popkov and S. M. Rubanov 83 70 Antifriction Characteristics of Neutron-Irradiated Steel?E. A. Markovskii and M. M. Krasnoshchekov 85 72 Method of Measuring Radioactive Preparations and Checking Stability?V. M. Malykhin . . . 87 73 The Role of Thermal Peaks in the FOrmation of Defects?L. G. Gurvich and N. S. Bespalova 91 76 SCIENCE AND ENGINEERING NEWS Agreement on Collaboration in Desalinization Efforts 94 78 International Conference on the Quantiim Theory of Systems Having Many Degrees of Freedom?P. S. Isaev - 96 79 All-Union Conference on Nuclear Meteorology?S. G. Malakhov and I. V. Yagodovskii . . . 99 80 Application of Methods of Nuclear Geophysics in Ore Prospecting, Exploration, and Development?S. I. Savosin and V. I. Sinitsyn 100 81 Radioactive Chlorine-36 in Monitoring the Production and Processing Of Hexachloran ?G. M4 Strongin and M. N. Kulikova ifiBLIOGRAPHY 104 84 New Books. 106 8S The Ibissian date "Podpisano k pechati" of this issue was 12/19/1964 . This is equivalent to "approved for printing." Publication did not occur prior to this date, but must be assigned to have taken place reasonably soon thereafter. Publisher Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 THE SEVENTIETH BIRTHDAY OF ACADEMICIAN A. L. Mints Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 3-4, January, 1965 Aleksandr L'vovich Minch January 8 marked the passage of 70 years since the birth of Hero of Socialist Labor, Academician Aleksandr L'vovich Mints? the Direction of the Radio Engineering Institute, Academy of Sciences of the USSR Alexandr L'vovich Mints is widely known in our country and abroad as a prominent scientist and engineer, talented or- ganizer, and director of the development and installation of high- power broadcasting stations and gigantic charged particle ac- celerators. In the Civil War, Aleksandr L'vovich was an active fighter for the victory of Soviet power, taking part in the battles in the Caucasus, on the Polish and Crimean fronts as a member of the legendary first mounted army, in the capacity of the Radio Divi- sion. After the end of the Civil War, A. L. Mints continued serving for some time in the Red Army, occupying a position of command in the advanced communications War College in the Scientific Research Communications Institute, and then, around 1924, he turned to the development and installation of high- power radio station in the Soviet Union, the installation of which to some extent or other was not connected with the name of Alexandr L'vovich. At that time, he was responsible for the de- sign of new high-power radio stations, and was in charge of construction. A. L. Mints developed and built dozens of radio stations and radio centers in the Soviet Union, starting with the 20 kilowatt ASPopov radio station (1925- 1927), and ending with the superhigh-power 1200-kilowatt radio station (1941-1943). This period clearly exhibited one of the basic characteristics of A. L. Mints ?the effort to bring his scientific developments to practical applica- non in the shortest possible time. The scientific work of A. L. Mints embraces literally all fields of high-power radio equipment: the theory and development of methods for designing radio telephone modulation systems, the development, investigation, and installation of new antenna systems for long and short-wave radio stations, the de- velopment of new vacuum tube devices, and much, much else. In 1930-1932, A. L. Mints proposed and brought to practical realization a completely new unit system, which has been used up to the present time in building all the large radio stations in the USSR as well as abroad. To a considerable extent, as the result of A. L. Mints' work, Soviet high-power radio work occupied a leading place in the world even in those years. The advanced ideas which A. L. Mints carried out in high-power radio stations exerted an enormous effect on the development of Soviet radio engineering, as well as the radio industry. Building radio stations and radio centers revealed the brilliant organizational abilities of A. L. Mints, who showed in practice that the time required to build and adjust large radio engineering installations may be greatly reduced by a correct and exact organization of the work. The creative and organizational abilities of Alexandr L'vovich were brilliantly revealed in the period which marked the .beginning of construction of the first large charged particle accelerators in the USSR In 1946, a group of specialists headed by A. L. Mints, M. G. Meshcheryakov, and D. V. Efremov took over the construction of the first high-power proton accelerator in the USSR ? the 500-MeV synchrocyclotron in Dubna (later its energy was raised 1 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 to 680 MeV). The accelerator was built in an unusually short time, and began to operate in 1949. Then, likewise in Dubna, a group from the radio engineering laboratory of the Academy of Sciences of the USSR, together with other institutes, engaged in the development and construction of what was at that time the largest proton accelera- tor the 10-BeV synchrophasotrOn, which was started up in 1957. Building acceleratorS required the solution of very difficult radio engineering problems: In the synchrocyclotron, the frequency of a high-power oscillator had to in- crease by a factor of two during a very short oscillation cycle (3 ft-Bee), While in the synchrophasotrori, the frequency had to be changed by as much as a factor of 10 according to a definite law, and at the same time the value of the frequency had to be maintained with an accuracy of 3 ? 10-4 at all times. These Very complicated problems were solved, not only successfully and elegantly from the engineering point of view, but with a high degree of reliability. In later years, the range of A. L. Mints' scientific interests continued to increase: In addition to radio electron- ic systems for the ring-type stiff focusing 7-BeV proton accelerator (started up in 1961 at the Institute of Theoretical and Experimental Physics) and the 70-BeV one (installed in the Institute of High-Energy Physics of the GKAt), Alexandr' L'vovich directed the development and building of the 30-MeV linear electron accelerator at the I. V. Kurchatov Atomic Energy Institute, the 20-MeV and 100-MeV linear proton accelerators, and other machines. Since 1962, development of a project for building a gigantic ring-type proton accelerator for energies of 1000 BeV has been going on under A. L. Mints' direction. This project includes new ideas among them, ideas for the cybernetization of the acceleration processes so-that the accelerator has been given the name cybernetic. At the same time a Model of this accelerator is being built for an energy of 1 BeV. .Since 1958, at the suggestion of-academician I. V. Kurchatov, a group from the Radio Engineering Institute of the Academy of Sciences,USSR, headed by A. L. Mints, has Started work on high-frequency plasma equipMent. In 1959, work began on the investigation of the ionosphere, of Space near the earth, and Of interplanetary plasma. The years that Academician A. L. Mints spent On building accelerator's were also the years of the ,founding and development of the Radio Engineering Institute of the Academy of Sciences, USSR, which grew from a small laboratory into a large scientific research center. A. L. Mints was the organizer of this center, and is its per- manent director. To the comparatively young group at the institute, A: L. Mints communicates his character- istic Scientific boldness, persistence in the achievement of a goal, and clearly defined organization, as Well as organic Unity in profound theoretical analysis of the most complex questions of present day radio engineering and experimental physics and the practical realization of Scientific ideas. A. L. Mints has educated many talented young scientists, known for their work, among them not a few State and Lenin prize winners, candidates and doctors of science. During the 45 years of his scientific, engineering, and social activity, A. L. Mints published more than 100 scientific and engineering science papers, books and pamphlets, made more than 30 inventions in various fields of radio engineering and electronics, and has presented more than 70 papers, popular scientific, and publicizing ar- ticles. A. L. Mints carries on a large amount of social work, and is a member of the Scientific Councils of several Institutes, a member of the Bureau of the Division of General and Applied Physics, Academy of Sciences of the USSR, as well as an honorary member of the ASPOpov Scientific and Technological Radio Engineering and Elec- trical Communications Society. The Scientific and Engineering accomplishments of A. L. Mints are highly esteemed by the Communist Party of the Soviet Union, and by the Soviet Government. He has been awarded three orders of Lenin, two Orders of The Red Banner of Labor, the Order of the Red Star, and medals. He has received the high distinction of Hero of Socialist Labor, and has been distinguished by two state prizes of the first grade, and by the Lenin prize, The Presidi- um of the Academy of Sciences of the USSR has awarded A. L. Mints the ASPopov Gold Medal. The high devotion to principle, ability as an organizer, profound feeling of responsibility, and great self criticism, scientific boldness and ability to act, harmoniously blended in Alexandr t'vovich with a fine and spritual relation to his fellow workers, have given him great and well deserved authority. Academician A. L. Mints is a splendid example of a prominent Soviet Scientist, Engineer and Organizer. 2 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 HIGH-FREQUENCY OSCILLATIONS EXCITED ON INTERACTION OF AN ELECTRON BEAM WITH PLASMA UDC 533.9 A. K. Berezin, Ya. B. Fainberg, L. I. Bolotin, and G. P. Berezina Translated from Atomnaya tnergiya, Vol. 18, No. 1, pp. 5-14, January, 1965 Original article submitted June 4, 1964 Some results of experiments on the observation and study of oscillations excited in a beam and plasma as a result of their interaction are presented. The experiments were made under condi- tions in which wo < cuil, where wo is the electron Langmuir frequency of the plasma, and WH is the electron cyclotron frequency. The conditions of excitation of the waves in the plasma were determined, together with their frequency spectra, phase velocities, and gain factors, the inten- sity of the electric field, and the absolute values and spectral distribution of the power of the os- cillations excited. The experimental results for the frequencies, gain factors, and phase ve- locities of the oscillations excited in the plasma are in satisfactory agreement with calculated data. As shown earlier in [1-3], on passing a heavy-current pulsed electron beam (current 5 to 8.5 A, energy 15 keV, pulse length 3.6 ?sec) through a plasma in a longitudinal magnetic field (intensity 400 to 1320 Oe), under certain conditions it loses a considerable part of its initial energy (10 to 25%). In these experiments the plasma is created by the beam itself. It follows from theoretical considerations [4, 5] that this energy must pass into excitation of oscillations in the beam and plasma, and also into heating them. As we know [4-6], in the case described in the present paper, forward waves (normal dispersion) should be ex- cited. For large electron beam densities, frequencies associated with the electronic Langmuir oscillations of the beam must be excited together with Langmuir electronic frequencies of the plasma. The measurements were made under standing and traveling wave conditions for current 5 and 8.5 A in a longitudinal magnetic field of intensity 720 to 1320 G. In the first case, a metal reflector plate (current collector) was placed at the end of the chamber, and in the second an adiabatic absorbing load (graphite cone 12 cm long). Study of Oscillations Excited in the Plasma The block diagram of the apparatus is shown in Fig. 1. Let us examine some of the components in more detail. For recording the Hgo-, Hp -, Hz-components of the hf field, the oscillations are detected by a loop, and for recording the Ez component by a half-wave dipole situated in the plasma and oriented in the appropriate direc- tion, connected via a movable coaxial cable to a power-calibrated resonance wavemeter (band half-width ?1.5Mc). Changing the wavemeter over to frequency and recording the power variation of the signal detected, the fre- quency spectrum of the oscillations excited in the plasma could be obtained for a fixed position of the loop or di- pole inside the chamber. By moving the coaxial cable bearing the loop or dipole in the direction of motion of the electron beam and recording the variation in the hf power of the oscillations excited in the plasma for given fre- quency, the intensity distribution of the corresponding components of these hf oscillations could be obtained. In order to eliminate vibration, the coaxial cable bearing the loop or dipole was moved inside a guide (copper tube 4 x 6 mm, with a side slot along the whole length). The guide was fixed inside the chamber near to the edge, parallel to the axis of the system. The movable cable came out of the side slot in the guide and ended in the loop (area ?1 cm2) or half-wave dipole. The loops and dipole were placed at a distance of 10 mm from the beam bound- 3 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Beam at e ray oscine ra h. Fig. 1. Block diagram of apparatus for studying oscillations excited in the plasma under standing and traveling wave conditions: 1) Guide; 2) loop or dipole; 3) chamber; 4) fixed dipole; 5) current collector; 6) movable coaxial cable; 7) leak; 8) synchronous motor. ary. The coaxial cable passed through to the outside by a way of a special vacuum seal, and was connected via a calibrated attenuator to a power-calibrated resonance wavemeter. The signal from the output of the wavemeter fell simultaneously on to an oscillograph and a wide band amplifier, then to a cathode follower with integrating circuit, and then to an automatic electronic potentiometer EPP-09. The envelope of the hf oscillations was ob- served on the oscillograph screen and its amplitude measured (to an accuracy of 5%). Calibration of the wave- meter for given frequency (in an assigned frequency range) consisted of the following. Oscillations of known power from a standard signal generator operating under continuous conditions fell on the wavemeter with crystal detector, the steady voltage at the output being measured. The generator power was determined with a low-power meter (IMM-6) to an accuracy of 7 to 10% Such calibration was carried out before and after measuring the hf power of the oscillations excited. Only measurements for which the calibration did not alter during the experiment were taken into account. On measuring the power in this way, the total error was ?17 to 20%, the error associated with the calibra- tion of the wavemeter being ? 7 to 10%, and that in determining the attenuator factors being ?10% The magnetic field strength of the corresponding components of the hf oscillations were calculated from the formula fr7los P p ? (OS (1) where P is the hf power Collected by the loop in W, p is the input resistance of the wavemeter (p = 7512), S is the area of the loop in cm2 (S = 1 cm2); and u.) is the oscillation frequency in cps. The Most intense oscillations in the plasma were excited in the range 825 to 835 Mc (half-width 50 to 70 Mc) in the pressure range 4 to 7 ? 10" mm Hg, An example of such an oscillogram taken for a frequency of 825 Mc appears in Fig. 2. From measurements of the hf field distribution in standing wave conditions, the phase velocities were deter- mined; measurements under traveling wave conditions gave the gain coefficient of the excited oscillations. The relative phase velocity 3 was calculated as follows: where X and X0 are the wavelengths in the plasma and free space respectively. from the relation 1 in P2 V = 2 (z2?zi) Pi (z2?z1 In -112 .115 The gain factor (2) was calculated (3) Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Fig. 2. Variation of the amplitude of the hf oscilla- tions with time. Oscillation frequency 825 Mc; volt- age pulse length 3.6 ?sec; scale 1 ?sec. 100 SO 70 50 40 30 .111 20 W, rel. units 10 7 3 2 0 3 6' 9 72 15 1, cm a 100 80 70 50 40 30 20 10 7 3 18 21 24 where H1 and H2 are the field intensities of the propagat- ing wave at points z1 and z2, while P1 and P2 are the cor- responding hf powers. Graphs of the distribution of the Hp -components of the electromagnetic hf field along the direction of motion of the beam (z axis) at frequency 835 Mc under standing wave conditions are presented for various mag- netic field strengths (1320, 960, and 720 G) in [2], in Fig. 7a,b, and c. In these graphs, the axis of ordinates represents the hf power proportional to lizp (in relative units) collected by a loop suitably oriented and situated at a given point along z. The axis of abscissas represents the distance (in cm) reckoned from the end of the region of interaction. Figures 3a and b show distributions of the Hp -com- ponent of the hf field in the plasma along the direction of motion of the beam for both standing and traveling waves. Analogous graphs were obtained for the Ha-, and Ez-components of the hf field in the plasma. The slight peaks on the curve of Fig. 3a may be explained by the fact that, owing to the imperfect load- ing, together with absorption, there is a partial reflection of the wave (cone length 12 cm, i.e., approximately equal to the wavelength in the system at frequency 835 Mc). Measurements show that on an average the wave- length of the oscillations in the plasma is ?10 to 12 cm, i.e., 3 0.3 (oscillation frequency 835 Mc). Below we give the gain factors as a function of the 27 longitudinal magnetic field intensity (frequency 835 Mc): = IIIIIIIIIMINNIMII MIII !Ilii II I ii 1 Sill r or= 16 IAN in IN 11 Wail , 111 3 6' 9 12 15 18 21 24, 27 1, cm Fig. 3. Graphs showing the spatial distribution of the H -component of the hf field at frequency 835 Mc. The electron beam has current 5 A and en- ergy 15 keV; the pressure of the working gas is 6 ? 10-4 mm Hg, and the magnetic field intensity 1320 G; a) traveling waves; b) standing waves. The beam moves from right to left. Magnetic field intensity, G Gain factor, cm 1320 0.21 960 0.23 720 0.26 On changing the current and velocity of the beam, the gain factors also change, increasing with increasing beam current and decreasing beam velocity. Thus, in the present experiments, when an elec- tron beam interacts with a plasma, slow electromagnetic waves are excited in the latter, and these rise in inten- sity along the direction of motion of the beam. The mag- netic field intensity of these oscillations at the end of the chamber, calculated from formula (1), reaches 0.3 to 0.4 G. Variation of the longitudinal magnetic field in- tensity from 1320 to 720 G hardly affects the frequency of the oscillations, but alters their intensity substantially: as the magnetic field intensity rises that of the oscilla- tions falls. The frequency spectra were measured in the fre- quency range 400 to 3200 Mc at the end of the region of 5 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 f ,Mc 1400 1200 7000 800 500 400 7 I I 2 1320 Oe '4 ' I ? I I I I 10x10-1 f , Mc 1400 1200 1000 800 600 400 2 960 Oe J, rel. units J, rel. units 250- 250 200 200 150 - 150 _ 100 1011 tjO 50 0 i Ii 2 4 6 8 10x10-1 2 ' !III :z 8 10x10 Pressure, mm Hg a J, rel. units 250 200 150 100 50 I I IL 0 4 6 8 7010-4 Pressure, mm Hg Fig. 4. a) Excited frequencies II and 12 and spectral half-widths, and b) maximum intensity of ex- cited oscillations as functions of air pressure in the plasma chamber for a 5-A, 15-keV electron beam for various longitudinal magnetic field intensities. 