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APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00854R004500040025-5 FOR OFFICIAL USE ONLY JPRS L/ 10379 11 March 1982 _J I USSR Report PHYSICS AND MATHEMATICS CFQUO -2/821 Fg~$ FQREIGN BROADCAST INFORMATION SERVICE FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00850R000500040025-5 NOTE JPRS-publications contain information primarily from foreign newspapers, periodicals and books, but also from news agency transmissions and broadcasts. Materials from foreign-language sources are translated; those from English-language sources are transcribed or reprinted, with the original phrasing and other characteristics retained. Headlines, editorial reports, and material enclosed in brackets are supplied by JPRS. Processing indicators such as [Text] or [Excerpt] in the first line of each item, or following the ]'.ast line of a brief, indicate how the original information was processed. Where no processing indicator is given, the infor- _ wation was summarized or extracted. Unfamiliar names rendered phonetically or transliterated are enclosed in parentheses. Words or names preceded by a ques- tion mark and enclosed in parentheses were not clear in the original but have been supplied as appropriate in context. Other unattributed parenthetical notes with in the body of an item originate with the source. Times within items are as given by source. The contents of this publication in no way represent the poli- cies, views or at.titudes of the U.S. Government. COPYRIGHT LAWS AND REGULATIONS GOVERNING OWNERSFiIP OF MATERIALS REPRODUCED HEREIN REQUIRE THAT DISSEMINATION OF THIS PUBLICATION BE P.ESTRICTED FOR OFFICIAL USE ONLY. APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504040025-5 JPRS L/10379 11 March 1982 USSR REPORT PHYSICS AND MATHEMATICS (goUO 2/82) CONTENI`S ASTROPHYSiCS AND CQSMOLOGX Combustion and Explosion in Outer Space and on the Earth........... 1 CRYSTALS AND SEMICONDUCTORS � Elec.cronic Processes in Island Metal Films ................6........ 6 FLUID DYNAMIC S ' Nonlinear veformation Waves 10 Numerical Modeling of Gasdyaamic Processes Occurring When Laser - Emission With Moderate Flux Densitq Acts on Metallic Obstacle in Air 13 LASERS AND MASERS Mechanisin of Pulsed La.sing in High-Pressure Electric Discharge Ar-Xe-Laser 20 Catalytic Recovery of Gas Mixture of Closed-Cqcle Electron Beam Preionized C02 Laser 31 _ Characteristic Features of Forming Radiation Pattern of Laser Emission in Resonators With Retroreflecting Mirrors 41 Determining Turbulence Parameters by Laser Beam Probing of the Atmosphere 53 I,aser Measurement Systems 71 Abstracts of Articles in Collection on Quantum Electronics.... 77 - a- [III - USSR - 21H S&T FOUOJ FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007142/09: CIA-RDP82-40854R040500040025-5 FOR OFFICIAL USE ONLY MAGNETOHXDRODYNAMICS = Science Session on Therinophysical and Electrophysical = Problems of MD Energy Conversion Method 81 � OPTICS AND SPECTROSCOPY Properties of Resonators With Mirrors Formed by Set of Inverting Elevients 83 OPTOELECTRONICS Electroluminescent Image Converter With Memory 89 PLASMA PHYSICS Plasma Heating im k:ute-Angled Flagnetic Trap Without Use os Injection 95 STRESS, STRAIN AND DEFGRMATION Precursors of Mechanical Destruction of Large Specimens............ 99 THEORETICAL PHYSICS . Absolute and Convective Instability in Plasma and Solids........... 103 - b - 4 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00854R004500040025-5 FOR GFF[CIAL USE ONLY ASTROPHYSICS AND COSMOLOGY COMBUSTION AND FJXPLOSION IN OUTER S�ACE AND ON THE EARTH lrioscow GORENIYE I VZRYV V. KOSMOSE I NA ZEhLE in Russian 1980 (signed to press 15 Jan 80) pp 2, 152-155 [Annotation, table of contents and abstracts from collection of articles "Combus- tion and Explosion in Outer Space and on the Earth", edited by E. I. Andriankin, doccor of physical and mathematical sciences, Vseaoyuznoye astronamo-geodezicheskoye obshchestvo pri Akademii nauk SSSR, 1000 copies, 156 pages] [Text] The collection contains articles that outline the results of theoretical and experimental research in the f ield of inechanics of a continuous medium as applied to problems of combustion physics. An examination is made of problems of the singular state of the universe, exuansion of the metagalaxy, questions of radiation in a shock wave in inert gases, of the mechanism and limiting condi- tions of ignition of mixtures, shock waves in the presence of magnetic fields, and also analytical methods of studying equations that describe the corresponding processes. The collec;tion is inteniled for specialists in the field of astrophysics, cosmology, physics o� explosion, shock wave physics, plasma physics and so on. Contents page Krechet, V. G., Nikolayanko, V. M. and Shikin, G. N., "Some Corollaries of the Theory of Interacting Fields in Cosmology and Astrophysics" 3 - Stanyukovich, K. P. and Mel'nikov, V. N., "Energetics and Mass Spectrum bf ' Planckeon and Gravitational Vacuum" " 20 Kiselev, Yu. N., "Total Output of Radiation From Shock Wave Front in Inert wlu Gases" 36 Kononenko, M.�M., "Electrothermal Analog of Detonation" 56 Ivanov. V. G., Ivanov, G. V. and Kuznetsov, V. P., "Investigation of Mechanism and Limiting Conditions of Ignition of Fuel Mixtures With Iodic Acid Anhydride" 61 Sarukhanov, Q. I., nAnalytical Studies of Equations of Unsteady Nonadiabatic One-Dimensional Flows of Continuous Medium Modeled by Viscous Thermally Conductive Perfect Gas" 76 1 FOR OFFIC[AL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540040025-5 FOR OFFICIAL USE ONLY Ageyev, A. N. and Andriankin, E. I., "Double Explosion in Water at Low Energy Densities" 109 Dolgov, A. A., "Some Classes of Solutions of the Monge-Ampere Equation for an Inhomogeneous Medium" 125 = Ivanov, M. Yu., "Rarefaction Wave in Medium With Equation of State including Section With Negative Pressure" 131 Andriankin, E. I. and Kononenko, M. M., "Motion of-Fluid in Magnetic Field Witb Clapping of lfao Plates" 014 o � t 41,,: . 138 ~ Andriankin, E. I. and Malkin, A. I., "Theory of Nonlinear Wave Propagati,on" 148 UDC 530.12:531.51 SOME COROLLARIES OF THE THEORY OF INTERACTING FIELDS IN COSMOLOGY AND ASTROPHYSICS [Abstract of article by Krechet, V. G., Nikolayenko, V. M. and Shikin, G. N.] [Text] An examination is made of the inf luence that terms of interaction of clas- sical fields have on the singular initial state and isotropization of the process of evolution of the universe. The problem of the cosmological background of quan- tum field theory and the mass of the Higgs boson is discussed. References 27. UDC 530.12:531.51 ENERGETICS AND MASS SPECTRUM OF PLANCKEON AND GRAVITATIONAL VACUUM. [Abscract of article by Stanyukovich, K. P. tind Mel'nikov, V. N.] [Text] nao fundamental relations, the Mach relation and Dirac`s equation, are derived from a model of a vacuum based on two hypotheses: a) dense packing of planckeons; b) density of de-excited energy coincides with the energy density of the field of the metagalaxy. References 12. UDC 5 35.89+535.21 TOTAL OUTPUT OF RADIATION FROM SHOCK WAVE FRONT IN INERT GASES [Abstract of article by Kiselev, Yu. N.] [Text] The article describes a method of ineasuring spectrally integrated radiation fluxes from a shock wave front using quick-response pyroelectric radiation re- ceivers, and gives the results of ineasurement of radiation fluxes from a shock wave front in xenon and argon, and also brightness temperatures of the front in the red ancl violet regions of the spectruan. It is shown that in xenon at velocities of 5.5-11 lun/s, despite considerable screen- ing in the red region of the spectrum, the total radiation output is close to the calculation from the shock adiabat.' With further increase in shock wave 2 FOR OFF[CIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R004500040025-5 FOR OFFICIAL USE ONLY velocity, radiation fluxes do not exceed 1.8�107 W/cm2. In argon at velocities of 6.8-15 km/s, the shock wave radiation is close to that of an ideal bYack body. The total radiation output is close to calculation up to 20 lan/s. At velocities of 20-37 km/s, considerable excess of radiation temperatures over brightness tem- peratures is observed. The radiation fluxes registered from the wave front in ~ argon are up to 1.2�108 W/cm2. The experimental results are used to estimate the spectral average absorption coefficients of shock-heated xenon and argon, which are much lower than the absorption coefficients in the visible region of the spectrum. References 8. UDC 534.222.2:539.63 ELECTROTHERMAL ANALOG OF DETONATION [Abstract of article by Kononenko, M. M.J [Text] Supply of energy from outside sources to a shock wave front with some conductivity leads to an effect similar to detonation. Joule heat.release on the front gives rise to the detonation mode. It is shown that the "shock adiabat" in such a mode coincides with that of a substance absorbing intense luminous flux. References 5. UDC 536.46 INVESTIGATION OF MECHANISM AND LIMITING CONDITIONS OF IGNITION OF FIJEL MIXTURES WITH IODIC A.CID ANHYDRIDE [Abstract of article by Ivanov, V. G., Ivanov, G. V. and Kuznetsov, V. P..] [Text] The mechanism and processes that limit spontaneous combustion of mixtures of inorganic fuels (metals and non-metals) with 1205 are studied by thermal dif- ferential analysis. It is shown that in contrast tu conventional mixtures, the mechanism of spontaneous combustion of t'he investigated mixtures is deteXcnined by the formation and properties of iodides of the fuels. The authors establish the lower limits of ignition of the mixtures as a function of their relative den- sity and fuel content. References 12. UDC 532.'5-1/-9:532:011.11 ANALYTICAL STUDIES OF EQUATIONS OF UNSTEADY NON-ADIABATIC ONE-DIMENSIONAL FLOWS OF CONTINUOUS MEDIUM MODELED BY VISCOUS THERMALLY CONDUCTIVE PERFECT GAS [Abstract of article by Sarukhanov, G. I.] [Text] An investigation is made of equations of unsteady non-adiabatic flows of a continuous medium modeled by a viscous thermally conductive perfect gas. Solutions of the equation of motion are obtained in the class of solutions of _ a continued system of equations by reducing the differential corollary of the initial equation to a Darboux equation. The resultant solutions enable evaluation of the way that temperature, heat flux and static pressure depend on time and mass coordinate, and can be used in studying some patterns of explosive processes: combustion, explosi.on, detonation. References 12. 3 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY UDC 539.1 DOUBLE EXPLOSION IN WATER AT LOW ENERGY DENSITIES [Abstract of article by Ageyev, A. N. and Andriankin, E. I.] - [Text] At low energy densities, a spherical explosion in water is described by an approximation that differs from the solution of the corresponding problem for an incompressible liquid anly in the accounting for delay time. The problem of double explosion in water is solved in such an approximstion. An analysis is made of the dynamics of the cavity formed as a result of double explosion. It is shown that the principal characteristics of pulsations of.the cavity as well as the magnitude and shape of the pressure pulse propagating in water can be varied over a wide range by controlling the parameters of the double explosion. References 7. UDC 532.11+534.222.2 SOME CLASSES OF SOLUTIONS OF THE MONGE-AMPERE EQUATION FOR AN INHOMOGENEOUS MEBIUM [Abstract of article by Dolgov, A. A.] [Text] An examination is made of one-dimensional plane movements of an ideal fluid with variable initial density and speed of sound. Exact solutions of the Monge-Ampere equation are found for some distributions of these parameters. References 3. ' UDC 533.1:5330.2 RAREFACTION WAVE IN MEDIUM WITH EQUATIdN OF STATE INCLUDING SECTxON WITH NEGATIVE PRESSURE [Abstract of article by Ivanov, M. Yu.] [Text] An 'investigation is made of qualitative peculiarities of rarefaction waves in a medium with an equation of state that includes a section with negative pressure. Assuming that the results of rarefaction processes may lead to breakup of Lhe medium into individual particles, the author evaluates the mass of such a particle. References 5. UDC 537.84:539.63 MOTION OF FLUID IN MAGNETIC FIELD WITH CLAPPING OF TWO PLATES [Abstract of article by Andriankin, E. I. and Kononenko, M. M.] [Text] The flow of a conductive fluid in a magnetic field resulting from conver- gence of channel walls may be of interest for getting strong currents in MHD oper- ation. This paper gives an exact solution of such an unsteady two-dimensional problem for a slit channel at low magnetic Reynolds number,when plates clap togeth- er in accordance with a special law. The solution depends on three constants that can be used for approximations. References 2. 