JPRS ID: 9142 USSR REPORT PHYSICS AND MATHEMATICS

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• Content Type: REPORTS

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JPRS L/9142
16 June 1980
- U SS R Re ort
p
- PHYSICS AND MATHEMATICS
CFOUO 5/g0)
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. JPRS L/9'142
16 June i.9 8 0 -
USSR REPORT -
- PHYSICS AND MATHEMATICS
(FOUO 5/80)
CON1'ENTS
ACOUSTICS
Diffraction of Sound Pulses By Elastic Bodies 1
CRYSTALS AND SEMICONDUCTORS
Crystallization Physics 6
FLUID DYNAMICS
Gas and Wave Dynamics 9 -
LASERS AND MASERS
Concerning Self-Oscill.atory Instability in Fast-Flow
Lasers With Unstable Resonators 12
Experimental Study of the Way That Rhodamine-6G Laser
Emission Acts on Aluminum 21
Particulars of Stimulating Emission in Vapors of Complex
Organic Compounds 29
A Multibeam Waveguide C02 Laser With AC Discharge
Excitation 39
Intensity Fluctuations oF Thermally Self-Stressed I.aser
Radiation in a Turbulent Medium 46
A Study of the Characteristics of Photoionization
Excimer Lasers 57
The Change in the Energy Characteristics of an Electro- _
ionization Discharge in Mixtures of C02-NZ-He and
Commercial Grade Ni~rogen Duxing Pulse Periodic Operation 65
Dynamics of Free Lasing of Solid-State Lasers 72
NUCLEAR PHYSICS
Collective Ion Acceleration by Electron Rings 78
- a- [III - USSR - 21H S&T FOUO]
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1
OPTICS AND SPECTROSCOPY
Interferometric Criteria for Radiation Focusing 81
SUPERCONDUCTIVITY
Semiconductors, Superconductors and Paraelectrics in ~I-
Cryoelectronics 89
i
1
-b-
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ACOUSTIC~
UDC 534.2
~ DIFFRACTION OF SOUND PULSES BY ELASTIC BODIE5 =
Moscow DIFRAKTSIYA AKUSTICHESKIKH IMPUL'SOV NA UPRUGIKH TELAKH in Russian
1979 signed to press 10 July 79 pp 2, 3-4, 238-239
[Annotation, foreword, and table of contents fror~ a book by Yaan Aleksandro-
vich Metsaveer, Naum Davidovich Veksler, and tinatoliy Svyatovslavovich
Stulov, Nauka, 1400 copies, 239 pages]
[Text] This monograph describes methods for calculating acoustic echo sig--
nals fr~m deformable bodies and the use of these signals for determining the
geometrical and physical parameters of the scattering bodies. The echo sig-
nals investigated come from thin shells and solid bodies of spherical, -
cylindrical, and arbitrary shape. Stress waves in thin elastic shells are -
investigated in the framework of the ~quations of motion corresponding to
Timoshenko's linear shell theory, while stress waves in solids are studied
by assuming the equations of linear elasticity theory. t'he medium surround-
ing the body is assumed to be infinite, and it3 motion is described by the
_ equations of an ideal compressible fluid. Acoustic echo signals are calcu-
lated primarily in the form of individual Acho pulses, but algorithms pri-
marily in the form of individual echo pulses., but algorithms are proposed
both for calculating the principal parts of the quasi-steady state approxi-
mations of. echo signals and for finding their wavefront regions. Numerical
results are given. Algorithms for determining the parameters of thin shells
from acoustic echo signals are described.
~ This monograph is intended for the use of a broad range of scientists, stu-
dents, and graduate students specializing in the fields of hydroacoustics =
and the mechanics of deformable solids. Figures 44; references 280: 146
Russian, 134 Western.
FOREWORD
The theory of the 3iffraction of acoustic waves by elastic bodies !s con-
- sidered in this book. The authors do not go beyond the linear formulation
of the problem. The basic working method involves integral transforms,
and the basic goal is the investigation of unsteady wave fields in a fluid.
- Systematic study is ~iven to reflected and emitted, peripheral and creeping
1
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- pulses, and also to pulses passing thr~ugh a liquid filler that are produced
by an acoustic pressure pulse incident ~n an elastic body. The results of -
an an~lysis of these pulses are used to develop algorithms for determining
- the parameters of an elastic body from an acoustic echo signal.
- Two-dimensional diffraction problems are considered in the monograph. Prob- _
- lem formulation is discussed in the first chapter. The second chapter con- �
_ siders the problems of diffraction by bodies of spherical shape: a thin
- elastic shell with a fluid filler and a hollow shell of revolution whose ~
meridian is clase to a circle. The third chapter discusses the problems of
diffraction by bodies having ttie shape of a cireular cylinder: a thin elas-
tic she11 with a fluid filler, a hollow cylindrical shell, and a solid elas-
tic cylinder. Dlffraction by bodies of arbitrary shape ia c~nsidered in the
- fourth chapter. The theory of peripheral waves on a noncircular cylinder is �
- generalized, a way of solving the problem of diffraction by the Bubnov-Galer-
kin ~ethod is proposed, the reflection ~~a~;~,s und waves from a solid elastir_
body is in~~estigated, and a method of salvi~g the nonstationary probl:m of
~iiffraction by elastic bodies with the use of integral boundary equations is
described. An algorithm for determining the parameters of a shell from a
recorded acoustic echo signal is proposed in the fifth chapter.
The book discusses th~ results obtainediby the authors in their research o�
hydroacoustics carrted out at the Institute of Cybernetics of the Academ;r
of Sciences of the Estonian SSR. ~
N. D, Veksler wrote sections 1-3, 5-7, 9, 11, and 15; Ya. A. Metsaveer wrote
sections 4, 8, 10, 13, 14, 17, 18, along with Sec. 5.2 and the problems re~-
ferring to pulses passing through.a filler in Sec. 5; A. S. Stulov wrote
Spca. 12 and 16; Yu. P. Pikk helped to obtain the reaults given in Secs. 4
and 8; M. E. Kutser discussed the problems referring to pulses passing through
a f iller in Se~. 9; V. M. Korsunskiy..helped to obtain the results in Sec. 6.5.
The authors are grateful to Profs. N. A. Alumyae, U. K. Nigul, and L. Ya.
Aynola for useful discussions that improved the manuscript.
TABLE OF CONTENTS
Foreword 3
Chapter 1. Formulation of Contact Problem 5
_ 1. Basic equations� 5
1.1. Two-dimensional equations of an ideal compressible fluid
(5). 1.2. Two-dimensional equations af linear elasticity
theory (7}. 1.3. Linear equations of Timoshenko shell theory (8).
2
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2. rormulation of the Problem 11
Chapter 2. Echo Signals from Spherical Bodies 14
3. Analytic methods for investigating diffraction of waves by
spherical bodies 14
- 4. Calculation of the echo signal from a spherical shell with
liquid Filler 17
4.1. Formal solution of diffraction problem (17). 4.2. Taking
the inverse Watson transform (21). 4.3. Taking the inverse
Fourier transform (25). 4.4. Numerical results of an echo
signal calculation (28).
5. Derivation of wavefront asymptotic behavior of an echo signal
from a spherical shell with liquid filler 35
_ 5.1. Formulation of the problem and its solution in the space
of a double integral transform (35). 5.2. Asysnptotic expan-
sione of cylindrical functions (39). 5.3. Asymptotic behavior
of the solution in the space of a double integral transform (44).
5.4. Finding the L-transform of the solution of the diffraction
problem (49). 5.5. Taking the inverse Laplace transform (53).
6. The procedure for calculating the echo signal from a hollow shell
of revolution with a meridian close to a circle 55
6.1. Equations of motion for a shell in a polar coordinate
system (56). 6.2. Formulation of the diffraction problem and
its solution by the perturbation method (61). 6.3. Formal
solution of the diffraction problem (65). 6.4. Taking the -
inverse Laplace transform (70). 6.5. Calculation of the echo
- signal from a nondeformable fixed body of revolution with a
meridian close to a circle (74). -
Chapter 3. Echo Signals from Cylindrical Bodies 93
7. Analytic methods and numerical results from an analysis of the
diffracti4n of waves by cylindrical bodies g3
8. Calculation of echo signal from a cylindrical shell with a
liquid filler 104
8.1. Formal solution of the diffraction problem (104). 8.2.
Performing inversion of integral transforms (108). 8.3. Nu-
merical results from an ec~o signal calculation (111).
9. Derivation of the wavefront asymptotic behavior of an echo signal
from a cylindrical she11 with a liquid filler 127
3 -
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9.1. Formulation of the problem and its solution in the space r
of a double integral transform (127). 9~2. Asymptotic behav-
ior of the solution in the space of an LF transform (129). 9.3.
Taking the inverse Fourier transform (132). 9.4. Finding the
inverse Laplace transform (137). 9.5. Physical consequences
of the solution of the problem (137).
10. Calculatfon of the echo signal from a cylindrical ~hell gen-
erated from a spherical probing pulse 139
10.1. Formal solution of the diffraction problem (139).
10.2. Performing inversion of integral transforms (144).
11. Finding the wavefront asymptotic behavior of the echo
signal from a solid elastic cylinder 149
11.1. Formal solution in the space of the LF transforma-
tion (149). 11.2. Taking the inverse Fourier transforr~
- (151). 11.3. Takir.g the inverse Laplace transform (157).
11.4. Physical consequences of the solution of the prob-
_ lem (158).
Chapter 4. Echo Signals from Bodies of Arbitrary Shape 160
12. Analytic and numerical methods for solving the problem of
the diffraction of waves by bodies of arbitrary shape 160 ~
13. Echo signal calculation by the Bubnov-Galerkin method 167
_ 13.1. Echo signal from a c3~lindrical shell (167). 13.2.
Echc+ signal from an elastic cyllnder (174).
14. Exr.ensi~n of peripheral wave theory to the case of a non-
. circular cylindrical shell. � 1~7
,
; 14.1. Calculation of the echo signal from a hollow cylindri- .
cal shel.l (178). 14.2. Calculation of an echo signal from -
a shell with a fluid filler (185).
15. Reflection of a plane sound pulse from an elastic body 187
- 15.1. Reflection of a plane sound pulse by a nondeformable
- fixed reflector (187). 15.2. Reflection and refraction of
a plane sound pulse by the interface between an ideal com-
pressible fluid.and an elastic half-space (190. I5.3. Ap-
plication of the "isolated element principle" (192)
16. Solution of the nonstationary diffraction problem by the `
integral equatio;~ m.ethod 192 ~
16.1. Integrai Kirchhoff equation (192). 16.2. Application
of integral ~~uations to the solution of the pulse diffraction
4
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- problem (194). 16.3. Numerical solution of integral equa-
- tions (199). 16.4. Results of calculation of an acoustic
pressure field (20?,).
Chapter 5. Determining Shell Parameters from Echo Signals 211
17. Sl~ell parameters and echo signals 211
.17.1. Introduction (211). 17.2. Parameters of ~ shell
and a filler (212). 17.3. Echo signal parameters (212).
,7 _
18. Determining the parameters of spherical and cylindrical shel~s 218
18.1. Determination of shell class (219). 18.2. Determina-
tion of shell radius (220). 18.3. Identif ication of sepa-
rate echo pulses (221). 18.4. Determination of the parame-
ters Sl and Sp (222). 18.5. Determination of the parame- _
ters Y, Yp (224). ^
COPYRIGHT: Izdatel'stvo "Nauka," 1979
(13F+-9370]
937U
CSU: 1862 _
~
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CRYSTALS AND SEMICONDUCTORS
.