2 4 8 8 10 x10 1- interaction of the beam with the plasma. For pressures below 8 ? 10-4 mm Hg, the frequency spectra have two (sometimes three) sharp maxima. For the high pressure region (8 ? 10-4 to 2 ? 10-3 mm Hg) there is a character- istic plateau in place of the maxima. From the data obtained, we constructed graphs on which the values of the excited frequencies, the spectral half-widths, and the maximum intensity of the excited oscillations are given as functions of air pressure in the plasma chamber, current (5 and 8.5 A), and longitudinal magnetic field intensity (720, 960, and 1320 G). The beam energy was 15 keV. The graphs for the 5 A current are shown in Fig. 4a and b. The graphs for the 8.5 A current are of the same form. The frequency ranges between the intensity maxima are shaded in this figure. The frequency of one of the intensity maxima (11) depends on the air pressure in the plasma chamber, increasing as this rises. On the other hand, the frequency of the second maximum (12) is independent of pressure, remaining almost constant; further, 11 > 12. We should note that f2 S20/27r, where 00 is the electronic Langmuir frequency of the beam. As seen from the graphs given in Fig. 4, the spectral half-widths of the excited frequencies rise on increasing the air pressure in the plasma chamber. This may evidently be explained by the fact that these half-widths are directly proportional to the frequency of collisions in the plasma, which increases on raising the pressure of the working gas. With increasing velocity of the electron beam, the frequency fj rises. Figure 4b shows the maximum intensity of the oscillations at frequency f as a function of the air pressure in the plasma chamber. From these graphs we may draw the following conclusions; 1) the intensity of the excited oscillations reaches a maximum at pressures 4 to 7 . 10-4 mm Hg; 2) on increasing or decreasing the pressure rela- 6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 ? Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 1 Current, A a A*, MC 520/2n, MC 5 0.53 450 560 8.5 0.44 600 730 tive to the optimum value the intensity of the excited oscillations falls; 3) on lowering the longitudinal mag- netic field intensity from 1320 to 720 G the intensity of the oscillations rises. Measurements also show that on raising the velocity of the electron beam the intensity of the excited oscillations falls. Similar laws were ob- served for experiments in both standing and traveling wave conditions. Since in our case the plasma density N is proportional to the air pressure in the chamber, we constructed graphs relating f to the plasma density for fixed current and energy of the electron beam. Such graphs appear in Fig. 5a and b for currents 5 and 8.5 A respectively. The values of plasma density as a function of air pressure in the chamber were taken from Fig. 3 of [2]. The plasma density was measured by two methods: by means of a hf interferometer (X 3.2 cm), and by means of a method based on the use of the dispersion properties of plasm-a waveguides. 14 12 10 \ 8 4 2 to fo 1 2 N, cm-3 a Cl U 2 /o 2 3 4 5 6 N, cm-3 Fig. 5. Variation of the square of the excited fre- quencies in the plasma (fl) as a function of plasma density for an electron beam of energy 15 keV and current (a) 5 and (b) 8.5 A: ED 1320 G; 0) 960 G; A) 720 G. mov As we know, there is a cutoff band in our wave- guide between the limits coo and (.0H [for the case WH > wo (see Fig. 9, curve ?o?)]. Hence after deter- mining the frequency corresponding to the beginning of the cutoff we may find the plasma density [2]. We may therefore suppose that the squares of the ex- cited frequencies (A) vary in direct proportion to the electron density of the plasma. The excited frequencies rise on increasing the current in the electron beam. The equation of the straight lines shown in Fig. 5a and b may be written in the form a21(2) (A*)2, (4) where a is the coefficient of proportionality between f and f, A* is the frequency of the excited oscilla- tions in the absence of plasma (fo = 0), and f = w0/27r. From the calculations made we obtain the values given in the table (remember that no is the electronic Lang- muire frequency of the beam). As seen from the table, the values Ai' = 450 Mc and A2* = 600 Mc are in agreement with the values of the Langmuir frequency for the electrons in the beam for the above current values. If we neglect a small correction in the investigated frequency region As to fi, the frequency of the excited oscillations fi is 0.53 f for a 5 A current and 0.44 f for an 8.5 A current. We also studied oscillations with frequencies in the 2400 Mc range. These oscillations were only ob- served under standing wave conditions. The measure- ments showed that these hf oscillations in the plasma had only Hz- and Hp -components. The intensity dis- tribution of the oscillations along the z axis at fre- quency 2405 Mc for current 5 A and energy 15 keV with magnetic field intensity 1320 G is shown in Fig. 6. As seen from the graph, the intensity variation of the oscillations along the z axis at frequency 2405 Mc dif- fers from the distributions found earlier., The radiation consists of narrow lines (two or three lines with a half- 7 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 I, rel. units 160 150 140 130 120 110 100 90 80 70 60 50 48 30 20 ? 10 %.? 0 ; 2 3 4 6. 6' Ju_ I 8 3 10 11 12 13 14 1516' 12L,cm Fig. 6. Distribution of the Hp -component of the hf field in the plasma along the axis of the system at frequency 2405 Mc. Beam energy 15 keV, current 5 A, longitudinal magnetic field intensity 1320 G. Direction of beam motion in the oscillogram right to left. width of the order of 3 to 5 Mc). The maximum field intensity of these oscillations is 0.05 to 0.15 G. The fre- quency of the oscillations is almost independent of the pressure of the working gas in the chamber and the magnetic field intensity, but depends greatly on the current and velocity of the electron beam, rising as these increase. Thus we may conclude that the excitation of os- cillations in the frequency region 2400 Mc depends on the boundary conditions, while in the range 825 to 835 Mc it is independent of these. The most distinctive feature of the oscillations at frequency 825 Mc is the fall in their intensity on lowering the magnetic field strength. Analogous measurements were made using argon and hydrogen as working gas instead of air. The de- pendence of Hp on z for air and argon was much the same if the working gas pressure in the chamber was roughly the same and other experimental conditions were identical. In order to obtain the same kind of os- cillations after admitting hydrogen to the chamber, its pressure had to be raised to 5 ? 10-3 mm Hg (i.e., to some six times the-value for air). These results maybe explained by noticing that the specific ionization co- efficients &(V) in air and argon are roughly the same, while for hydrogen the value is six or seven times smaller [7]. Study of Oscillations Excited in the Electron Beam After Passing through the Plasma The block diagram of the apparatus for studying these oscillations is shown in Fig. 7. The electron beam (not modulated at the input), after interacting with the plasma, passed through a helical junction, by means of which hf power in the beam was selected. 8 tEl rEl0tEl 00 o ZICZ1 I1,21/NNYMMMY11111 IVIVIVAIIIINI7A7AVAVNIAMVAltim G') 0000000 Pumping Cs4 Attenuator , i!meri CZ0 ShU-1 0 0 scillo- graph I Pumping Integrating CirCuit To oscillograph Fig. 7. Block diagram of the apparatus for studying oscillations excited in the beam: 1) Tube for creating pressure drop; 2) chamber; 3) inner helix of helical junction; 4) glass tube; 5) outer helix; 6) .current collector; 7) solenoid for creating longitudinal magnetic field; 8) leak. Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 It 3 c.) k 2 The helical junction was made in the following way. In- side a vacuum-sealed glass tube of internal diameter 18 mm was placed a helix of 1.5 mm diameter molybdenum wire. The pitch of the helix was chosen so that the phase velocity of a wave propagated along the helix should be equal to the velocity k- 7 of the electron beam passing inside the same helix. On the out- side, the helix was surrounded by a second, shorter helix with turns in the opposite direction. This latter was connected to a coaxial cable, the wave resistance of which was 75 O. At one end, the inner helix was connected to an electrode at zero ("ground") potential. The ends of the glass tube were covered with a layer of aquadag. Thus electrons falling on the ends of the glass tube and the inner helix spiral flowed to ground. 'The length of the helical junction was -15 cm. The standing wave voltage coefficients (SWVC) of the input into these helical junc- tiorfs-clid not exceed 2.0 in the frequency range 650 to 5000 Mc. These measurements were made on systems without an electron beam. Beyond the helical junction was placed a collector, and the electron beam fell into this. The experiments were mainly carried out with a 5-A electron beam of 15-keV energy at a pressure of 6 ? 10-4 mm Hg, and a longitudinal magnetic field intensity of 1320 G. Measurements showed that the spectra of the frequencies excited in the beam were analogous to the earlier described spectra of oscillations excited in the plasma under the same conditions. The power of the oscillations was determined by a method similar to that described earlier, using fixed attenuators and a calibrated wavemeter. As the measurements showed, the absolute power of the oscillations at frequency 825 Mc was of the order of 150 to 200 W, and at frequency 2400 Mc some 1 to 2 kW. The total power of the oscillations radiated in the 825-Mc frequency range was 3 to 4 kW pulsed. Thus, the total power of the radiation recorded in the beam was 6 to 8 kW pulsed. Estimates show that, for the above beam and plasma parameters, the electric field strength of the excited wave at the end of the beam-plasma interaction region (f - 825 Mc) equals 0.5 to 0.6 kV/cm. The properties of the oscillations excited in the beam in the frequency region -.825 Mc are analogous to those of the oscilla- tions excited in the plasma and described earlier. The time at which the oscillations excited in the beam at frequencies in the range 825 to 1100 and -2400 Mc appeared was also determined. This time was determined from oscillograms similar to those shown in Fig. 2. The time was reckoned from the beginning of the voltage pulse applied to the cathode of the electron gun up to the maximum amplitude of the high frequency envelope. A graph showing the variation of the time of appearance of the oscillations with the air pressure is shown in Fig. 8. As seen from the graph, oscillations at frequency 2400 Mc are excited in the beam earlier than oscillations in the frequency range 825 to 1100 Mc. With increasing pres- sure, the time of excitation of the oscillations in the beam diminishes. 0 104 2 6 810-4 2 It 6 8 10-3 2 p, mm Hg Fig. 8. Time of appearance of oscillations excited in the beam as a function of the pres- sure of the working gas; 1) Frequency 825 Mc; b) frequency -2400 Mc. Discussion of Results Obtained and Comparison with Theoretical Data Let us compare the experimental results obtained with theory. As indicated in [3-6], the interaction of an electron beam with plasma situated in a longitudinal magnetic field may result in the development of instabilities in both beam and plasma owing to the Cherenkov-Vavilov and anomalous Doppler effects. In order to determine the possible spectrum of excited frequencies and gain factors we used a dispersion equation describing the interac- tion of a bounded electron beam with a bounded plasma situated in a longitudinal magnetic field, obtained by M. F. Gorbatenko [611 In the case in which the radius of the plasma column b equals the radius of the beam a, the dispersion equation has the form where 11 1 + + it- 9 N'Y2 [ U.- X- ?(y ?x)" x2 ( 81 n y?x)2J b2coti SY,2, k3v N' = 8= , 0 = (")2 , y = , x = ? A.pv2 wo (00 (00 'All the succeeding calculations were also made by M. F. Gorbatenko. Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 (4) 9 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Li-311 Y Wo -2-u 2 -1 0 1 2 u ?? 4 Fig. 9. Solution of dispersion equations; ?0-0? for plasma, ? for beam with plasma (values of parameters indicated in text). (here k3 = w /v, v = beam velocity, vo = constant lying within the limits 2.4 to 3.8). Dispersion relations for our beam and plasma parameters are given in Fig. 9, where u2 = 8, N' = 2, e = 0.125, which corresponds to N 2 ? 1010 cm-3, H = 1200 G, current = 5 A, v 6 ? 109 cm/sec, and b = 2.5 cm. It follows from an analysis of the dispersion equation that in our case the regions of excitation of the oscilla- tions are situated close to the frequencies coo and WH. In the wo region the excitation may be caused by the Cherenkov-Vavilov effect (region 1) and anomalous Doppler effect (region 3) on the forward wave. In the WH re- gion excitation may be caused by the Cherenkov-Vavilov effect (region 2) and the anomalous Doppler effect (re- gion 4) on the backward wave. The growth increments (imaginary part of x) calculated for these regions in our case have the following values; for region 1 the maximum growth increment equals 0.26, for regicn 2 it is 0.12, for region 3 it is 0.07, and for region 4 it is 0.06. Thus the growth increment has the largest value in region 1, in which the oscillations are excited by the Cherenkov-Vavilov effect on the forward wave (normal dispersion). The frequency fi of these oscillations is close to the electronic Langmuir frequency of the plasma f, but not coincident with this (fi ?0.6 f 0) owing to the bounded state of the beam and plasma and the influence of the strong magnetic field. The experimentally measured frequency of the oscillations most amplified is fi ? 0.53f for a current of 5 A (see Fig. 5a and table), in very good agreement with calculated data. The frequency of the most amplified oscilla- tions was also measured for an 8.5 A current; this equals 0.44 f 0 (see Fig. 5b and table). It follows from the calculations that in our case slow electromagnetic waves with a wavelength of about 7.2 cm in the plasma (frequency 835 Mc) must be excited. The measured wavelength in the plasma is 10 to 12 cm (13 0.3) (see Fig. 3a). Thus slow waves with a phase velocity approximately equal to the beam velocity (vo v) are in fact excited in the present experiments. The calculated value of the gain factors for the conditions ruling in the experiment equals 0.32 cm-1; the ex- perimental values lie between 0.21 and 0.26 cm-1 (see above). Thus the gain factors are also in agreement with calculated values. 10 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 As indicated in [8, 9], on interaction between an electron beam and plasma a convective (transport) instabil- ity should be developed. The graphs of Fig. 3a and b confirm the validity of this principle. During the measurements we failed to observe any marked excitation of frequencies in the neighborhood of the electron cyclotron frequency WH. This corresponds to theory, since in our case the increments in this region of fre- quencies equals 0.12, which is considerably less than that for frequencies in the neighborhood of coo (0.26). Hence the oscillations excited in the frequency range ?800 to 1100 Mc are longitudinal waves in the beam and plasma caused by the Cherenkov-Vavilov effect (forward waves). The experimental results agree with the main theoretical principles. Together with oscillations in the frequency range 800 to 1100Mc, for certain conditions oscillations of fre- quency 2400 Mc are also excited. The frequency of these oscillations is practically independent of the plasma density. In time, they develop earlier than the oscillations in the frequency range 800 to 1100 Mc (see Fig. 8). Their frequency does not depend on the longitudinal magnetic field strength, but depends on the velocity of the electron beam. The intensity of the oscillations in the region of 2400 Mc, in contrast to the plasma oscillations, rises on increasing the longitudinal magnetic field strength. It should be mentioned that the excitation of oscillations at frequencies of 2400 Mc only takes place in the case in which a reflecting metal surface is placed at the end of the region in which beam and plasma interact. All this strongly suggests that such oscillations are caused by the electron beam itself, not depending on the param- eters of the plasma. It may be assumed that in the present case parametric excitation of oscillations takes place. Additional measurements must nevertheless be made in order to decide the question completely. It follows from the measurements made in [1-3] that, for current 5 A, energy 15 keV, and pressure 4 to 6. 10-4 mm Hg, the electron beam loses up to 18% of its initial energy as a result of interaction with the plasma (-13 kW pulsed). This energy goes into excitation of oscillations in the beam and plasma, and also into "heating" these. As measurements show, the power of the excited oscillations is 8 kW pulsed, i.e., at least 60% of the total beam energy loss. We must note, however, that in the experiments carried out the coupling of the beam with the helical junc- tion, and hence the power of the excited oscillations was not optimal, so that it is quite possible that only part of the power in the hf oscillations was taken off from the electron beam during its passage through the helical junc- tion, and hence the power of the excited oscillations may be in fact higher. Some part of the energy goes into heating the beam and plasma. The authors express their thanks to M. F. Gorbatenko for carrying out the calculations. LITERATURE CITED 1. A. K. Berezin, et al., Atomnaya energiya, 14, 249 (1963). 2. A. K. Berezin, et al., Collection; Plasma Physics and Problems of Controlled Thermonuclear Synthesis [in Russian] (Kiev, Izd. AN UkrSSR, 1963), Vol. 3, p. 125. 3. A. K. Berezin, et al., Atomnaya energiya, 18, No. 3 (1965). 4. ya. B. Fainberg, Dissertation [in Russian] (FIAN SSSR, 1960); Atomnaya energiya, 11, 313 (1961). 5. V. D. Shapiro and V. I. Shevchenko, ZhtTF, 42, 1515 (1962); V. D. Shapiro, ZhtTF, 44, 613 (1963); Dis- sertation [in Russian] (0IYaI, Dubna, 1963). 