4 FOR OFFICIAL USE ONLY , APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504040025-5 FOR OFFICIAL USE ONLY UDC 539.9 THEORY OF NONLINEAR WAVE PROPAGATION [Abstract of article by Andriankin, E. I. and Malkin,'A. I.] [Text] A method is proposed for studying nonlinegr waves in weakly dispersing media. The evolution of initial perturbation reduces to propagation of a certain number of modes. In the first order of the method, modes interact with near phase velocities. References 4. COPYRIGH.T: Unknown 6610 CSO: 1802/79 5 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY CRYSTALS AND SEMICONDUCTORS UDC 539.216,535.33,537.533 ELECTRONIC PROCESSES IN ISLAND METAL FILMS Kiev ELEKTRONNYYE PROTSESSY V OSTROVKOVYKH METALLICHESKIKH PLENKAKH in Russian 1980 (signed to press 17 Nov $0) pp 4-8 [Annotation., preface and table of contents from bodk "Electronic Processes in Island Metal Films", by Petr Gri.gor'yevich Borzyak and Yuriy Aleksandrovich Kulyupin, Institute of Physics, UkSSR Academy of Sciences, Izdatel'stvo "Naukova dumka", *1200 copies, 240 pages] [Text] The book examines new problems in the physics of island metal films: "cold" electron emission and "cold" luminescence, the relation between these ef- fects and conduction current, and between luminescence re:aulting from conduction current and a new kind of luminescence when metals'are bambarded by electrons. An investigation is made of the.nature of conductivity of island films, the rela- tion between their characteristics and structure determinel by the conclitions of growth. Also examined are problems of the physics of small metal island parti- cles that are new with respect to their solution. The book is intended for scientific workers, specialists in the field of elec- tronic technology and electron microscopy, and also for graduate atudents and upperclassmen majoring in physics and physical engineering. Figures 127, tables 2, references 355. Preface Our attention was f irst drawn to island metal films and small particles during research on the nature of silver-oxygen-cesium photocathodes. A study of the very interesting optical and photoelectric properties of silver island films, especially when coated with cesiwa and its.oxide, enabled us to explain the ap- preciable influence of small silver particles on the properties of these photo- cathodes., Later we were to observe completely new effects occurring in gold films. In studying the emission,of hot electrons from.silicon p-n junctions, we had to apply a gold film on the end face of the junction. At a certain voltage across the junctions, electron emission was abserved that sec-:aed to emanate fram the gold fi1.m. Numerous control experiments with fi1;,s of different thicknesses on different dielectric backings confirmed the effect of electron emission from gold films upon application of sufficient voltage and with passage of current. Tha emission was only from island films, and only cold, i. e. not associated wiCh 6 FOR OFFIC[AL USE OA1LY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY _ heating of the film by the transmitted current. Moreover, we learned that cold electron emission is accompanied by cold luminescence of the films, i. e. by lumi- nescence of film islands that are not incandescent. It is not surprising that these striking and completely unexpected effects have long riveted our attention on island metal films and small particles. The desire to explain the nature of observed new effects, and the mutual relation between these effects and conducLion current has led to many experiments and theo- retical studies. The very effect of conductivity of films consisting of individual metal island particles on dielectric substrates is of irndependent interest, and it has been necessary to give attention to the mechanism of this conductivity as well. Some interesting properties of island f ilms have also been observed in the study of conductivity. Some of these properties have been associated with peculiarities of film structure, which has necessitated a study of the problem of growth of islands and the structure of the films. In studying the properties of island films, we cannot avoid dealing with the properties of the separate is- lands themselves, which are microparticles of the'metallic substance. And since physical arguments.tell us-that the properties of such particles with suff iciently small dimensions must.differ from those of massive metals, their investigation is of considerable physical intErest. In studying the nature of lwninescence, island metal f ilms were subjected to elec- rrnn bombardment. In doing this, unknown luminescence was observed. It was found that bombarding continuous films and massive metal with the same kind of electrons produces the same kind of luminescence. It was necessary to study ~the nature of this effect, the moreso as it promises important applications. Generalization of these studies has been the content of this book. But if the work delineates research in the given area, it does so on an initial stage. The physics of fine solid particles and island f ilms is still far from complete study, and our main goal has been to call attention to this interesting field. The wider the class of people who are involved in the area, the greater the depth and the faster the pace of investigation will be in studying these interestirig ob3ects, and the more intense will be the generation of new physical and practical ideas and the acceleration of their realization. If the publication of this book is in any way conducive to the attainment of this goal, the authors will feel that their labor has been rewarded. Contents page 7 Preface 9 List of Symbols 11 Chapter 1: INTRODUCTION TO PHYSICS OF ISLAND FILMS 11 1. Thin Films. Classification and Description 20 2. Basic Information on Mechanism of Film Growth 31 3. Specifics of Electronic Processes in Island Films 3.1. Physical model of island film (31). 3.2. Properties of f3ne metal particles (33). 3.3. Electrical conductivity of films. Emission and optical ghenomena (38). 3.4. Specifics of experimental studies of physi- cal phenomena in island films (41) 44 Chapter 2: ELECTRONIC PROPERTIES OF FINE METAL PARTICLES 44 1. Quantizing Spectrinn of Single-Particle States 7 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00854R000540040025-5 FOR OFFICIAL USE ONLY = 1.1. Quantum size effect and electric conductivity of continuous films (44). 1.2. Film potential, carrier scattering mechanism, and calculation of the way thaz bismuth film conductivity depends on thicknesG and tem- perature (46). 1.3. Structure and electric conductivity of bismuth films. Quasi-size effect (50). 1.4. Quantization of single-particle electron states in islands with few atoms (SS). 5~ 2. Collective State of Electrons in Metal Islands 2.1. Frequency of collective vibrations in massive metals and fine. particles (57). 2.2. Electron-photon radiation by island silver films (66). 10 3. Dynamic Polarizability of Fine Metal Particles 3.1. Theoretical concepts of size dependence of dynamic polarizability of fine particles (70). 3.2. Methods of determining polarizab ility of fine particles (74). 3.3. Dimensional and frequency dependences of polariza- bil.ity of f ine silver particles (79) 85 4. Average Internal Potential of Fine Metal Particles 4.1. Relation between index of ref raction of electron waves and average internal potential of metal (85). 4.2. Principal equation of interference microscopy. Direct and inverse problems (89). 4.3. Internal potential of bismuth and silver particles (95). 4.4. Internal potential of f ine metal particles (102). 4.5. Nature of size dependences of properties of fine particles (104). 106 Chapter 3: ELECTRONIC PROPERTIES OF ISLAND FILMS 1. Electric Conductivity of Island Films. Case of We.ak Fields and Low 106 Powers of Conduction Current 1.1. Principal problems of theoretical and experimental investigation of electric conductivity (10i;). 1.2. Distribution of electric field and potential in island filtis (109). 1.3. Electric conductivity of island films with statistically homogeneous structure (117). 1.4. Electric con- ductivity of f ilms with statistically inhomogeneous structure (125) 2. Electric Conductivity at Large Inserted Powers and Hot Electron Emission 134 2.1. Electron heating in film. Electric conductivity at large inserted power (134). 2.2. Electron emission from island films (137). 2.3. Electron emission current as a function of voltage across the film and inserted power (143). 2.4. Estimating magnitude of electric field in the vicinity of the emission center (151). 2.5. Electron emission from island films in micro- wave field (155). 2.6. Electron temperature in emission center (159) 164 .3. Island Metal Films as Unheated Electron Emitters 3.1. Cold cathodes (164). 3.2. Equipoteatiality of cathode and electron energy distribution (164). 3.3. Plate characteristics of emission current (165). 3.4. Time stability of emission characteristics (168). 3.5. Inter- ference imnunity and temperature stability (171). 3.6. Cathode efficiencv and economy. Break-in time (172). 3.7. Effect of vacuum conditions (173). 3.8. Ways to improve emission characteristics of cathodes (173). 3.9. Island films as sensors of physical quantities and microelectronics components (17i~$ 4. Current-Excited Light Emission by Island Films 4.1. General information on current-excited emission (178). 4.2. Spectra of light emission by films of different metals (181). 4.3. Power of ltnninous radiation from individual center (185). 4.4. Dependence of intensity and spectral makeup of emission on power input to the film (186). 4.5. Fluc- tuations of characteristics of light emission (188). 4.6. Influence of substrate temperature on emission characteristics (191). 4.7. Relation between emission of light and electron emission.(194). 4.8. Mechanism of current-stimulated emission of light (196) 8 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2407/42/09: CIA-RDP82-40850R000500440025-5 FOR OFFICIAL USE ONLY 5. Electron-Photon Emission of Light Frem Thin Metal Films and Massive Metals 203 5.1. Characteristics of electron-photon emission (203). 5.2. Mechanism of electron-photon emission of light from metals (209). 5.3. Relation ~ between current-stimulated and electron-photon emission (218) . References 221 Subject Index .238 COPYRIGHT: Izdatel'stvo "Naukova dumka", 1980 6610 CSO: 1862/73 9 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R004500040025-5 FOR OFFiCIAL USE ONLY FLUID DYNAMICS UDC 350.145.6 NONLINEAR DEFORMATION WAVES Moscow NELINEYNYYE VOLNY DEFORMATSII in Russian 1981 (signed to press 4 Ma.r 81) PP 2-4, 256 . [Annotation, preface and table of contents from book "Nonlinear Deformation Waves", by Yuriy Kustavich Engel'brekht and Uno Karlovich Nigul, USSR Academy of Sciences, ESSR Academy of Sciences, Institute of Cybernetics, Izdatel'stvo "Nauka", 1700 copies, 256 pages] [TZxt] On the basis of general equations of the mechanics of continuous media, by introducing appropriate supplementary postulates, nonlinear mathQmatical models are constructed for describing wave processes of deformation of thermoviscoelastic, thermoelastic, viscoelastic.and elastic solids and ideal compressible liquid. An examination is made of the construction of solutions of wave problems by sequential integration'of simpl,if ied quasilinear equations (systems) derived by the ray meth- od. Some specific examples are given. In contrast to the conventional approach of rionlinear acoustics, where sine-wave pulses are considered as a rule, this book examines finite pulses of arbitrary shape. . � The publication is intended for scientific workers, graduate .students and upper- classmen interested in the theory of nonlinear waves. Tables 11, figures 44, references 161. Preface Mathematical modeling of nonlinear wave~ processes has lately become more and more - topical in mechanics, acoustics, plasma physics, electrodynamics, oceanology, ' seismology, astronomy and other areas of science and engineering. This can be attributed to the fact that an in-depth understanding of physical phenomena that take place in wave propagation, as well as their use in various technical applica- tions in many cases are beyond the capacity�of the linear theory of wave propaga- tion. Although non-linear wave processes have�their own specific features in the different areas of science, it should be noted that systems of equations used to model the wave process, as well as efficient methods of constructing solutions, are in many cases analogous-or even identical from the mathematical standpoint. 