CRYSTALLIZATION PHYSICS
Kalinin FIZIKA KRISTALLIZATSII: MEZHV[JZOVSKIY TEMATICHESKIY SBORNIK (Crys-
tallization Physics: Thematic Anthology for Higher Schools) ir~ Russian 1979 _
signed to press 20 Apr 79 pp 2, 143-144
[Annotation and table of contents from book edited by T. V. Mikushin, 300
copies, 144 pages]
[Text] The thematic collection for higher achools, "Fizika kristallizatsii"
chisfly deals with sub~ects relating to the research into the mechanism of
crystal gro`arh, the kinetics of growth and dissolution, the eff ect of grow-
= ing conditions on morphology, and crystal defects and impurities. Cl.early,
the ti�iews of crystal growth expressed by the authors of the papers published
_ in this collection may not coincide. _
The Editorial B~ard strives to enlist participation in this collection by ex-
perts in the f ield of industrial crystallogeny. Papers on crystal properties
are not accepted for this collection unless they deal with a direct relation-
' ship between properties and growth. In this respect Spedding`s co~nent is -
pertinent: "If some property has to be measured, 8~D percent of the effort
, and ingenuity is usually expended on either obtaining the metal or alloy in
a highly pure form and on growing a single crystal of corresponding purity -
_ or 'characterizing' the obtained crystal in order to know exactly what is
_ represented by the material which is to be used for the measurements. And
only 20 percent of all effort is usually expended on tihe measurement of the
investigated property itself."
The Editorial Board regards as highly desirable participation in this collec-
tion by the leading experts in the genesis of natural crystals, thus empha-
sizing the universality of the laws governing the commercial synthesis of
crystals and the growth of crystals in nature. .
The next issue in this series will be devoted to morphological aspects re-
lating to the formatiAn and gr~wth of crystals.
Editorial Board: Can3idate of Engineering 5ciences Yu. M. Smirnov (Coordi-
nating Editor), Doctor of Physical-Mathematical Sciences Professor L. M.
_ Shcherbakov, Doctor of Physical-Mathematical Sciences D. D. Mishin, Doctor
6
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of EnginPering Sciences V. N. Romanenko, Candidate of Geological-Mineralogi-
cal Sciences B. N. Litvin, Junior Scientific. Co-Worker V'. A. Shmidt (Techni-
cal Secretary).
Contents Page
Salli, I. V., Dzenzerskiy, V. A., Sakhno, G. A. The Mechanism
of Crystal Growth 3
Salli, I. V., Tremba; T. S., Sakhno, G. A. On the Kinetics of
the Dissolution and Growth of Crystals 9
Smirnov, Yu. M. Instantaneous Growth Rates of Single Crystale 12
Lyubalin, M. D. Certain Features of the Fo-rmation of Twinned
Crystals With Diamond Type Structure lg
Buzynin, A. N., Bletskan, N. I. Morphology and Special Features
of the Growth Mechanism of Induced-Shape Cxystal~ 25
Krylov, A. S,, Romanenko, V. N. Synthesis of Bismuth-Base
"~ompensated" Alloys 34
Dashevskiy, M. Ya., Savei'yeva, L. I., Isaakyan, V. A., Kibizov,
R. V., Ivanchenko, V, I. Comparative Investigation of Inter-
dendritic Strips and Single Crystals of Silicon 42
Skornyakova, K. P., Pis'mennyy, V. A. Morphology of Crystals of
Yttrium-Aluminum Garnet and Its Relationship to Growth Conditions 50 _
Makeyev, Kh. I., Pogodin, A. I., Eydenzon, A. M. Determination of
Axial Components of Temperature Gradients at the {III} Faces
on the Crystallization Front of Dislocation-Free Single Crystals
of Silicon 5~
Glikin, A. E., Nikolayeva, V. P., Petrov, T. G. Crystallization
of Potassium Biphthallate From Neutral and Alkaline Aqueous
Solutions 63
Litvin, B. N., Bebikh, D. G. Cr~stallization of Neodymium
Fentaphosphate 72
Franke, V. D., Bubnova, R. S. Growth Kinetics and Structural
Features of MKP Crystals Grown From Solutions of Various
Composition
7
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Contents Page -
. Franke, V. D., Treyvus, E. B., Ivanova, T. Ya. A Study of the
Crystallization of the Nitrate Series in Aqueous Solutions
With Nitric Acid ~ gg
Belyustin, A. V., Levina, I. M., Perepelova, I. I. Relation-
ship Between the Rates and Mechanism of the Dissolution
and Growth of the Faces of Epsomite Crystals 99 _
Stepanova, N. S., Belyustin, A. V. Effect of Impurities on the
Crystallization of Granules of Potassium Acid (MKP) 107
Pushkar', Yu. E., Shul'pina, I. L., Dedegkayev, T. T. Structural
Defects in a High-Antimony Germanium Alloy 113
Kuznetsov, V. N., Kolesnikov, A. I. Investigation of Defects in
Large-Diameter Single Crystals of Germanium by the Ultrasonic
Flaw Detection Method 119
Akhsakhalyan, S. D., Portnov, V. N. Model of Impurity Capture
During the Movement of an Isolated Fracture 124 ;
Romanenko, V. N., Vasilevskiy, S. A., Kuznetsov, V. N. Analysis ~
of Growth Modes of Doped Semiconductor Crystals With Uniform
Distribution of Electrophysical Properties Over Crystal Length 128 -
Summaries � 138
COPYRIGHT: Kalininskiy gosudarstvennyy universitet, 1979
[134-1386]
~
1386 -
CSO: 1862
~
- 8
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FLUID DYNAMICS
GAS AND WAVE DYNAMICS -
Moscow GAZOVAYA I VOLNOVAYA DINAMTKA, VYPUSK 2[No 2] in Russian 1979
_ signed to press 9 Jan 79 pp 2, 199-200 -
[Anr~otation and table of cont~nts from book edited by Khalil Akhmedovich `
Rakhmatulin, Izdatel'stvo Moskovskogo Universiteta, 200 pages]
[Text] This collection contains articles reflecting both traditional and
new trends under develapment in the department of gas and wave dynamics
of the mechanics-mathematics faculty. A ma~or part of the studies pre-
sented is devoted to problems of gas dynamics and the dynamics of a de-
: rormable solid.
This collection is intended for specialists in the field of the mechanics
~ of a continuous medium and for graduate students and students.
CONTENTS pag~
Rakhmatulin, Kh.A. and Khamiduv, A.A. "Solution of Ztao-Dimensional '
Problems of the Jet Flow af an Ideal Gas" 3
Sagomonyan, A.Ya. "Approximations in Formulation of the Problem of
Piercing a Barrier" 1~
Bunimovich, A.I. and Sazonova, N.I. "Analytical Method of Determin-
ing Aerodynamic Forces and Moments in Nonstationary Movement of
Bodies in a Gas with Differing Negative Pressure" 32 ~
Zverev, I.N., Zverev, N.I. and Smirnov, N.N. "Evolution of ~ao-
Phase (Gas-Film Fuel) Detonation" 44
Pavlenko, A.L. and Zvyagin, A.V. "Mation of Thin Bodies in a
Linearly Elastic Medium" 5~
Grigoryan, S.S. and Kuksenko, B.y, "Possibility of the Existence
of Fronts for the Appearance ~nd Disappearance of Wrinkles on a
Diaphragm with the Normal Impact on Tt of a Cone" (g
9
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Maksimov. V.F. and Osnach, L.A. "Interaction of a Longitudinal
Wave with a Discontinuifiy in a Filament" 72
Sabodash, P.F., Mardonov~ B. and Kadyrbayev, Sh.T. "Thermo-
elastic Spherical Waves Caused by the Tnstantaneous Release of
Heat in a Closed Spherical Space''' 77
Vorotyntsev, M.A., Grafov, B.M. and Martem'yanov, S.A. "Change in
Concentration Near a Spherical Electrode Performing Slight Vibra- -
tions in a Solution of Electrolyte" 85
Guvernyuk, S.V. "Problem of the Motion of a Shock Wave in a Con-
vergent Channe]." 91
Rakhmatulin, Kh.A. and Kuliyev, Yu.N. "Propagation of Qua.si-
Rayleigh Waves in Piezoelectric Media" 100
Rakhmatulin, Kh.A., A1laverdiyev, A.M. and Kuliye~, Yu.N.
"Theory of Coupled Vibrations of Piezocer.amic Disks" 108
Rakhmatulin, Kh.A. and Varpiyev, A.O. "Propagation of ~wo-
Dimensional Stationary Unloading Waves " 118
Sagomonyan, A.Ya. "Fundamental Solution of Wave Equations for
Cylindrical Shells" 127 ~
Sagomonyan, A.Ya. "Shock Effect on a Spherical Shell" 134 i
Bunimovich, A.I. and Sadykova, L.G. "Nonstationary Motion of
One Class of Three-Dimensional Bodies with High Speeds" 140
Bunimovich, A.I. and Khots, O.A. "Analytical Method of Determining
Aerodynamic Forces Acting on a Solid of Revolution When Streamlined
Under Conditions of the Localization Law" 146
Ramodanova, T.V. and Zverev, I.N. "Two-Phase Detonation in Tubes" 155
Zverev, I.N. and Gayevskaya, I.S. "Detonation in a Porous Plate
Impregnated with Liquid Oxygen" 159
~
Kuksenko, B.V. and Abdulgalimov, A.M. "Approximation Method of
Solving the Problem of Forced Vibrations of a Thin-Walled Hemi-
spherical Shell Made of a Piezoceramic on a Rigid Base" 166 -
Mardonov, B., Mansurov, F.K. and Yaminova, R.Sh. "Motion of a
Rigid Smooth Ba:~d in a Linearly Elastic Medium" 171
~
Vorotyntsev, M.A. and Kornyshev, A.A. "Electrical Properties of
a Nonconducting Metal - Solid Electrolyte Contact" 176
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Rakhmatulin, Kh.A. and Lubashevskiy, ~.y. "Radia]. Cylindxical
Source" 182
Zverev, I.N. and Ramodanova, T.V. "Chemically Reacting Non~
Self-Similar Boundary Laqer Behind a Shock Wave" 185
Mardonov, B., Osmonkulov, D.S. and Barayev, A.K. "Determination
of the Zone of Separation of a Beam of InfiniCe Length from a Base
with the Effect on the Beam of Concentrated Forces" 191
COPYRIGHT: Izdatel'stvo Moskovskogo Universiteta, 1979
[132-8831]
8831
CSO: 1862
.
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.fi
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LASERS AND MASERS
_
UDC 621.373.826.038.823
CONCERNING SELF-OSCILLATORY INSTABILITY IN FAST-FLOW LASERS WITH UNSTABLE
RESONATORS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 7, No 2(92), Feb 80
pp 237-243 manuscript received 3 Apr 79
[Article by V. V. Likhanskiy and A. P. Napartovich, Institute of Atomic
Energy imeni I. V. Kurchatov, MoscowJ
[TextJ 1. At the present time, unstable resonators are extensively used
in fast-flow lasers. In a theoretical paper [Ref. 1] it has been shown
by the example of the simplest modeT of an active medium that a self-
oscillatory mode of operation may arise in such systems. Experin~ents ;
[Ref. 2, 3] have shown modulation of the output emission of a C02 laser ;
with characteristic frequencies corresponding to the time of flight of
the active medium through the resonator region. In Ref. 4, by a method
analogous to Ref. 1, a condition was derived for the distribution of
i.ntensity through the resonator of a laser with steady-state pumping
in the volume that gives rise to instability. It was shown that pumping
of ttie active medium in the reaonator region may lead to atabilization of
the steady state. '
It was numerically shown in Ref. 5 that exchange of excitations between
molecules of Nz and C02 stabilizes the steady state, while accounting
for the finiteness of time of emission output from the laser cavity for
ordinary conditions essentially changes nothing. In Ref. 6 in the model
of the active medium of a C02 laser with approximate consideration of
exchange N2 ~ C02, the boundary of development of self-oscillatory insta-
bility was numerically found. In particular it was found that when
kin~kth~2~ instability arisea when TtfXC~~TNCXN~ Here kin is the gain
at the input to the resonator zone; kth is the threshold gain; Ttf is the
time of flight of the medium from the inlet to the axis of the resonator;
TN~ = KpNxN; Kp is the rate constant of exchange of �vibrational excitation.
between NZ and the upper laser level of C02; N is the total gae density;
x~, xN are the molar percentages of C02 and N2 in tha laser mixture.
The influence that the enumerated factors (exchange between N2, C02 and
pumping in the resonator zone) have on lasing stability in a fast-flow
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~ laser has been studied numerically heretofore. Analytical criteria are
derived below for laser working stability as a function of the parameters
of the working medium and the pumping parameters.
_ 'L. Our c~xam-Lnati.on will be carried out within the framework of th~ modc:l
of tlie worki.ng medium of a COZ laser presented in Ref . 6. 1,eC uK bri.ef l.y
outline the derivation of this model.
