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Cover Rukhadze A.A., Alexandrov A.F., Bogdankevich L.S. Principles of Plasma Electrodynamics

Id: 166939

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Rukhadze A.A., Alexandrov A.F., Bogdankevich L.S. Principles of Plasma Electrodynamics Ed.2

URSS. 504 pp. (English). ISBN 978-5-396-00482-5.

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Summary

Principles of Plasma Electrodynamics deals with plasmas and plasmalike media. The text is divided into three parts. The first part treats the linear electrodynamics of homogeneous plasma in equilibrium; the second is dedicated to linear electrodynamics of a spatially inhomogeneous non-equilibrium plasma, i. e., the theory of plasma instability. Finally, the principles of nonlinear plasma electrodynamics are outlined. The textbook contains a large number ...(More)of exercises with solutions.

This textbook is based on the course of lectures that was given by professor A.A. Rukhadze for the students of the department of physical electronics of Lomonosov MSU during the 1966–2006 years.

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Physics > Plasma Physics. Electronic and Ionic Phenomena ; Electrodynamics, Special Theory of Relativity

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Preface				XIV
Part I Electromagnetic Properties of a Plasma in Thermodynamic Equilibrium				3
1. Basic Concepts of Plasma Physics				3
1.1 Definition of a Plasma				3
1.1.1 Plasmas in Nature				4
1.2 Plasma Parameters				4
1.2.1 Plasmas in Thermodynamic Equilibrium and Quasi-equilibrium. The Maxwell and Fermi Distribution Functions				5
1.2.2 Characteristic Values of Plasma Parameters				7
1.3 Quasi-Neutrality, Plasma Frequency and Debye Length				7
1.4 Gas Approximation and Plasma Parameter				9
1.5 Exercises				10
2. Principles of Eletrodynamics of Media with Dispersion in Space and Time				15
2.1 Equations of the Electromagnetic Field in the Medium and Boundary Conditions				15
2.1.1 Material Equations of Linear Electrodynamics				17
2.1.2 Derivation of Boundary Conditions				17
2.2 Tensor of Complex Conductivity and Dielectric Permittivity				18
2.2.1 Dispersion in Time and Space				19
2.2.2 The Case of the Isotropic Medium				20
2.2.3 The Kramers-Kronig Formulas				21
2.3 Energy of the Electromagnetic Field in the Medium				22
2.3.1 The Dispersion of the Dielectric Permittivity Tensor				24
2.3.2 Average Force Affecting the Plasma in the In-homogeneous High-Frequency Field				26
2.4 Electromagnetic Waves in the Medium				27
2.4.1 The Case of the Isotropic Medium				28
2.4.2 Longitudinal Waves in an Anisotropic Medium				28
2.5 Initial Value Problem				30
2.6 Boundary Value Problem				32
2.6.1 The Phase and Group Velocities of Waves				33
2.6.2 Correlation Between the Initial and Boundary Value Problems				33
2.7 Electro-and Magnetostatics				35
2.8 Exercises				37
3. Equations of Plasma Dynamics				46
3.1 Simplest Plasma Models				46
3.1.1 The Model of Indepedent Particles				46
3.1.2 The Нуdrodynamic Model				47
3.2 Kinetic Equation with a Self-Consistent Field				49
3.3 Boltzmann Kinetic Equation				50
3.3.1 The Fokker-Planck Equation				53
3.4 Collision Integral of Charged Particles				54
3.4.1 The Case of the Degenerate Plasma				56
3.5 Model Integral for Elastic Particle Collisions				57
3.5.1 The Case of the Degenerate Plasma				59
3.6 Discussion of the Simplest Plasma Models				60
3.6.1 Two-Fluid Hydrodynamics of a Cold Collisionless Plasma				61
3.6.2 One-Fluid Hydrodynamics of the Nonisothermal Plasma				62
3.6.3 The Hydrodynamic Description of a Degenerate Plasma				65
3.7 Exercises				66
4. Dielectric Permittivity and Oscillation Spectra of Unmagnetized Plasmas				75
4.1 Dielectric Permittivity of a Collisionless Homogeneous Isotropic Plasma				75
4.1.1 Cherenkov Absorption and Radiation Emission of Waves				77
4.1.2 The Longitudinal and Transverse Dielectric Permittivities of an Isotropic Plasma				79
4.1.3 The Dielectric Permittivity of a Degenerate Plasma				80
4.2 Longitudinal Oscillations of a Collisionless Nondegenerate Plasma				81
4.2.1 High-Frequency Plasma Waves				81
4.2.2 Landau Damping				82
4.2.3 Ion-Acoustic Waves in a Nonisothermal Plasma				83
4.2.4 The Low-Frequency Range, Debye Screening				85
4.3 Longitudinal Oscillations in the Collisionless Degenerate Plasma				85
4.3.1 High-Frequency Plasma Waves and Zero-Point Sound				85
4.3.2 Ion-Acoustic Waves in Degenerate Plasma				87
4.3.3 Debye Screening in Degenerate Plasma				87
4.4 Transverse Waves in Collisionless Isotropic Plasmas				88
4.4.1 Transverse Electromagnetic Waves				88
4.4.2 The Anomalous Skin-Effect				89