10 FOR OFFIC[AL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY Therefore the nonlinear theory of wave propagation has now begun to take shape as a discipline developing at the confluence of several sciences. This book is an attempt to treat a certain class of problems in the nonlinear theory of deformation wave propagation from a uni�ied standpoint. Its content is divided into two parts. . The f irst part (chapters 1 arid 2) deals with problems of construction o.f mathe- matical models (systems of equations) to describe the mechanics of nonlinear wave processes,of deformation of thernaoviscoelastic, thermoelastic, viscoelastic and elastic solids and ideal campressible liquid within the framework of classical (newtonian, nonrelativistic) mechanics. . The second part (chapters 3-5) examines methods of reducing the problems to sequential integration of simrlif ied equations, as well as methods and results of construction of solutions of these simplified equations in the case of actions by f inite pulses of arbitrary shape. In choosing material for the second part of the monograph, the authors took into consideration that U. K. Nigul's monograph "Echo Signals From Elastic Ob3ects" (Tallin: Valgus, 1976, Vol 1) contains a detailed description of a method of sequential integration of linear equations of hyperbolic type, which has been used to solve many direct and inverse problems of propagation of one-dimensional pulses in laminar media. Therefore, to avoid repetition, this book has focused its main attention (chapters 3-5) on a dif�erent asymptotic approach known as the ray method, reducing the initial problem to se- quential integration of simplif ied nonlinear equations. Of the two asymptotic approaches mentioned here, the former is more simply realized, but is suitable only in the region of minor nonlinear distortions of the pulse, while the latter, which is more complicated, enables description of the principal part of a nonlinear solution on any stage of pulse prapagation. Let us note that other important aspecCs of nonlinear wave theory have been exam- ined recently in monographs by 0. V. Rudenko and S. I.''Soluyan "Theoretical Prin- ciples of Nonlinear Acoustics" (Moscow, Nauka, 1975), and [Dzh.:Uizem] "Linear and Nonlinear Waves", Moscow, Mir, 1977. Chapter 1 was written by U. K. Nigul, chapters 2-5--by Yu. K. Engel'brekht. Contents page - Preface* 3 Introduction 5 PART I: NONLINEAR MATHEMATICAL MODELS OF CONZ'INUOUS MEDIUM Introduction ~ Chapter 1. Elements of Classical Mechanics of a Continuous Mediian 9 1. Initial assiunptions. Description of motion and deformation 9 2. Velocity, acceleration and stress 35. 3. Principal laws (postulates) 47 References . 60 Chapter 2. Specific Mathematical Models of a Continuous Meditun 61 4. Theory of nonlinear dissipative medium without memory 62 5. Mathematical models of solids in specific coordinates 72 ii FOit OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY 6. Mathematical model of liquid in langrangian coordinate systPm 7. Integral form of equations of state References PART II: NONLINEAR DEFORMATION WAVE THEORY Introduction Chapter 3. Ray Method in Nonlinear Wave Theory 8. Principal equations and conditions'of asymptotic approximations 9. Construction of transport equations 10. Properties of transport equations References Chapter 4. Multiple Wave Problems . 11. Ray method for interacting waves 12.. Interaction of counter waves 13. Waves in a la}er 14. Influence of reflected wave interaction 15. Interaction in inhamogeneous medium &eferences . Chapter 5. Analysis of Wave Processes 16. Nonlinear elastic meditmn 17. Nonlinear viscoelastic medium 18. Nonlir;ear thermoelastic mediinn 19. Nonl3.near dispersing mediimn 20. Nonlinear inhomogeneous medium 21. Accounting for diffraction divergence References Appendix COPYRIGHT: Izdatel'stvo "Nauka", 1981 6610 CSO: 1862/61 12 FOR OFFICUIL USE ONLY 91 99 107 110 112 113 125 134 139 140 141 145 149 160 166 169 170 172 178 197 202 221 2 38 251 254 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2407/42/09: CIA-RDP82-40850R000500440025-5 F'OR OFr':C:Ai USE ONLY NUMERICAL MODELINa OF GASDYNAMIC PROCESSES.OCCURRING WHEN LASER EMISSION WITA MODERATE FLUR DENSITY ACTS ON METALLIC OBSTACLE-IN AIR . Novosibirak FIZIKA GORENIYA I VZRYVA in Ruseian-Vol 17�, No 6, Nov-Dec 81 (manu- script received 3 Oct 80) pF 77-82 . � � [Article by G'. S. Romanov.and Yu.'A. Stankevich, Minsk] [Text] The mechanisms of formation and development of a plaema layer at the sur- face of. a metal target that ia located in air and abaorbs intense laser emission have been both experimentally and theoretically investigated in a number of:papers. Ref. 1-8 are most thorough and definite from the standpoint of tying in measurement data to laser pulae parametera (smooth neodymium laser pulse with duration of -1 us). These papers cover experimental and (in of the phase of one-' dimensional planar expansion of the plasma layer) theoretical investigation of mechanisms that successively replace one another as radiation flux density in= � creasea: subsonic radiation wave, light detonation wave and supersonia radiation wave. In view of the fact that time-profiled radiation pulaea are generally realized in experiments, while calculations are done for constant density of the radiation f1ux, eMperiment and theory are'compared in these,works for certain selected param- _ etera of the process such as maximimm pressur.e on, maximum rate of dis- _ persal of the plasma layer and-certain others in time intervals t*.- ra/c* limited by the condition of one-dimensional dispersal (ra is the radius of the irradiated area on the target, c* is the characteristic speed of sound in the plasma layer, c* - 105-106 cm/s). This comparison ahowed satisfactory qualitative'agreement, and with respect to the series of parameters named above, quantitative agreemerit as well between theoietical concepts and observed phenamena. � At the same time, available experimental information that ia much more detailed than that used in theoretical analysis of phenomena in Ref. 1-8 enables us to consider the problem of direct numerical modeling of the aggregate of observed pfienomena based on a gasdynamic computational model [Ref. 9-131 that accounts for one-dimensional and two-dimensional movement of plasma and of the ambient medium under the action of radiation pulses with the intensity distributiona over the beam cross section and in time that are realized in an experiment. Such a computational model and comparison of the data that it yields on the dynamic' char- acteristics of phenomena with the quite complete results of ineasurements given in Ref. 7 are considered in this article. In accordance with the data of'Ref. 7 ].3 - FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY - we study below the gasdynamtc -p.rocesses that take place at the surface of a bis- muth target irradiated by bell-E;haped laser radiation (with duration at half gower level of T~= 0.4-0,5 us) with wavelength a= 1.06 um in the range of maximum radiation flux densities Qmax"'S-200 W/cm2 (so-called "moderate" flux densities) in which the subsonic radiation wave and light detonation wave con- ditions are realized. 1. The computational technique that is used here was described in Ref. 9-13 where it was used to model processes of formation and dynamics of the light detonation . wave and supersonic radiation wave at the surface of an aluminum target in air. The method includes solution of the unsteady axisymmetric problem of heat conduc- tion on heating and vaporization of an obstacle under the action of absorbed laser radiation on a,circular spot of radius ra, and solution of the unsteady axisyimnet- ric gasdynamic problem of movement of vapor and the displaced ambient gas (air). We will briefly describe the procedure as applied to the given problem. It was assumed in accordance with Ref. 7 that radiation traveling toward the sur- face of the target has intensity qo= qo(t) that is constant withi.n'the limits of the cross section of a cylinder with radius of 0.4 and 0.2 cm, and has a time dependence that is tabulated (Fig. 1). The quantity qmax and the total energy density E on the target are related by the expression E= 0.53qmax, and the total PIaT - ener E for a tar et with r =0 4 cm 800 400 gY o g a is defined by the relation Eo = 0.27 x qmax� Here qmaX is expressed in MW/cm2, E--in J/cm2, and Eo--in J. Surface reflectivity R was determined by surface temperature To in accor- dance with data of Ref. 14,�1. e. the vapor and the air heated by the vapo::-generated shock wave partly or totally absorbed both the incident radiation and that reflected fram the surface. The obatacle was heated ar.u vaporized in region r S ra under tlie action af incident radiation with ilux densiCy qa (r,, t) = qo (t) [1- R(To)] X - , t~ us >C eap - fx~ (r, a) dz (here K~ is the co- 0 1 o R'/4max l ~ 0,8 1 1 I 1 I ~ 12, 1 1 345 2 ~ 0,4 MA t 6 3 8 g ~ ' Fig. 1. Time dependence of laser emission efficient of absorption of radiation intensity and pressure in the center of by vapor and air, z is read out along exposure spot on target surface: qmaX the normal to the surface). Heat [MW/cm2] 1--200; 2--140; 3--70; 4--45; transfer was disregarded in the tar- 5--25; 6-16; 7--10; 8--7; 9--5 get in the radial direction, heating into the target (z < 0) was determined by the magnitude of the energy flux qa(r, t) delivered to the surface. The boun- dary parameters for vapor at the surface were assigned in accordance with Ref. 15 with consideration of ambient counterpressure; in accordance with this,�vapor motion started upon heating of the surface above the boiling point, equal to Tb.= 1830 K for 'bismuth [Ref. 161. 14 FbR OFF[CIAL USE ONLV APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY To describe the movement of vapor and air in an eulerian coordinate aystem, the f inite difference method of "coarse particlea" was used [Ref: 17], generalized to the case of accounting for absorption of incident and reflected radiation by the vapor-air plaema. In contrast to Ref. 12, 13, re-radiation of energy by the plasma was disrzgarded due to a lack of data on the group coefficients of absorp- tion of bismuth vapor. Motion of the contact bouridary between vapor and sir was followed by using markers--paesive particles having a'velocity equal to the lo- calized'velocity of motion of the medium. The equatian of state and coefficienta of absorption were tabulated in the form of dependences p= p(p,e) and KVO KV(p,e), where p is presaure, p is density, e is the internal energy-of a unit of mass of the medium, for air in accordance with the tables of Ref. 18, aiid for bismuth vapor in accordance with data.of Re~. 19. The computational grid for'solving the problem,[had] up to 34 cells'along the r-coordinate (over the surface) and up to 60 celle along the z-coordinate (normal to the surface), providing satisfactory spatial resolution of.flow parameters. � Aa the gasdynamic perturbations approached one of the boundaries of the campu- tational region, the dimenaions of the camputational cells in this direction were doubled, and as a result development of flow of the medivan wae traced over a fairly long time interval. In the given case motion was nearly one-dimeneional over a considerable part of the emission pulse (up to t -1 �s), agpreciably improving the.detail'of motion description at the beginning of the process through intro- duction of cells Az�Or. 2. Calculations are 140 and 200 MW/cm2. R,M done for versions with qm~ = 5, 7, 10, 12, 16, 25, 46, 70, . We begin examination of the results with Fig 2, giving the distributions�of parameters in a plasma 'Mm . jet formed by an emiasion pulse with qm~ = 200 MW/cm2 acting on a bismuth tar- get with ra = 0.2 cm. Time t- 1.3 �s corresponds to nearly total cessation of energy release.The given example is of interest in particular in the re- spect that here in the process of energy release there is a change in the condi- tions of propagation of the plasma front contrary to the radiation: the mode of the;aubsonic radiation wave is replaced by that of the light detonation wave when the radiation flux density on the target M � reaches qa - 130 MW/cm3on the leading edge of the pulse (at t=0.5 us). The distri- Fig. 2.. Distribution of tempera- ture T and density p in plasma jet at time t= 1.3 us. T, eV: 1--5.6; 2--3.2; 3--2.5; 4--1.8; 5--1.6; 6-- 1.4; 7--1.3; 8--1; 9--0.4; 10-0.022. p�103, g/cm3: 1--10; 2--3.2; 3--1.6; 4--1.3; 5--0.6; 6--0.5; 7--0; 8--0.3; 9--0.25 bution of density in the jet shows a pro- nounced minimum of -5�10- g/cm3 (sir dens3ty outside of the jet p= 1.29�10'3 g/cm ) in the middle part in a region at a distance of from 2 to 5 mm from the surface. Schlieren photographs for the same kind of conditions given in Ref. 6, 7 for an aluminum target (as calculations 15 FOR OP'FICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2447102/09: CIA-RDP82-44850R444544444425-5 FOR OFFICIAL USE ONLY show, the latter circumstance does not alter matters since the vapor is situated much nearer the surface zhan the indicated