In the approximation of a small degree of vibrational excitation [Ref. 7)
and assiuning rapid relaxation from the lower lasing level of C02, the
kinetic equations will take the form
art~ dn~ x~ vln~ n~
dt - v az = - Ro1Vxn ~nC - xN nN ) - h~ - zP Qc ; ~ ~ )
dnN an;~ ( XK 1 2
ar - v . az = - KoNxc ;n?v - z~ nc ~ -i- QN ~ . ( )
where n~ is the population on level (001) of C02; nN is the concentration
of vibrationally excited nitrogen; v is the velocity of the gas flow; c~ is
the cross section of stimulated emission; ~w is the transition energy; I
is the intensity of laser emission; T is the time of relaxation of
level (001) of C02 as calculated for mixtures according to known rules
(the relaxation of nit,rogen is disregarded); Q~, QN are the rates of ex-
citation of C02 and N2 by an external source (discharge). When x~�xN
equations (1), (2) are simplified since the degree of excitation of COZ
qUasi-steadily follows the change of concentration nN. The transition
region is small compared with the dimension of the resonator along the
flow, if Ttf~~l/(KpNxN),(QI/ w)"'1. This requirement actually coincides
with the condition of high efficiency of energy extraction in the reso-
nator when x~+v. (6)
This equation must be supplemented by two conditions
k (0)=d, k (1)=ko,
where k 2Lkin/ (M - 1) , defining k(~, T) and u(T) .
Without writing out the steady-state solution of problem (6), (7), let us
go on to the linear analysis of its stability. We represent the func-
tions k and u in the form
u=u~T -i-u exp ('y'r)~ k=kcs ~~)-F~k eXP ~'Y'~)~ ~8~
[The subscript cT indicates "steady-state"]. Here k satisfies the
equation
ai~a~=tuaT +~n-1+~') F~-I-k~t u (9)
and the conditions
k(0)=k(1)=0. (10)
Solving (9), (10), we find the equation for eigenvalues Y
� ~
~ 1-e-y= ~~qe-~~~:tn 1)E(e-v~_e-Y)d~, (11) _
; When q= 0, obviously Ym = 2irmi. Thus in this model there is no self-~ -
oscillatory instability.
When q�2~rm, we can approximately find ReYm:
~ 14
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Re ym ~ 9~~~ (1- ~os 2rtim,~,) d~,. (12)
~ ~ k _
' In a resanator w.~.th rotating field, pumping leads to attenuation of per-
turbations. The onset of instability in an ordinary unstable resonar_o:
is due to inhomogeneous distribution of intensity over the cross section.
Exchange of excitations be*_ween N2 and C02 also leads to damping of per-
turbations in a resonator with rotating field. In the model with ex--
change saturation (4) it is convenient to convert to the following dimen- '
sionless variables : ks =(x~/xN) 2LQnN/ (M - 1) , uS = a/TN~/t~w, T= tv/Z ,
x~Z, aS = xCZ/(xNvTN~), in which equation (4) takes the form
' ak,/ch-8k,/a~=-a,uek,/(1-~-u,). (13)
The conditions at the reaonator input and on its axis are written as
follows:
k~ (1)=ko; k, (0)=d(1-Fu,). (14)
Using tlie linear theory of stdbility of the steady-state solution of
(13), (14) we find the dispersion equation for Y(see (8)):
exp ~ 1')=1-~'Y~1~'ue~z)~as~ ~15)
which can be approximately solved in two extreme cases: -
2nmi a,-1 (2nm(a~-1)1'~1-f-u,)Z, ~1'�ti~�ae~ (16)
_ C as ) 2as -
~m - ~
2JLL ~m�- 4 1- IIl ( 21C ~ aa ~e) ~1 (js~1 ~ ~ ~m I aa� ~17~
1 L .1
4. Let us go on to answer the question of the influence that pumping has =
on self-oscillatory instability jRef. 1]. To describe the field struc-
ture in an unstable resonator we take a quasi-one-dimensional geometric
model that was proposed in Ref. l, valid for M- 1� 1, Neq �1 (where Ne~
is tt~e equivalent Fresnel number). The equation for the overall inten-
sity in tfiis model takes the form
1 8 (xd!) 2Lanc I. (18)
z~=1 ax - M -1
(For spherir_al mirrors (d = 2) equation (18) is written for a straight
line along the flow passing through the axis of the resonator). In
dimensionless variables we get '
~duld~= (k-c~u. (19)
Attempts to get a steady-state solution in explicit form have so far been
_ ur.successful, and in the linear theory of stability (see (8)) now u(~)
satisf ies the equation
~dc~ld~=(k,;T-c~u-i-u~T k� . ~20)
System of equations (9), (20), with conditions (10) can be reduced to
a boundary value problem for an equation of second order for the quantity
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~v = exp - 2 J~ ry ~ -r u~.~l d~l
1
~ r
~ ~ kcru ~g~) eXP I ~ ~Y -i- -I- uo~r) dy dgl. . _
The equation takes the form
d~~D 1 / , 1 d]n (uk) `2 �
dy1' T~~- 4 I Y T u-- d~ - I
~ 1
- 2 d~ ~ d~ dsku~ - ul d~ 1=: 0. ~21) -
L - ~ ~
Its solutions satisfy the boundary conditions ~(0) _~(1) = 0. Multiply-
ing (21) by integrating and taking the real part from tlie resultant
equation we get
~ N~*~5,. I ~1U* d~~u .
Re ~y = � , � � (`'2)
~ ~D~� d~
0
Expression (22) implicitly determines the increment of development of
instability since the f unction generally speaking, is unknown. How- I
ever, if the gain of the medium at the input is close to the threshold ~
i .
gain, kp - d�1, and pumping is small, oq (~)d~~~1, then ~ ImY I Rey ~ and the
eigenfunctions of the perturbations are found
cUm(~)=sin (nm~), Imym=2nmi. (23)
Since the coefficients of ~~m~2 in (22) are small, in order to find Reym
the zero approximation in calculation of ~m is sufficient. As a result
we get
~
R~' Y~n = 2 O( ucT d
d6~ - k~T) ) sin= (nm~) d~. (?4)
Expression (24) defines the region of stability, the frequencies of de-
veloping perturbations and the rate of their increase. In particular,
if pumping is uniform over the cross section of the resonator, q=(d + ~)/n ~
and kp = d+ ~ when 1, then Reym is independent of the number of the
mode of perturbation: ReY~ _-1/n + In dimensionless variables
ZLk
ReYm = Z~ M- 1- d vT ~en pumping along the fl4w is inhomogeneous,
preferential development of high-frequency perturbations is possible.
_ Let kin = d, and let the pumping be concentrated on a small section half-
way between the edge of the mirror and the axis of the resonator. Then
perturbations will develop with a frequency that is a multiple of 2v/Z.
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Such distribution of pumping leads to modulation of the intensity of the
output emission with a period equal to half the time of flight Tpf. From
(22) we can get an expression for the rate of development of high-
frequency perturbations at k~T(~), q(~) (not necessarily small). At
liigh frequencies (m-~~), the eigenfunctions of the perturbations coincide
with (23) and
~m = - cT ~1~
Re m ~ k(~) d~ + ln u~T (o) ' ~25~
i -
The inequality 1n u()]~ k~~j d~ is a sufficient condition of instability
_ of steady-state laser operati~n. From the simple model of an active
- medium in an unstab].e resonator considered above we can draw the fol].ow-
ing conclusions.
An increase in parameter y= 2L1 �QN X~ leads to stab ilization of the
v M - 1 zN
5tc~acly state c~f laser operation. This conclusion explains the experi-
m~~t~ral data of Ref. 2 In which a reducCion of M led to attenuation of
pulsations.
The frequencies of developing perturbations depend on the distribution -
of pumping and on kin. A reduction of kin stabilizes the working mode
of the iaser. '
For stability of steady-state laser operation with respect to small per-
turbations, it is necessary at least that the inequality
t xc 1 ! QN (x)
ln ~~o~ C zN v~' R~ ~x~ dx
be satisfied. �
5. Let us consider the question of the waythat saturation of exchange
N2-C02 affects the developr~ent of self-oscillatory instability. To sim-
plify the equations we introduce the new function
b
~ c~~ _ ,k~
u, eXp _ ~(~y -l-- u8) dyl d~.
~ ,
For this function, from linearized equations (13), (18) with conditions
(14) we can get the second-order equation
ds~P d~P aeus d k9u8
~ ~~a d~ (Y -f- j
+
uD d~ It~ ~ + ue~ l =
~
ksus dcp aek�us 26
- . - (1 ue)a dE (I ue)e ~ ~ )
with conditions
~~l)=0 d~' I _ ae
, d~ ~ao _ ~ u8 ~27~
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The problem of stability is solved by finding the eigenvalues Yn and the
eigenfunctions ~n(~) of boundary value problem (26), (27). This problem
can be solved analytically in the case where the lasing threshold is
slightly exceeded (kp - d� 1) and at high frequencies (lyn~ �1). In
these cases we can use perturbation theory as in Ref. 9.
Let kp - d= ~�1. With accuracy to terms of the order of 0 from (26) we
get .
d2~ d~ ea, d~ dy~ eae 1 28
d~z -f-Y ds = 1,+a, d`-, li a, d; - I..~ ad ~PJ �
When A= 0, the eigenfunctions ~pn that satisfy boundary conditions (27) i
take the form (~~~i=Q-y0n~"'-e-vOn, whjle the eigenvalues YOn are solutions
of transc~ndental equation (15). Applying perturbation theory with re-
spect to the small parameter ~ and following Ref. 9, we get
_ ~
R~ Yn - I 2acsl (1-~- u� (0)~Z -I-1 + ~ a~ ~ Yon , (29)
.
't'he eigenfunctions and eigenvalues take the form
cp�= e-vnE._-e-v~
a, --1 20a, i 2'u` 1- cos x +
Yn =`Z7t/2l ( aQ ad 2t~n ~ X dz
~ 0
Aa, (2nrt (a, - 1)]~ ~30~
1 as - 2us � . '
~
The equation ReYl = 0 defines the boundary of the region of stability of
the steady-state solution. When as � 2n, the equation of the boundary
takes the form ask = 2n 2~. For a C02-N2 mixture we get the condition of
stability of the st~ead -state mode of operation of a fast-flow laser
XCTtf~~XNTNC~ ~ 2n~'' Numerical calculations in Ref. 6 showed an
abrupt increase in the parameter ask with approach to the lasing
CI~ res I~o.ld .
lf ~he saturation parameter is sufficiently large, 2~rn/ 2~
. o .
.�.s can be seen �rom the last formula, the .radiat~on intensity fluctuat~.ons
of an incoherent source increase with distance more slowly than the -
- fluctations in a plane wave, in which case, they do not depend on The
attenuation of the fluctuations is explained by the fact that a~ any point
- at a distance z in a turbulent medium, the intensity is the sum of the in-
tensities of plar:~ waves arriving at this pa9:~t from the region of the med-
ium bounded by a cone.with an apertiD:e angle of 9. As a result, the small
scale spikes in the intensity are averaged in a manner similar to the avera-
- ging of the fluctuations of the light flux by ~n ab~ective of radius Z=
_ = Az. Only overshoots ~aith dimensions on the oLuer of Z lead to intensity
�luctuat3ons in this case, .
The formula for the fluctuations of in the case of parfi~,ally coherent
radiation can be derived from formula (2.0~ f~.,:r a plane wave, by su;;stitut3ng
(6z)'1 for Km in it. It will agree with ~:orm~~a ~'`1) *-'th a prec ision of
down to a constant factor.
Similar arguments can also be adduced for estimates of the influence of in-
coherency on the sel~-stress effect. In accordance with them, the quant~ty
K~ in the expression for the parameter ~p (17), which characterizes the
influence of nonlinearity, shoi~ld be replaced by (9z)'l. The influence of
nonlinearity will then be determin2d by the quant3ty:
~~=n9, t/T/e~ ~22> -
where n is a coefficient on the order of unity.