6. M. F. Gorbatenko, Zh. tekhn. fiz., 33, 173, 1070 (1963); Dissertation [in Russian] (Khar'kov Gos. Univ., 1964). 7. A. Engel' and M. Shteenbek, Physics and Technology of the Electrical Discharge in Gases [in Russian] (Moscow- Leningrad, ONTI, 1935), Part 1. 8. P. Sturrock, Phys. Rev., 112, 1488 (1958). 9. Ya. B. Fainberg, V. I. Kurilko, and V. D. Shapiro, Zh. tekhn. fiz., 31, 633 (1961). 11 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 INTERACTION OF PLASMOIDS WITH AN ELECTROMAGNETIC WAVE (UDC 621.384.623) V. I. Veksler, I. R. Gekker, . Ya. Gol'ts, G. A. Delone, B. P. Kononov, 0. V. Kudrevatova, G. S. Luk'yanchikov, M. S. Rabinovich, M. M. Savchenko, K. A. Sarksyan, K. F. Sergeichev, V. A. Silin, and L. E. Tsopp Translated from Atomnaya biergiya, Vol. 18, No. 1, pp. 14-18, January, 1965 Original article submitted April 22. 1964 Some preliminary results of a study of plasma acceleration in circular waveguides are presented. The study was made in the 10-cm range on systems with H01 and Hli type waves and various plasma injectors. Plasmoids with initial particle concentration 1012 cm-3 and above were in- jected with an initial velocity of 5 ? 106 cm/sec from a spark source, or formed directly on the waveguide axis by means of a plasma source with pressure drop, the working vacuum in the accelerator being 10-7 to 10-6 mm Hg. Diagnostics were conducted by means of electric probes uhf methods, and an electrostatic particle energy analyzer. The plasma was contained by auxili- ary external magnetic fields of various configurations. ,Accelerated ions of energy greater than 10 keV were obtained. A proposal was made in 1954 [1] to use the coherent interaction of charged particles with an electromagnetic wave for accelerating plasma. Subsequent theoretical studies showed that, on fulfilment of certain conditions, prolonged acceleration of plasmoids could be achieved, their form and dimensions remaining unchanged [2, 3]. In the present investigation, the initial stage of acceleration and the behavior of the plasma in the wave- guide in the presence of a strong electromagnetic wave were studied experimentally. No attempt was made in these experiments to secure stable acceleration of the plasmoids or reach high energies of accelerated particles. Two systems were prepared; these differed in the type of accelerating wave used and the method of plasma injec- tion. External magnetic fields were used to reduce the diffusion of plasma to the walls of the waveguide. Plasmoids were created in the waveguide at a vacuum of 10-7 to 10-6 mm Hg, both with a spark injector [4] and a pressure- drop plasma source [5]. The investigations thus made enabled us to obtain the first experimental data on the radia- tion acceleration of plasma. Acceleration of Plasma in an H01 Wave The choice of the H01 wave was determined by the following considerations; 1. The field configuration of the H01 wave is such that it permits metal rods of small cross section to be in- troduced along the radius and along the axis without seriously distorting the field pattern. This enables us to place the plasma gun and probes inside the accelerating waveguide. 2. The H01 wave is a wave of the lower type and quite easily excited. 3. The electric field configuration of the H01 wave eliminates the occurrence of uhf discharges to the wave- guide walls. In order to achieve radiation acceleration of plasma in an H01 wave, the system shown schematically in Fig. 1 was constructed. Power from the uhf generator passes into the waveguide tract through a ferrite valve into a King- type wave transformer. Here the H01 type wave in the rectangular waveguide is transformed into an H01 type wave in the circular waveguide. The accelerating waveguide is formed by a stainless steel tube with wall thickness 1 mm. This kind of tube ensures low damping of the uhf waves (around 0.2 dB), and screens the external pulsed magnetic field very little. Between the accelerating waveguide and the transformer lies a vacuum-tight uhf window. The 12 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Fig. 1. H01 wave accelerator (schematic): 1) uhf gen- erator; 2) ferrite valve; 3) wave transformer 4) accelerating waveguide; 5) spark plsma injector; 6) magnetic system; 7) pumping section; 8) uhf absorbing load; 9) screened electric probe; 10) diagnostic window; 11) vacuum-tight uhf window; 12) section with two de- tector heads; 13) high-vacuum line. Fig. 2. Screened electric probe ion current oscillograms: 1) uhf power switched off; 2) uhf power switched on; 3) calibrating signal, period 2 ?sec. ??????\ 3 Fig. 3. Signals from an uhf probe placed at the window of the accelerating waveguide (time base 23 ?sec): 1) Envelope of uhf pulse without the plasma; 2) the same on discharging the plasma gun; 3) signal from gun. 2 Fig. 4. Signals from two detector heads displaced by a distance of 10 cm (time base 17 ?sec): 1) First head; 2) second head. accelerating waveguide is terminated by an absorbing uhf load coinciding with the pumping section. Windows for plasma diagnostics are set in the accelerating wave- guide tube. The 10-cm wave uhf generator operates on a single pulse 8 ?sec long. The mean power flow density through the cross section of the accelerating wave- guide is not greater than 8 ? 103 W/cm2. The standing wave coefficient (voltage) of the whole waveguide sys- tem of the accelerator (without plasma) is not worse than 1.3. A plasma injector of the spark type is introduced along the radius into the center of the waveguide and has a symmetrical "counterweight," reducing distortion of the fundamental wave. The maximum current through the gun in the aperiodic condition is 1.8 kA for a duration of 0.3 ?sec. The spark gun creates a plasma containing around 50% ions of atomic hy- drogen. The total number of ions is 1018 to 1018. In order to reduce the passage of plasma to the walls of the accelerating waveguide, both a longi- tudinal magnetic field and also a magnetic field created by a system of straight conductors parallel to the waveguide axis, fed by currents moving in al- ternate directions, are employed. During the motion of the plasma in the accelerating waveguide (20 ?sec), the magnitude of the magnetic fields remains prac- tically unaltered. The accelerated ions are recorded by means of screened electric probes [6] introduced from the end of the waveguide. Figure 2 shows a superposition of two oscillograms giving the probe ion currents for uhf power "on" and "off"; the longitudinal magnetic field here equalled 300 G, and the gun to probe distance was 45 cm. We see from Fig. 2 that switching on the accelerating field leads to a shift in the velocity dis- tribution of particles in the bunch in the direction of higher velocities. It was not possible to determine the total number of accelerated particles using the probe method, since this can only separate out particles with velocities exceeding the maximum particle velocity in the ab- sence of the uhf accelerating field. Estimates showed that there were not less than 1012 accelerated par- ticles, the maximum velocity of some of the ions ex- ceeding 108 cm/sec. It should be noted that these ex- 1)erimental values agree satisfactorily with calcula- tions in order of magnitude, if we assume that the momentum of the uhf wave is transferred completely to the plasma. Varying the number of particles created by the plasma injector by an order of magnitude (by varying the conditions of the spark gun) does not great- ly affect the number of accelerated particles. 13 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 1 2 Gas Fig. 5. Principle of H11 wave accelerator; 1) uhf generator; 2) ferrite valve; 3) detector head; 4) wave transformer (H ri---03-.14)1); 5) vacuum-tight uhf window; 6) high vacuum pumping line; 7) electric probe; 8) absorbing uhf-load; 9) electron multiplier; 10) electrostatic (127?) par- ticle energy analyzer; 11) magnetic system; 12) accelerating waveguide; 13) pressure-drop plasma source. Fig. 6. Oscillograms (time base 6.4 psec); 1) uhf envelope; 2) signal from electric probe. I, rel. units 1,0 0.6 0,4 0,2 0 2 4 6 8 10 12 14 Energy, keV Fig. 7. Energy spectrum of accelerated ions; 1) uhf wave power P = Pmax ; 2) P CI. 5 Pmax? Operation with the magnetic field created by the system of straight conductors required the introduction of a glass tube inside the metal accelerating waveguide, since, as experiments proved, the plasma losses during motion in a metal tube with this field were large (two orders in density lost in a distance of 1 cm). This is connected with the fact that the polarization of the plasma arising from the presence of the transverse magnetic field is taken by the metal walls, and polarization currents flow constantly in the plasma, retarding its motion. The introduction of a glass tube leads to the insulation of the plasma from the metal walls. The results obtained on accelerating plasma by an uhf wave in this field were analogous to those described earlier. 14 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 By means of an uhf probe (detector head) set at the diagnostic windows of the accelerating waveguide, it was observed (Fig. 3) that, after discharge of the plasma gun, the waveguide practically cut off, that is a "block" was set up for the uhf-wave independently of the external magnetic field. This was confirmed by measurements made with the help of two detector heads [7] in respect of uhf power reflected from the plasma. The presence of the reflected wave appeared in the form of modulation of signals sent from the detector heads (Fig. 4). Analysis of the experimental data showed considerable reflection of the uhf wave from the bunch, reaching some 900/o. Acceleration of Plasma in an H11 Wave The intensity polarized H11 wave is a wave of the lower type in a circular waveguide. A possible failing of the H11 wave is the considerable electric field strength at the waveguide wall, facilitating the development of uhf breakdown. On the waveguide axis, in a condition well removed from critical, the H11 wave takes on a form close to a plane wave, and in certain cases rthis may make for easier comparison between experimental and computed data. Figure 5 shows the principle of a system for accelerating plasma in an H11 wave. The uhf generator is the same as that in the arrangement of Fig. 1. Excitation of the linearly polarized Hn wave is effected by smooth transition from a rectangular waveguide. The accelerating waveguide also consists of a stainless steel tube 1 mm thick. The magnetic field is formed by a system of six straight conductors with currents flowing in alternate di- rections. A pressure-drop source is used to form the plasma. The principle of this source is described in [5]. A plasma pinch with particle concentration above 1012 cm-3 is formed in a discharbe between electrodes A and K (see Fig. 5) in a longitudinal magnetic field. The pressure of the hydrogen admitted at, the anode A and cathode K equals 104 mm Hg. The pressure in the accelerating waveguide is 10-6 mm Hg. The pressure difference is maintained by means of four diffusion pumps. After the plasma pinch has been formed, the A-K voltage is switched off and the magnetic field of the straight conductors is switched on (the time of growth of-the field is 25 ?sec). After the magnetic field has reached a value of the order of 103 G (at the stops) and the plasma is squeezed away from the walls, the uhf field is switched on. A displacement of the standing waves takes place in the waveguide as the plasma moves. This is recorded by a detector head (see Fig. 5). The observed modulation of the uhf oscillation envelope is analogous to that shown in Fig. 4. The accelerated particles were recorded by an electric probe screened from the uhf field (asymmetrical double probe); this was introduced on the side of the uhf-load and could be moved along the waveguide axis. Figure 6 shows an oscillogram of the uhf oscillation envelope and signal from the electric probe situated at a distance of 30 cm from the point of injection. In the absence of the uhf wave, no signals are observed from the probe. From the delay in the arrival of the plasma we may estimate its mean translational velocity, which in or- der of magnitude is 107 cm/sec. In order to measure the energy of the accelerated ions, an electrostatic analyzer rotating the particles through 127? was used together with an electron multiplier as ion detector. The analyzer enables us to measure ion energies within the range 1 to 100 keV; it is placed at the end of the accelerating waveguide, 70 cm from the injector. Figure 7 shows the detector current as a function of the energy of the recorded ions. With increasing uhf power the energy spectrum shifts towards higher energies. On increasing the sensitivity of the system, ions with en- ergies up to 50 keV were recorded. Conclusions As a result of the experiments described, radiation acceleration of plasma was established. Accelerated ions were obtained in both systems, independently of the type of wave in the waveguide and the form of the plasma in- jectors. The energy of the accelerated ions increased on raising the uhf power. The total number of accelerated particles is of the order of 1012, which corresponds to the momentum of the uhf wave transferred to the plasma. The maximum energy of the accelerated particles is up to 50 keV. Regarding the small value of the mean energy obtained in the experiments, there is a number of explanations. 74: First, our plasma injectors give a very large number of particles (up to 1013 to 1016) which, for a given uhf field power, cannot all be markedly accelerated. The background of unaccelerated particles blocks the waveguide. Secondly, almost all the hf power is reflected from the plasma. Thus the acceleration region is small (a few cm), and the length of the accelerating waveguide (30 to 100 cm). Thirdly, a wave of the H11 type evidently cannot 15 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 exert a stabilizing influence on the size and direction of motion of the bunch, as would be expected from theory, owing to the large dimensions of the bunch [2]. The results obtained for the acceleration of plasma in waves of the H01 and H11 types are similar to one another (a wave of the H01 type should not stabilize the dimensions of the bunch in thedirection of acceleration). This is also explained by the action of the background particles in screening the uhf wave. Higher energies can evidently be obtained not only by increasing the uhf power but also by forming com- pact bunches at the beginning of the acceleration. The use of inhomogeneous fields [3] for stabilizing the transverse dimensions of the bunches justified itself completely. We had hardly any plasma losses to the walls of the waveguide on using quadrupole or sextupole,mag- , netic fields. Up to the present, however, we have not succeeded in stabilizing the longitudinal dimensions by means of an inhomogeneous field [3]. This is explained by the low initial velocity of the bunch and its small conductivity. It would appear, that, in the initial stages of acceleration at least, we should use two types of wave simultaneously in the circular waveguide, as was proposed earlier [2]. Thus the preliminary experiments carried out offer a basis for developing a fairly clear program to increase the energy and number of accelerated particles. LITERATURE CITED 1. V. I. Veksler, CERN, Symposium, Geneva (1956), Vol. 1, p. 80; Atomnaya energiya, 2, 427 (1957). 2. M. L. Levin, M. S. Rabinovich, and G. A. Askar'yan, Proc. Internat. Conf., CERN (1959). 3. G. A. Askar'yan, et al., Nucl. Fusion, Suppl., Part 2, 797 (1962). 4. W. Bostic, Phys. Rev., 104, 292 (1956). 5. B. P. Kononov and K. A. Sarksyan, Zh. tekhn. fiz., 31, 1294 (1961). 6. K. D. Sinernikov, et al., Plasma Physics and Problems of Controlled Thermonuclear Synthesis [in Russian] (Kiev, Izd. AN Ukr.SSR, 1962), p. 102. 7. A. Bloch, F. Fisher, and G. Hunt, Proc, IEE, 100, 93 (1953). 16 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 DETERMINING THE PERTURBATIONS OF THE PARAMETERS IN THE MAGNETIC AND ACCELERATING SYSTEMS OF AN ELECTRON SYNCHROTRON ON THE BASIS OF AN ANALYSIS OF INFORMATION REGARDING THE BEAM (UDC 621.384.60) I. P. Karabekov Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 18-22, January, 1965 Original article submitted May 13, 1964 A method of selecting and analyzing information regarding the center of gravity of the beam in the cross section of an accelerator vacuum chamber is proposed; on the basis of this, the deviation of certain fundamental parameters of the electron synchrotron may be obtained. The various components making up an accelerator can only be constructed with finite accuracy. Thus the parameters of the magnetic and accelerating systems also can only hold to a certain accuracy around their cal- culated values. The deviation of these parameters by more than the permissible values leads to a considerable loss of particles. Hence the question of measuring the parameters of the magnetic and accelerating systems from beam data and also stabilizing them (by introducing special corrections) demands special attention in setting up modern accelerators. At the present time, methods of controlling the frequency of the accelerating voltage from information regarding the radial position of the beam [1, 2], methods of measuring and stabilizing the frequency of betatron oscillations [3, 4], and a method of correcting the space harmonics of the magnetic field from beam data [3, 5] have been or are being developed. Also being developed are methods of correcting the magnetic field before injection in order to make the start-up of the first rotation of the beam automatic [6]. Different arrangements of the mutual disposition of the sensory beam elements and controlling devices are considered, as well as the number of controllable sections of orbit required [7]. The distortion of the beam trajectory depends on many factors associated with the deviation of various ac- celerator parameters from their nominal values. For effective correction of the beam trajectory and reduction of particles loss during acceleration, it is important to determine the distortion arising correctly, i.e., to separate out the perturbations corresponding to the various parameters. The possibility of separating the perturbations due to different parameters on the basis of an analysis of beam information and of determining the operations required to correct these perturbations enables us to make the tolerances laid on various components of the accelerator less stringent, so making construction cheaper and more rapid. In the present paper, methods of handling beam information and determining therefrom the perturbation of certain leading parameters of the magnetic and accelerating systems are discussed. Determining the Value of the Field Perturbation of the Magnetic Sections of the Ac- celerator, and Corrective Operations for Compensating These Let us suppose that we know the coordinates of the trajectory of the center of gravity of the beam and its derivative with respect to azimuth at the ends of the magnetic section at points 01 and 02. Let us 'assume that our magnet has no field deviation; then the motion of the particles within the magnet in question must be described by the differential equation (1) 2np where 1 is the length of the period of the magnetic system; p the radius of curvature in the magnets, n(0) the field falloff index. Hence 17 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Col% CV*, r' =C0F' cv*/, (2) where F and F are the Floquet function and its complex conjugate, Co arid Co* are complex conjugate conStants, and 6 Varies by 2it Within the lirnits of the gradient period. Solving the algebrait system of equations (2) with respect to Co at points 61 and 02; we obtain r1F1' ? riFt ?2i c 02_ r2Fr ?2i ' (3) (4) in which C01 is identically equal to CO2 for AH /H0 = 0. The existence of some perturbation, however, destroys this identity; AC =CO2 ? C = r1PI ?2i (5) At the same time, the quantity AC, as we know already [8], is associated with the value Of the perturbation(AH /H0)8 via the expression 02 ( 's 2 I (. AC = ) 2i01 \ (6) Let us measure ri, r2, ri, and 4 and determine AC from (5). Expression (6) connects the quantity AC with the per- turbation (Ai-1/ tio)8 in the unit; this connectian, however, is clearly not unequiVocal. What is important in prac- tice is not the exact measurement of the function (AI-I /1-10)e , but the determination of such equivalent Corrective perturbations as will restore the condition AC = 0, i.e., make the atilt perturbation-free. (The deviation of the beam inside the unit must not be tOo great.) Since AC, generally speaking, is a complex quantity, two parameters are required in order to compensate it. Let us divide the unit into two parts (these may, for exampit, be focusing and defocusing parts). Then expression (6) may alas be written in the form On 02 AC = '\ 2 1 ( AHI r ) F* -F K 92-t ) 2ip Ho /eq. 61 (7) where (Alli /H)N is the required equivalent perturbation created by the first correcting cbil,andK is the ratio be- tween the value8 of the perturbations created by the first and second correcting coils. By due choice of the signs arid Magnitudes of (A1-11/Ho)e,4 and K, the right-hand sides of formulas (5) and (`7) may be made equal. EqUating the arguments of the complex expressions iii (5) and (7), we obtain where on On, r ? 