region when aluminum and bismuth tar- gets are used) clearly show a more t*ansparent disk-shaped region at distances of -3-5 mm that can be 'identified with the above-+mentioned density minimum. The general shape, as well as the dimensions of the jet in the axial and transverse directions as measured from the schlieren pattern from Ref. 6, 7 and also with respect to Fig. 2 are likewise similar to one another. Even this implies that the given calculation satisfactorily transmits the dynamics of the phenomenon over the entire duration of the emission pulse. Let us examine in more detail the space-time dependences of parameters for twa typical versions of calculations. The distributions of parameters in the z direc- tion at r= 0 for different instants within the duration of the emission pulse are shown in Fig. 3 and 4 for qmaX = 45 and 140 MW/cm2 respectively. Under these p,a7 800 400 0 ae,cM ' II I 80 II l~ I 2 I r~ 40 I 31l A 1 ~4 1~5 6 i ~ 2 3 Fig. 2. Distribistion along the z-axts for pressure p(-) and absorption coefficient Kv at qmax = 45 MW/cm2 ac times t, us: 1--0.5; 2--0.63; 3--0.795; 4--0.9; 5--1.0; 6-- 1.26 . p,a1 l20G 90l 40G 0 2 3 Z,MM Fig. 4. Distribution along the z-axis for pressure p( ) and absorption coefficient Kv at Qmax � 140 MW/cmZ at times t, us: 1--0.4; 2--0.5; 3--0.63; 4--0.795; 5--0.9 ae,cM I - t ~ /20 t I 1~ ( I I I J~~2 3 I ~ 4 f 5 ~ 40 ~ conditions the pattern of motion in the paraxial region of the jet is still close - to one-dimensional although its lateral distribution along the surface of the target may influence the integral characteristics (recoil momentum, etc.). It can be seen that the optical thickness of the vapor is great for both versions at t? 0.6-0.8 us, but formation of light detonation wave is possible unly at suf- ficient magnitude of q: for the second version at t- 0.6 us, when q= 130 MW/cm2. The intensity of the shock wave generated by the vapor in sir is here sufficient - for the shock-compressed layer to begin to completely absorb radiation in the vicinity of the wave front, and to form a light-detonation complex. Both versions of calculation are characterized by considerable vapor temperature - --up to 5-7 Ev. These temperatures, calculated without consideration of.processes 16 FOR OFFIEIAL� USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY of radiative cooling of vapor, are apparently overstated by about 30%, which as noted in Ref. 5 is implied by the estimate of equality of the radiative and out- wardly incident emission f luxes. The air temperature between the contact boundary and the shock wave front is considerably lower: in the first version it is less than 1 eV; in the second version by time -0.6 u$ and later it begins to exceed 1 eV, which is suff icient to change absorption from vapor to air [Ref. 20]. Transition from the subsonic radiation wave to the light detonation wave in.the given case takes place under the action of gasdynamic forcesv the piston action of vapor on air is decisive in the:.process of increasing its temperature to the point of :Cnitiation of absorption T* -1.2-1.5 eV [Ref. 20]. However, estimates of the.rat:e of propagation of a subsonic radiation wave according to Ref. 20 show that under the given conditions the difference between the propagation velocity and the mass velocity of the medtwm in the vicinity of the contact boundary is still small, i. e. actually the motion of the plasma front is'~determined by gas- dynamic processes. Supplementary to this, let us mention the nearly complete coincidence of ineasurements in Ref. 7 and the chlculated maximum velocities of dispersal umaX of the plasma front from the surface both in the region of existence of subsonic radiation wave conditions and in the region of values qmaX > 130 MW/cm2 that ensure transition to the light detonation wave conditions in the process of action: at qmaX = 50, 140, 200 MW/cmZ these velocities were umaX = 4, 8, 11 km/s respectively. The measured and calculated,hodographs of the 3et front also coin- cide. Let us consider the time dependences of pressure in the center of the target for versions of calculations with different values of qmax (see Fig. 1). Here, just as in the experiments of Ref. 1, 7,. two pronounced pressure maxima can be observed: the first corresponding to vaporization of the target, and the second corresponding to arrival of perturbations from the absorption spike on the vapor-air interface at the surface. In the calculations the time of onset.of the second maximiun is somewhat less than in the experiment of Ref. 7, and its value pmaX at Qmax > 100 MW/cm2 is somewl:at greater. It must be borne in mind here that pressure averaged over the surface of the sensor (and target) was recorded in the experiment. If the calculated pressure were averaged over the target, the value.of pmaX would be reduced (due to two-dimensional vapor movement); these differences continue to decrease with increasing averaging surface, although-some discrepancy'remains. This can be attributed to the peculiarities of the registration system in Ref. 7 (some time lag of the pressure sensor, some arbitrariness in cambining the emission pulse and pressure oscillograms and so on), as well as to incomplete reproduction of the emission pulse parameters in the calculation (for example the nonuniformity of distribution of radiation intensity over the spot that was unaccounted for in the calculations was estimated in Ref. 7 by a value of t20%). At the same time, just as in Ref. 7, pmaX falls off somewhat beginning at Qmax"'130 MW/cm2. A quantity of definite interest is the specific recoil momenttnn r1: the ratio of the recoil momentum I acting on the target to the energy Eo delivered to the target (n= I/Eo) � The quantity time t= 20 us from the start of the emission pulse is plotted as a function of qmax on Fig. 5, from which we see that the dis- crepancy between calculation and experiment does not exceed the spread of ineasure- ment resu'lts. The nature of the dependence of n on qmaX is also reproduced--the 17 FOR OFF[CIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAi. USE ONLY ti ~ z w N ~ ~ ~ so � to 80 3 0 2 1 3 10 30 f00 300 qmax' MW/cm2 Fig. 5. Specific recoil mo- mentum as a function of maximum flux density of laser emission: 1--calculation; 2--Ref. 7 rise in n up to qmaX= 10 MW/cm2 due to increase in vapor mass and reduction in losses to thermaZ conduction in the target, the relatively smooth fall-off in the region qmaX < 100 MW/cmZ due to.absorption of'emission in the vapor and re- duction of energy losses on vapor heating, and finally the steeper drop at qmaX > 100 MW/cm2 due to formation of the light detonation wave and more rapid departure of the absorption front from the surface as well as to the considerable influence of two-dimensionality. - Thus, the aggregate of the cited computational data and their comparison wifih the � experiment of Ref. 6, 7 show that the described computational model properly im- parts the behavior of gasdynamic processes at the surface of a target in the one- dimensional and two-dimensional phases of development. REFERENCES .1. Kozlova, N. N., Petrukhin, A. I., et al., FIZIKA GORENIYA I VZRYVA, Vol 11, No 4, 1975, p 650. 2. Kozlova, N. N., Markovich, T. E., ez al., KVANTOVAYA ELEKTRONIKA, Vol 2, No 9, 1975, p 1930.. ' 3. Petrukhin, A. I., Nemchinov, V. A., Rybakov, V. A., PIS'MA V ZHURNAL TEKHIdI- CHESKOY FIZIKI, Vol 3, No 4, 1977, p 158. 4. Nemchinov, V. A., Orlova;l: I., FIZIKA PLAZMY, Vol 4, No 4, 1978, p 949. 5. Nemchinov, V. A., Polozova,.I. A., KVANTOVAYA ELEKTRONIKA, Vol 6, No 6, 1979, � p 1223. � 6. Nemchinov, V. A., Petrukhin, A. I., et al., DOKLADY AKADEMII NAUK SSSR, . Vol�244, No 4, 1979, p 877. 7. Markovich, I. E., Petrukhin, A. I., et al., FIZIKA GORENIYA I VZRYVA, Vol 15, No 4, 1979, p 30. 8. Markovich, I. E., Nemchinov, V. A., et al., FIZIKA GORENIYA I VZRYVA, Vol 15, No 4, 1979, p37. 18 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE OIVLY 9. Romanov, G. S., Stankevich, Yu. A., DOKLADY AKADEMII NAUK BELORUSSKOY SSR, Vol 21, No b, 1977, p 503. ' 106 Romanov, G. S., Stankevich, Yu. A., in: "Dinamika sploshnoy. sredy" [Dynamics of Continuous Medium], No 9, Novosibirsk, 1979. 11. Romanov, G. S., Stankevich, Yu. A., "Tezisy dokladov Tret'yey Vsesoyuznoy konferentsii po dinamike izluchayushchego gaza" [Abstracts of Reports'to the Third All-Union Conference on I}ynamics of a'Radiating Gas], Moscow, 1977. 12. Bonch-Bruyevich, A. M., Zinchenko, V. I. et al., "Tezisq dokladov Chetvertogo Vsesoyuznogo soveshchaniya po nerezonansnomu vzaimodeystviyu opticheskogo izlucheniya s veshchestvom" [Ab stracts of Reports to the Fourth All-Union Conventiun on Nonresonant Interaction of Optical Radiation With Matter], Leningrad, 1978. 13. Yel'yashevich, M. A., Romanov, G. S., Stankevich, Yu. A., "Tezisy dokladov Chetvertogo Vsesoyuznoy konferentsii po dinamike izluchayi�sshchego gaza" [A,b- straces of Reports to the Fourth All-Union Conference on Dynamics of a Ra- diating Gas], Moscow, 1980. , 14. Golub', A. P., Markovich, I. E., et al., Article deposited in the A?~-t?nion Institute of Scientific and Technical Information, No 3300-79, 1979. 15. Anisimov, S. I.., Imas, Ya. A. et al., "Deystviye izlucheniya bol'shoy moshchnosti na metally" [Action of High-Power Radiation on- Metals], Moscow, Nauks, -1970. � 16. Slavinskiy, M. P., "Fiziko-khimicheskiye svoystva elementbv" [Physicochemical Properties of Elements], Moscow, Metallurgizdat, 1952. 17. Belotserkovskiy, 0. M., Davydov, Yu. M., ZHURNAL VYCHISLITEL'NOY MATEMATIKI I MATEMATICHSKOY FIZIKI, Vol 11, No 1, 1971, p 182. 18. Kuznetsov, N. M., "Termodinamicheskiye funktsii i udarnyye adiabaty vozdukha pri vysokikh temperaturakh" [Thermodynamic Functions and Shock Adiabats of Air at High Temperatures], Moscow, Mashinostroyeniye, 1965. 19. Yel'yashevicli, M. A., Borovik, F. N. et al., "Tezisy dokladov Chetvertogo Vsesoyuznoy konferentsii po dinamike izluchayushchego gaza" [Abstracts of Reports to the Fourth All-Union Conference on Dynamics of a Radiating Gas], Moscow, 1980. 20. Rayzer, Yu. P., "Lazernaya iskra i rasprostraneniye razryadov" [Laser Spark and Propagation of Discharges], Moscow, Nauka, 1974. ~ 21. Bergel'ston, V. I., Loseva,- G. V., Nemchinov, V. A., ZHURNAL PRIKLADNOY t MEKHANIKI I TIICHNICHESKOY FI2IKI, No 4, 1974, p 12.. COPYRIGHT: Izdatel'stvo "Nauka", "Fizika goreniya i vzryva",'1981 6610 CSO: 1862/85 19 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/49: CIA-RDP82-00850R040500040025-5 FOR OFFICIAL USE ONLY LASIItS AND MASERS UDC 621.373 - MECHANISM OF PULSED LASING IN HIGH-PRESSURE ELECTRIC DISCHARGE Ar-Xe-LASER Moscow KVANTOVAYA ELEKTRONIKA in Rusaian Vol 8, No 11(113), Nov 81 (manuscript received 13 Feb 81) pp 2425-2432 - [Article by V. N. Lisitsyn and A. R. Sorokin, Theraaophysics Institute of the Siberian Department, USSR Academy of Sciences, Novosibfrsk] [Text] On the basis of studying the characteristic behavior of spontaneous and induced emission during pulsed electric discharge in*a mixture of Ar and Xe, an analysis was made of the population processes of the atomic laser levels of xenon, and the efficiericy of excitatioq transfer from argon to xenon atoms was estimated. A con clusion was drawn regarding the excitation of laser levels by direct electron impact from the ground state. Improvement of the energy char- acteristics of the lRser and variation of the spectral composi- tion of the emission with an increase in xenon pressure and the addition of argon are connected with significant variation of the electron distribution function with respect to energies. It is possible to neglect the excitation transfer from argon to xenon atoms in the electric discharge. The latter is important for creating electron beam preionized'and electric discharge XUV . lasers utilizing Xe2 dimers. This paper is devoted to the study of the processes of exciting xenon levels in the working mixture of a high-pressure Ar-Xe laser. It is known [1] that in low-pressure lasers utilizingIR transitions of inert atoms, the output power of the emiscsion does not exceed a few tens of watts with an efficiency of =10-5. Increasing the heavy inert gas content in mixtures with helium made it possible significantly to increase the radiation power (-105 watts) and efficiencv (-10'3) [2, 3]. The replacement of helium by argpn in an electron beam preionized Ar-Xe-laser led to further increase in O-fficiency (10'2) [4]. The use of discharge through a dielectric having increased stability expanded the operating range of the Ar-Xe-laser to 7 atm [5]. The transition to high pressures was accompanied by vaxiation of the spectral composition of the emission. The level population processes in an Ar-Xe mixture were investigated in an elec- tric discharge with small 0.1%) [6] xenon content and in an electron beam pre- ionized laser with large (0.7%) [4] xenon content. The excitation transfer from 20 FOR OFF[CIAL USE ONLY ' APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02109: CIA-RDP82-00850R000504040025-5 FOR OFFICIAL USE ONLY argon molecules to xenon atoms on excitation by an electron beam and with a xenon content pXeZ0.3pAr was investigated in [7]. In an electric discharge laser Gyith optimal xenon content (-1.5%) such studies were not performed. The discovery of population channels of atomic levels in an Ar-Xe mixture is important not only for the Ar-Re-laser, but on the whole for high-pressure lasers in which, as a rule, inert gases are used, in p articular, to create electron beam preionized [8] and electric discharge [S] lasers utilizing Ar2, Xe2 dimers. The purpose of*this experiment was to deter.nine the basic mechanisms participating in the excitation of laser levels of the electric discharge Ar-Re-laser and estimation of the efficiency of the excitation transfer from argon to xenon atoms b ased on studying the characteristic behavior of spontaneous and induced emissions of a gas discharge plasma under various conditions. Experimental Results and Discussion 1. Experimental Setup. Two discharge cell designs were used in the experiments: for investigation of lasing, a cell with double transverse discharge [2] 60X1.5x 0.6 cm (electrode spacing 1.5 cm); to study spantaneous emission, a cell with exposure through a cathode grid 44.94.5 cm. The exposure discharge was realized between an awd liary electrode coated with glass and the grid. For attenuation of the radiation reabsorption, the observations were made across th e cell so that the thickness of the plasma column focused on the MDR-2 monochromator was 0.5 cm. Y,umNed (1) 0 Axe-xe 100hie S�;rxe 10 m- ~ a~-Yt 004 0,1 0,7 94 ,o,om.Y (2) Figure l. Spontaneous emission power on the 0.47 micron line for the first and second (5A") glow components as a function of the pressures of Ar-Xe and He-Xe mixtures (the subscripts on ,gD); pXe=0.01 atm; the current was kept constant. Key: 1. relative units . . 2. atmosplieres 21 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00850R400540040025-5 FOR OFF[CIAL USE ONLY ~ a Z" 3 0 0,2 0,4 tNMC a~ (A) ~ b 3 p 10 ZO t,Hc . (B) Fi gure 2.' Os ci llograms emission at X=0.47 (a) He-Xe (2) and Ar-Xe (3) Key: A. microseconds B. nanoseconds of.the current (1) and spontaneous and 0.98 microns (b) in mixtures of for p=0.5 atm, PXe�0.01 atm. A cable energy storage element couanuted by a gas-filled discharger through a transmitting cable line to the cell was used to excite the discharge. The ratio of the maximum voltage on the cell to the closest secondary peak was 60, the discharge current duratian was b4 (4) ~ Figure 3. Discharge current Jp(1), carbon dioxide concentration c in the gas mixture in a laser with regenerator (2) and with out regenerator (3), oxygen concentration cp in a laser without regenerator (4) as a fim ction Af operating time (a) and self- maintiained discharge power Pel in the initial C02:N2:He:Xe = = 1:30:16:0.5 as a function of voltage (b, see the text). Key : A. JP, relative units B. Pel, relative imits C. t, minutes . D. U, kv . The mass spectrometric analysis of the gas mixtsre from the).ampules demonstrated a decrease in C02 concentration by approximately 20% of the initial concentra- tion and also the appearance of CO and excess 02. The 02 and CO formed were sometimes not in a stoichiometric ratio. This obviously is explained by the processes on the inside surfaces of the GDC elements and release of vapor and gas from them during heating. For example, the presence of watex vapor in the amount of 0.1% can have a significant influence on the gas mixture composition as a result of the reaction [13] CO-}-OH - CO2-{-N� ' ' - (20) If the GDC elements were degassed as a result of prolon ged operation of the laser, then the products of decomposition of the C02 molecules formed would be in a stoichiometric ratio. ' 36 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504040025-5 FOR OFFiCIAL USE 01%Y Y. 10'', ~r~~j~ (2) . g�NM pA1,fIQ~ ~:3 Key:. 1. 2. 3. Figure 4. Activity of the catalyet K as a function of concentration c.y and presaure py of carbon. monoxide litera/ (sec-kg) moles/liter mm Hg . Continuous monitoring of the. gas composition demonstrated that after 15-20 minutea of ope'ration 15% of the C02 decompoaes, 8% of the excess 02 forms,, and then the ,gas compositian atabilizes (see Figure 3, a). A camparison of the curves in . 4gure�3, a ahawe that a decrease: in conductivity correlates with changes in the g'as mixture composition. Considering the sensitivity of the mass spectrometer, it is poseible to state that the nitrogen oxtde concentration in the given case did not exceed 0.1X. 6. From what has been stated it is clear that for stable operation of a closed- cycle laser it is necessary to regenerate C02 from CO and 02. The regenerat:ion of the gas mixture ia best realized by a catalyst on the surface of the active medium; here the iaaterials of the GDC elements and the regeneration systemg mns.t not disturb the stoichiometric ratio of the decomposition products. A"by-pass" system for connectin g the regenerator to the GDC parallel to the cooler in the discharge chamber, that is, the elements making the basic contrib ution to the total resistance of the GDC, was realized in the laser. This made it possible to insure calculated va].ue of a=0.1 withoilt using additional pumping devices. Measurement of the velocity and'temperature profile of the gas f low after the regenerator using Pitot tubes and thermocouples demonstrated that the mass flow rate of the gas thxough'the regenerator with connected heating element reaches 10% of the total flow rate ta the GDC. � If we set T=60 seconds, which corresponda to the time of decreasing conductivity of self-maintained discharge by 5%, then for Tk=0.4 second and am0:1, the required degree of recovery x-0.067. By formula (15) it is then possible to deterndne the steady-state concentration of the carbon dioxide. If decomposition of the CO2 takes place as a result of reaction (1), then for a value of the ratQ � constant of this reaction K=10'12 cm3/sec under our discharge� canditions a C02 concentration on the level of 987 of the initial value must be egtabliahed. 37 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-00854R000540040025-5 FOR OFFiCiAL USE ONLY 7. Initiall:y a study was made of the possibility of using induetrial catalysts ShPK-2 and ShPK-0.5 to recover the gas ffixture 3:n the C02-laser. These cata- lysts are y aluminum granules on which platinum or palladium has been deposited. In spite of'the f act that these catalysts are characterized by quite high catalytic activity, they have a number of signi.ficant disadvantages: in particular, they absorb carbon dioxide from the gas mixture and have high heat capacity. The latter leads to the necessity for prolonged heating of them when reaching operating conditions. In addition, on loas of seal of the GDC these catalysts absorb water vapor and atmospheric air intensely, which creates an inconvenience in maintainin g the laser. During operation the granulated catalyst in the regenerator becomes packed as a result of vib rations, which leads tu varia- tion of the linear flow rates through a cross section of the catalyst layer and = requires additional filling of the regenerator with catalyst. Therefore a catalyst free of the notecl deficiencies was specially developed and manufactured. It is a metal base on which palladium is applied. The catalyst has quite high activity, it does not form dust an vibration, it-does not absorb carbon dioxide and water vapor, it has law gas dynamic resistance and other advantages. The characteristics of the catalytic activity for the metal-based catalysts are presented in Figure 4. The activity K does not depend on the CO pressure, which indicates the first order of the reaction with respect to carbon monoxide (for 0 order with reaction with respect to carbon monoxide (fcr 0 order with respect to oxygen) in the corresponding pressure range. Mass spectrometric analysis demonstrated that operation of the laser with a regenerator cant3ining a metal catalyst at a temperature of 300�C and pumping of the gas mixture which amounts to 10% of the total flow rate in the circulating loop leads to decomposition of 2% of the carbon dioxide (see Figure 3, a). The catalyst temperature was estimated by the temperature of the gas passing through the regenerator. ' Thus, the measured value of the steady-state C02 concentration in the gas mixture agrees with the calculated value. As the experiments demonstrated (see Figure 3, a), the decomposition of carbon dioxide in the GDC is described by the linear dependence on time only in the initial section. Then even withour the regeneratur, the decomposition rate slows sharply. This indicates the presence of the processes of recovering C02 from CO and 02 which can take place either in the discharge o'r on the surfaces (for examplex the heat exchanger having branched surface, coated with copper oxides). The application of a catalytic regenerator in a C02-laser with circulation of the working mixture made it possible to obtain stable operation-of the laser forseveral hours. Figure 3, b illustrates the stability of the volt-watt character-, istic of independent dis charge when using a catalytic regenerator (curve 7, t=15' minutes).- As is known, the oxygen content in the 3nitial components of the gas -mixture has a negative effect on the characteristics of a C02-laser [12]. In the presence of a regenerator and on addition of CO to the gas mixture, there is no necessity for using high-purity gases. 38 POR &FICkAL USE 6M,Y APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY 8. Thus, the "by-pass" gas mixture regeneration system with catalytic reg e rLc r _ is optimal for use in lasers of the selected type. The regenoator cataly: t inus _ have higln catalytic activity at temperaturea of 100-300�C and large volumetric flow rates of the gas flaw; stability of the catalytic activity; law gas dynamic resistance and heat capacity; absence of gas and vapor absorption. As a result of using a catalytic regenerator in an electron beam preionized closed-cycle C02-laser it was possible to atabilize the gae mixture composition in the laser; the degree of decompoeition of the carbon dioxide was decreased by almost an order in thie case. This permits maintenance of the discharge and generation characteristics of the laser on the required level for a long period of time and awidance of replacement of the gae mixture in the laser. In conclusion, the authora expreas their sincere app reciation to G. G. Dolgow Savel'yev for useful discuasion of the ob tained results and also 0. F.�Saprykina and Ye. G. Isayeva for the manufacture of a new type of catalyat. BIBLIOr,RApHY 1. Lock, E. V. PROC. SPIE, No 2, 1976, p 86. 2. Kosarev, F. K.; Kosareva, N. P.; Lunev, Ye. I. AVTOMASHICHESKAYA SVARKA [Automatic Welding], No 9, 1976, p 72. 3. Basov, N. G.; Belehov, E. M.�; Danilychev, V. A..; Kerimov, 0. M.; Kovsh, I. B.; Sucttkov, A. F. : PIS'MA V ZHETF [Letters to the Journal of Experimental and Theoretical Physics], No 14, 1971, p 421. 4. Hoag, E.; Pease, H.; 5tga1, J. J. ZAR. APPL. OPTICS, No 13, 1974, p 1959. _ 5. Basov, N. G.; Babayev, I. K.; Danidychev, V. A.; Mikhaylov, M. D.; _ Orlov, V.K.; Savel'yev, V. V.; Son, V. G.;'Chebuxkin, I. V. KVANTOVAYA - ELEKTRONIKA [Quantwn Electronics],'No 6, 1979, p 772. 6. Eckbreth, A. C.; Blazuk, P. R. "A.I.A.A. 5th Fluid and Plasma Dynatqics Conferetice," Boston, June (1972); A.I.A.A. Paper, No 72-723. 7. Clotov, Ye. P.; Danilychev, V. A.; Zvoxykin, V. D.; Leonov, Yu. S.; Soroka, A. M.; Cheburkin, N. V. KVANTOVAYA ELERTRONIKA, No 7, 1980, p 630. 8. Nighan, W. L.; Wigand, W. J. PHYS. REV., No A10, 1974, p 922. 9. Sheilds, H.; Smith, A. L. S.; Noris, B. J. PHYS. D., No 9, 1976, p 1587. 10. Napartovich,�A. P.; Starostin, A. N. FIZIKA PLAZMY [Plasma Physics], No 2, 1976, p 843. . 11. Belomestnov, P. I.; Ivanchenkov, A. I.; Soloukhin, R. I.; Yakobi, D. A. ZHURN. PRIKL. MEKH. I MEKHN. FIZ. [Journal of Applied Mechanis and Technical Physics], No 1, 1974, p 4. � 39 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504040025-5 m FOR OFFICIAL USE ONLY 12. Lancashire, R. B. PROC. SPIE, No 86, 1976, p 11. 