3. Experimental Resu'lts ~
The spatial structure of a pulse3 laser beam after it passed through an
absorbing turbulent medium was studied experimentally. A GOR-300 laser
genera~ted multimode radiation in a pulse with a width of about 8 msec. The
pulse energy was monitored with an IKT-1M meter and varied in a range of _
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L'va\ vl a .LVaaW Vvu ~/~.ua
30 - 120 J. The beam diameter at the input to the turbulent medium was 2 cm
and the angular divergence of the beam was 10-2 rad. The beam passed ~hro~gh
a cell with ethyl alcohol which was dyed with methylene blue to produce the -
monitored absorption a. Flat heat exchangers were placed at the upper and
lower boundaries of the 7.iquid to produce convective turbulence. The re-
sults given below were obta3ned w3th the folloFring parameters: the absorp-
tion coefficient was a= 0.04 cm-1; the temperature of the upper and lower
boundaries of the liquid was 52 and 14� C respectively; the spacing between
the heat exchangers was 4.5 cm. The values of C and K~ ~n formula (16)
can be estimated in accordance with [6]: C= 5.4 � 10-8 cm-2~3 and K~ _
= 57 cm"1. The distribution of the intensity at the rear wa11 of the cell -
was photographed with an SKS-2 camera at a rate of about 4,000 frames/sec ~
using MZ-2 motion picture fi1m.
The photographs were computer processed for quantitative studies of the
change in the intens3ty fluctuations. The distribution of the light
intensity Jk~l = J(xk, yl) at the corners of a grid with dimensions of
b/(m-1), where b= 1.32 cm is the width of a side of the square located
= in the center of the beam; m= 128 is the number of subdivision points
along each axis, was computed taking into account the charateristic
density curve for the film, Two-dimensional spectra of the intensity
fluctuations were computed using a fast Fourier transform:
m-I
~i~p~ 9) = ~ ~v~ e ~v. v= m~ ~n~ t exP (i ~(kP + l9)1 ~23)
k, 1a0 ~ ~
i
- as well as one-dimensional spectra of the relat3ve fluctuations in the i
intensity: ,
m/2 - i '
F~~P) = 2 ~ ~i~P+ 9)l~0,0�. ' ~24~
Q-o
~xamples of experimental one-dimensional intensity fluctuation spectra _
1, which illustrate their timew.Lse evolution are shown in Figure 5. A1so
depicted here are theoretical curves for Fi(K/~c~, ~3 )[~3~ _~e��], com-
~uted from the two-dimensional spectra of ~X taking ~nto account the iso-
tropicity of the fluctuations:_. _
Fi~x~xM~ ~e~~ = 476m f 4~x ~ x2/xm -f- t2 ~~8~~ dt.
~
For convenience in making a comparison with experimental values, a dimen-
sionless spectrum F~ was introduced so that the dispersion of the relative -
intensity fluctuations was ~2 =4(xa)=fF~(x/xm)d(x/x~. . In order to
take into account the influence of both the radiation incoherency and the
_ thermal nonlinearity, the ~x spectrum was chosen as follows in accordance
with formulas (14), (19) and (22): �
~x 24e2 ze~ e~x~ x~f ~~a~~ ~ ~ x2Z ) � (25 )
0
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~9 fi .
e
e .
. -2 ~ e: ' ~~~=0 . .
� . �o . . ' .
'o : Q
o
i' ; .
- o.a
3 o e
~ y� Figure 5.
~ ,
' � The change in the one-d~nensional intens-
~ � 4 ity fluctuation spectra with time.
o . �ae
~ � The solid 13.nes are computed from Formula
� ~ ~ ~ � � �~.~o ~ ~ (27) where B = 280; tAe dots are experi-
,6a mental values where W= 23 (solid black
~ , , dots), 100 J(tr~angles, light circles9
� black triangles) and t/T = 1/27 (black
. ~ ~ dots), 1/35 (light triangles), 2/5 (cir-
cles with a dot in the center) and 31/35
~ .-q4 `r-o,2 02 ~black triangl.es) .
The function defi;ned by expression (20), can be approximated by the
following expression with an error of no more than 5%:
~~J)=~1~-4ye/3Yn)-1~ _ (26)
Taking into account the values of the parameters C and K~, we derive the
following expression for the spectrum F1. (when z= 25 cm):
x
Ft (xm ~ ~ed~) = l~sf ~~a~) ~ y~/se-u~l +,By3/s~-id~~ (27)
where y=xs~xm~'~s~ B=(4/3~)(xm8z/2)s. . The theoretical curves shown in
Figure 5 were computed for the case of V= 280, which corresponds to A=
= 10 mrad.
When 200 < B~ 300 and 0.4 < K~Km < 2, logFi as a function of B can be
approximately descr3bed by the formula:
IgFi(B, x/xm)=1gF~(250, x/xm)-2, 5~ 10-'(8-250).
Curves corresponding to ~3~ = 0, 2 and 3 are shown in r'igure 5. The
values of these parameters for the experimental curves were computed from -
the formula: �
~a~(t) = e ~ - ~ aT ~ ~tT
a 'ap
where W= 100 J, a= 0.04 cm-1, a= 1 cm, and will be ~eff = 1�~7n .for the
14th frame (t/T = 14/35) and ~eff = 2.64n for the 31st frame. A comparison
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of the experimental curves with the theoretical ones makes it possible to
specify the value of the undetermined coeffic3ent n more precisely.
When r~ = 1.1, good agreement is observed between the theoretical and
experimental spectra in a range of wave numbers of 0.4 = ~c/K~ ~ 1.3. _
However, there is no such agreement outside of this range, something which
is related to the influence of the boundedness of the beam on the low
frequency portion of the spectrum (~c/km < 0,4), and apparently, Co the
difference between the tur~ulent spectrum ~E(K) and the spectrum specified
by formula (16) in the region of high frequencies (~c/~ > 1.3). As can
be seen from Figure 5, in the absence of self-stress, the ex~erimental i
spectra of F~ when ~c/~c~ = 2 fa11 off more slowty than exp (-~c /Km) , as
follows in the case of tR~ function ~F in the form of (16). Tt is
desirable to pergorm an eaperiment us~ng a coherent source in order to
come to more definite conclusions concerning the behavior of the spectrum
in the high frequency reg~on.
The authors are grateful to V.P. Trusov for assisting in the performance
of the experiment.
BIBLIOGRAPHY
1. B.S. Agrovskiy, et al., KVANTOVAYA ELEKTRONTKA IQLTANTUM ELECTRONICS], ~
7, 59, (1980). Isic] '
- 2. M.I. Mordukhovich, IZV. WZOVo SER. RADIOFTZTKA [PROCEEDINGS OF THE
HIGHER EDUCATIONAL INSTITUTES, SERTES ON RADTOPAYSTCS], 13, 275, 1970.
3. G.A. Pasmanik, ZhETF jJOURNAL OF EXPERTMENTAL AND THEORETTCAL PHYSICS],
66, 490, (1974).
4. D. Klauder, E. Sudarshan, "Osnovy kvantoboy aptiki" ["The Principles of
Quantum Optics"], Moscow, Mir Publishers, 1970, p 36.
5. A.S. Burvich, A.I. Kon, V.L. Mironov, S.S. Khmelevtsov, "Lazernoye
izlucheniye v atmosfere'~ ["Laser Radiation in the Atmosphere"], Moscow,
= Nauka Publishers, 1976, p;227.
6. A.S. Gurvich, M.A. Kallistratova, F.E. Martvel~, IZV. WZOV. SER.
RADIOFIZIKA, 20, 1020, (1977). -
COPYRIGHT: Izdatel~stvo '~Sovetskoye radio'~, "Kvantovaya elektronika", 1980.
[135-8225]
- 8225
CSO: 1862
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UDC 621.373.826.038.823
- A STUDY OF THE CHARACTERTSTICS OF PHOTOTONTZATTON EXCTMER LASERS
Moscow KVANTOVAYA ELEKTRONIKA in Russian Vol 7 No 3(93), 1980 pp 593-598
manuacript received 24 Aug 79 -
[Article by V.M. Borisov, F.I. Vysikaylo, S.G. Mamonov, A.P. Napartovich
- and Yu.Yu. Stepanov] -
[Text] The results of experimental and theoretical
studies of the characteristics of photoion~zat3on
excimer lasers as a function of the pre~on~zation con--
ditions, the charging voltage and the partial composi-
t3on of the gaseous mixture are given. Optima'1 condi-
tions for laser operation are found, under which the
lasing energy for the KrF molecule amounted to one
Jou1e.
The possibility of easily and efficiently producing a volumetric discharge
with the free ionization of gas by ultraviolet radfiat~on has generated
interest in studying its electrical and 1as~ng characteristics. In
particular, it was established in paper j1~ that there exists a threshold
concentration of photoelectrons for TEA C02 lasers, which when reached,
the discharge acquires a volu~etric character. A further increase in the
photoelectron concentration 3n a wide range by virtue of the increase in
the energy contributed to the auxiliary discharge did not change the
discharge and lasing characteristics. The presence of a significant amount
of halogens (0.1 - 1%) in the Zaorking mixtures o� excimer lasers sub-
stantially changes the governing laws related to preionization which
apply to C02 lasers. A study of the effic~ency of XeF and KrF lasers as
a function of the free ionizat~ion delay time with respect to ~he primarp
discharge was carried out 3n papers [2, 3]. The functions which were
obtained are explained by the presence of fluorine in the working gas
mixture. A power supp'ly circuit including an LC oscillator j4] or a
Blumline line is used in almost a11 electrical discharge excimer lasers
known at the present time, while preionization is accompl3shed bp one
row of sparks positioned on the side and along the center of the inter-
electrode gap. The ~yptcal 1as~ng energy obtained in such lasers amounts
to 0.1 J. The laser described in paper [6] is an exception. The authors
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rvc~ ~rri~.icaa, uai, .,..i+l
of this work obtained an energy of 0.8 J using a complex system of
energy repumping and discharge voltages of 140 KV; in th~s case, the
efficiency of the laser amounted to about 0,1 percent. Tt should be
noted that such high charging voltages are extremzly ~nconvenient for
the design of lasers operating in a frequency mode.
The resul*s of experimental
~ and theoret3cal studies of the
- B g, characteristics of photoioniza-
tion excimer lasers are given
_ A A~ in this w~ork as a function of j
+ ~ y,: zf; �,r the preionization cond3tions,
~ x r x x-~' ~r '`s~ ~ u%~ i~ charging voltage and partial
U c, cz c= � composition of the gas mixture.
, Opt3mum conditions are found
for laser operation, under which -
the lasing energy for the KrF
Figure 1. A schematic of the experi- molecule amounted to 1 Jo A
mental setup. schematic of the experimental
setup in shown in Figure 1o The
metal housing of the chamber is
grounded, the cover is made of plexiglass, and four rows of inetal rods
5 mm in diameter are placed in it, with 11 rods in each row, The discharge
electrodes are fabricated from aluminum bar stock 40 mm in d~~meter and ;
60 cm long; the interelectrode spacing is 5 cm. A KMK-100-0.06 capacitor
with a capacitance of 0.06 ~Fd was~used as C1; C2 was bu~Llt up with KVI-3 ,
capacitors, so that the capacity of a single element was 150 pf, while the
equivalent capacitance of all of the elements of one row was 1,650 pf. The
resonator was formed by a fu11y enclosed aluminum reflector and a plane-
para11e1 plate made of CaF2. When C1 is swStcRed, pulse charging of C2
takes place, and in thia case, two series of sparks (A and A') occur close ~
f'Q"~ Joules -
O,B Figure 2. _
- The XeF (solid line) and KrF (dashed line)
ay p lasing energies as a function of the volt-
6~ 4~ 3 age for various preionization levels. =
d -
~1 2 Key: 1, 4a I1lumination only by the B and B'
/ ~
/ d rows of sparks;
4~ d ~ f ~ 2, 5. On1y by the A and A' rows of
~ ~ sparks; -
g05 ~ ii 3, 6. Total illumination.
~ U~ ~CV ~
40 SO 60 U,rB
to the high voltage electrode and two series (B and B') on both sides of the
discharge gap. The ultraviole~ radiation of the sparks produces the pre-
ionizati.on of~the gas volume.
