JPRS ID: 10379 USSR REPORT PHYSICS AND MATHEMATICS

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JPRS L/ 10379
11 March 1982
_J I
USSR Report
PHYSICS AND MATHEMATICS
CFQUO -2/821
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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
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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
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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
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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
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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.
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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
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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
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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
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_ 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
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= 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)
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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
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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.
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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 initi.al 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
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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
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91
99
107
110
112
113
125
134
139
140
141
145
149
160
166
169
170
172
178
197
202
221
2 38
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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 the.case 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 the.target, 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
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- we study below the gasdynamtc -p.rocesses that take place at the surface of a bis-
muth target irradiated by bell-E;haped monopul.se 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
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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
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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
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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 n.by 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
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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
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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
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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
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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
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~
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. '
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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.
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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 oxi.de 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.
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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. �
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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
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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
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_ 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.
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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 let.us break down the lasing region into n small regians dx so that
8x= Ax/n;~_-1/an.
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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
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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 radiat3.an 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 regul.ai :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. .
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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 corresponding.to 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 tt-.at 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.
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. ~ /
. .
. / \
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 p.laced.in 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
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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
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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.
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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
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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
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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 .
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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.
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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
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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
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