13. Ochkin, V. I.; Shubin, N. A. RHIMIYA VYSOKIKH ENERGIY [High-Energy Chemistry], No 6, 1972; p 26. . . COPYRIGHT: Izdatel'stvo "Radio i svyazl", "Kvaatovaya elektronika", 1981 4 , 10845 CSO: 1862/75 40 Vbg UFFICIAL USit (OAN APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00854R004500040025-5 FOR OFF'ICIAL USE ONLY UDC 535.417.2 CHARACTERISTIC FEATURES OF FORMING RADIATION PATTERN Ok' LASER EMISSION IN RESONATORS WITH RETROREFLECTING MIRRORS Moscow KVANTOVAYA ELEKTRONiKA in Russian Vo1 8, No'11(113), Nov 81 (manuscript received 12 Feb 81)pp 2397-2407 �[Article by,Z. Ye. $agdasarov, Ya. Z. Virnik, S. P. Vorotilin, V. B. Gerasimov, V. M. Zaika, M. V. Zakharov, V. M. Razanskiy, Yu. A. Ralinin, V. K.'Orlov, . A. R. Piskunov, A. Ya. Sagalovich, A. F. Suchkov, N. D. Ustinov, Physics Institute imeni P. N. Lebedev of the USSR Acsdemy of Sciences, Moscow] [Text] A study is made of the characteristic features of shaping the radiation pattern of laser emission in resonators with retro- . reflecting mirrors. The characteristics of exchange lasing and methods of suppressing it are investigated. The dynamic and static optical inhomogeneities of a medium and optical channel are compensated with five to ten-fold reduction of beam divergence. Intracavity beam steering and the formation of complex radiation patcerns of ginen canfiguration have been . implemented, and. radiation homtng on a mirror target with angular dimensions of 30 urad has been realized. In recent years significant 'attention has been given to the study of a new physi- cal phenomenon wave front reversal (WFR) of optical radiation (see, for - example, [1]). . � The use of WFR is connected,with s.olving such problems as reduction of laser beam divergence, transmission of optical radiation through nonuniform media, opti- cal focusing of radiation on a target in laser fusion devices. Along with WFR by the methods of nonlinear optics [1], it appears useful in practice [4, 5] to create devices that use classical optical elements such aa corner reflectors, triple prisms, rectangular prisms and Dove prisms, lenses and mirrors to solve analogous problems. This arises from the fact that devices based on the enumerated optical elements are less critical with respect to radiation wavelength, width of the radiation spectrum, polarization and power. In 1970 A. F. Suchkov proposed the study of a mosaic of corner reflectors (triple prisms) and a raster of telescopes with unit power to reduce 'laser beam divergence for the first time. Then the first experiments were run by V. M.. Kazanskiy, However, a systematic approach to this type of system'was 41 FOR OFF[CIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FUR OFFICIAL USE ONLY _ started in 1977 after the creation of the first multielement triple%prism mosaic _ mirrors called, by analogy with [2], retroreflecting mirrors (RM).. T1ie first experimental results pertaining to compensation of optical inhomogenei- ties occurring during punping of a neodymium glass rod in a two-pass amplifier were published in [3]. In references [4, 51 which appeared somewhat late.r, the possibility of transmitting an.image through an optically inhomogeneous medium [4] and compensation of optical inhomogeneities in a laser cavity [5] by plastic retroreflecting "gratings" with reflector sizes.of 150 microns [4] and 2.5 mm [5] was demonstrated experimentally. Let us note that in contrast to the,authors of [4, 5] we have not used a grating with comparatively small "spacing," but RM, that is, a set of'many (From 7 to SOO) quite large (from 5 to 35 mm). triple prisms inasmuch as we have stated the goal of obtaining a beam with small divergence. The p recision of the angle at the apex of the prisms was no less _ than 1-2"; for the large prisms it was even higher. . The RM used in this experiment are sets of identical total internally reflecting (TIR) triple prisms assembled into a single module without glueing using a special frame. 1. Characteristic Features of Compensation of Dynamic and Static Optical Inhomogeneities of the Active Medium in a Resonator with RM As is known, the beam divergence of lasers with open resanators, as a rule, is determined by the magnitude of the spatial inhomogeneity of the real part of the dielectric constant of the active medium. If within the limits of. the lasing _ region the real part of the dielectric constant varies with respect to the transverse coordinate by Ide'l, then the angle of divergence of the emission in a flat cavity [6] e_- 2 yF6E' Usually A is much greater than the-diffraction limit. Accordingly, a significant amount of attention has been given to finding static and dynamd.c methods'of com- pensation of optical inhomogeneities. In this section we shall consider the method of partial compensation of quite smooth nonsteady optical inhomogeneities based on using RM. In cases�where W(x) has a regular nature and does not depend on time, static compensation of the optical inhomogeneities is possible. Actually, if, for example, Se'(x) is equivalent to a negati~ve lens (dE'(x)-ax2), the laser beam divergence can be estimated by formula (1) qufte precisely. However, it is known that in this case the lasing wave front has a shape close to spherical [7]. The spheri- calness of the wave front in such a slightly unstable resonator can easily be compensated by a positive lens located.outside the resonator so that after this compensation the beam divergence can become close to diffraction. In the majority of cases, however, aptical inhomogeneities are not subject to monitoring and vary during the lasing pulse time. Static compensation of wave front deforma- tions turns out to have little effect. - 42 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R040500040025-5 FOR OFFICIAL USE ONLY ' The problem of dynamic compensation ariaes in connection with which the WFR phenomenon is of great interest. Let ba considgr a laser in which the exit mirror ie flat and the blind ffirror ie � reversing. A plane wave from the exit mirror, passing through an optically inhomogeneous active medium, ia deformed. On reflectioa from the revereing mirror the wave front retaias the apatial shape of the inddent wave, but the direction of propagation changea to the opposite. On the return path through the active msdium the wave froat deformations will, consequently, be compensated. Thus, the phenomenon of WFR theoietically*permits the,creation of lasers with beam divergence determined by the light diffradtion in the laser aperture and not the optical quality of-the active medium. In a number af cases for dynamic compensatian of wave front deformations and-impxove- ment of the beam divergence, RM can be used. Using RM, it is poasible sharply to improve the radiation pattern if the inhomogeneities of the real part of the dielectric constant are comparstively large with respect to absolute magni- tude and vary quite amoothly in the direction X transverae to the optical axis of the laser. � � Let us note first of a11 that formula (1) includes the variatinn of de' in the , entire lasing region. Therefore if we somehow break down the lasing region into a number of subregions'between which there is no radiation exchange and within the limits of which the optical inhomogeneities vary monotonically, the diver- gence of each such smgll oacillator diminishes. Actually, with a decrease in the tranaverse dimensions of the lasing region Ax for smooth variation of de'(x) the abaolute variation of 18e'(x)l also, diminishes within the limits of each small lasing region; therefore the overall divergence of the laser beam diffinishes. For more specific definition let ua conaider the case where the inhomogeneity de'(x) varies by an exgonential law . 8e'(x),eo exp (-a,z) . (2) with a b road active region Ax..l/a. The situation close to (2) can be rQalized, for example, in a laser with optical pumping when the ptmmping emisaion damps by an exponential law on being propagated into the active mediwn [8]. Estimating the radiation divergence 6l for a leser with laeing region 0;Ax51/a by formula (1), we obtain 0 1 2 R1 , Now break down the lasing region into n small regians dx so that 8x= Ax/n;~_-1/an. 43 FOR OFFICIAL USE ONLY (3) APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2407/42/09: CIA-RDP82-40850R000500440025-5 FOR OFFICIAL USE ONLY The inhomogeneity dF' (x) in a small laser with number m(0Sm5�+) with accuracy to terms of second order of smallness Sem (x) =eo exp [ - (m + 1/Z) 8x] [ 1- ax + (ax)2/2], (4) and the mean divergence 82 C 2V~ so 1 aS x. (5) The linear part of the inhomogeneity Se'm(x) can be compensated if we use a corner reflector which is a set of three mutua.lly peipendicular mirrors instead of the blind mirror in a small laser. After triple reflection the ligh t beam changes direction of propagation to the reverse. A glass pyramid with right angles at the apexes - (a triple prism) can be used as the corner reflector. In order to avoid tmnecessary losses the base of the prism must be made in the form of one of the centrally symmetric figures: a hexagort, square, rectangle. A small laser, the resonator of which is formed by a blind mirror made as a corner reflector will be insensitive to inhomogeneities de' of the wedge type. Dropping the linear term in (4), for the divergence of such a laser 63 from (1) and (4) we obtain - ~3 ~ 2 V ~ Ea I (a t)3/2 = BtaSx/(2 (6) Of course, formula (6) is validif 93>6d, where Ad is the diffraction divergence determined by tlie corner reflector aperture. Considering the diffraction diver- gence, the total divergence of the emission of a large laser in the first approx- imation eo;Z_' e3+a.18'1C . (7) It is easy to see that if appropriate meas ures are not taken, exchange lasing between any two corner reflectors occurs in the proposed resonator. Exchange lasing will proceed through a section of the exit m3.rror, projecting these reflec- tors on eachcther. Exchange lasing will exit at angles of On= f n6z/2L, where L is the resonator length. - S * . ? 3 4 6. 7 Figure l. Diagram of the experimental setug for studying exchange lasing 44 FOR OFFfCtAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY In order to suppress exchange lasing small lasers can be separated by partitions that scatter the emission. For this purpose we have built a sectional active neodymium glass element consisting of 19 thin rods with frosted lateral surface traYtsparent to pumpirig emission. Rods 30 cm long and 1 cm in diameter were used. The resonator was formed by a flat semitransparent mirror R=50% and 19-element RM with 70 cro spacing between the adrrors. The sectioning of the active element made it possible to prevent exchange lasing. However, this type of sectioning of the active medium is provided in far from all types of laser active media. Therefore we have given significant attention to investigating the characteristic features of the suppression of exchange lasing by using angle selection of the emission. 1.1. Exchange Lasing Conditions. The experimental study of the peculiarities of the formation of the pattern in resonators with RM was carried out on a tube-pumped iodine laser. A cylindrical quartz cell 80 cm long and 3.7 cm in diameter had openings fixe3 at the Brewster angle.. Four IFP-20000 tubes with aluninum foil reflector w.ere used to pump the working medium n=C3F7I. The capaci- tance of the capacitor bank was 4 millifarads. Here, the pumping.pulse duration (measured with' respect to a level of 10% of the maxitnum current) was 800 micro- seconds. Depending an the operating mode of the laser, the energy in the lasing pulse varied from 2 to 9Joules. . The exchange lasing conditions were. observed on a device, the optical di,agram of which is shown in Fi gure 1. The resonator was formed by the ItM 1 and a semi- transparent flat mirror 3 with reflection coefficient R 20y. Using an optical wedge 4 part of the emission .was tapped to the caloximeter 5 to measure the energy in the.pulse and to the lens 6 with focal length F=2 meters, in the focal plane of which a screen 7 or photographic film was installed to record the angular distribution of the emissian. Adjustment of the resonator was as simple as possible and consisted in setting the semi-transparent mirror normal to the axds of the laser cell by eye. The pressure of the working medium in the cell 2 was varied from 12 to 80 mm Hg and the resonator length L, from 100 to 250 cm during the experiment. Figure 2 shows the evolution of the angular distribution of the output emtssion during exchange lasing with an increase in the pressure of the working mix for a resona- tor length of 1 meter. (In the experiments to study the characteristics of exchange las3.--.g a seven=element RM made of triple prisms with bese 'in the form of a :1exagon 10 umi high was used f or greater descriptiveness of the ob- tained angular distribution pattem of the emission.) . For small pressures of the working,medium of 12-20 mm Hg, which corresponded to small optical inhomogeneities, the charaateristic pattern of exchange lasing was observed (Figure 2a [not reproduced]) with 19 channels (as follows from the corresponding'theoretical analysis) and with maximum intensity in the main lasing channel directed normally to a semi-transparent mirror. . 