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We measured the lasing energy and simultaneously recorded the oscilloscope
voltage and current traces when various rows og sparks were covered with
shields opaque to UV radiation. The results o~ measurements of the Xer and
KrF lasing energie~ are shown in Figure 2 as a function of the charging
voltage and the i1lum~nation geometrq~. The dependence of the 1as~ng eneLgy
on the geometry of the UV prei~onization for the XeC1 molecule is very close
to similar funct~ons for XeF. Tt can be seen from Figure 2 that preioniza-
tion by only the sparks of rows A and A' is more effective as a rule than
preionization by the sparks of only rows B and B'. This can be explained
_ by the generation of a lower concentrat3on of photoelectrons in the working
volume by virtue of the greater distance of spark rows B and B' from ttte
discharge gap. The utilization of the illumination from all the roFrs of
sparks leads to an even greater increase in the lasing energy. It can also
be seen from Figure 2 that preionizat3on yields the strongest effect in the
case of low charging voltages (30 - 40 KV).
U,~B U, Ky
60 \ ~a~ a
40 ~
i
?0 ~
J ~
~ i i 1 i
f"A Figure 3.
~6 1 6 The computed osc311oscope traces of
11 /I ~~l the voltage (a) and current (b) in
/ ~ the case of high (solid line) and
B ~ ~ an order of magnitude lower (dashed
4 ~ ; ~ line) preionization level.
/ ~
~ t, nsec
0 d0 /60 2k0 t,,vc
Thus ir~ contrast to the well-known laser desi ns 1- 6
~ g j where preion-
- 1.zation was realized by a set of sparks powered from an individual ~
_ capacitor and located to the side of the discharge at a spacing of 4 to 6 -
cm, we have sh~wn tha~ the preionizer sparks must approacR the d3.scharge
gap in a manner similar ~o A and A'. Tt is innportant to underscore the
_ ~act that it is specif~cally the production of powerful homogeneous pre-
- ionizat~on which has made it ~ioss~ble to use a simple discharge supply
circuit configuration with one switcher, 3n contrast to the previously
used circuits [4, 5]. Tn such a circuit configuration (see Figure 1),
a type TGT-2500/50 thyratron,.operating at a voltage of 35-50 KV can be
used in place of the dischargei, and a pulse-periodic laser operating
_ mode is realized. The circuit we us~d for this operation likewise has
the advantage that preionizat~.on fs accomplished automatically, wi.thout
a second switcher.
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run vrri~lcu~ u~n v~vLi
The computed oscilloscope current and voltage traces are shown in Figure 3,
in which case, the current is of an oscillating nature with a sharply
pronounced first peak. An analysis of the oscilloscope traces shows
that the energy contribution to the discharge over the t3me of the first -
- current peak amounts to about 50 percent of the total stored in the
capacitors. Since the contribution to the discharge following the first
current peak is realized at low values of the parameter E/13 (as compared
to its value at the maxiTnum of the f~rst current peak), the excitation
of the lower resonance and metastable levels of Xe and Kr [7] becomes -
ineffectual, and for this reason, from the viewpoint of laser efficiency
only the energy contribution in tt~e first current peak is important.
In the following, we sha11 understand the words "energy contribution to
the discharge" to mean tRe energy contribut3on in the first current peak
and will designate it as
- It was found from the experimental oscilloscope traces of the voltage and
current that ~ increases with an increase in the charging voltage, as
well as with the introduction of halogens (0.2 percent) into the pure
helium and does not change substantially with a char.ge in the preioniza-
tion level. Thus,.the increase in the lasing energy observed with an
increase in the preionization 1eve1 (see Figures 2, 3) cannot be explained
by the change in the energy contribution to the bulk discharge.
The current and voltage oscilloscope Craces were calculated using a homo- ~
geneous discharge model in a manner similar to j7] to explain the ob- '
served functions. The equations which describe the main elementary pro- '
cesses in this case have the form:
dn~
dt - y~ nHe yt ne -f- Ki~ 11Kr ne'- va ne 9~ (1)
dn ~ . . . .
dte =vu n.-y~ nHe-~r ~nHe~~~ ~2)
_ dnKi ,
, dt = ve nr - Kic nKr ne vr nKrr ~3~
*
where ne is the electron concentration; nge and n~. are the concentrations
of He and Kr atoms in the metastable states; v~ is the Penning ionization
frequency of the easily ionizing molecules and atoms by the helium atoms
in the metastable states; vi is the frequency of direct ionization of
He, F2 and Kr by electron impact; va is the frequency of dissociative
adhesion of electrons of to F2 molecules; vB and vB are the excitation
frequencies of the helium and kryptan atoms respectively to metastable
- states; q takes into account the formation of photoelectrons due to
ultraviolet preionizat3on; Ki~ 3.s the ionization rate constant for Kr atoms
in metastable states due to electron impact; v~, is the extinction rate of
krypton atoms in metastaDle states by heavy particles; K~ is the Penning
ionization rate constant for the case of collision of two helium atoms ~
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i~i metastable stateso The Penning ionization rate constant of F2 moleculas
and Kr atoms was chosen as Ki = 10-10 cm3/sec, ~ust as for nitrogen [8].
The remaining ionization a:ld excitation rate constants due to electron
- impact were sele~ted in accordance with paper [7J. (We will note the close-
ness of the results of the calculations of the various constants in papexs
[7] and [9].)
As a result of calculations using the model described here, pretty good
agreement was achieved betw~een tiae experimental and ca~.culated voltage ar.d
current oscilloscope traces.
U, K6
� Ffgure 4. Oscilloscope traces of the current
40 ~~r1 / and voltage computed for the fol-
~ lowing mixtures:
?o F2:He = 0.2:99.8 (1); -
FZ:He:Kr = 0.2:94,~:5 (2); and for
~ pure He (3);
I'KA 2 U0=50KVandp=l.5atm.
30 6 ~
d` ~
20 ~
!0 3 ~l
D SO 100 t,yc _
The increase in e when fluorine is added to the helium (a 0.2%) can be
explained by the increase in the breakdown valtage which ~s due to the
acceleration of electron extinction due to their adhesion to FZ and the
reduction in the ionization rate due to the decrease in the tail of the
electron distribution function, as we11 as by the increase in the r.?aximum
value of the current due to the growth in the ionization when the Penning
reaction of He with F2 starts. At significant concentrations o.f fluorine
1%), electrons are formed primarily by virtue of direct ionization of
the fluorine. The oscilloscope traces of the voltage and current in this
case take on a shaTply pronounced osc~7.latory character, and flashover is -
visually observed in the form of several bright channels agafinst the back-
ground of the diffusE disct~arge. -
The results of a numerical calculation of thE voltage and current oscillo-
scope traces at a pressure of 1,5 atm and a charging voltage of Up = SQ KV
for various mixtures are shown in Figure 4 by way of illustration. The
- energy contribution to the discharge in pure He amounted to 38 J/lo
With the addition of 0.2% F2, the energy contribution increased up to
= 53 J/1, and with the addition of Kr to the lasing mixture, it fe11 off to
44 J/l.
- An increase in the preionization level, as calculations have shown, leads
to a somewhat greater growth in the concentration of inetastable He atou~s
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with respect to the increase in the concentration of electrons. The delay
in the generation of electrons because of the Penning reaction leads to
a slight increase in the current in the first peak. However, this effect
is sma11. It can be seen from Figure 3 that an increase by a factor of 10
in the preionization 1eve1 Zeads only to a 20% incr.ease in the energy con-
tx~Dut~on, something which is in agreement with experimental results.
The analysis of the numerical calculation of a discharge in an He-F2 mix-
ture made it possible to ascertain four stages in the development of a dis-
charge, each of which is descr~~ed in a simplified fashion. Ionization due to
the ~ltraviolet sonrce predominates in the first stage, ionization due to
the Penning reactfion w~th metastable He predomir.ates in the second, direct
ionization of He and ~2 in the fiRird, and in the fourth stage, stepwise
ionization proves ~o be the primary formo
We sha11 ~rrite sianplified expressions for ne(t) and nHe(t) in each of the
stages:
r
~ ~
- ne= q/vo, nHe ~ qve/v~t;
u
r l
2. n~ ~ n~, eXp f~ ve ya - vi) dtJ , n H~ ~ Yva/vi ~n; - C~ ;
a .
3. n, ~ rc~z exp (vc - va) dt] ~ nH~ y: n. C3 :
vi
v~
n~ Kr~ n. vi ne + C.i~ ,
Here nel, ne2, C2, C3 and C4 are constants whic'h can be found from the
conditions of blending the salutions.
The possibility o� the breakdown into the indicated stages is determined
both by the con~ditions in ~he discharge network and by the gas composi-
tion. When the condit3.ons change, ~he duration af the individual stages
chang~s as well as the parts they play in the vverall current rise.
- Subsequently, t~?e fourCf~ sCage is replaced, obviously, by a current ~
reduction s~age wh~ch is related to the d~ap in the voltage. The same
type of breakdawn iaCo st~g~s 'is also observed for laser mixtures (with
the addition of Kr, Xe). We wi11 note that 3n the first tAree stages,
khe growtl~ in ne is proport.ion~1 ~o the orig~nal concentrafiion, while
there is a peaking ~~n tne fou~th stag~ wt~icFx is related to stepw3.se
ionfzation. Tt was ass~ned in accordance with fihe estima~es that the
recombination is 1ow i,n a11 sxag~s. Under these conditions, steady-state
burning of the ~d~schaxge is unstabZ~ j10]. Soth the experiment and the
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Table
ne0 nel
U~, KV E, J T, KA E/N, Td npM~ n~il E~planations
50 15.4 25,3 23 1/2 85 The basic calculation.
- 50 14.9 27.8 20.7 10/20 122 nel and nep increased by a.
factor of 10.
50 15.3 27.7 22.8 1/2 76.3 The following reactions are `
considered; He* + Kr e and
H*+F2-~e.
50 14.8 27.4 22.1 1/2 39 The reaction rate constants _
for He* + Kr e and He* + F2
e were increased by a fac-
tor of 10.
70 21.6 40.7 24.4 1/2 64.6 The following reactions are
considered: He* + Kr } e,
He* + F2 + e.
Note; U~ is the charging voltage; nep and n~p are the initial and maximum
electron concentrat3ons in the main discharge; ne1 and n~1 are the `
same in the segregated current column.
calculations demonstrated that the growth in laser power with an increase
in the ultraviolet illumination power is not related to an increase in '
the energy contriBution to the discharge. To studp the in#Suence of the
inhomogeneity in the preionization 1eve1, we sha11 modify the discharge
model, segregating from tAe wAole $amogeneous volume tRat col~mn with an
~nitial concentratfion which differs from the mean value. We sha11 like-
w~se asswne that the dimensions of the coliann are small enough that its
contribut{on to the overall cur,rent 3s sma11, and for this reason, the
field is determined Dy tAe ma~n vo1~Q of the discRarge.
As follows from the preceding anal}*sis, the initial difference in the
concentrations can be increased only in ~he fourth stage, something which
is a manifestation of instability [i0]. Numerical calculations have ~
shown that under the conditions of the discharge, tRere occurs amplifi-
cation of the initial oversAoot of the electron concentrat~on by a factor
of 50 to 100 (Tab1e). Tt has been nated that with an 3ncrease in ~he
charging voltage, the ampli�ication of an inhomogeneitp fa11s. This
correlates with the experimentally observable increase in discharge
stability w~th a rise in tRe c~harging voltage. Tri the general case,
d3,scharge stability~ is fimp~oved wRen the contribut3.on of tAe fouzth
stage to its deve7.opment ~s reduced.
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L'va~ va' L' 1v1~1L V~Ili Va\Li ,
Thus, calculations show that the equalization of the ultraviolet pre-
ionization 1eve1 promotes the development of a more~homogeneous discharge,
something which sfiouid have a positive effect o~ the lasing characteris-
tics.
BIBLIOGRAPHY
1, V,M. Borisov, Yu.A. 5atov, V.V. Sudakov, KVANTOVAYA ELEKTRONTKA ~
[QUANTUM ELECTRONTCS], 3, 2460, (1976).
2. R.P. Akins, G. Tnnis, Shao-Clu Lin, J. APPL. PHYS., 49, 2262, (1978),
3. J. Hsia, APPL. PHYS. LETTS., 30, 101, (1977).
- 4. R. Burnham, N. D~eu, APPL. PHYS. LETTS,, 29, 7~J7, (1976).
5. I.M. Isakov, A.G. Leonov, V.Ye. Ogluzdin, PIS~MA V ZhTF [JOURNAL OF
TECHNICAL PHYSICS], 4, 1228, (1978).