1 IM dO e 1 F* a'0 1 //i1(Z) Re (Z) 01 81 K 02 Z Ini() [ F* aqj [ F* (101 Re (Z) Cid Olt Correspondingly the quantity (Mi. /1-ideci is determined by the expression 18 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 (8) 1 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 i AH, _ r2F:' ?riF;.?riFf' -F-riFt \, Ho )eq ? ?N. 62 , ( ?12 a - Y -= { F* dO+K S F* (10} 271 Q el en (9) where en is the coordinate of the middle of the block. For the simple case in which AH/ Ho = const over the whole length of the block, K = 1 and (Nil/ Ho)eq = AH /Ho. Formulas (8) and (9) do not depend on normalization and the initial phase of the Floquet function. Still more im- portant, the results of determining (6111/H0)eq .and K do not depend on the number of passages of the beam through the magnet over which the quantities r and r' trieasured by the signal electrodes are averaged. This enables us to increase the precision of determining (Alii /H0)eq and K for a given precision of measuring the momentary values of r and r'. In order to determine the sensitivity of the method, calculations were made for, the Erevan annular electron accelerator EKU with the FOFDOD magnetic structure; the radius of curvature of the magnets was -25 m, and the mean ring radius -30 m. Calculations showed that use of the values of r and r' measured at the ends of the block yielded a reliable value of AH /Ho = 0.5% for the perturbation. Thus, the occurrence of a deviation AH /Ho = 0.50/0, constant over the length of the bloc, leads to a change of Ar2 = 1.21 mm and Ari = 1.18 mm/rad in the coordinate at the exit from the block. The coordinates of the beam axis are conveniently measured at the ends of the mag- netic block, since the derivatives with respect to azimuth do not alter in the free spaces. For greater reliability in the determination of the derivatives we may then use information from sensing devices situated at the entrance and exit of two neighboring blocks. The fair distance between these points ensures good precision in determining r'. Thus for the EKU accelerator for the length of the free space between the blocks AO = 0.86 rad and .l-1/ H0 = 0.50/0, Ar'6,0 = 1.00 mm. The value of the derivatives may be made more exact by additional measurements in the free spaces. The method enables us to determine and compensate perturbations in the magnetic system caused by im- precise installation of the blocks and chance displacements. In the case in which the beam-sensing elements are fixed in the vacuum chamber, such perturbations will be sensed as phase shifts of the Floquet function. In order to distinguish the case of loss of beam inside the magnetic block from that of its, emergence with zero parameters, we must use the total signal from the sensing elements situated at the end of the block. If the over-all signal at the block entrance is zero, then a special signal proportional to the maximum possible displacement of the center of gravity of the beam at the block exit must be applied to the analyzing device. From this signal and the measured values of 1.1 and r1 we may determine the values of (AH1 /H0)eci and K. For successive correction of the blocks, however, this case in not very probable. Thus, for the EKU, loss of the beam inside the block in the case of zero entrance parameters (r1 = 0, r1 = 0) means a field deviation of AH /Ho r:-.1 300/0 in the block. Determining the Magnitude of the Frequency Deviation of Betatron Oscillations Suppose we know for certain that in one of the magnetic blocks the magnitude of the perturbation is constant along the whole length. If r1, ri and r2, 1.2 are the measured values of the coordinates and the derivatives of the beam center of gravity at the ends of this magnetic block, then the value of K I determined from Eq. (8) is in- dependent of the value of AH /Ho. Let us suppose that the frequency of the betatron oscillations varies by Av. Here we obtain a new distribution of the Floquet function with respect to azimuth, leading to an additional dis- tortion of the beam trajectory. If the values of r1 and r1 remain the same as for Ay = 0, the r2 and ti acquire cer- tain increments Ar2 and A*. If the new values of r2 and r2 are put into expression (8), the value of K will differ from unity. Let us examine the variation with Ay of the phase of the expression Z d-r;Fi*. (10) The new values of the Floquet function and its derivative for a change of Lv in the frequency of the betatron os- cillations will to a first approximation be given by the expressions; FejAv? F iAv0F, cp'= iAvFeim'e?F'eim'o F' (1+ iAv0)? iAvF. 19 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 From the measured values of r1 and ri and the new values of the Floquet function, we determine 72 and Making some fairly simple mathematical transformations and rejecting terms containing Av2, we obtain r2= rzfr ?r2fo ?Re {K (riri)+ L (rolAv, (12) r2= r2 fr -1- r2fo ? Re {N (riri)+ E (n)} Av , (13) where r2fr and r2fr, are the values of the coordinate of the center of gravity and its derivative at the point 02 for Av =0 and AH /Ho = 0 ("free"), and r2f0 and r2f0, are the "forced" solutions at the point 02 for A v = 0; K(ri, ri) and N(ri, ri) are functions determined by the values of r1 and ri, and L(II) and E(II) are functions determined by the magnitude of the perturbation in the magnetic block. These functions have the form K (r jr) = ? F2 (02? 01) ? riF:F 21, (14) N (riri) = ?4-{[F2--F; (02 ? 01)] [riF ,*" ? ? riF:F;} , (15) Here 82 92 L (n) = F211F*0 d0 ?02 c F* do) , Eli ea 02 E (n) = -2- [ (02F; ?F2) F* de ? F; F*0 de . ?2t,IQ Ho ? Substituting expressions (12) and (13) into (10), rejecting terms containing Av2, and allowing for the condition r2fr we obtain (16) (17) (18) (19) Z = r2 fo F:' ? AvRe {K (r iri)+ L (n)} F:' ?r fo F; + Av Re {IV (r tri)+ E (II)} F. (20) Let us form the ratio of the imaginary part of expression (20) to the real part. Expanding the resultant expression in series in powers of Av and restricting consideration to the term containing the first power of Av, we obtain; Im ()= r2 fo ImFt" ?ri fo InzF Av T Re (Z) r2f0 Rely ?r'2 fo ReF An expression for T(ririlI) can easily be found by making some simple transformations. In expression (21) 02 m F* T2 fo I mFt' ?r 2' fo IniF; r2 fo ReFr fo 02 ,"="- const. Re F* del (21) (22) 'Thus for the t KU accelerator this quantity equals ?0.195. The function T(ri,rilI) is a linear function of the prin- cipal coordinates, their derivatives, and the value of the perturbation. Hence the value averaged over many rota- tions of the beam is = T(II), i.e., constitutes a certain constant determined by the magnitude of the perturbation specially introduced into the block. Substituting expression (21) into (8) and averaging over many turns, we determine the deviation of K from unity. This deviation may, for a known value of T(11), be graduated in units of A v. 20 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Determining the Amplitude and Frequency Coherent Phase Oscillations In electron synchrotrons calculated for a particle energy of the order of several BeV, owing to the high mul- tiplicity of the high frequency voltage the direct method of measuring the. amplitude and frequency of coherent phase oscillations presents considerable difficulty. This information may be obtained far more simply by measuring the coherent deviation of the particle energy from the equilibrium value arising for phase oscillations. It is known [8] that for Es >> mc2 da) AE dt E, (1), (23) where q is the multiplicity of the frequency of the accelerating voltage, c4)0 is the frequency of rotation of the par- ticles in the orbit, and cc is the logarithmic derivative of the length of the orbit with respect to momentum. Let us suppose that the momentary phase of the accelerating voltage for which the center of gravity of the beam passes through the middle of the accelerating gap under the influence of an external perturbation, is given by the expression 0= Os+ Acp cos Qt, (24) where cps is the value of the equilibrium phase, Acp the amplitude of the phase oscillation, and Q the oscillation frequency. On this assumption, expression (23) will have the form AE ? ? AyS2 sin SU Tooa (25) Let us measure the coordinates and their derivatives with respect to azimuth at the ends of one magnetic block and determine the value of the total perturbation arising as a result of deviations of the magnetic field values in the block and the mean particle energy in the beam: 02 * All 7.21T ?r;F* ?riF,*: +r/?* =(?-)2 1 ?c (0) dO ( 1 2 AE F* dO. 23t 'CO . Ho 23t j es el. 0.1 The deviation of the magnetic field in the blocks during the acceleration cycle changes considerably more slowly than the coherent deviation of the particle energy, owing to the phase oscillations. Hence the duly separated high frequency component of expression (24) determines the amplitude and frequency of the oscillation of (AE/E)t. The frequency of the variation of (AE/E0)t may be measured by many well known methods. The amplitude of the phase oscillations will be connected with the maximum deviation of the beam energy by the expression qcooa AE = Q max. Ao In conclusion, the author considers it his pleasant duty to thank S. M. Rubchinskii, t. L. Burshtein, A. A. Vasil'ev, Yu. F. Orlov, S. A. Kheifets, and V. M. Kharitonov for discussion of the work, and M. A. Garzoyan for help in carrying it out. LITERATURE CITED 1. A. A. Vasil'ev, A. A. Kuz'min, and Yu. S. Ivanov, Pribory i tekhnika eksperimenta, No. 4, 111 (1962). 2. 'k . L. Burshtein, Yu. S. Ivanov, and A. A. Kuz'min, Pribory i tekhnika eksperimenta, No. 4, 102 (1962). 3. t. L. Burshtein, et al., Atomnaya energiya, 12, No. 2 (1962). 4. A. A. Vasil'ev, A. A. Kuz'min, and V. A. Uvarov, Pribory i tekhnika eksperimenta, No. 4, 134 (1962). 5. A. A. Vasil'ev, Transactions of the International Conference on Accelerators, Dubna, 1963 [in Russian] (Moscow, Atomizdat, 1964), p. 871. 6. A. A. Vasil'ev, Dokl. AN SSSR, 148, 577 (1963). 7. A. I. Dzergachard, V. A. Karpov, See [5], p. 867. 8. S. A. Khaifets, The Electron Synchrotron [in Russian] (Erevan, Izd. AN Arm. SSR, 1963). Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 (26) 21 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 PHASE STABILITY OF A SYSTEM OF PARTICLES IN SELF-REGULATED ACCELERATORS (UDC 621.384.60) f. A. Zhil'kov and A. N. Lebedev Translated from Atomnaya tnergiya, Vol. 18, No. 1, pp. 22-28, January, 1965 Original article submitted February 13, 1964 The problem of the phase stability of a sytem of particles in a cyclic accelerator with frequency autocorrection of the accelerating field along the beam is considered. The stability of nonlinear synchrotron oscillations is investigated by the kinetic-equation method for arbitrary characteristics of the self-regulating system. Some general stability criteria are obtained. One of the most promising routes in the development of cyclic accelerators is the wide application of beam autocontrol systems, which peimit a considerable reduction to be made in the allowance for different parameters of the magnet and high-frequency systems [1, 2]. In practice the most important and at present most widely used system of this type is the system of automatic frequency trimming of the accelerating field by radial (or phase) shift of the accelerated particles, thus permitting considerable increase in the stability of coherent synchrotron os- cillations relative to various perturbations. An investigation, which was carried out in linear approximation [3], showed that the frequency of coherent synchrotron oscillations, i.e., oscillations of the beam center, is increased by a factor of (1 + K)112 where K is the amplification factor in the self-regulation cycle with respect to the radial shift of the beam. In addition, it was proved possible to achieve strong damping of the coherent oscillations. The oscillations around the beam center, discussed in [3] in linear approximation, are not subject to the effect of self-adjustment and have the normal frequency of synchrotron oscillations. Naturally, the nonlinear nature of the phase motion should alter this picture, leading to coupling of the beam-center oscillations and the free oscilla- tions around it. The representation of the nature of this coupling can be obtained in this case if the first moments of the distribution are considered as in [4] and, more rigorously, in the first and second sections of this paper. However, for the subsequent statement of the problem the discussion should center on the stability of a system having a large, almost infinite number of degrees of freedom corresponding to a large number of accelerated par- ticles. It is shown below that this investigation can be carried out by the kinetic-equation method with self- consistent interaction. It was found possible to obtain a very general characteristic equation, useful for a wide class of regulatory systems and giving in principle an answer to the problem .as posed. The paper has been limited to the investigation of certain general properties of this equation which are in- dependent of the choice of the feedback circuit parameters. The calculation of an actual system, requiring com- putation of a number of purely radiotechnological considerations, will be carried out in a separate report. 1. Statement of the Problem In order to describe the synchrotron oscillations of an individual particle, we shall use the canonical conjugate variables 23520 dE eV sin cps (E) ' Es where w(E)is the rotational frequency of a particle with energy E; V and ca are the amplitude and phase, respec- tively, of the accelerating potential; 00 is the frequency of the linear synchrotron oscillations in the absence of self-regulation. We shall neglect the explicit time dependence of the parameters 00, V, etc. 22 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 If we choose T = Qt as an independent variable, then the synchrotron oscillation equation can be written in the form uF (q)) ?-= cos q)? cos cps Sin cp.= u+ A (T), (1.2) where A(T) is the correcting adjustment to the frequency of the accelerating field, associated with the energy of the self-regulation system and expressed in units of Q. According to Eq. (1.2) the kinetic equation which describes the change of the distribution function has the form f(u, T) [-I-q, T) = O. (1.3) The quantity A can be related to the various characteristics of the beam as a function of the following (or tracking) system parameters: to the coordinates of its center of gravity, dimensions, etc. In the general case, if we denote by K(u, , w) the reaction of the system with frequency u.) to a shift of a point-like beam with respect to u, and yo, then in Fourier presentation the quantity A(w) can be described in the form of a linear function of the dis- tribution function A (6)) =K (u, cp, o) f (a, cp, co) du dcp. (1.4) Equations (1.3) and (1.4) represent a closed integral-differential system describing the behavior of the entire buildup of particles in an accelerator with self-regulation. We shall proceed further from the fact that this system permits a stationary (equilibrium) solution: f o(u, co), Ao = const. We note that the constant component of the cor- rection signal Ao, associated with the equilibrium distribution, can be set equal to zero without limiting the gen- erality, since this leads simply to an insignificant indeterminacy of the equilibrium energy. It is not difficult to see that an extremely wide range of equilibrium distributions is possible, on which a unique requirement is im- posed ? the constancy of f 0 along the phase trajectory [see Eq. (3.2)]. In the general case, the center of the equi- librium phase cos as a consequence of the nonlinearity of the synchrotron oscillations, i.e., in conseque ce of the deviation of the potential well ? f Fcico from parabolic. This shift is found to be greater, the larger the equilibrium phase of the beam. In accordance with the assumptions made above concerning the absence in the equilibrium state of a correction signal Ao, it should be assumed that the center of the equilibrium distribution with respect to energy coincides with Es, i.e.; uo = 0. 2. Method of Moments First of all we shall consider the case of a beam of quite small dimensions, since by this example it is easier to trace the physical significance of the relationships obtained below. Multiplying the kinetic equation (1.3) by ( ? 