45 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY As the pressure of the working medium increased from 20 to 80 mm Hg (Figure 2,b-d [not reproduced]) and with a corresponding increase in inhomogeneities of the medium, the characteristic spot size in different lasing channel5 grows, and the brightness of the spots on the screen decreases. Figure 2, c, d[not repxoduced] sh aus the angular distributions of the emission corresponding to an ordinary flat cavity of the same length (1 meter) as the resonator with RM with reflection coefficients of the mirrors R1=98% and R2=20% and the same pressure of the work- ing medium, at the top for comparison. As a result of significant inhomogeneities of the working medium, for a flat resonator the spot (see Figure 2, d[not reproduced]) has the form of a ring which indi cates absence of axial emission. At the same time in a resonator with RM the naximum radiation intensity falls on the axis, which indicates compensation of the optical inhomogeneities o-ccurring even under exchange lasing conditions. In a resonator with RM under exchange lasing conditions, in addition to a decrease in the beam d�ivergence, a 25-30% increase in pulse energy was observed by compari- son with a flat cavity with the same base. Let us note that no special measures (such as selecting the working mix, use of high-quality optical system, high-precision adjustment and prevention of mis- alignment of'the flat cavity during the aperating process) were taken to achieve small divergence in the laser with flat cavity. The nature of the inhomogeneities of the working medium of the laser was also not specially investigated. There- fore we sh all not compare the obtained results with the results of other authors dealing with beam divergence of an iodine laser with flat cavity. In order to determine the angular scale (see Figure 2[not repxoduced]), it is possible to use the fact that the angular spacing between the central spot and the nearest spot the inclined lasing chennel is 5 mrad. Figure 3[not reproduced] shaws the evolution of the angular distribution of out- put emission during exchange lasing with an increase in resonator length. For comparatively short resonator lengths (1 meter, Figure 3, a[not reproduced]) the main part of the radiation is included in the axial lasing channel; the angular spacing between adjacent channels which, just as above, can serve as the angular scale, is d/2L, where d is the height of the base of the triple prism of the RM, L is the resonator length. As the resonator length increases, the angular spacing between adjacent channels 6k decreases in accordance with the formula 0k=d/2L, and the intensity distribution by channels becomes more uniform (L=2 m, Figure 3, d[not reproduced]). Obviously, the latter fact arises from a decrease in losses to vignetting for tilted lasing channels with an increase in the resonator length. Let us -note with an increase -in the length of a. resonator with RM from 1 to 2 m(in contrast to'a flat cavity), no decrease in pulse energy was observed, which also indicates partial compensation of the optical inhomogeneities in a resonator with RM under exch ange lasing conditions. 46 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102/09: CIA-RDP82-04850R000500040025-5 FOR OFFICIAL USE ONLY . ~ / . . . / \ Figure 4. Suppression of exchange lasing by a telescope For a number of applications, energy concentration in one axial lasing channel is of interest. As applied to a resonator with RM,� this implies the necessity for suppressing exchange lasing. For this puapose we introduced. a Replerian tele- scope into the resonator (see Figure 4). It is known (see, far example 171)3, that putting a Replerian telescope with magnification M=1 ,in the resonator leads to a decrease in equivalent length of the resonator Le to L-IL-21s1~ (i) ~2) Key: 1. e=equivalent; 2. resonator (9) where L is the actual resonator length equal to the distance between the flat mirror Pand the RM; 2LT is twice the telescope length. Selecting the telescope' length such that Le is appreciably less than the cell length with �active mediimm Lk, it�is possible to suppress the lasing of the off-axis channels. Actually, on satisfaction of the condition d/Le>D/Lk, where D is the cell"diameter, the lasing of the tilted channels will be impossibleas a result of incidence of the emission on the side walls of the cell. Ir`igure 5[not reproduced] shaws the behavior of exchange lasing with a decrease in Le from 2 meters (Figure 5, a) to 0.(Figure 5, c, [not reproduced])'. As Le decreases, the nuab er of lasing channels decreases and the spacing between them increases (Figure 5, b[not reproduced]); for a defined value of Le ane axial channel remains (see Figure 5, c[not reproduced]). However,. decreasing the equivalent length of the resonator, eliminating the exchange lasing, simultane- ously increases the beam divergence in the axial channel (see Figure 5,, c). (The angular scale of Figure 5 is easily determined from the ratio d/2Le (where� d=1 cm), which is equa.l to the spacing between the'central and sdjacent spots.) We have also investigated another possibility of suppression of exchange lasing as a result of introducing an angle sele ctor into the resonator. 1.2. Resonator with RM and Angle Selector. In the diagram in Figure 4 an iris with apertures such that the axis of angle selector is normal to the semi-trans- parerit mirror was the focal glane of the telescope. Be low, the RM with base height of the triple prisms of 0.5 cm was used in al�1 the described experiments. , . The angle selector formed a light beam w3th divergence equal to the pass band of the selector 6c=dc/Fc from,spontaneous noise, where dc is the iris aperture diameter; Fc is the focal length*of the telescope lens: The greater part of the emtssion was coupled out through a semt-transparent mirror, R=20y, and the smaller part returned to the active medium. Here it was amplified in two'passes 47 FOR OFFIC[AL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/42/09: CIA-RDP82-40854R040500040025-5 FOR OFF[CIAL USE ONLY with reflection from the RM, which permitted exact "fitting" to the hole in the selector iris even in the presence of significant optical inhomogeneities of the active medium. Selecting the pass band of the angle selector 6c 15 kGa. Time base 8 msec. Arrowshows;noment ofinjection blocking: 1-radiointerferometer signal; 2-etream of ions to reflectors; 3-noise signal frosn probe; 4-electron atream to an electrode beyond the plasma edge. . The virtue of injectionl.eae heating is ita obvious technical simplicity which might even be termed "ideal', since the heating zequires nothing more than that combina- tion of electric and magnetic fields which make;s up the very trap. Another advan- tage,lies in phyeical character and consiets in the fact that with such heating,. the electron bunches that usually give rise to instabilities in the plaema are nat in evidence. Thus, one can expect better confinement in thie inetance, which is qualitatively cbnfirmed by the ATOLL experimetits. It can be seen in Figure 3� that while the density of the plasma in tYte trap is practically unchanging during transition to the injectionless mode, ion losses decrease. It can also be seen that the noise1evel and inteneity of electron transfer acrosa the magnetic field are reduced. . BIBLIOGRAPHY 1. Azovskiy, Yu. S., Karpukhin, V. I., Lavrent-tyev, 0. A: et al., FIZIIKA PLAZMY, Vol 6, 1980, p 256. - 2. Zaleaskiy, Yu. G., Komarov, A. D., Lavrentlyev, O.A. et al., Ibid., Vol 5, 1979, p 954. . ' � - 3. Gormerano,' C., NUCL..FUS., Vol 19, 1979, p 1094. COPYRIGHT: Izdatelletvo""Nauka", Pislma v BHETF, 1981 5454 CSO:' 1862/81 98 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007142/09: CIA-RDP82-40854R040500040025-5 FOR OFF[CIAL USE ONLY STRESS, STRAIN AND DEFORMATION UDC 539.2.219 PRECURSORS OF MECHANICAL DESTRUCTION OF LARGE SPECIMENS Moscow DOKLADY AKADEMII NAUK SSSR in Russian Vol 260, No 3, 1981 (man6script received 2 Apr 81) pp.616-619 [Article by A. A. Semerchan, G. A. Sobolev, B. G. Salov, V. N. Badanov, V. A. Budnikov, A. V. Kol'tsov, V. F. Los', R. M. Nasimov, A. V. Ponomarev, I. R. Stakhovskiy and V. A. Terent'yev,.Inatitute of Phyaics of the Earth imeni 0. Yu. Stmiidt,USSR Academy of Sciences, Moscow] [Text] The construction of high dams, nuclear electric plants and other large structures in recent years, frequently situated in territories subject to earth- quakes, has brought to the fore the question of predicting damage to large-scale objects under the zction of prolonged mechanical stresses. This problem is closely associated with prediction of the destruction of a rock massi: by earth- quakes, rockslides and so on [Ref. 1]. The model of avalanche-unstable crack formation developed in the Soviet Union states that the proceas of preparation for fracture of an inhomogeneous medi!un is qualitatively repeated on different scale levels [Ref. 2]. The patterns ot this process can be studied therefore on models of materials in different stressed states. However, in the case of a small-sized specimen we cannot avoid the in- f luence of the boundaries and the loading device, and no detailed investigation can be made of the spatiotemporal patterns of the different physical fielde that reflect the internal- state of the material under strain.. Transfer of these results to full-scale conditions necessitates a quantitative'study of the acale factor as well. � The unique 50,000 metric ton press at the Institute of High-Pressure Physics, USSR Academy of Sciences, has given us the capability of studying�the d'estruction process on large specimens. Some results in this direction have been obtained on concrete [Ref. 3]. This paper is the f irst to make a detailed investigation of the process of prepa- ration for fracture by simultaneous registration of six mechanical, acoustic and electric parameters. A sigtiificant feature of the experiment was the use of many pickups placed in different :;--,ctions of the specimen;: enabling determination o.f the spatial structure of the investigated fields, and the change in this structure as the instant of fracture approaches. 99 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2047/02/09: CIA-RDP82-00850R000504040025-5 FOR OFFiCIAL USE ONLY The experiments utilized two granite specimens with measurements of 50 x 50 x 70 and 70 x 70 x 70 cm that had been previously studied petrographically and also by irradiation with respect to area by elastic waves, and by mapping the electric potential of the surface. Each specimen underwent several uniaxial loading cycles with an increase in the- - maxi.miun load on each succeeding scle. On t:-.a initial stage of a cycle, the load - was applied at a rate of (2-8)�10 Pa per hour, and then increased more slowly at a rate of 4�106 Pa per hour. The experiment was terminated upon appearance of macrocracks commensurate in length with the dimensions of Che specimen. The strain Eield was studied by strain gages cemented on two faces of the specimen. There were 84-104'sensors on each face, measuring displacements of the surface in the direction of application of the load uy, in the perpendicular direction uX, and at an angle of 45� to these directions. Thus, all components of the two- dimensional strain -~:ensor were studied for elements of area measuring 5 x 5 and = 3 x 3 cm covering the. entire surf ace of the f aces . Measurement accuracy was 6�10-5. In contrast to results found on small specimens, where deformation is an effective characteristic of the entire specimen, it was found in the given case that the surface is divided up into elements with different behavior. Side- by-side with elements undergoing mainly compression are neighboring expanding sections on individual stages of loading. The differences that show up on early loading stages are f irmly retained and amplified as the instant of fracture ap- proaches. Fig. 1(curves 1, 2) shows the change in the quantity auX/aX + auy/ay - that characterizes the reduction or increase in area of two neighboring elements as the load 3i increased. It can be seen that the rates of change in area for the elements are appreciably different. Macrocracks had a tendency to arise at boundaries between zones of compression and expansion. -60 -40 -10 0 20 v, kn/s X.X. ~-'x y 6 Q !0 !Z l4 d~ � /0'Pa Fig. 1. Change in area of adjacent elements of the surface of a.specimen (1, 2) and the velocities of longitudinal elastic waves over neighboring paths (3, 4) as a funr_tion of the me- chanical stress applied to the specimen 100 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007102109: CIA-RDP82-00850R000500040025-5 FOR OFF[CIAL USE ONLY In the course of the experiment, the specimen was periodically exposed to elastic waves on frequency of 70 kHz. The tocation of the transmitting and receiving sensors enabled determination of zones of reduced or elevated velocities