~ 6. R.S. Taylor, W.J. Sar~eant, A.J. Alcock, K.E. Leopold, OPTICS COMMS.,
25, 231, (1978).
" 7. V.Yu. Baranov, et al., Preprinty IAE jTnstitute of Nuclear Power Pre- ~
printsJ Nos. 3080 and 3081, Moscow, 1979.
8. P.W. I,ee, C.B, Co~lins, .?q CHk~o ~HXS.~ 65, 5189, (1976~.
9. A.E. Greene, C.A. Brau, IEEE J. QE-14, 951, (1978), "
10. J.B. Daugherty, J.A. Mangano, J.H. Jacob, APPL. PHYS. LETTS., 28,
581, (1976).
COPYRIGHT: Izdatel~stvo "Sovetskoye radio", "Kvantovaya elektronika~', 1980
[135-8225]
~ 8225 .
CSO: 1862
r
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UDC 533.92 -
THE CHAPdGE IN THE ENERGY CHARACTERTSTICS OF AN ELECTROTONTZATION DISCHARGE
TN MTXTURES OF C02-N2-He AND COI~ZERCTAL GRADE NTTROGEN DURTNG PULSE
PERIODIC OPERATTON
Moscow KVANTOVAYA ET.EKTRON~KA in Russi,an Vo1 7 No 3(93), 1980 pp 630-633
manuscript received 28 Aug 79 . _
[Article by Ye.P. Glotov, V.A. Danilychev, V.D. Zvorykin, Yu.S. Leonov, -
- A.M. Soroka and N.V. Cheburkin, Physics Institute imeni P.N. Lebedev bf
USSR Academy of Sciences, Moscow]
jText] The effect of the change in the characteristics of
an electroionization discharge is atudied in mixtures of -
C02-NZ-He and connnerciaZ grade nitrogen for the case of
pulse period~c operation of an electrical ionization laser,
It is feund that when E/p < 5 KV/(cmoaL~n) and with specific
energy inputs which do not exceed 500 J/(1�ahn), the change _
in the discharge characteristics of the indicated mixtures
of COZ-N2--He and ccmmiercial grade nitrogen is determ:tned
only by the action of the elecfron beam. The drop in the
energy contribution is related to the formation of oxides
of nitrogen as a result of plasma chemical reactions, where -
the molecules of ~he nitrogen oxides possess very high
_ electron adhesion rate constants 10-10 cm3/s),
When designing CW and q>>asicontinuous closed cycle jl] electrical ionization
?asers (EIL) with r.epeat use of the lasing mixture, one o~ the most 3~nport-
r_nC problems is that of mixture degradation, since 3t is specifically this
process which determines the gas consumption during the operation of a C02
laser in pulse-periodic and C~T modes. This paper is devoted to an inve5ti- -
gation of the discharge characteristics of the lasing mixture of [2] during
pulse-periodic operation of an ETL.
The experiments were performed using a laser installation with an acrive
volwne of "l~ liters, which was described in paper [3J. The ionization of
_ the medium was accomplished by an electron beam with a current density of
j e= 0.5 A/cm2 and a pulse width of T= 1.5 microseconds, which was genera-
ted by an electron gun with a point catAode. The high voltage pulses were
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i va~ va a iviau. a.u.. -
W�q,w/n J!�!0'sc-~ s"~
- 600- i4,5 Figure 1. The specific energy contribution
~I, J/ltr, q in commercial grade n3.trogen (light circles),
electron beam current without discharge
40a- ~ (light triangles) and tRe adhesion rate cons-
tant S(dark triangles) as a function of the
� number of preceding d~scharge current pulses,
n. The light circles with short horizontal .
200 ~ t,5 lines above and below them correspond to the
1 values of s computed from the results of mass
n spectrometer measurements of the concentra- j
~ puleee o tions of the nitrogen oxidea formed in the '
o /0 7o n,uM~ discharge.
Figure 2. Mass spectrograms of commercia).
grade nitrogen before (a) and after (b) 3C'
energy contribution pulses.
- a a ~
0
' N ze
N t
Hz0 N29 Ar
ON O= Ki0
b.6
generated by a Marx generator with impulse capacitance of 0.04 ufd. The
discharge current was measured by a Rogowski 1oop, operating in the RC
integration mode (R = 300 ohms, C= 0.05 ufd).
In the course of the experiment, mass spectrometer studies of the composi-
tion of the gas m3xture were performed as a function cf the number of energy
contribution pulses, as a result of which it was established that in an
electrical ionization d3scharge in m3xtures of C02-N, cyanogen CN and hydro-
cyanic acid HCN are formed, which in being electranegatfive, can increase -
the effective electron adhesion rate. Fo1low~ng 30 discharge pulses, which
- corresponds to an overall energy contribution averaged over the ent3re vol-
ume of the laser ce11 (a passive volume of 200 liters) of 0.5 KJ'/1, and `
0.06% CN and 0.03% HCN were formed in a m3xture of C02:N2 = 1:5. However,
as further experiments demonstrated, the formation of cyanogen and hydrocyanic
acid is not the main reason for the reduction in the energy contr.ibution
to electrical ionizat3on discharge, s3nce the elecfiron adhesion rate in-
creases not only in~mixtures of C02 - N2, but also in co~nercial grade ni-
trogen where CN and HCN can, in p-~~inciple, not be produced. The energy -
~ontributed to the discharge is shown in Figure 1 as a function of the num-
ber of preceding pulses for ccammercial grade ni~rogPn with an oxygen con-
tent of 0.4%.
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In order to determine what contrib,ution is made by the electron gun in the
absence of discharge to the formation of electronegative additives, the
energy W introduced 3.nto the discRarge was recorded as the funcL~~n of -
the number ~f preceding p~ectron gun pulses without discharge, which
agreed (see Figure 1) witA the curve for the energy contribut3on as a
function of.the number of discharge current pulses. This makes it possible
to draw the conclusion tRat ~he formatinn of electronegative impurities
in an electrical 3onization d3seharge in a range of field intensities of
E/p 6 5 KW/(cm � atm) and the energy contr3butions W= 200--500 J/(1 � atm)
is determined only by the action of the electron gun on the gas mixture.
A ma~s spectrometer analyais ehowed that as a result of the action ef the
electron gun, the oxygen content in commercial grade nitrogen is reduced, -
and a peak with a mass number of 44 appears in the mass spectrogram,
which corresponds to nitrous oxide N20. Characteristic mass spectrograms
for commercial nitrogen be~ore (a) and after (b) 30 energy contribution
pulses are shown in Figure 2.
It is well known that molecules of the~nirogen oxides N20 and N02 have
very .large electron adhesion dissociative cross-sections ~ j4J correspond-
ing to the reactions N02 + e-~ NO + 0- and N20 + e-* N2 + 0'-. Tn this
case, the adhesion rate S is determined bp the distribution of the
electrons with respect to the energies n(e):
~
R = o ne(e)uQ (e)de,
and is a sharply increasing function of the field intensity. Besides
dissociative adhesion, there also exists a proceas of triple frequency
electron adhesion to the molecules of nitrogen oxide (N02 + e+ M-*
NQ~ + M; N20 + e+ M-~ M+ N2Q-), the r.ate of which is likewise high,
but in contrast to the preceding case is a declin3ng function of E/p.
To derive quantitative expressions which define the influence of nitrogen
oxides on the energy characteristics of an electrical ionization discharge,
experiments were carried out in which fixed amounCs of the impurities
N02 and N20 were added to nitrogen of especial~y high purity. Oscilloscope
traces of the discharge current corresponding to the various concentra- '
tions of nitrous oxide are shoWn in ~'ignre 3. Tt can be seen that N20
molecules possess a very high electron adhesion cross-section, wh.ich
significantly exceeds tlte cross-section ~or adhes~on to oxygen znolecules.
At a concentration of N20 = 1 percent, the energy contribution drops off
practically to zero, wfiile ~he amplitude of the discharge current does -
not exceed tite thi.ckness of the beam on fihe screen of the oscilloscope.
xhe energy contribution as a funct~.on of the concentrations of nitrous
oxide and nitrogen d3oxide are~l3kewise shown in Figure 3; *_he energy
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- - - ;
~ . .
a o y�, dt.,o=~a~,K cg~ cb~
~ 3 ~
~ ca)
os ~
Z
~ ~l
, ' ,
a o~ 0,2 fN:o~.[nozJ,%
Figure 3. Characteristic oscilloscope traces of the discharge '
current in nitrogen with N20 added and the curvea
for the integral of the d3scharge current as a func-
tion of the concentration of nitxous oxide (1), nitro-
gen dioxide (2) an3 oxygen (3):
a-eo 1, 0.1, 0.01, 0.005 and 0.002 % N20 respectivelyi
f. Co~ercial grade nitrogen.
contribution due to the concentration of the oxygen impurity is also shown
for the sake of comparison.
At small concentrations of electronegative impurit3es, the electron adhesion
rate constant can be determined with a sufficient degree of accuracy from
measurements of th~ post-pulse energy contribution, the size of which for ~
commercial grade nitrogen is comparable to the energy contributed to the dis- ~
charge during the electron current pulse. The voltage, up to which Che -
capacitor bank is charged, is determined from the formula:
.
UN_Ul~p _ 1 dt
C ,J~ R (t) �
(1)
_
U,=U, - ~ ~ dr ,
where ~ is the voltage corresponding to the
ends~of the current pulse of the electron gun; R(t) is the resistance of
the decaying plasma as a function of time; C is the capacitance of the
capacitor bank. The resistance of the discharge gap is determ~ned from
the formula:
R-1(t)=�~~(!)S/d, ~ ~2~
where d is Che spacing betw~en t he electrodes; ue is the electron
mobility; S is the area of the electrodes; ne is the electron density.
In order to compute the integral we shall
~ dt/R (t) _ ~ �~en~ (t) Sd-1 dt,
t i
employ the electron balance equation for a decaying plasma:
dn~/dt=-an; -~ne.
'
_ ~ 68
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Then:
~ �~en~S dt n~ �~tS dn~ _ �~eS i~ n,: -f- ~la
d a an. Cda R~ ~~a (3)
eo
The quantity nei corresponding to the electron density at which the
plasma conduct~vity ceases to be determined by tfie electron component,
_ while the volt-ampere characteristics correspond to Thomson's formulas
[5] was taken as the upper integration limit. The value o~ ne amounts to
109 - 1010 cm-1 [6].
_ By taking the logarithm of both sides of equation (1) and substituting
(3) in it, we obtain an expression for S in the case where ~/a � ne:
~=n,oa/[(ul/uh)A-lI, A=Cda/(�eeS). (4)
The physical meaning of the coefficient A becomes understandable if the
numerator and denominator of the fraction are multiplied by the electron
density nep, corresponding to tAe moment of campletion of the current
pulse of tA,e electron gun: A= Cdan~a/'(e}~QnepS) = CRp/Tpp, where TPp =
_(a ne~)-1 is the characterist3c initial recombtnation time; Rp ss the
discharge resistance at the moment of pulse completion. The coef~icient
A can easily vary in a wide range w~en performing experiments as a
_ result of changes in the capacitance of the capacitor bank, wh~ch in the
process of making the measurements was chosen so that the relative measure-
ment error would be the least, When ane0/S � 1, the optimal value of th~
parameter A is determined from the formula Aop~ ~ 1?1[(aneO/~)eT~/Tpp].
The maximum relative measurement error using the given procedure when A=
Aopt does not exceed 12% if the voltage at the capacitor bank is measnred
with a prec3sion of no worse than 2%.