0)Juk and integrating with respect to the entire phase space, we obtain a system of equations for the set of distribution moments Mi,k = (99 ? vo)juk (the bar denotes the average): II; j-1, /AM5,h kF (9)) =0. (2.1) In accordance with the assumption made above concerning the smallness of the beam, the distribution moments should be reduced rapidly with increase of their number. Having expanded the quantity F(yo) in a Taylor series around the point cpo, Eq. (2.1) leads conveniently to the form j, Pi 41? /A (t) M_1, co F (1) (W m? 1! j+17 h-1-= 0. 1=0 (2.2) We note that the system of equations (2.2) is, generally speaking, nonlinear since the correction signal A is con- nected with the moments by the relationship (1.4). We now use the fact that the phase dimensions of the beam 23 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 A > 1) the "rigidity" of the oscillations of the center of gravity of the beam can be increased strongly and even damping of them can be originated (for example, for Re K2 < 0). The natural oscillation frequency of the second moments, which in this approximation remain free, is equal to twice the frequency of the synchrotron oscillations in the ab- sence of self-regulation. By taking into account terms ?A4, the corrections to the natural frequency of the first two moments can be found (terms ?A3 make it possible to determine only the partial frequencies a the third moments, equal of course to ?1 and ?3). These calculations are quite cumbersome since they are associated with the calculation of a deter- minant of the 10th order. We shall mention only the most important result ? the correction of the first approxima- tion to the real partial frequency w = 2 of the second moments, since small corrections to the complex frequency (2.6) cannot change the nature of the motion qualitatively. If we assume that 0./ = 2 + a(1 a I 0) and buildup (Im a < 0) of the oscillations are also possible at this frequency. The con- dition of stability for I K1,2 >> 1 is, obviously, the inequality Kt Re ?K2 1 Po?(Atillo)Pie(131-p?)1+ (A:1/140) Pie(Pi?P?)t (13) In order to select the cycle for the reactivity measurement with respect to the positive period, calculations were carried out of values of 6 for various reactivities and holding times of the system at a constant power level. The results of the calculations are given in Figs. 1 and 2. The deviation of the measured period from asymptotic was determined experimentally for a reactivity of 0.10/0 in the critical beryllium oxide assembly being investigated. As the asymptotic period in these measurements, the steady state period was used as measured over 200 sec after a positive reactivity surge (for the stated time the value of 6, as shown by the calculations, does not exceed 0.1% The results of?the experiment and of the calculation are compared in Fig. 3. Measurement of Reactivity The calculated and experimental data obtained concerning the magnitude of the deviation of the measured period from asymptotic permits selection of the reactivity measurement cycle to be made. 38 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 In the experiments on the critical assembly, .the results of which are given in the present paper, the holding time at constant power was taken equal to 1000 sec, A shorter holding time, although advantageous from the point of view of reducing 6, is inadvisable since prior to measurement of the positive period it is necessary to determine the critical state of the assembly. The positive period was measured over 100,200 sec after the reactivity range. The measurement results were analyzed by the "inhour" equation.. The cycle taken for the measurement of the period and the equipment used permitted the reactivity to be measured to an error not exceeding ?1.55. A section of the control rods was,cali- .. brated by the method mentioned. The data obtained are shown in Fig, 4, In addition to the positive reactivities, the negative reactivities were measured by an integral method [7]. It has been shown that after a Laplace transform of Eq. (1) and (2) expression (5) is obtained which, for Ulieff ,lXicio/keffRiTio and for p = 0 is transformed to the form where whence N (0) ? -Q keff ' co N (0) = n (t) dt, to no xi lkicio yipi N (0) k p?n 2,,? ? eff o If the reactor has previously operated for sufficiently long at stationary power, so that the condition ci0Xil/k5in0 = 1 is fulfilled for all the delayed neutron groups, then -p is determined from the expression __ Pole \-1 ViN N(0)1t-eii ? In contrast from the "inhourn equation, Eq, (14) depends to a great extent on the quantity )Li. The presence of photorieurrons in the system increases the significance of this fact. However, the difficulties can be overcome, to a considerable extent, if the photoneutron precursors do not reach saturation and if the quantity cio be deter- mined, i.e? ci at the instant of time to, when the source is eliminated from the solution of the equation (14) (14') dci (t) kpi = n (t) Xici (t). dt 1 For the case of constant value of k, the solution has the form to c0 (t)----= (143i11) e?mo n (t) ekt Cit. 0 After substituting Eq. (16) in Eq. (14), the equation for the reactivity being measured assumes the form Q to k E viPiS n(t) (t-td dl (15) (16) (17) The effect of long lived groups of photoneutrons on the magnitude of the reactivity can almost be eliminated by change of to, and the time of the experiment can be shortened significantly. 39 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 1.0 0 4 RIO Delay time, sec a ZOO Relative contribution reactivity 40 Delay time, sec Fig. 5. Undersaturation factor of delayed photoneutron groups (a) and relative contribution to reactivity injected by the photoneutron groups (b) as a function of holding time of the neutron source in a sub- critical assembly for p = -1 ? 10-3 (figures near the curves are the number of groups). Preliminary results of the use of the integral method in the absence of saturation of photoneutron precursors were obtained on an analog computer, by which the behavior of the reactor was reproduced with six delayed neutron groups and four photoneutron groups. By choice of scale factors it was presumed that as a result of saturation of the precursors Un = Ucn and then nokikeff E (v/k)cucio/und ?Q = n (t) dt to (17') The complex yi i3i/ Xi of each group of delayed neutrons enters into this formula with its undersaturation factor .13 = U /Uno, depending on the holding time of the source in the recator. cio The data obtained (Fig. 5a and 5b) permit conclusions to be drawn concerning the magnitudes of the under- saturation factor and the relative contribution to the reactivity of each photoneutron group as a function of the holding time of the source in the reactor, and to distinguish two possibilities for measuring the reactivity by the integral method; by using the undersaturation factor [Eq. (17)] or by choosing an operating cycle which will permit the photoneutron groups to be neglected, within the limits of the stated accuracy. We have used the first possibility. A section of the control rod was calibrated by the integral method discussed in the critical assembly being in- vestigated. The data obtained are given in Fig. 4, where both methods of reactivity measurement are compared. Determination of the Efficiency of the Delayed Neutrons and Photoneutrons In describing transient processes or in measuring reactivity, it is necessary to know the value of y or 13eff = y i3, the effective fraction of delayed neutrons and photoneutrons. For the critical assembly being investigated the quantity y was measured by the method of substitution of fuel by absorber and by determining the change of reactivity originated by this substitution. It follows from perturbation theory [8, 9] that the change of reactivity of the system as a result of changing t he quantity of fuel and absorber is expressed as L\keffI beff = r dv VC?r fa ,u +1 fTvTF TFT ) dv vF*SE/Fdu-F6X/FITT] ? SE,F*F du? 6M,T.F TF1,1 , n, - tir u where F is the neutron flux; F* is an adjoint function; the suffix T denotes a thermal group. 40 (18) Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 If the absorption in the absorber inserted is equal to the absorption in the spent fuel at the site of location of the absorber, then (SEc = 0 and there will be no terms in expression (18) which will take absorption into account. If the system is divided into N parts and this substitution of fuel by absorber is performed each part, then we can write 1=1 S vF*SEfF du dv + . . . + S S vF*15EfF du dv eff ti v N u k eff 5 5 vF*.EfF du dv V u =1 (19) (for brevity of writing, the thermal group is included here under the integral sign). The value of Akeff/keff = ky/keffEi Sipo/(po + Xi) is determined in the experiments to measure the reac- tivity, if y is assumed constant for all groups of delayed neutrons and photoneutrons. Then, = N PiPo 1=1 keff )t 1 (20) If the absorption cross section in the absorber inserted, Ea, does not match the absorption cross section of the fueld, c E c, than we obtain from Eq. (18) Akeff S (I! F*F du dv keff vu vF*F.Ef du dv U (21) and the correction to unity should be obtained by a numerical method. Expression (21) was used to determine the experimental error associated with the inaccuracy in Ete and 4, since rs (Av+ Ica) F*F du dv i) U L Ay = 1 k ek ff 1=-1. iPo 5 S vF*F2/ du dv v Po+ki u (22) Experiments to determine y were carried out on a critical beryllium oxide assembly with fuel elements on a Teflon-4 base [10]. Specially prepared plates of Teflon-4 with a boron filler were used as the absorbing elements. The ex- periment consisted in the substitution of the fuel elements by absorbers and in measuring the change of reactivity caused by this substitution. Usually, one or two fuel elements were substituted during a single procedure. As a re- sult of this, in order to reduce the number of substitution and measurements the symmetry used for the assembly was represented by a rectangular prism with square cross section. In order to ascertain the inaccuracy in the quan- tity y, the same experiments were carried out for two cases when the absorption in the absorbing element was not equal to the absorption in the fuel element. It was found for the assembly being studied that y = 1.15; the experi- mental error was 4%. For comparison with the experiment, calculations were undertaken of the quantity y. The difference between the prompt and delayed neutrons, as is well known, is due to their different initial energy. The energy.of the de- layed neutrons from U235 fission products was used in accordance with [2, 11, 12]. The energy of the photoneutrons was determined from consideration of the Be9(y, n)Be8 reaction and from analysis of the y -radiation which forms the photoneutrons (see table). In the formation of a Be% nucleus in the ground state as a result of the reaction Be9(y, n)Be8, the energy of the photoneutron of the i-th group was determined from the expression E.= ?1_67 MeV, where EY i is the average energy of the gamma radiation for the i-th photoneutron group; 1.67 MeV is the Be9(y,n)Be8 reaction threshold. The average energy with which photoneutrons are formed was found to be 670 keV. 41 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Since in the experiment carried out the value of y obtained was relative to all groups of delayed neutrons and photoneutrons, the calculated value of y was determined in accordance with [13] from the expression y eX2 AT, where AT is the difference between the increase of fission neutrons and delayed neutrons, and photoneutrons, whose spectrum was obtained. For the assembly investigated x2A T = 0.13 and y = 1.14, Thus, consideration of the effect of the Be9(y, n)Be8 and Be9(n, 2n)Be8 reactions on the kinetics of systems con- taining beryllium has shown the necessity for taking these reactions into account for reactivity measurements and in choosing the measurement cycle. Analysis of the data obtained shows that by choosing the holding time of the reactor at a constant power level to be about 1000 sec, by measuring the period over 200 sec after the reactivity surge, the deviation from asymptotic of the period to be measured does not exceed 0.1% for periods within the inter- val 10-100 sec. In measuring negative reactivities the taking into account, as suggested, of changing the amount of photo- neutron precursors by the undersaturation factor makes it possible to use the integral method, which gives ? as com- parison with positive period measurements show ? a satisfactory result. Determination of the efficiency of the delayed neutrons and photoneutrons by the method of substituting fuel by absorber and comparison of the experimental and calculated data showed the good applicability of the numerical formula for the case with photoneutrons. The special significance of the experiment in substituting fuel by absorber consists in the fact that it makes - possible the determination of the constant in front of the summation in the expression yk/keff 6ipo Apo + Xi) in the "inhour" formula, by eliminating the effect of existing inaccuracies in the delayed neutrons, lphotoneutron and neutron parameters of the Be9(n, 2n)Be8 on the result of the reactivity measurement. It is desirable always to carry out a normalized experiment of this nature prior to the precision experiments associated with reactivity measure- ments. In conclusion, the authors tender sincere thanks to N. N. Ponornarev-Stepnoi for valuable advice and interest in the work, and to Ya. V. Shevlov for discussion of the results. LITERATURE CITED 1. G. Keepin, et al., Phys. Rev., 101, 1044 (1957). 2. G. Keepin, et al., J. Nucl. Energy, 6, No. 1/2 (1957). 3. G. Keepin, Nucleonics, 2, 151 (1962). 4. A. K. Krasin, et al., In the Book: Proceedings of the Second International Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958 [in Russian] (Moscow, Atomizdat, 1959), Vol. 2, p. 39. 5. P. Benoist, et al., Proceeding of the 2nd Intern. Conf, United Nations, Geneva (1958), Vol. 12, p. 89. 6. S. Bernstein, et al., J. Appl. Phys., 27, 18 (1956). 7. U. Hojgn, Nucl. Sci. and Engng., 8, 518 (1960). 8. L. N. Usachev, Reactor Construction and the Theory of Reactors. Report of the Soviet Delegation at the International Conference on the Peaceful Uses of Atomic Energy [in Russian] (Moscow, Izd-vo AN SSSR, 1955), p. 251. 9. G. I. Marchuk, Numerical Methods of Assessing Nuclear Reactors [in Russian] (Moscow, Atomizdat, 1958), p. 205. 10. N. N. Ponomarev-Stepnoi, S. S. Lomakin, and Yu. G. Degal'tsev, Atomnaya energiya, 15, 259 (1963). 11. R. Batchelor and H. McHuder, J. Nucl. Energy, 3, 7 (1956). 12. D. Hughes, et al., Phys. Rev., 73, 111 (1948). 13. E. Cross and J. Marable, Nucl. Sci. and Engng., 7, 281 (1960). 42 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 THE CRYSTAL HYDRATE UF4 ? 4/3 H20 (UDC 546.791.4) Yu. V. Gagarinskii, E. I. Khanaev, N. P. Galkin, L. A. Anan'eva, and S. P. Gabuda Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 40-45, January, 1965 Original article submitted July 24, 1964 X-ray diffraction, refractometry, infrared spectroscopy, nuclear magnetic resonance and thermo- graphy are used to study a new hydrated form of uranium tetrafluoride, UF4 ? 4/31120, and its de- hydration products. This is a hitherto unknown monoclinic crystal hydrate of UF4. Its water of crystallization is attached by a hydrogen bond to the fluorine. The water molecules can be divided into three groups of different bond strength, corresponding to three peaks in the absorption bands of the valence and deformation vibrations of the 0 ?H bonds. The substance dehydrates in two stages. Its crystalline class is retained down to the composition UF4 ? H20. On further dehydra- tion down to 0.5H20 it undergoes a phase transformation accompanied by change of structure. The crystalline lattice thus formed is very close to that of the cubic hydrate. [1] and [2] describe two crystal hydrates of uranium tetrafluoride: UF4 ? 2.5H20, which is orthorhombic, and UF4 ? nH20 (0.5 < n < 2), which is cubic. We have found another, previously unknown, hydrate, whose properties are described below. It is a bright grass-green, contrasting with the deep green cubic and pale green orthorhombic hydrates. Its water content, after washing with alcohol and ether and drying in air, corresponds approximately to the composition UF4 ? 1.4H20. By the calorimetric method [3] it was established that the formula is UF4 ? 4/3H20. We investigated this hydrate by x-ray diffraction, optical methods (refractometry and infrared spectroscopy), thermography and nuclear magnetic resonance (NMR). Under the microscope it appears as long thin greenish crys- tals with spherical concretions. It is homogeneous: the crystals are optically anisotropic and have normal and oblique extinctions, showing that they belong to the monoclinic system. Table 1 gives the refractive indices n of a specimen of composition UF4 ? 1.4H20 (measured by immersion, error of order ?0.005), and the density(deter- mined by pycnometry in toluene with error ?0.01 g/cm3). For comparison, the same data, taken from [4], are given for the cubic and orthorhombic hydrates and the monoclinic anhydrous form of UF4. Table 1 shows that the new crystal hydrate differs markedly in crystallographic properties from the cubic and orthorhombic hydrates. The refractive indices are close to those of anhydrous UF4 (only nmin differs appreciably). These optical data show clearly that this actually is a new crystal hydrate of uranium tetrafluoride. X-ray diffraction photographs of the substance were taken with a URS-50I apparatus in filtered Cu radiation. For comparison, photographs were also taken for the stable monoclinic form of anhydrous UF4, the higher, ortho- rhombic, crystal hydrate UF4 ? 2.5H20 and the lower, cubic, hydrate UF4 ? 1.5 H20. They show that the substance under investigation does not resemble any of the previously known forms of UF4 and is not a mixture of them. This confirms the conclusion, drawn from the optical data, that it is a new substance. The x-ray diffraction spectra are shown in Fig. la. To determine the nature of the water bonds in the new hydrate, we investigated its infrared absorption spectra and nuclear proton magnetic resonance spectra. The method of measuring the former spectrum is given in [4], that for the latter in [5]. The infrared absorption spectrum of monoclinic UF4 ? 1.4H20 is given in Fig. 2 (curve 1), the positions of the absorption maxima in Table 2. The absorption band corresponding to valence vibration of the 0 ?H bond has three maxima at 2950, 3365 and 3480 cm-1, that corresponding to deformation vibration of the 0?H bond has less clearly visible maxima at 1565, 1625, and 1645 cm-1. The presence of absorption in this region shows that the compound is of the crystal hydrate type, the water being present as molecules. The absorption band corre- 43 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 44 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 ,130 020 ,110 ,100 ,90 ,80 ,I0 ,60 ,50 ,130 ,120 ,t10 ,I00 190 ,40 ,_30 ,20 , to 180 170 ,60 _,50 ,40 ,30 20 130 100 ,90 ,86 ,70 ,60 28 Fig. 1. X-ray diffraction spectra of UF4 ? 