of elastic waves in the body of the specimen within 0.4%, as we11 as tracking the evolution of these zones with the approach of fracture. It was found that such zones measuring several centimeters arise and disappear as strain increases. Regions with elevated velocities may form around a zone with reduced velocities and vice versa. This effect is apprently due to a fall-off in stresses within such a"soft" zone, while at the same time the stresses increase in adjacent sec- tions. Fig. 1(curves 3, 4) shows an example of origination of anomaly of veloci- ties on two neighboring paths. Ultrasonic emission from cracks arising in the specimen was registered in an ex- periment with the participation of U. S. specialists H. Spetzler and C. Sonder- held, using the Nicol-2090 apparatus. Simultaneous recoxding of these signals at eight points enabled determination of crack location. Most of the registered signals had a frequency in the range of 50-150 kHz, corresponding to an emitting crack length of the order of 1 cm. Development of such crack systems was confirmed by visual inspection of the specimen after the experiment. Investigation of the apace-time distribution of ultrasonic emission showed that localized actively emitting regions of enhanced crack formation arise that are separated by "silent" zones. Migra��.ion of the active regions through the volume. of the specimen is observed; an increase in activity in one region leads to a simultaneoue reduction of activity in other regions. On the last loading stage, ultrasonic emission from all regions fades, and then increases abrputly just before macrocracks appear. Electric resistance of the specimen was measured with accuracy of SX by a four- electrode method on direct current with switching of polarity. One supply elec- torde was placed on each of the four lateral faces of the specimen, and the 20 reception electrodes were distributed over the surface of two faces. It was found in the'experiment that when an active region of acoustic emission appeared at a distance commensurate with the spacing of tlie reception electrodes (10 cm), it was also registered by the change in resistance. A typical characteristic was anisotropic anomaly of electric reaistance such that upon an increase in one direction, a drop was observed in the perpendicular direction. Fig. 2 shows an dP/p, % 40 -10 - 20 / 2 3 4 Fig. 2. Change of electric re- sistance (1, 2) and electric surface potential (3, 4) of speci- men in the region of development of microcrack formation 0 2 4 6. d 10 12t,hr 101 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY example pf an anomaly calculated from the readings of two mutually perpendicular pairs of electrodes (curves 1, 2). The source of the anomaly in this case was located in the depth of the specimen 15 cm from the reception electroaes, and coincided with the zone of intense crack formation revealed by ultrasonic emission. The anisotropy of anamalies of electric resistance is apparently associated with the presence of preferential orientation of the cracks that arise in the specimen. Use of unpolarized silver Ghloride electrodes enabled observation of variations of the electric surface potential of the specimen with accuracy to 1 mV. The - initial state of the specimen is characterized by a smoothly changing field with deviations of the potential on the surface of about 5 mV. The regions of crack formation distinguished by ultrasonic emission and by electric resistance are also revealed by an increase in density of isolines of potential with maximum values up to 30 mV. The lifetime of electric potential anomalies is determined by the intensity of the strain process (crack formation) and electric relaxation = phenomena, and is of the order of tens of minutes to hours for granite specimens of the given dimensions. Fig. 2(curves 3, 4) shows an example of the change in potential difference AV between the far (zero) electrode and two others installed 15-20 f.m from the same zone of crack formation that was revealed by changes of electric resistance p. The nature of the variations of electric potential is.apparently associated with the ion transport mechanism. . Generation of rf electromagnetic radiation that may arise during crack formation [Ref. 41 was monitored by a frame tuned to 157 or 775 kHz. At sensitivity of the reception equipment of 1.8 mV/m on the low frequency and 0.24 mV/m on the high frequency, no correlation was observed between the recorded electric pulees and acoustic emission of cracks. . These experiments done on lar ge specimens brought us to the following conclusions. Regions of active strain and microstresses with mechanical, electrical and acoustic properties that differ sharply frnm the ambient medium appear in the material long before macrofracture. Comprehensive observation of t'he evolution of these regions by measuring the strain f ield, elastic wave velocities, acoustic emission, electrical resistance and electric potential enables us to keep track of the state - of the specimen, and to determine the place and time of development of macrocracks. REFERENCES 1. Sadovskiy, M. A., VESTNIK AKADEMII NAUK SSSR, No 11, 1971. 2. Myachkin, V. I. et al., IZVESTIYA AKADEMII NAUK SSSR: FIZIKA ZErfLI, No 10, ~ 1974. Semerchan, A. A. et al., DOKLADY AKADEMII NAUK SSSR, Vol 251, No 2, 1980. 4. Deryagin, B. V., Krotova, N. A., Smigla, V. G., "Adgeziya tverdykh tel" [Adhe- sion of Solids], Moscow, 1973. COPYRIGHT: Izdatel'stvo "Nauka", "Doklady Akademii.nauk SSSR", 1981 6610 . = CSO: 1862/92 102 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY THEORETICAL PHYSICS UDC 533.9 ABSOLUTE AND CONVECTIVE INSTABILITY IN PLASMA AND SOLIDS Moscow ABSOLYUTNAYA I RONVEKTIVNAYA NEUSTOYCHIVOST' V PLAZME I TVERDYKH TELAKH in Russian 1981 (signed to press 15 May 81) pp 2-6 . [Annotation, preface and table of contents from book "Absolute and Convective Instability in Plasma and S.olids", by Adol'f Mikhaylovich Fedorchenko and Nikolay Yakovlevich Kotsarenko, Izdatel'stvo "Nauka", 3000 copies, 176 pages] [Text] The problem of instability is closely related to the most important prob- lems of modern physics: the problem of stabilizing processes in fusion devices, as well as the problem of developing up-to-date methods for generating and ampli- fying electromagnetic and acoustic waves. This book is the first monograph in worZd Ziterature on the theory of absolute and convective instability in plasma and solida. Criteria are derived for con- vective and absolute instability, spatial amplification, and are used as a basis for analyzing specific systems encountered in electrodynamics of microwaves, optics, acoustics, gas plasma and plasma of solids. The book is intended fbr a broad class of specialists working in the field of microwave electronics, the theory.of wave processes and plasma phyaics. It will also be useful to graduate'students and upperclassmen of the corresponding specialties. Figures 34, table 1; referencea 67. Pref ace The problem of instability of physical systems described by partial differential equations first came up in the solution of hydrodynamic problems. The theory of hydrodynamic instability has been dealt with in a number of detalied monographs by both Soviet and non-Soviet authors. However, in the fifties in connection with fusion research the problem of instability.was once more on the agenda, but with much broader scope. Research on the theory of plasma instability in turn stimulated research in other areas of physics,and par.ticularly in solid state physics. The same problem was closely associated with the problem of gener- ating, amplifying and converting wave processas over a wide range of frequen.cies and wave modes. The need has arisen for sound crite.ria of absolute and convec- tive instability, as well as spatial amplification. It was also necessary to develop practical methods of analyzing the dispersion equation that is *_he basis of the theory of instah{?ity of phyaical systems with distributed parameters. 103 FOR 'OFFICIAL U3E ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02109: CIA-RDP82-00850R000500040025-5 FOR OFFICIAL USE ONLY At present, such work is basically complete, but all resultG are scattered through separate journal articles with the exception of a short survey by A. I. Akhiyezer, R. V. Polovin published in 1972 in USPERHI FIZICHESKIKH NAUK. In the Soviet liter- ature there is no complete and systematic exposition of questions associated with the theory o� instability of systems with distributed parameters. Therefore the time has arrived for writing a monograph that would fill this breach, if only in part. The authors hope that this book will sarve the purpose. This book presents from a unified standpoint the theory and methods of studying - the nature of instability of physical systems of various types that are described by partial differential equations. These methods are grounded in the theory of wave processes in linear systems since the development of an instability on the initial stage may be described by the concept of snall perturbations of the investi- gated state. It has turned out that it is sufficient to l.rnow only the'dispersion equa.tion that relates the wave vector to the frequency of the given wave process in order to establish the threshold of the instability and its nature. This has made it possible to develop a unified approach to investigation of instabilities in different systems regardless of their nature and frequency band. The first part of the book is devoted to introducing basic concepts and substan- tiating criteria of instability and spatial amplification. This part also points out the simplest methods of analyzing the dispersion equation, and in particular a rigorous pr.esentation is given of the widely used method of weakly associated waves. Understanding of the first part of the book assumes that the reader is acquainted with certain concepts from the theory of functions of a complex varia- ble. The theorems used in the book from the theory of functions of a complex variable are presented without proof at the end of the book in the form of an Appendix. The second part of the book contains a detailed examination and analysis of exam- ples of unstable systems from various fields of physics: lasers and masers, acou- stic amplifiers and oscillators, Gunn diodes, systems of the TWT and backward-wave TWT type, two-beam amplifiers and so on. The bibliography on the given topic is eno?_mous, and Cherefore only those mono- graphs and papers'are listed at the end of the book to which citations are made in the text. Most of the book is an exposition of results that have already been published tn the literature, but that have been presented here from a unified standpoint. A considerable portion of the materfal is based on lectures given by one of the authors at Kiev University starting in 1970. � The 4.uthors thank the reviewer of this book, Doctor of Physical and Mathematical Sciences P. Ye. Zil'berman for constructive camments, and also Professor V. L. Bonch-Bruyevich of Moscow University upon whose initiative the book has been written 'A. M. Fedorchenko N. Ya. Kotsarenko 104 FOR OFFICIAL USE ONLY APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5 Cortents Preface FOR OFFICIAL USE ONLY Chapter 1: CRITERIA OF SPATIAL AMPLIFICATION, CONVECTIVE AND ABSOLUTE INSTABILITY 1. Intraduction 2. Criterion of absolute and convective instability 3. Criterion of spatial amplification 4. Applying Laplace transformation with respect to two variables to the problem of spatial amplification 5. Analysis.of dispersion equations for two and three associated waves 6. Transition of absolute to convective instability. Influence of boundaries on nature of instability 7. Absolute and convective instability and amplification in systems with parametrically interacting waves Chapter 2: ANALYSIS OF DIPSERSION EQUATIONS OF SOME PAYSICAL S'iiSTEMS 8. Cyclotron waves in moving cold plasma ' 9. Acoustic instability in piezoelectric semiconductors. 10. Analysis of dispersion equation of laser 11. Instability in medium with negative differential conduction 12. Recombination instability in semiconductors 13. '16-orkscrew instability in semiconductors 14. Analysis of dispersion equation for two collid3ng beams 15. Interaction of curvilinearelectron fluxes with fast electromagnetic waves . � 16. Parametric instability af electromagnetic waves in electron fluxes 17. R-f instability in electron-hole plasma 18. Three-wave parametric instability Mathematical supplement Referenco-s COPYRIGHT: Izdatel'stvo "Nauka". Glavnaya redaktsiya fiziko-matematicheskoy literatury, 1981 6610 CSO: 1862/93 - END - 105 FOR OFFiCIAL USE ONLY page 4 7 7 13 23 32 38 49 63 71 71 77 83 94 107 118 128 136 146 152 157 165 174 APPROVED FOR RELEASE: 2007/02/09: CIA-RDP82-00850R000500040025-5