The condition S/a � ne is always met with a considerable margin under
actual experimental conditions. The electron adhesion rate constant is
shown in Figure 1 as a function of the number of preceding electron c~~rrent
pulses, determined using the procedure described here. The light circles
with horizontal marks above and below on this curve correspond to the values
of s computed for the concentrations of the N20 and N02 impurities formed
in commercial grade nitrogen with the action of the electron beam. The
adhesion rate constants N2p and N~2 Were determined experimentally ~
in the processing of the osc311oscope traces of the discharge current in
commercial nitrogen with monitored added amounts of the oxides; the con-
centration of N20 was determined from mass spectrograms based on the intensity
of the peak with a mass number of 44, while the N02 concentration was deter-
mined from the reduction in the oxygen in the commerc3al nitrogen, taking
into account the formation of N20. Tt can be seen from Figure 1 that the
values of S computed ~rom the concentration of the nitrogen oxides formed
in the electrical ionization discharge, w`.Lthin the limits of the measurement
error, is related basically to the inadequate precision of the determination
of the N02 concentration, and the values fa11 on the experimental curve for
69
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S(n). This makes it possible to conclude that the main reason for the
degradation of the mixture during Che operation of an ETL in a pulse
periodic mode is the formation of nitrogen oxides, the moleculea of which
have very high electron adhesion rate conatants, ~ 10-10 cm3/sec,
which exceed the cross-section for electron adhesion to oxygen molecules
by a factor of more than 100. To prevent nitrogen dioxi.de formation from
reducing the power of the energy contribution, and corres-
pondingly, the output radiation power, it is necessary to cool the work3ng
mixture down to a temperature at which the density of the saturating
N02 vapors is much less than the quanti:.y jC02]C02~~~~N02o For a ;
_ mixture of C02:N2:He = 1:5:4 at a temperature of -70� C, the contribution
of the impurity to the overall rate constant does not exceed 10 percent =
(without taking into account adhesion to N20).
We will note that cooting the mixture is necessary not only to avoid
nitrogen dioxide, but~also to increase the lasing efficiency and the
specific power output [7]. The task of cleaning the lasing mixture
of the nitrous oxide is a technically much more complex one, since N20
has a lower boiling point (-88� Cj. For this reason, to completely
prevent the degradation of a laser mixture during long term c~ntinuous _
and pulse-periodic operation of an ETZ, along with cooling the gas, it
is also necessary to introduce a nitrous oxide recovery system into the
gas dynamic loop.
~
BTBLIOGRAPHY
1. NaG. Basov, I.K. Babayev, V.A. Danilychev, M.D. Mikhaylov, V.K. Orlov, "
V.V. Savel~yev, V.G. Son, N.V. Cheburkin, KVANTOVAYA ELEKTRONIKA [QUANTUM
ELECTRONICS], 6, 772, (1979),
2. A.F. Vitshas, Ye.P. Glotov, V.A. Danilychev, V.K. Orlov, N.V. Cheburkin,
V.V. Chulkov, "Preprint FIAN" ["Preprint of the Institute of Physics
imeni P.No Lebedev of the USSR Academy of Sciences"], Moseow, 1979,
No 192.
3. I.Ao Berezhnoy, V.A. Boyko, V.A. Danilychev, V.D. Zvorykin, V.V.
Ignat~yev, I.V. Kholin, A.Yu, Chugunov, PTE [EXPERT'MENTAZ TNSTRUMENTS
AND ENGINEERING], No 5, 172, (1977).
4. R.E. Fox, J. CHEM. PIiYS., 32, 285, (1960).
S. L.A. Leb, "Osnovnyye protsessy elektricheskikh razryadov v gazakh" -
["The Ma~or Electrical Discharge Processes in Gases"], Moscow-Leningrad,
Gostekhizdat Publishers, 1950. -
- 70
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6. V.V. Aleksandrov, V.N. Koterov, A.M. Sor~ka, ZHURN. VYCH. MAT. I MAT.
FTZ. [THE JOURNAL OF COI~UTATTONAZ MATHEMATTCS AND MATHEMATTCAL PHYSTCS], -
18, 1214, (1978).
7. D.H. Douglas-Hamilton, R.M. Feinberg, R.S. Lowder, J. APPL. PHYS., 46,
3566, (1975). -
COPYRIGHT: Izdatel~stvo ~'Sovetskoye radio~', "Kvantovaya elektronika", 1980.
_ [135-8225]
- ,8225
CSO: 1862
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~
DYNAMICS OF FREE LASING OF SOLID-STATE LASERS
Novosibirsk DINAMIKA SVOBODNOY GENERATSII TVERDOTEL'NYKH L~?ZEROV in Russian -
1979 ~igned to press 31 Oct 79 pp 2-5, 263-264
- [Annotation, Fv~eword and Tabl.e of Contents from the book "Dinamika svobod-
noy generatsii tverdotel'nykh lazerov" by K. G. Folin and A. V. Gayner,
_ Institute of Semiconductor Physics, Siberian Department of the USSR Academy
of Sciences, Izdatel'stvo "Nauka," 1,550 copies, 264 pages]
[Text) The physical factors and mechanisms which determine the time varia-
tion of the spectrum, intensity and spatial characteristics of output emis- ;
sion are analyzed. Because of the identity of experimental conditions for I
different types of lasers, a sharp difference in the dynamics of free lasing ~
of ruby and neodymium lasers was established. The analogy between lasing
and specific mechanical motion was shown theoretically, which made it pos-
sible to analyze the general properties of solutions of equations over
_ practically the entire range of variation of laser parameters.
The book is intended for scientific workers, engineers, postgraduate stu-
dents and students engaged in study and application of lasers.
roreword
The development of modern radio-frequency amplifiers and oacillators has
become possible due to the many years of careful study of the physical pro-
cesses occurring in them. Similar investigations in the optical range,
where the physical fundamentals of constructing devices is considerably
_ more complex are now being continued intensively. Existing optical masers
and lasers are still far from their maximum capabilities and the processes
occurring in them are still far from complete understanding.
The foregoing is also true of the class of solid-state lasers which includes
those based on dielectric crystals and glass activated by luminescent im-
purities. A. M. Prokhorov, in his foreword to the book "Fundamentals of
Laser Technology" [1], notes that these lasers are the most widely used in
scientific research and in technical applications since they have maximum
emissivity over a wide range of pulse lengths and lasing frequency. It
72
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should be taken into account that we are talking about lasers based on two
or three of the most efficient media, while etimulated emission ia achieved
in more than 200 media at wavelengths from 0.31 to 3 microns. This reserve
in combination with the prospects for development of the physics and chem-
istry of laser crystals [2] and glass indicates the high potential capabili-
ties of solid-state lasers.
The needs of scientific and technical applications, on the one hand, and the
complexity of the laser as a physical system, on the other, are the reason
that investigations on the discussed topic now number in the thousands.
And whereas only sections were firat allocated to solid-state lasers in
monographs (see, for example,.[3,4]) or the entire complex of problems con-
cerning this class of devices was considered [5], there are now papers de-
voted entirely to individual aspects of the problem [1, 2, 6-8].
_ The dynamics of free lasing of solid-state lasers is mainly investigated in
the present book. The specifics of the free lasing mode are determined by -
_ a number of characteristi~s of a given class of devices. Specifically, the
half-width of the amplification line of the active medium in a solid-state
laser exceeds 103-104-fold the distance between ad~acent cavity frequencies, ~
which leads to excitation of a large number of modes. The lifetime of an
atom at the upper working level is 104-105 times greater than the field re-
laxation time in the cavity, which is the reason for the occurrence of a
prolonged oscillatory relaxation process. The process of mode interaction _
is complex in nature under these conditions in combination with the low rate
of spatial migration of excitations and the partial dispersion of the excita~
tion volumes of the modes in the active medium. This complexity signifi-
cantly increases in the most widespread case of pulsed lasing when neither
the shape nor the position of the amplification line nor the cavity configura-
tion remains constant. Therefore, despite the fact that the main equations
which describe lasing have long been known [9], ~t was possible until quite -
recently to find a solution only within the framework of simplifying assump-
tions (see, for example, [10]), which undoubtedly made comparison with ex-
periment diff icult. The derived solutions in the matn range ~f laser parame-
ter variation are weakly attenuating oscillations and the nature of lasing
can be changed qualitatively due to the effect even relatively weak factors r
related to competition of modes or by disturbances whose effect should be
carefully analyzed. The high level of technical disturbances and the high
sensitivity of solid-state lasers to them severely aggravate experimental
investigations.
The circumstance that there was until now no satisfactory agreement between
theoretical and experimental results on some essential problems was appar-
ently caused by the enumerated characteristics of free lasing. It is suf-
ficient to recall, for example, the problem o� the spike nature of solid-
state laser emission, when the situation can be characterized by the thesis:
"There are just as many opinions as there are investigatars." The fact that
73
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the experimental resulta found for a specif ic type of laser and valid only _
_ fur that type were transferred to the entire class of solid-state lasers* _
- contributed to this to a significant degree.
Thus, analysis and generalization of available results are now apparently
no~less timely than new investigations. Among the known publications de-
voted to this problem, two concern special types of lasers (traveling-wave
lasers [llJ and lasers wit~ large angular divergen~e [7J) and only theoreti-
cal problems are considered in papers [12, 13]. The theoretical aspects of ~
the dynamics of lasing of gas, solid-state, liquid and semiconductor lasers
and also molecular and paramagnetic oscillators are analyzed mainly in the
recently published monograph [10]. Practically all the known lasing modes
are discussed. Naturaliy, with this wide range of considered problems, main
- attention is devoted to the principles common for all types of lasers.
New theoretical and experimental results which, in combination with known
results, permit more complete characterization of free lasing of solid-
state lasers, are presented in the present monograph. The conclusions out-
lined in the book are formulated as a result of analysis and generalization
of experimental data found both by the authors with their colleagues and by
other collectives. The main characteristic of constructing the thPOry is
the use of the analogy between lasing and specific mechanical motion, which ,
makes it possible to establish the general properties of solving multimode i
balance equations and to consider specifically the effect of deviations ,
from balance approximation and some disturbances on these solutions. It is
shown experimentally and theoretically that, besides techni.cal dusturbances,
there are dynamic factors whieh lead to non-attenuating fluctuations.
- A detailed discussion of free l~sing, on investigation of which the main
efforts of the authors and colleagues were concentrated, is feasible with
regard to the need for prir~ary anal~sis and understanding of this main
mode. The results obtained during investigation of it made it possible to _
solve problems of controlling the emission parameters of interest to prac-
tice, including those in the giant pulse operation and mode locking [14, 15].
Problems of controlling the output emission parameters are considered to the _
extent that they are closely related to investigation of the main principles
of lasing dynamics. Successful solution of problems of ~his type of control
is the criterion of truth for the developed concepts.
The authors are deeply grateful to Corresponding Member of the USSR Academy
of Sciences V. Ye. Zuyev, who took upon himself the a_abor of editor-in-
chi~f, to Corresponding Member of the USSR Academy of Sciences S. G. Rautian
and Candidate of Physicomathematical Sciences G. E. Surdutovich for useful
commenta and also to V. S. Pivtsov and I~. P. Komarov for the timely
The authors of the given book also held this view st one time.
74 -
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presented data on experimental investiga~ion of neodymium lasers and sweep-
laser theory.
V. V. Antsiferov, V. D. Ugozhayev, V. G. Gladyshev, B. M. Chernobrod, V. A.
Shvets and Yu. N. Luk'yanov rendered great assistance in formulati~n of the
text and preparation of the illustratibns, for which the authors are truly
grateful.