4/31-120, and the products of its dehydration and subsequent rehydration. a) Original crystal hydrate; b) UF4. H20; 8 0F4 ? 0.70H20; d) UF4 ? 0.45H20; e) UF4 ? 0.20 H20; f) UF4 ? 1.40H20, obtained by hydrating specimen of composition UF4 ? 0.20H20. 0 ,60 140 ,30 ,j0 00 0 (D (I) (I) (D -To -To (D -n (D (T) (D o.) 0 0 -0 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 1. Refraction Constants of the Various Forms of Uranium Tetrafluoride Composition Crystal class nmax nmed nmin Ti d425,g/cm3 f2D,cm3 UF4.1.4H20 Monoclinic 1.596 1.586 1.567 1.582 5.79 19.77 UF4.1.5H20 Cubic ? 1.523 ? 1.523 5.08 20.51 UF4.2.5H20 Orthorhombic. ? . 1.545 1.537 1.529 1.537 4.70 23.86 UF4 Monoclinic 1.594 1.584 1.549 1.576 6.68 15.58 TABLE 2. Maxima of Absorption Bands (in cm-1) in Infrared Spectra of Specimens Obtained by Dehydrating Crystal Hydrates of Monoclinic Uranium Tetrafluoride Curve 14o. in Fig. 2 Composition Dehydration temperature,?K Deformation vibrations of 0?H bond, cm-1 Valence vibrations of 0?H bond,cm-1 1 2 3 4 5 UF4 ? 1.401126 U F4 ? 1 00H20 U F4 ? 0 . 301120 U F4.0.101120 ' UFO . 401120 150 200 250 Obtained by hy- drating I UF4 ? 0.101-120 1565; 1625; 1645 1590; 1645; 1675 1615; 1640; 1675 1650 1680 2950; 3365; 3480 2935; 3365; 3480 3465 3470 3400 sponding to valence vibration of the water molecule is markedly broadened and displaced towards longer wave- lengths. It follows that in the new hydrate the water is also attached by a hydrogen bond. The presence of three maxima in the absorption bands corresponding to valence and deformation vibration of the 0?H bond leads to the supposition that in UF4 ? 1.4H20 the water molecules can be subdivided into three groups according to bond strength. Figure 3 shows the NMR spectrum of the crystal hydrate, taken at 290?K, and the derivative spectra at 90 and 290?K. The second moment of the NMR lines is 27.5 ? 0.3 0e2 at 90?K and 23.6 ? 0.9 0e2 at 290?K. At 290? the relative intensity of the central peak, which determines the fraction of mobile water molecules, is about 50/0. The shape at 90? of the new hydrate's NMR spectrum can be explained by the presence of a hydrogen bond be- tween the water molecules and a fluorine atom, OH?F. In this case we should have a three-spin system whose spec- trum should be a triplet (or unresolved triplet degenerating into a singlet). At 90?K the second moment of the NMR spectrum is less for the monoclinic hydrate than for the other hy- drates [6]. This means that, provided the distance between the protons in the water molecules remains constant, the mean H?F distance in this hydrate is relatively greater tharrin the other hydrates of UF4. Figure 4 shows the thermogram for dehydration of the new-hydrate in a vacuum, recorded by means of an PFK-59 Kurnakov pyrometer. The graph shows that the dehydration takes place in two stages. As in the cases of the other two hydrate, an unstable form of anhydrous UF4 is produced and on further heating this undergoes an ir- reversible transformation to the stable form. This process is accompanied by heat evolution, as shown by the exo- thermic peak at 330?K. X-ray and optical investigations were made of the products formed by dehydrating UF4 ? 1.4H20 in a vacuum at various temperatures. The results are given in Tables 2 and 3. As seen from Table 3, during vacuum dehydra- tion the crystal class of the original substance remains unchanged at least until the composition UF4 ? H20 is reached; only its refractive index changes slightly. The x-ray diffraction spectra show that the structure remains unchanged. On reaching the composition UF4 ? 0.45H20 and after further dehydration, the optical properties and x-ray diffraction patterns change appreciably. If a specimen of composition UF4 ? 0.20H20 is washed with alcohol and ether, dried in air for 24 h and then rehydrated, the resulting substance has a very slight anisotropy; all the strong and medium lines in its x-ray diffraction spectrum correspond to those for the cubic hydrate. Additional, very weak lines betray the presence of a small quantity of another phase (which apparently causes the slight anisotropy). Figure 2 gives the infrared absorption spectra of similar specimens obtained by dehydrating the monoclinic hydrate in various degrees. The positions of the absorption maxima are given in Table 2. This table shows that, 46 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 3. Optical Properties of Substances Obtained by Dehyrating Monoclinic Crystal Hydrate of UF4 Composition Dehydration temperature, ?K N Remarks UF4?1.40H20 1.582 Anisotropic spherulites UF4?1.00H20 150 1.570?0.008 The same UF4. O. 45H20 175 1.52?0.01 Almost isotropic UF4?0.20H20 250 1.504?0.006 Weakly anisotropic UF4?1?10H20 Obtained by hydrating 1.545?0.003 Weakly anisotropic UF4?0.20H20 e-60 0-40 .g.2? 4 400 600 1400 1800 2800 3200 3600 4000 Fig. 2. Infrared spectra of monoclinic lower crys- tal hydrate of uranium tetrafluoride and of speci- mens obtained by dehydrating it. 1-5) Specimen numbers in Table 2. 210 -14-12-10-8-6-4-2 0 2 4 6 8 10 12 14 Fig. 3. a) Derivative NMR spectra of monoclinic crystal hydrate of uranium 184 tetrafluoride of composition UF4?1.40H20 at 90 and 290?K; b) [integrated] spec- trum at 290?K. ) spectrum at 290?K; ----) broad component; - .-.-.-.) narrow component corresponding to highly mobile water. Vertical scale chosen so that total area is equal to unity. in the frequency region of valence deformation vibrations of the 0?H bond, the absorption bands of the specimen of composition UF4 ? 1.00H20 retain the structures of the corresponding bands for the original crystal hydrate. On transition to composition UF4 ? 0.30H20 the spectrum of valence vibrations of 0?H becomes simpler. The maxima at the long-wave end disappear, the spectrum being left with one band at 3470 very similar to the absorption band for valence vibrations of 0?H for the cubic hydrate of identical composition [4]. Fig. 4. Thermogram for dehydration of monoclinic lower hydrate UF4 ? 1.40H20. Heating rate 4 deg/min. 47 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 UF4 1.401120 obtained by hydrating UF4 ? 0.10H20 has an absorption even more like that of the cubic hydrate of identical composition. The maxima of its infrared absorption spectra are at the same positions as those of the cubic hydrate. The above results thus show that the original hydrate undergoes a phase transition between the composition UF4 ? 1.00H20 and UF4 ? 0.5H20, accompanied by a structural change; dehydration products containing less than 0.5H20 per UF4 molecule cannot be rehydrated to the original UF4 ? 4/3H20. In conclusion, the authors would like to thank S. S. Batsanov for the refractometric work, recording the in- frared spectra and discussing the results, and L. A. Khripin for recording the thermograms. LITERATURE CITED 1. W. Zachariasen, Acta crystallogr., 2, 388 (1949). 2. J. Dawson, R. D'Eye, and A. Truswell, J. Chem. Soc., November 3922 (1954). 3. Yu. V. Gagarinskii and V. P. Mashireev, Zh. neorgan. khim., 4, 1246 (1959). 4. S. S. Batsanov and Yu. V. Gagarinskii, Zh. struktur. khim., 4, 387 (1963). 5. S. P. Gabuda, et al., Zh. stxuktur. khim., 5, 303 (1964). 6. Yu. V. Gagarinskii, S. P. Gabuda, and G. M. Mikhailov, ibid., p. 383. 48 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 ? ? Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 THE RELATIVE VOLATILITY OF SOLUTIONS OF HTO IN H2O (UDC 546.23:536.432.1) Ya. D. Zel'venskii, V. A. Shalygin, V. S. Tatarinskii, and D. A. Nikolaev Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 46-48, January, 1965 Original article submitted January 27, 1964 A method of simple distillation, with calculations performed according to Rayleigh's equation, was used to determine the separation factor a of solutions of HTO in H2O in the 38-100?C tem- perature range. The results obtained are expressed by the equation logna = 38.80/T ?0.0935. The data of our study are close to the separation factor values calculated on the basis of earlier measurements of the vapor pressure of T20 (see Atomnaya Energiya, Vol. 8, No. 5, p. 420, 1960). The data available in the literature regarding the values of the relative volatility (separation factor) a of so- lutions of tritium water are unreliable and contradictory. In [1] it was stated that the boiling point of hydrogen- tritium water, HTO, is lower than that of ordinary water, H20, i.e., that the former is more volatile. This con- clusion was contradicted by the data obtained by Price [2], who used the ratio of the activities of the liquid and gaseous phases to determine the separation factor of HTO and H2O solutions in the 25-80?C temperature range. According to Price, for example, at 55?C the separation factor of the HTO-H20 system is 1.13. Considerably lower values of a were found in [3] by a method using a fractionating column: a = 1.051- 1.053 at 70?C and a = 1.036 at 100?C. At the two temperatures investigated, according to [3], (aT ?1) /(aD ?1) = 1.37 ? 0.02, where aD is the separation factor of the HDO ?H2O system. Theoretically, the ratio of the enrichment factors, (aT ?1)/ (aD ?1) should be 4/3[4]. In 1960 M. Popov and F. Tazetdinov published the results of their measurements of the vapor pressure of triti- um water, T20, in the 12-95?C temperature range [5]. Using water specimens with concentrations of 83.40/o and 98.12% T20, the authors of [5] conducted their measurements by a static method. The resulting values of vapor pressure, converted to the values for 100% T20, are expressed by the generalized equation igp = 7.9957 1654.9 t ? 222 ? Popov and Tazetdinov computed the vapor pressure of HTO on the assumption that it is equal to the geometric mean of the vapor pressures of T20 and H20. At 25?C, according to [5], a 'PH20/PHTO = 1.097, instead of the value of 1.295 found in [2]. There is less disagreement between the data of [5] and [3]. In order to check and improve the accuracy of such very divergent data on the value of the separation factors of solutions of tritium water, the study described below was carried out. Experimental Procedure In order to determine the separation factor, we used the method of simple distillation, with calculations per- formed according to Rayleigh's equation. This method is relatively simple and, at the same time, sufficiently rigorous and free from unverified assumptions, which makes it possible to obtain accurate results [6]. The experi- mental technique consists in evaporating a large amount of the initial solution, under isobaric equilibrium condi- tions, until a small residual amount is left. For dilute solutions of the less volatile component, the separation factor is calculated by means of the equa- tion [6]: Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 49 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Fig. 1, Schematic of equipment used for determining separation factor: 1) Still; 2) shell of air thermo- stat; 3) heater; 4) autotransformer; 5) stirrer; 6) magnet; 7) motor; 8) water condenser; 9) drying column with zeolite; 10) manometer; 11) manostat; 12) vacuum pump; 13) condensate collector. 1g (Wo/WE) a =-- lg (Wo/WR)+ Ig (Ao/Als) (1) where Wo/Wf is the ratio of the amount of the initial solution to the amount of the final solution, and Ao/Af is the ratio of specific activities. A schematic of the equipment used for the distillation is shown in Fig. 1. The still 1 was placed in an air thermostat 2, whose temperature was kept 10-20?C higher than the boiling point of water in order to prevent con- densation of vapor on the walls of the still. The still was equipped with a magnetically driven stirrer. In accord- ance with the results of the preliminary tests, the rotation rate was kept between 80 and 100 rpm. The steam, being liquefied in be condenser 8, flowed into the collector 9. A predetermined constant pressure was maintained in the apparatus by means of a vacuum pump 12 and an automatic manostat 11. The distillation was carried out at a slow rate, in order not to disturb the vapor-liquid equilibrium. For a separation factor a which is close to unity, it is desirable to increase the ratio Wo/Wf if we wish to im prove the accuracy of the results. However, if the volume of the still is made excessively large, this will upset the conditions on which Eq. (1) is based (according to our data, the residual liquid at the end of the distillation should be not less than 1% of the original amount). We therefore carried out the distillation in two stages, with a volume reduction factor of Wo/Wf = 50-60 in each stage. To achieve this, after the first stage all of the residual liquid was poured into a smaller still, in which the second stage of the distillation was carried out. The amount of water before and after the distillation was determined by weighing. The activity of the triti- um water before and after the distillation was measured by a scintillation method. The scintillator used was a so- lution of paraterphenyl in dioxane containing an admixture of the preparation POPOP (5 g of paraterphenyl and 0.1 g of POPOP per liter of dioxane). To make the measurements, on the basis of preliminary, tests, we mixed 0.1 ml of the water to be analyzed w th 9.9 ml of a scintillating solution of the indicated composition. The resulting sOlution was poured into a glass cuvette sealed with Canada balsam to the face of the FEU-19M photomultiplier. The latter was combined with a "Volna" instrument complex. When we measured the back- ground, we poured a mixture consisting of 9.9 ml of the scintillating solution and 0.1 ml of ordinary distilled water into the same cuvette. The activity was measured with an accuracy of lob. The specific activity of the tritium water used was about 0.5 mCi/ml. 50 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Results of the Measurements factor determined 11111111111=1111111111 The separation of dilute solutions of tritium water was 1111M1111?111111111 at pressures of 50-750 mm Hg, which corresponds to varying the boiling point from 38 to 100?C. The results obtained are given below. 1111111MMIMIIII MINE1111111111N1111 7.15 11111111111?11111111111M Pressure, mm Hg 50 100 300 750 111111UMMIIIM Boiling point, ?C 38.1 52.0 76.8 100.0 M111111?111111111111110 Volume reduction in first 61.0 59.2 56.4 62.2 1113111111111111111= stage of distillation, , Wo/WI 11111111111111=1011111 410 RIRIUi Volume reduction in 52.8 61.6 52.3 52.5 second stage of distilla- tion, Wi/Wf 1?1111111111MINII Total volume reduction, 3220 3646 2940 3260 11111?111110111111111 1.0 1111111111?11111172111111111 Wo/Wf Activity, Ao, of original water, pulses per 100 sec 58,600 58,720 58,740 58,790 111111111MMIN. 11111111111111MMIk Activity, Af, of remainder 95,400 105,330 80,670 72,760 after distillation Separation factor a cal- 1079 1064 1041 1027 11111111111111111111M Fig. tion data Present 0 20 411 60 80 t.?C culated according to 2. Comparison of separa-Eq. (1) factors according to the Separation factor acalc of various studies: 0) calculated according study; A) [2]; -F) [3]; to Eq. (2). 1080 1065 1041 1027 The variation of the separation factor as function of temperature can be represented by the equation log10 a = A/T - B. Accordingly, the resulting ex- perimental data can be expressed by the general equation g a = 38.80 0.0935. As can be seen from the tables, the deviation of acak from the experimental values of a is no more than 0.01. (2) Figure 2 shows the values of the separation factors in comparison with the data obtained in other studies. As can be seen from the figure, the results of the present study are in satisfactory agreement with the data of [5], which were obtained by a different method. There is also comparatively little difference between the two values of a ob- tained in [3] by a third method. Price's data [2] are considerably higher and must be considered erroneous. The assertion of Libby and Cornog [1] that the vapor pressure of HTO is higher than that of H20 is also incorrect. LITERATURE CITED 1. W. Libby and R. Cornog, Phys. Review, 60, 171 (1941). 2. A. Price, Nature, 181, 262 (1958). 3. P. Avinur and A. Nir, Nature, 188, 652 (1960). 4. I. Bigeleisen, Tritium in the Physical and Biological Sciences, Vienna, IAEA (1962), Vol. 1, p. 161. 5. M. M. Popov and F. M. Tazetdinov, Atomnaya Energiya, 8, 420 (1960). 6. Ya. D. Zel'venskii and V. A. Shalygin, Zh. prikl. khimii, 31, 1501 (1957). 51 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 DETERMINATION OF y -RAY AND NEUTRON ABSORBED DOSE IN POLYMERS (UDC 639.121.7) F. A. Makhlis and I. M. Kolpakov Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 48-52, January, 1965 Original article submitted January 9, 1964 Together with results, a method is given for calculating the 7-ray and neutron absorbed dose in several polymers which is based on the elemental composition of the materials and the energy of the radiation. In radiochemical studies and in the radiation treatment of various materials and biological subjects, the basic physical problem is the determination of the amount of energy which is absorbed by the irradiated medium, i.e., the determination of absorbed dose. Strictly speaking, this criterion, although it is fundamental, need not be unique. Clearly, radiochemistry lacks a concept resembling the coefficient of relative biological effectiveness (RBE) in radiation biology. Actually, for the same absorbed energy, the changes in the properties of a polymer under neutron irradiation can differ from the corresponding changes under 7-irradiation [1]. However, the required quan- titative data are lacking, and we are forced to proceed solely on the basis of the magnitude of the absorbed energy, on which the final effect of the irradiation process depends to a considerable extent, other conditions being equal. Gamma Irradiation With the exception of calorimetry, there are no known experimental methods by which one might determine the magnitude of the absorbed dose for each specific material under 7 irradiation. However, the use of the calori- metric method is made difficult by the complex configuration of the absorbed dose field which is produced by ac- tual irradiation equipment. Consequently, one ordinarily resorts to indirect methods for determining the absorbed dose, using various liquid dosimetric systems of air ionization. A number of important considerations connected with the determination of absorbed dose from the results of radiation dose measurements were discussed in [2]. Knowing the magnitude of the absorbed dose D1 in a definite volume occupied by one material, one can ob- tain the corresponding magnitude of the absorbed dose D2 for another material, other conditions being equal, from the relation D (1-ta/Ot n (N/Q)2 (1) where (p a /p)1 and (p a /p)2 are the true mass absorption coefficients for y radiation in the first and second ma- terials. If the radiation dose in air is known, then the conversion to absorbed dose in the irradiated material is ac- complished on the basis of formula (1). Indeed, if it is assumed that the energy needed for the formation of an ion pair in air is 34 eV, the energy equivalent of the roentgen in air with fulfillment of electron equilibrium is 87.7 erg/g. From that, we obtain DM == 0.877 (ILta/Q)m- [rad/R], (11aMair (2) where the subscript "M" indicates the irradiated material. The true mass absorption coefficient for a multicomponent system (pa /p)syst consisting of n elements is defined as (Ra/Q)syst = ti?gi (11.70i, where gi is the fractional weight of the j-th element in the system. 