Contenta P3ge
Foreword 3
Notations 6
Chapter 1. Main Physical Characteristics of Solid-State Lasers 9
1. Extent and Nature of Broadening of Amplification Lines of
Active Media in Solid-State Lasers and the Lasing Character-
istics Determined by Them 9
2. Lifetime at the Upper Working Level and the Related Lasing
, Characteristics 17
3. Lasing Characteristics Related to the Rate of Spatial
Migration of Excitations 23
Chapter 2. Fundamentals of Ti~eoretical Description of the Lasing
Dynamics of Solid-State Lasers 34
1. General Propositions 34
2. Single-Mode Lasing Theory Under Conditions of Spatially
Homogeneous Inversion 42 -
2.1. Semiclassical Description 43
2.2. Balance Approximation 48
2.3. Mechanicai Analogy 57
- 2.4. Onset of Lasing 59
3. Dalance Approximation in Multimode Lasing Theory 68
4. The General Nature of Solutions of Balance Equations 78 -
4.1. The Steady Solution 78
4.2. The Nature of Solutions of Balance Equations and
Disregard of Read~ustment of the Spatial Config-
uration of Modes 79
4.3. The Nature of Solutions of Balance Equations with _
Regard to Variation of the Spatial Configuration
of Modes 83
4.4. Mechanical Analogy 86
5. Combination Interaction of Modes Related to Intermode
, Time Divisions of Inversion and Its Effect on Lasing
Dynamics $9
5.1. The Zfao-Frequency Mode 91
5.2. The Single Mode 94
. 75
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5.3. The One-Frequency Double Mode 95
5.4. Emission of a Laser With Moving ~`.cCive or
Absorbing Medium 101
6. Some Quantitative Characteristics of Free Lasing in
Solid-State Lasers 105
6.1. Single-Mode Lasing 105
6.2. Emission of a Laser With a Short Active Medium 110
6.3. The Effect of Spatial Migration of Excitations 114 ,
6.4. Multimode Lasing li7
Chapter 3. Free Lasing of Solid-State Lasers 122
1. The Main Technical Characteristics of the Optical System
in Solid-State Lasers 123
2. Claseification of the Free Lasing Modes in Solid-State
Lasers 128
3. Some Characteristics of Experimental Realization of the
Steady State in Soltd-State Lasers 138
- 4. The Dynamics of Free Lasing in Longitudinal Modes Under
Pulsed Pumping Conditions 142
4.1. The Results of Comparative Investigation of Pulsed
Lasing in Longitudinal Modes in Ruby and Neodymium
Lasers With Reduction of the Effectiveness of
Technical Disturbances 145
4.2. The Properties of the Spectral-Kinetic Character- ~
istics of Pulsed Free Lasing in Longitudinal Modes 155
5. Free Lasing in Modes With Non-Zero Transverse Indices 165
5.1. Transverse Mode Lasing in a Laser With Flat Mirrors 166
5.2. Transverse Mode Lasing in Lasers With Spherical
Mirrors 1~2
6. Spiking in a Ruby Laser 189
6.1. The Spiking of Degenerate and Non-degenerate Modes 190 .
6.2. The Characteristics of the TEMO~q Spiking of a
Ruby Laser 199
7. Some Dynamic Mechanisms of Undamped Spiking 208
8. The Effect of Technical Disturbances on Lasing Dynamics 213
Chapter 4. Some Methods of Controlling the Lasing of Solid-State
' Lasers 21~
1. The Electro-Opticai Method of Smoothing Spatial Inversion
Holes 21~
2. Some Characteristics of the Lasing Dynamics of a Laser
With Frequency Sweeping 221
2.1. The Quasi-Steady Mode 223 '
2.2. The Stability of Quasi-Steady Lasing 228
2.3. Experimental Results 234
3. Control of Solid-State Lasing By Using the Light
Injection Mehtod 239
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3.1. Free Lasing 240
3.2. The Giant Pulse Mode 241
3.3. The Ultraehort Pulae Lasing Mode 243
Conclusions 249
Bibliography 251
COPYRIGHT: Izdatel'stvo "Nauka," 1979
[138-6521]
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- NUCLEAR P1iYSICS
~
COLLECTIVE ION ACCELERATION BY ELECTRON RINGS
- Muscow KOLLEKTIVNOYE USKORENIYE IONOV ELEKTRONNYMI KOL'TSAMI in Russian
1979 signed to press 27 Feb 79 pp 2-4, 216 -
[Annotation, Foreword and Table of Contents from book "Kollektivnoye uako-
reniye ionov elektronnymi kol'tsami" by V. P. Sarantsev and E. A. Perel'-
shteyn, Atomizdat, 1,290 copies, 216 pages] _
[Text] Collective ion acceleration by electron rings is a new effective
method of acceleration which was developed during the past decade. The
~ book contains tt~e results of theoretical and experimental investigations on
collective ion acceleration. Problems of shaping the electron rings, loading
them with ions and acceleration are considered. The stability of electron-
_ ion rings in collective ion accelerators is analyzed. ;
The book is intended for scientific workers and postgraduate students work- _
ing the field of accelerator technology and plasma physics and also for
students of upper-level coursea in physics specialties.
Foreword
Work has been conducted on the problem of collective ion acceleration by
electron rings for the past decade in many laboratories of the world.
After the first canmunication at the Internation Conference on Accelerators
in 1967 (United States) on the theoretical and experimental results achieved
at Dubna under the supervision of V. I. Veksler, groups engaged in collec-
tive ion acceleration were created at ITEF [Institute of Theoretical and Ex-
perimental Physics] (Moscow), IYaF [Institute of Nuclear Physics] (Tomsk),
Berkeley (United States), Garsch{ng and Karlsruhe (West Germany) and other
scientific centers.
The advantage o� the new method is its universality--collective ion acceler-
ators can essentially cover the entire range of energies of interest to
physics investigations. Construction of collective ion accelerators is much
more economically advantageous than construction of traditional accelerators.
- Heavy-ion collective field accelerators find the most diverse applications
- in industry, chemistry, biology, medicine and so on.
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The intensive work of many investigators of the collective ion method is re-
flected in the large number of ~ournal articles and in the proceedings of
conferences and symposia. There are no monographs which generalize the nu-
merous papers on the given topic. We feel that this book should partially
f ill the existing gap in survey papers on collective ion ~r.celeration by
electron rings. -
In working on the book, we attempted to solve many problems. On the one
hand, this book shovld provld~ an overa?1 concept of collective ion acceler~-
tion by electron rings and, on the other hand, it should be useful to people
directly involved in design of collective ion accelerators and experiments
on them. Therefore, materials of a calculation-theoretical nature are in-
_ cluded, Moreover, development of collective ion acceleration, like investi-
gations on relativistic particle storage, stimulated careful stuciy of the
dynamics of heavy-current ring-shaped beams. The most significant aspects
of this problem for the method are reflected here. Thus, we w~re forced to
proceed toward an obviously nonuniform exposition.
We also note that the given book is far from a complete survey ,~n c.ollective -
ion acceler.ation, We feel that established facts are reflected in it. Many -
problems touched on in the boo~ still await final solution. We hope that
the book will be useful in this respect as well. Tn surveying the litera-
ture, we did not attempt to provide an exhaustive bibliography on the con-
eidered problem, but limited ourselves on13~ to necPSSary references,
We had invalc~able help when working cn the book from collea~:.~ ~ of the De-
partment of New Methods of Acceleration of 0 I Y a I [Joint Instl.tute for
Nuclear Research], specif ically from V. S. Aleksandrov, Yu. I, Aleksakhi.n,
N. Yu. Kaxarinov, A. A. Popov, V. A. Preyzendorf, A. P. Sumbayer, V, S.
Khabarov, Va F. Sheftsov, B. G. Shchinov, G. Shchornak and others. We ex- ~
press deep gratitude to all oi them.
We are also very grateful to I. A. Zolina, N. A. Filippova and V, Yu.
Shevtsova for the extensive w~rk which they did in formulation of the manu-
' script. -
Contents Page
Foreword 3
Introduction 5
Chapter 1. The Princi~l.e of Collective Ion Acce7.~~ration. Types
of Collective Ion Accelerators and Typic~al Parameters 7
1. The Principle of Collective Ion ~cceleration by Etectron -
- Rings 7
79 ~
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2. Types of Collective Ion Accelerators With Electron Rings.
Diagrams for Shaping Electron Rings 10
3. The Design Features of the Heavy Ion Cbllective Field _
Accelerator of OIYaI la
4. Systems for Observing the Electron Ring in the Adherer 22
Chapter 2. Formation of Elecr:ron-Ion Rings in Adherers 26
5. Particle Motion in trp Adherers 26
6. The Magnetic Field of Adherers 31 ~
7. The Natural Electromagnetic Field of an Electron-Ion Ring 44
8. The Shielded Electromagnetic Fields of an Electron Ring 50
9. Injection of Electron Beams Into Adherers 56
10. Formation of the Magnetic Field of Adherers 65
~ 11. Experiments on E1.ectran Ring Compression 72
12. Ion Storage in Electron Rings 7'
Chapter 3. The Stability of Electron-Ion Rings 88
13. The Resonances of Betatron Oscillations Caused By Non-
Ideal Magnetic Fields of Adherers 88
14. Azimuth (Longitudinal) Instabilities of Electron Rings 93
15. Transverse Coherent Instabilities of Electron-Ion Rings 119
Chapter 4. Acceleration of Electron-Ion Rings 139
16. Methods of Ring Extraction and Acceleration 139 ~
17. The Maximum Permissible Accelerations of An Electron-Ion ~
Ring 147
18. Focusing an Electron-Ion Ring During Acceleration 158
19. Interaction of Electron Rings With the Accelerating System.
Energy Losses of the Rings to Radiation During Acceleration 163
~
Conclusions
The Possibilities of Collective Field Particle Acceleration 170 _
Appendix
- The Magnetic Field and the Field Decay Index for a Thin Circular
Current-Carrying Turn 180
Bibliography 208
COPYRIGHT: Atomi2dat, :l!~79
[137-6521] -
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OPTICS AND SPECTROSCOPY
UDC 535+538056:530.145
INTERFEROMETRIC CRITLFciA FOR RADIATTON FOCUSING
Moscow KVANTOVAYA ELEKTRONTKA in Russian Vo1 7 No 3(93), 1980 pp 500-505
manuscript received 8 Jul 79
[Article by M.A. Vorontsov and V.I. Shmaltgauzen, Moscow State Uni~ersity
imeni M.V. Lomonosov] -
[Text] A method is proposed to increase the operational
efficiency of an adaptive focusing system f4r light beams,
which propagate in an inhomogeneoua nonlinear medium. A
case uf practical importance is considered, where the size
of the target exceeds the size of diffraction limited light
spot. The results of a numerical experiment are given,
which provide evidence for the efficiency of the method. -
Introduction
Adaptive optical systems in existence at the present time take the form of
closed systems for the control of the phase front of light beamso The pur-
pose of such control is the optimization of the system characteristics in
presence of random external perturbations. Phase control is realized :tn
transmitting systems of coherent optical adaptive technology (KOAT) to in-�
crease the light wave power density incident on an ob~ect, and in KOAT re-
ceiving systems to achieve the greatest angular res~lution when observing
through a turbulent atmosphere, -
Two main classes can be ascertained among KOAT systems: phase tracked and
aperture probe types [1]. The phase tracktng systems are basQd on the use
: of the principle of invertibility, in accordance with which the phase dis-
_ tortions arising during the propagation of a light beam t:o an ab~ECt can be
compensat~ed by in~roducing a certain pre,listortion of the pha~:e into the
i.nitial phase profile of the transmitted wave, where tnis p~~edistortion is
obtained by tracking the phase of the waL�e propagating ~n tY~e opposite di-
rection. The principle of phase invertibil~ty is employed only for a linear
m~dium; rinder nonlinear medium conditions, 3t is preferable to utilize the
ai~zrture probe method.
In this method, the focusing criterion is ':he power of the light wave scat-�
texed by the ob~ect within the bounda of the receiving aperture (the
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1 V~\ VL L aV+~~L~ vvu a.~~ua
definition functional). It is assumed in this case that maximizing the defi-
nition functional in the receiving aperture of the ob~ect [2J. This is ~us-
tified only in the case where the reflecting surface of the ob~ect has a
hri~htly pronounced eingle shining apot, the area of which is leas than the
dir~meter of the incident beam [3].
A system which maximizes the definition functional has little effect if
there are many highlights on the surface of the ob~ect which are similar
in intensity or if the reflecting surface is homogeneously rough. Motion
ox rotation of the ob~ect likewise leads to a degredation of the converg-
ence and random fluctuations in Che criterion [4]. i-
Interferometric criteria for radiation focusing, which can be used in
KOAT systems are proposed 3n this paper. These criteria utilize informa-
tion on both the phase and the amplitude of the scattered wave, and can
be interpreted as a measure of the identicalness of the transmitted and
scattered fields. The comparative analysis of the well known algorithm
for the maximization of the definition functional and the interference
algorithm performed here provides evidence of the efficiency of the utili-
zation of the latter when KOAT systems work with ob~ects having uniform ~
surface roughness, i.e., in those cases where the maximization of the
definition functional does not provide for efficient focusing of the _
radiation.
1. A Mathematical Model of an Optical System with Feedback i-
~
We shall consider an optical system with feedback which transmits the ~
light wave energy over a certain distance zp in a homogeneous nonlinear
medium. Let the transmitting aperture of the system produce a light beam, '
limited in space and time, with an initial distribution of the complex
amplitude of the electrical field of: _
E(r, 0~ ~=Eo(r)e~"