52 (3) Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 1. Values of Dm for Different Elements, rad/r . '2' y -Energy, MeV 0.1 0.2 0.5 1.0 2.0 5.0 10.0 H 1.54 1.73 1.74 1.74 1.74 1.60 1.36 C 0.811 0.870 0.877 0.877 0 877 0.864 0.834 N 0.844 0.873 0.877 0.877 0.877 0.876-0.866 0 0.877 0.883 0.877 0.877 0.877 0.880 0.894 F 0.905 0.845 0,832 0.830 0.835 0.850 0.880 Na 1.072 0.870 0.837 0.840 0.843 0.877 0,832 Mg 1.255 0.912 0.864 0.852 0.870 0.910 0.990 Al 1.395 0.899 0.845 0.842 0.852 0.900 0.991 Si 1.70 0.96 0.875 0.867 0.876 0.945 1,06 S 2.28 1.01 0.884 0.870 0.877 0,968 1.100 Cl 2.55 1,02 0.850 0.832 0.840 0.940 1.11 K 3.37 1.11 0.864 0.850 0.859 0,970 1.55 Ca 4.13 120 0.894 0.870 0.877 1.01 1.213 Fe 8.34 1.60 0.864 0.819 0.820 1.0 1.261 In order to simplify the computations, values of Dm are given in Table 1 for elements frequently en- countered in radiochemistry and radiobiology. These values were obtained by using the values of ga/p in [3]. Table 2 gives values of Dm for water and a number of polymers. Neutron Irradiation For reasons which are given in [4], radiation treat- ment of materials with neutrons is possible under very limited conditions, but the calculation of absorbed dose is necessary in order to estimate the radiation resistance of materials intended for operation in nuclear reactors. In the calculations given below for the absorbed dose in polymer irradiation with thermal and fast neutrons, the assumption was made that the neutrons undergo only one collision during penetration of the irradiated material. The validity of such an assumption is verified by the following considerations. 1. The thickness of polymer products (for example, rubber products) which are irradiated usually does not ex- ceed the neutron mean free path. Thus, the thermal neutron ranges in water and polyethylene are 0.28 and 0.24 cm, respectively; for 1 MeV neutrons, they are 2.45 and 2.3 cm, and 11.0 and 7.7 cm for 10 MeV neutrons. 2. The value of the absorbed energy we obtained was close to the maximum absorbed energy for the thickness of the irradiated object. This followed from a comparison of the experimentally determined distribution of neutron absorbed depth dose in a paraffin phantom [5] with computed values which were obtained with the "first collision" approximation. The deviation between the corresponding values did not exceed 40/0 for neutron energies of 0.24- 1.0 MeV. Thermal Neutron Irradiation For the elements which are present in a majority of the materials used in radiochemistry, the following basic reactions are characteristic of interactions with thermal neutrons: N14 (n, p) C14, a = 1.76 barn, Q = 0.623 MeV, K = 0.996, 0" (n, a) C", a -= 0.5 barn, Q = 1,72 MeV, K = 0.00039, C135 (n, p) S35, a = 0.17 barn, Q = 0.62 MeV, K = 0.7543. Here, a is the cross section for the respective reaction, cm2; Q is the energy of the emitted particles, MeV; K is the isotopic fraction in a natural mixture of isotopes. The contribution from the 017(n, a)C14 reaction is negligibly small, because of the insignificant amount of 017 in a natural mixture of isotopes. One can assume that the energy transferred by the products of the other two reactions is absorbed in the immediate vicinity of the location of the neutron-nucleus interaction. Then the absorbed dose, normalized to unit neutron flux, is Du= 1.6?10-8NiKiQuaii (rad/(neut.cm-2.)]. Here, Ni is the number of atoms of element j per cm3; the subscript i identifies the\ reaction under consideration, and the subscript j, the material under consideration. For the N14(n, p)C14 reaction, Do is 7.5 ? 10-10 rad/neut-cm-2 and for the C135(n, p)S35 reaction, it is 0.239 ? 10-1? rad/neut-cm-2. In the emission of protons or a-particles, one can neglect the energy of recoil nuclei. (4) 53 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 2. Values of Dm for Water and Several Polymers, rad/R Polymer y-Energy, MeV 0.1 0.5 0.8 i 1.5 2 5 10 Polyethylene, SKEP, butyl rubber 0.91 1.0 1.00 1.0 1,0 1.0 0.97 0.91 Natural rubber 0.90 0.99 0.98 0.98 0.99 0.99 0.96 0.90 SKS, SKB 0.89 0.97 0.97 0.97 0.97 0.97 0.94 0.90 Nitrile rubber 0.88 0,96 0.96 0.96 0.96 0.96 0.93 0.88 Silicone rubber 1.2 0.95 0:94 0.94 0.94 0.94 0.95 0.97 Fluoresin, "Viton" type 0.89 0.86 0.76 0.76 0.76 0.86 0.87 0.87 Iiy2alon 1.38 0.95 0.95 0.94 0.94 0.94 0.95 0.96 Teflon 0.88 0.84 0,84 0.84 0.84 0.84 0.85 0.86 Water 0.96 0.97 0.97 0.97 0.97 0,97 0,96 0.94 TABLE 3. Values of the Absorbed Dose, Normalized to Unit Neutron Flux, for Water and Several Polymers, rad/neut-cm 10-10-2. Material Neutron energy, MeV thermal 0.1 0.5 0.8 1 2 5 10 Polyethylene, SKEP, butyl rubber 0.155 9.0 21.9 28.5 31.6 42.7 61.2 75.5 Natural rubber 0.136 8.1 20.6 25.8 28.6 38.8 55.5 .69.0 Nitrile rubber 0.67 6.74 17.2 21.5 23.9 32.5 46.7 58,7 Silicon rubber 0.124 5.15 13.3 16.6 19.1 24.9 35.8 44,4 Fluoresin, "Viton" type 0.091 2.19 4.35 5.5 6.0 8.8 12.9 18.0 Fluoresin, Kel-F type 6,10 0.77 2.67 3.43 3,74 6.04 8.53 12.6 lIy2alon 4.05 5.9 15.0 18.8 20.9 28,2 40.8 50.7 Tenon ' 0.019 1.03 1.39 1.84 1.93 7.3 5.1 9.0 Water 0.139 6.8 17.8 21.6 27.0 32.4 45.5 56.8 TABLE 4. Values ofDij Normalized to Unit Fast Neutron Flux, rad/neut-cm-2 ? 10-1? Element Neutron energy, MeV 0.1 0.2 0.5 1.0 2.0 5.0 10.0 II 60.5 92 148 205 278 390 455 C 0.512 0.96 1.94 2.93 3.95 7.41 13.1 N -- 0.64 1.03 2.00 2.86 6,42 12.0, 0 0.23 0.47 1.67 5.0 9.07 4.33 8.15 F 1.07 0.39 0.65 1.09 3.10 4.46 7.72 Na 0.11 0.49 0.35 1.20 2.01 3.77 7.55 Mg 0.25 0.35 0.77 0.83 1.91 3.24 1.86 Al 0.15 0.22 0.43 0.64 1.67 2,71 4.19 Si 0.023 0.50 0.35 1.04 1.08 2,75 4.12 S 0.13 0.18 1.19 0.47 1,04 2.07 1.6 Cl 0:025 0.064 0.16 0.33 0.90 1.99 3.05 Ca 0.005 0.022 0.11 0.23 0.46 1.15 2,30 Fe 0.23 0.05 0.09 0,13 0.28 0,70 1.01 The energy released in radiative capture can also be found with formula (4), the only difference being that Qij is understood to be the binding energy released with the addition of a neutron to the nucleus [6]. Then the y -ray energy which is absorbed by a thin layer of irradiated material of thickness r can be approximated by the relation 54 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 = Duliar, (5) where ma is the y -quantum linear absorption coefficient for the material under consideration. If a single y -quantum is emitted in neutron capture by the hydrogen nucleus and, with some approximation, by the carbon nucleus, then one can assume with a reasonable amount of accuracy that three y -quanta with energies each are emitted in the case of the materials of interest to us. The contribution of nuclear recoil energy and induced activity to the absorbed dose is negligibly small in this case [7]. Results from a computation of the magnitude of the absorbed dose, normalized to unit thermal neutron flux, are given in Table 3 for water and several polymers. Fast Neutron Irradiation The energy which is transferred to a polymer as the result of elastic scattering of fast neutrons is determined from the relation Di; =1.94-1016E E [rad/neut-cm-2], (AJ-1-1)2 (6) where o ij is the neutron elastic scattering cross section for nuclei of element j, cm2;g ? is the proportion of element j in the mixture; Aj is the atomic weight of element j; E is the neutron energy, MeV.l In hydrogenous materials, the principal process which is responsible for the transfer of energy to matter is scattering by hydrogen. The fraction of the energy which is transferred by this process is 85-90% of the total absorbed dose [8]. To facilitate computations using formula (6), values of Dij (rad/neut-cm-2) are given in Table 4 for ele- ments often encountered in radiochemistry (only elastic scattering of neutrons was considered in the calculations). The relative role of inelastic neutron scattering as compared with elastic scattering increases with increasing energy and with the atomic number of the irradiated material. Of the light elements which make up polymers, only fluorine has an inelastic scattering cross section of 1.25-0.5 barns for neutron energies of 0.5-1.0 MeV; further- more, y-quanta with energies of 0.109 and 0.197 MeV are emitted. At neutron energies exceeding 1 MeV, inelastic scattering is also possible in aluminum, magnesium, iron, and other metals found in resins. The energy of the ac- companying y -quanta is approximately 1 MeV. Therefore, the contribution of y -radiation from inelastic scatter- ing to the absorbed dose can compete with the contribution from elastic scattering only for neutron energies above 0.5 MeV and only if the proportion of metal in the composition of the irradiated material is sufficiently great. The fast neutron radiative capture cross section is hundreds of times smaller than the scattering cross section, and only a small fraction of the energy released is absorbed in light elements in the case of thin, irradiated objects; consequently, one can neglect the contribution to the absorbed dose from y -rays in (n, y) reactions. A similar conclusion is reached with regard to secondary charged particles, recoil nuclei, and induced activity. The results of absorbed dose calculations, normalized to unit fast neutron flux, are given in Table 3 for water and several polymers. With reactor irradiation, the contributions of fast and thermal neutrons to the total absorbed dose depends on the composition of the polymer. For the majority of polymers, the absorbed dose from fast neutrons exceeds by far the corresponding value for thermal neutrons. Polymers which contain a considerable quantity of fluorine are an exception. Calculations which were carried out for the irradiation of polyethylene and Kel-F in the core of the VVR-M thermal reactor [9] showed that the thermal neutron absorbed dose in polyethylene did not exceed 1%, and for Kel-F was 501o, of the fast and intermediate neutron absorbed dose. For irradiation in the vicinity of the beryllium reflector, the analogous values were 3% for polyethylene and 100% for Kel-F. In conclusion, we wish to thank E. N. Smagin for valuable discussions. LITERATURE CITED 1. A. Charlesby, Nuclear Radiations and Polymers [Russian translation] (Moscow, Izd-vo inostr. lit., 1962). 2. Yu. V. Sivintsev, Atomnaya energiya, 9, 39 (1960). 55 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 3. R. Berger, Rad. Res., 15, 1 (1961). 4. F. A. Makhlis and A. Kh. Breger, Kauchuk i resina, No. 8, 18 (1964). 5.. A. M. Kogan, et al., Atomnaya energ i y a , 7, 351 (1959). 6. B. Price, C. Horton, and K. Spinney, Nuclear Radiation Shielding [Russian translation] (Moscow, Izd-vo inostr. lit., 1959). 7. M. L Shal'nov, Neutron Tissue Dose [in Russian] (Moscow, Atomizdat, 1960). 8. R. Eger, Dosimetry and Radiation Shielding [in Russian] (Moscow, Gosatomizdat, 1961). 9. V. V. Goncharov, et al., Proceedings of the Second International Conference on the Peaceful Use of Atomic Energy [in Russian] (Dokl. soy. uchenykh, Moscow, Atomizdat, 1959), Vol. 2, p. 293. 56 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 INCREASING THE DEPTH OF PROSPECTING FOR CONCEALED URANIUM ORE BODIES BY MEANS OF THE PRIMARY AUREOLE (UDC 550.8/546.791) S. V. Grigoryan Translated from Atomnaya Energiya, Vol. 18, No. 1, pp. 52-57, January, 1965 Original article submitted February 14, 1964 A study of the primary uranium aureoles in one hydrothermal deposit showed that, by using sys- tematic chemical analysis (sampling analysis of the mobile uranium content), the primary aureole can be more fully revealed, and the depth of aureole prospecting for hidden uranium ores thus increased. It is shown that this method of analysis is most effective for elements whose aureoles are of small extent and intensity, owing to high background content in the country rocks, low ore content, etc. Recent investigations have shown that uranium ores of hydrothermal origin are surrounded by aureoles of urani- um and other elements; these can be used in prospecting for concealed uranium ore bodies [1, 2]. The main ele- ments used as indicators of uranium ores are those forming the most extensive aureoles. A study of the distribution characteristics of elements in a number of hydrothermal uranium deposits showed that, in any cross section, as one moves laterally away from the ore, the concentrations of uranium and its ac- cessory minerals decrease in geometric progression [2, 3]. The distribution of any element around the ore can thus be represented by a graph (Fig. 1). Since the concentration decreases in geometric progression, the distribution is represented by a straight line in semilog coordinates. In practice, aureoles are mapped with respect to the least anomalous content of an element, just as in prospec- ting for deposits the limits of commerical ores are determined from the boundary content of the required component [2]. In Fig. 1 the half-width of the aureole corresponds to the intercept cut off by the distribution graph on the horizontal line representing the least anomalous content. In actual fact the aureole will be considerably wider; with increasing distance from the ore body, the element concentrations introduced during ore formation decrease, not down to the least anomalous content, but to the content in the interstitial solutions which saturated the rocks when the ore and aureole were formed. This is due to the fact that, when the primary aureoles were formed, the element contents were equalized between the ore-bearing solutions and the interstitial solutions saturating the country rock. The aureoles formed by this equalization will also have the maximum possible size. Let us call them "true," and those mapped from the least anomalous content "apparent." The difference between these aureoles will increase with the least anomalous content of any element. The vertical extent of the apparent aureoles is much less than that of the true ones. The relation between the dimensions of the apparent and true aureoles was studied in detail on one hydrothermal uranium deposit occurring in granites. The deposit appeared as numerous fine tarry fluorite veinlets, forming stockwork ore bodies of various sizes, elongated in a northwesterly direction. The dip of the ore bodies is steep. The boundaries of the commerical ores are known from the results of assays. In mapping the aureoles of the elements, the least anomalous uranium content was determined from the geo- chemical background value and standard deviation in the rocks [4]. The method of mapping is given in more de- tail in [2]. 57 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Least anomalous content (apparent aureole) 71i Geochemical background /0 a.) 8 : ? 6 0 U 4- ? 3 Content of element in interstitial solutions (true aureole) Cs I I 2 ? 4,1 Distance from ore deposit, m Ore body 444,. ? 1%. Fig. 1. Distribution of a chemical element around an ore deposit. To determine the vertical extents of the apparent and true aureoles, we drew graphs of the linear productivityl of the uranium aureoles in a vertical cross section through the ore body (Fig. 2). The linear productivity of the aureole at a given horizon was found by multiplying the mean uranium content by the width of the aureole. The abscissae in Fig. 2 represent the linear productivity calculated from the aureole of mobile uranium [2, 4]. The or- dinates represent the distance of the sampling horizons from the ore body, plotted on a linear scale. It is seen that the linear productivity of the uranium aureole is represented by a nearly straight line. To determine the vertical extent of the uranium aureole above the ore body, this line must be produced to meet the line corresponding to the least anomalous linear productivity. (This productivity corresponds to the aureole of minimum breadth and with mean content equal to the least anomalous content.) The apparent minimum breadth is equal to the sampling inter- val (5 m). However, we took it as 10 m, since the aureole must be mapped by at least two samplings. Conversely, samples in which the high concentration of elements is caused by random factors (e.g., background variation) may be mistaken for an aureole. For the ore deposit described, the least anomalous uranium content was taken as 0.00161, which exceeds the geochemical background (GB) of the surrounding granites, 0.0007%, by twice the standard devia- tion (GB + 2a). The minimum anomalous productivity will thus be 0.0016 ? 10 = 0.016m %. The extent of the uranium aureole above the ore body was found by extrapolation to be 180m (Fig.2). That of the true aureole above the same ore body was determined in a similar manner. It is equal to the distance from the ore body to the point of intersection of the straight line representing the productivity with a vertical line corre- sponding to the linear productivity (given by the product of the uranium content in the interstitial solutions and the minimum aureole breadth, 10 m). Graphical determination shows that, in this cross section, the true aureole ex- tends about 500 m above the ore body, i.e., more than 2.5 times the extent of the apparent aureole. From the above it is clear that the depth of an aureole survey can be increased by decreasing the least anom- alous productivity of the aureole (preferably by reducing the least anomalous content, since decreasing the sampling interval leads to a considerable rise in working expenses). To choose an appropriate method of systematic sample analysis (the essential point of the problem), we studied the forms of uranium occurrence within the aureole. The uranium content of an aureole accumulates from the primary distribution in the country rock (the Clarke content) and from uranium introduced by the hydrothermal solutions and forming the aureole. Many investigators, having studied the occurrence of primary uranium in magmatic rocks, remark that part of the uranium can be extracted from the rocks by relatively weak solvents, but the whole is extracted only by breaking down the crystalline structures of the rock-forming and accesory minerals. Tauson [6] distinguishes be- tween two main forms of uranium in granitoids: non-isomorphic and isomorphic. He assigns the name "non-iso- iThe idea of linear productivity of a diffuse aureole is due to A. P. Solovov [5]. 58 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 TABLE 1. Degree of Uranium Extraction by Na2CO3 from Pitchblende and Sooty Uraninite Sample No. Uranium mineral Total U content, oh Extraction into so- lution, oh A-3 Pitchblende 3.6.10-4 75 A-12 * 9.10-4 89 A-5 # 8.10-4 75 C-89 * 0.2 90 C-1 # 0.31 74 A-9 Uraninites 3.6?I0-4 100 s400 .0 z jog morphic" to that part of the uranium which can be extracted by boiling with 507o ammonium carbonate solution containing hydrogen peroxide. In these con- ditions the crystalline lattice of the rock-forming and accessory minerals is practically undisturbed. Tauson considers that, with this method of analysis, the urani- um from separate minerals (such as oxides) also passes into solution. Experiments have shown that granitoid rocks have a negligible content of non-isomorphic uranium. Our investigations showed that uranium, intro- duced into the country rocks during the formation of an ore body, occurs mainly as the individual minerals pitchblende and the sooty uraninite group of oxides [2]. In order to bring. the latter into solution without destroying the crystal lattices of the rock-forming and accessory minerals, weighed samples were boiled for 30 min with 20h soda solution containing hydrogen per- oxide as oxidizer. o To determine the degree of uranium extraction 0 0 from pitchblende and oxides, an artificial mixture of I I . . "8 - . these minerals with pure quartz sand was treated as 0 E ? Zoo 02 Surface ?E o s o . . described. The total uranium content of the samples was determined by melting weighed portions with soda. O 2 Horizon I ..1). II % The results showed that pitchblende and uraninite are satisfactorily dissolved by soda solution (see Table 1). w foo "8 ...47 It should be noted that Na2CO3 solution ex- Horizon III -8 % N tracts only a tiny part of the primary, so-called mobile Horizon IV .ct Yi VI % . uranium from the country granites outside the limits of . the aureole [6-8]. The least anomalous content of - ? . Horizon V ... ' o ? ?r .0 0 r- mobile uranium for the granites of the deposit de- 4 HorrizonVI -o. ; scribed is equal to 2 ? 10-407, which also exceeds the o geochemical background (0.000040h) by twice the stand- cool o.00t aot of to to ard deviation (GB + 20). The (linear) least anomalous ' productivity for mobile uranilum is 0.002 m ?A As shown by the graphical determinations, the extent of Fig. 2. Extent of uranium aureoles above an ore body. the mobile uranium aureole above the ore body is I, II, III) Linearized changes of productivity of urani- more than 11/2 times that revealed by measuring the urn aureole in a vertical direction. total U content (see Fig. 2). In other words, the above method of systematic sample analysis considerably increases the effective depth of prospecting for concealed ore bodies by means of uranium aureoles. This conclusion, based on graphical construction, is confirmed by mapping the aureoles in a vertical Cross section through the ore body. Figure 3 shows the uranium aureoles around a concealed ore body. The graph of the linear productivity in this cross section is given in Fig. 2. The aureole is mapped twice, according to sample assays of mobile uranium and of total U content. To reduce the number of analyses, the total U content was determined only for the samples taken at the surface and first horizon (see Fig. 3). The mobile uranium aureole is the wider and longer of the two. The mobile U content of all the surface samples was anomalous, whereas that of total U in the same samples was less than the minimum anomalous value ? i.e., no total-U aureole is observed at the surface of this cross section. At the first horizon the width of the U aureole is small. It follows from Fig. 3 that, if the total U aureole were used in prospecting for this ore body, it would not be located. A Horizon II 1/4 1/4 ? HorizonVII ?..? ? . . Linear productivity of uranium aureol, m% 59 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 a Scale 20 0 20 'Cm 1=1 ZNN1 4[= 5=I 6LJ 7E-1 8 Fig. 3. Primary uranium aureoles; a) Aureole of total U content; b) aureole of mobile urani- um. 1) Granites; 2) ore body; 3) faults; 4) workings and boreholes; 5) sampling intervals. Uranium contents, 0/0; 6) 0.002-0.0015; 7) 0.0015-0.005; 8) >0.005. a Scale 10 0 10 20 30 40.m Wimi==imamichnowni CSO 2R 3 MOE F-1 VW 6M 7 Fig. 4. Primary uranium aureoles; a) Of total U content; b) of mobile U. 1) Ore body; 2) working and boreholes; 3) sampling intervals. Uranium contents, 010: 4) 0.0002-0.0005; 5) 0.0005-0.0015; 6) 0.0015-0.005; 7) > 0.005. Figure 4 shows the uranium aureoles around two contiguous concealed uranium ore bodies. The latter are revealed at the surface by only two samples, if the least anomalous total U contents are used. For mobile U, how- ever, all the surface samples fall within the aureole. Furthermore, at the surface directly above the ore bodies an anomalous field of mobile uranium is found, its width exceeding that of the aureole of total U content (see Fig. 4). 60 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 The method of analysis for mobile uranium is easier than that for the total content: It facilitates the bulk sample analysis which is so necessary in geochemical prospecting. We can expect this systematic analysis method to be most effective for elements with small apparent aureoles of low intensity. Figure 2 shows that the use of sys- tematic analysis increases the extension of the apparent maximum-productivity aureole of uranium by a factor of 1.2 (curve III), while the extension of the aureole with minimum productivity is increased nearly ten times (curve II). The following conclusions may be drawn. 1. The use of systematic chemical analysis (determination of the mobile uranium content) permits fuller ex- posure of primary uranium aureoles and increased depth of prospecting for concealed uranium ores by means of pri- mary aureoles. 2.- The use of systematic chemical analysis will be most effective for elements with apparent aureoles which are, owing to high background concentration in the country rocks, low concentration in the ores, etc., of small dimen- sions and intensities. 3. By means of systematic chemical analysis it will be possible to find primary aureoles for a number of new elements which cannot be discovered by total content determinations, as their background levels are high and, con- sequently, so are their least anomalous contents. LITERATURE CITED 1. A D. Kablukov and G. L Vertepov, Geologiya rudnykh mestorozhdenii, No. 2, 20 (1960). 2. E. M. Yanishevskii, et aL, Endogenous Diffusion Aureoles of Certain Hydrothermal Deposits [in Russian] (Moscow, Gosgeoltekhizdat, 1963). 3. H. Morris and T. Lovoring, Econ. Geol., 47, 7, 685 (1952). 4. S. V. Grigoryan, Razvedka i okhrana nedr, No. 2, 26 (1964). 5. A. P. Solovov, Razvedka i okhrana nedr, No. 4, 48 (1952). 6. L. V. Tauson, Geokhimiya, No. 3, 9 (1956). 7. L. S. Evseeva and A. I. Perel'man, Geochemistry of Uranium in the Supergene Zone [in Russian] (Moscow, Gosatomizdat, 1962). 8. A. S. Saukov, Radioactive Elements of the Earth [in Russian] (Moscow, Gosatomizdat, 1961). 61 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 LETTERS TO THE EDITOR PHASE STABILITY OF PARTICLE BLOBS IN ACCELERATORS WITH AUTOMATIC CONTROL (UDC 621.384.60) A. Zhil'kov Translated from Atomnaya Energiya, Vol: 18, No. 1, pp. 58-59, January, 1965 Original article submitted May 8, 1964 The characteristic equation for a system of particles performing nonlinear synchrotron oscillations in an ac- celerator with automatic correction of the accelerating field's frequency (4)0= qws with respect to the beam was derived in [1]; +03 d/0 K _hk2Th 1=2ni, deQ(e) E co?kg2 (e) ? de ?Co (1) Here, u) is the natural oscillation frequency in 11(0) units, where 0(o) is the frequency of linear synchrotron oscilla- tions; e and Q(e) are the energy and the frequency of nonlinear synchrotron oscillations; fo(e) is the equilibrium distribution function of the blob; K(w) is the system's reaction to the shift of the point blob with respect to u and 9 at the frequency w; 9k and K_k are the coefficients of the expansions of 9(c, T) and K(e, T) as periodic func- tions of the variable T ,)u (e,) Wi in Fourier series at the section Es ( u 2n Q (0) ?dE Q(e) 12(e)) ' ? eV sin Ws .1 cos (E) Certain general stability criteria for small-size blobs were found in [1] under the assumption that the automatic control system corrected the position of the blob's center of gravity. Here, we shall investigate the stability of small blobs in the presence of a system of automatic control with respect to second moments and also the stability of higher moments. Consider the stability of a small blob [1] in the case where feedback with respect to the blob dimensions is provided [2], i.e., when not only the center of gravity, but also deviations of the blob dimensions with respect to vo their equilibrium values 4,(1= = e;W0 = 0 are corrected. The automatic control system is described by the equation K (w) = K (0)) u K2 (C)) (P+ K3 (0))('Y?i'0) + K4 (a)) (17 ?TM+ K5 MI 4 7, (2) where Ki(w) are the transfer constants of the feedback circuits with respect to the corresponding blob characteristics, and 4, = ? 90)2 , V = u2 and W = (9 ? 90)u are the characteristics of the blob dimensions. By substituting Eq. (2) in (1) and using the dependence of the phase 9 on the time T [3] where (T) cos QT ctg cps e L 8 ctg cps cos 2QT 8 Y28 2 m 6 96 1 5 Q 1 --8- e (1+ ?3 ctg2ps) , (1 + ctg2 Ts) cos 3QT + (3) we find the characteristic equation for determining the natural oscillation frequency of the blob; 62 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 a 1 ';Tr?max -411.6max. Fig. 1. Regions of stability (I) and instability (II) of a blob in the plane of the convex variable El. a) Linearly falling equilibrium distribution; b) linearly rising equilibrium distribution. correcting don cycle the center of gravity. This makes it possible by choosing suitable transfer constants K3 K while 5 s -=???:(J. (1+ vtg2ip,3) , (5 1 + -3- ctg2 cps ) (3 + 2iK2-1C1) 4i ctg cps [ et% (Ps (K2+ 2iKi)? + K3 iK5 e2 de j =C dfo 3 de (02_4+e ( ?5 ctgq),) 3 (4) ' (5) ce=2 (6) If we consider that the distribution is uniform [1], we obtain the solution of (4) in the following form: co-2 ?1 (1 +1 ctg2 cps) i ctg cps-8 [ etg6 (Ps (K2+2iKi)?K4+ K3 i K5 3+2iK2?Ki --e_cmax where 2 co-2'M The results obtained in [1], where the parameter g denotes the expression defined by (5), remain valid for a triangular distribution. Consequently, the introduction of feedback with respect to the blob dimensions produces the same effect as the consideration of a slight nonlinearity in to secure the blob's stability throughout the entire accelera- 4, and K5. We shall analyze the stability of a blob described by the three first distribution moments. In - (1 5 + ? ctg2q) {8 + 3iK2-1Ci?ie [K2 (0.94 +0.12 ctg2 TO+ ilf (0 8+0.1 ctg2 cps)? 3 8} ?3.2 ctg cps (K3?K4-1.5iK5)]} this approximation ( 0 3 (8) (0=3. (9) (10) 3 c t g2 Ts) [4. (1+ ctg2 cps) (K2+ 3iKi)?ctg cps (21(4?K3+ 1.5iK5) For a uniform distribution, we find from expression (1) is2 [-h-(1 + ctg2 cps) (K2+ 3iKi) + cg cps kK3 (1 6tg2 21C4-1.5iK5 .co (1+ ?5 ctg2cps + cps) 4 3 8 8+3iK2-1Ci If we use a triangular distribution, the characteristic equation assumes the following form: 1 y 1 max 4(9...2) Y-= 5 9emax (1 + ctg2 cps ) ? The logarithm branch is chosen in such a manner that the logarithm value for Im y > 0 lies on the first sheet. The figure shows the stability region for the blob, plotted in the plane of the convex variable g for the linearly falling (a) and the linearly rising (b) distributions. 63 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6, The stability criteria for blobs characterized by higher moments are established in a similar manner. It should be mentioned that it is rather difficult to consider the stability of higher moments by using the method of moments [1]. We shall formulate a general statement concerning the stability of higher moments for a small blob. The char- acteristic equation for the k-th moment is given by it--2=gtfit. (1+-35-- ctg cps) , where gk_2 is a (k -2)-power polynomial with respect to &max, and j dfo eh de 4(k2_2) h 3 de e?x ' 5 k2emax (1?-3-ctg2cPs) (12) For a uniform distribution (natural damping is absent), the correction for the frequency of the k-th moment ak that is secured by the automatic control system is proportional to the (k -1)th moment of the equilibrium distribu- tion function [al, ehm-atx = 810 (e) de] . By calculating Jk for any other equilibrium distribution function, we readily see that the order of natural damping for the k-th moment is ekm-a2x. Therefore, the effect con- nected only with the automatic control system, which is a small quantity of a higher order with respect to &max, is less important. Thus, the stability of higher moments is basically determined by natural damping, i.e., by the form of the blob's equilibrium distribution function. For small blobs, the moments rapidly decrease with an increase in their numbers. The stability (instability) regions of higher moments given by Eq. (11) became narrower. In prac- tice, the stability criterion for small blobs depends on the first, the second, and, perhaps, the third, moments. Higher moments apparently have no significance. At high frequencies co >> 1, the stability of small blobs is determined by the criterion for the stability of the center of gravity. The above results naturally cannot be applied to blobs whose dimensions cannot be considered as being small, since expansions of the type (3), cannot be used in this case. The author acknowledges his deep gratitude to A. N. Lebedev for his guidance in the work and to A. A. Kolomenskii for the discussion. LITERATURE CITED 1. E. A. Zhil'kov and A. N. Lebedev, Present issue, p. 22. 2. H. G. Hereward, Proc. of Intern. Conf. on High Energy Accel. Brookhaven (1961), p. 236. 3. L. D. Landau and E. M. Lifshits, Mechanics [in Russian] (Moscow, Fizmatgiz, 1958), Paragraph 29. 4. E. A. Zhil'kov, Pribory i tekhnika jksperimenta, No. 1 (1965). 64 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 SIMPLE METHOD FOR MEASURING THE FREQUENCY OF FREE TRANSVERSE OSCILLATIONS IN CYCLOTRONS (UDC 621.384.612) S. A. Khe,ifets and. S. K. Esin Translated from Atomnaya nergiya, Vol. 18, No. 1, p. 60, January, 1965 Original article submitted January 29, 1964 The usual method I'm measuring the frequency of transverse oscillations of particles in cyclotrons consists in exciting coherent betatron oscillations and measuring the frequency of the voltage induced at the signal electrodes [1, 2]. The energy scattering of particles in the circulating beam leads to a rapid disappearance of the coherent part of oscillations. If it is necessary to measure the frequency fairly often (in comparison with the damping time), repeated pulse excitations of oscillations may result in a considerable increase in the beam's aperture. We shall demonstrate that the frequencies of transverse oscillations can also be measured by introducing local perturbations of the equilibrium orbit which are constant in time. We shall assume that a certain perturbation exists at the azi- muth so. In this case, the right-hand side appears in the equation describing transverse oscillations; where d2x + (02 (s) x =llso (s), ds2 f 0, 0 ;:: Shield i :?..4.c 10 20 30 40 Fig. 1. Density of sources of capture y -rays in steel. qVo ) Without a boron screen; ql ) with a boron screen. V 5 0 5 10 15 pt Fig. 2. Dependence of the reduction factor for cap- ture y -radiation secured by the boron screen on the "optical" thickness pt (in mean free path units) in the shield. N Experimental result given in [2]. reducing the strength of sources of capture y rays in the steel mass, a boron-containing screen also influences the form of their angular distribution at the steel surface. In this case, the angular distribution assumes a predominantly cosine character. It is well known that sources with equal strength, but different angular distributions (all other con- ditions being equal), produce different dose rates. This is due to the fact that, along the path of attenuation of y - rays in the shield, isotropic sources are transformed into anisotropic sources due to intensive filtration, so that the reduction factor for the dose of capture y radiation (the blocking factor) constitutes a function of the "optical" thickness pt (measured in mean free path units) between the sources and the detector. For the confirmation of what has been said above, we calculated the spatial and energy distributions in steel screens and the reactor vessel by using the 18-group meth- od in the P2-approximation by means of an electronic com- puter for reactors with and without a boron-containing screen. Figure 1 shows the spatial dependence of the density of capture y -rays, calculated for the entire thickness of the steel mass with and without a boron screen. By using these sources of capture y -rays, we can readily calculate the dose rate produced by these sources for different "optical" thicknesses pt (measured in mean free path units). The ratio of the dose rate produced by a source without the boron screen for the thickness pt to the dose rate produced by the same source with a boron screen characterizes the 'advantage provided by the boron screen. This factor is given by S0 q7(r) _.:_vy-sou (r') dr' 0 4rc I r 12 dV 4;0/.12 dV Figure 2 shows the reduction factor for the dose produced by capture y -radiation in dependence on the "optical" thickness pt between the source and the detector. For pt 0.5, the calculated value of the above factor is in satis- factory agreement with the experimental value given in [2, 3]. If a boron screen is provided in the reactor structure, the screen reduces the dose by a factor of 13(pt) for the thickness pt. This factor can be useful in selecting shield variants, where the dose at the point pt in question is cal- culated without considering a boron screen and is theh reduced by'a factor Of 3 if a boron screen is to be provided. It should be noted that the factor 8 depends on the composition and thickness of the steel screens and the re- actor vessel as well as on the spec rum of incident neutrons. 81 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 The authors are deeply grateful to S. G. Tsypin and Yu. A. Kazanskii for their interest in the work and critical remarks. LITERATURE CITED 1. G. I. Marchuk, Methods for Calculating Nuclear Reactors [in Russian] (Moscow, Gosatomizdat, 1961). 2. A. G. Bakov, et al., Atomnaya Energiya, 13, No. 7 (1962). 3. D. L. Broder, et al., Atomnaya nergiya, 8, 49 (1960). 82 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 Declassified and Approved For Release 2013/09/24: CIA-RDP10-02196R000700010001-6 DEPENDENCE OF THE DENSITY OF RADIATION DAMAGE TO THE REACTOR VESSEL ON THE COMPOSITION OF THE FERRO-AQUEOUS THERMAL SHIELD (UDC 621.039.553.3) K. K. Popkov and S. M. Rubanov Translated from Atomnaya ?Energiya, Vol. 18, No. 1, pp. 70-71, January, 1965 Original article submitted January 15, 1964 The present article is concerned with an investigation of ferro-aqueous mixtures with different compositions for thermal shields from the point of view of the effect of the mixture composition on the radiation damage to the reactor vessel caused by neutrons. For this purpose, we considered a primary-shield composition consisting of 25cm Fig. 1. Geometry of the compo- sitions. 1) Reactor core; 2) ferro-
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