4.5 Dielectric Permittivity and Oscillation Spectra of Weakly Ionized Plasmas with Account of Particle Collisions				90
4.5.1 Collisional Damping of Longitudinal Waves				92
4.5.2 Damping of Transverse Waves				94
4.5.3 Degenerate Plasma				94
4.6 Dielectric Permittivity and Oscillation Spectra of Fully Ionized Plasmas Taking Account of Particle Collisions				95
4.6.1 Damping of Longitudinal High-Frequency Waves				97
4.6.2 Collisional Damping of Ion-Acoustic Waves				98
4.6.3 Damping of Transverse Waves				98
4.6.4 Degenerate Plasma				98
4.7 Exercises				99
5. Dielectric Permittivity and Oscillation Spectra of Homogeneous Magneto-Active Plasmas				110
5.1 Dielectric Tensor of the Homogeneous Collisionless Magneto-Active Plasma				110
5.1.1 Dielectric Tensor of the Quasi-Equilibrium Max-wellian Plasma				113
5.1.2 Dielectric Tensor of the Degenerate Plasma				114
5.2 Dielectric Permittivity and Oscillation Spectra of the Cold Collisionless Magneto-Active Plasma				115
5.2.1 Wave Propagation Along the Magnetic Field				116
5.2.2 Wave Propagation Across the Magnetic Field				118
5.2.3 An Arbitrary Direction of Wave Propagation				120
5.2.4 Longitudinal Oscillations of the Magneto-Active Plasma				120
5.3 Oscillations in Collisionless Magneto-Active Plasmas Taking Account of Thermal Effects				122
5.3.1 Collisionless Damping of Waves in the Magneto-Active Plasma				123
5.3.2 Spectra of Low-Frequency Slow Waves				125
5.3.3 Degenerate Plasma				127
5.4 Cyclotron Waves				128
5.4.1 Cyclotron Waves in the Nondegenerate Plasma				129
5.4.2 Cyclotron Waves in the Degenerate Plasma				130
5.5 Dielectric Tensor of Weakly Ionized Magneto-Active Plasmas Taking Account of Particle Collisions				131
5.5.1 Dielectric Tensor of the Quasi-Equilibrium Max-wellian Plasma				132
5.5.2 Degenerate Plasma				133
5.6 Dielectric Tensor of Completely Ionized Magneto-Active Plasmas Taking Account of Particle Collisions				135
5.6.1 The High-Frequency Range				135
5.6.2 The Range of Slow Waves				137
5.6.3 Degenerate Plasma				137
5.7 Electromagnetic Waves in Magneto-Active Plasmas Taking Account of Particle Collisions				138
5.7.1 Damping of Waves in the Cold Magneto-Active Plasma				138
5.7.2 Collisional Damping of Low-Frequency Waves in the Hot Magneto-Active Plasma				140
5.8 Exercises				141
Part II Electromagnetic Properties of Nonequilibrium Plasmas				155
6. Interaction of Charged Beams with the Plasma				155
6.1 Dielectric Tensor of the Homogeneous Anisotropic Non-equilibrium Plasma				155
6.1.1 The Lorentz Transform of the Dielectric Tensor				158
6.2 Instability of the Plasma with Anisotropic Temperature of the Particle Components				160
6.2.1 Plasma Instability with Anisotropic Temperature in the Absence of Magnetic Field				162
6.2.2 Instability of the Magneto-Active Plasma with Anisotropic Temperature				165
6.3 Interaction of a Straight Electron Beam with the Plasma. The Cherenkov Instability				167
6.3.1 Interaction of a Straight Electron Beam with Cold Isotropic Plasma				168
6.3.2 Cherenkov Instability of the Electron Beam in the Cold Magneto-Active Plasma				170
6.3.3 The Resonance Cherenkov Amplification of Waves				172
6.3.4 The Effect of Thermal Motion on the Cherenkov Instability of the Electron Beam				173
6.4 Interaction of a Rotating Electron Beam (Beam of Oscillators) with the Plasma. Cyclotron Instability				175
6.4.1 Conditions for Resonance Cyclotron Interaction of a Rotating Beam with Electromagnetic Waves in the Plasma				177
6.4.2 Convective and Absolute Cyclotron Instabilities				180
6.4.3 Screening of the Cyclotron Radiation in the Plasma				181
6.5 Exercises				181
7. Plasmas in an External Homogeneous Electric Field				195
7.1 The Distribution Function of the Charged Particles in an External Electric Field				195
7.1.1 Plasmas in a Strong Constant Electric Field				195
7.1.2 Runaway Electrons				196
7.1.3 The Stationary Distribution Function of Electrons in a Weak Constant Electric Field				197
7.1.4 Plasma in a High-Frequency Electric Field				199
7.2 Stability of the Nonmagnetized Plasma in an External Constant Electric Field				200
7.2.1 Buneman Instability of Nonmagnetized Plasma in Strong Electric Field				201
7.2.2 Ion-Acoustic Instability of Plasma with a Current				202
7.2.3 The Critical Velocity				203
7.2.4 The Effect of Collisions on the Development of Instabilities				204
7.2.5 The Case of the Degenerate Plasma				205
7.3 Stability of the Magnetized Plasma in an External Constant Electric Field				206
7.3.1 The Buneman Instability of the Magneto-Active Plasma				206
7.3.2 The Ion-Acoustic Instability of Plasma with a Current in a Magnetic Field				207
7.3.3 Effect of Collisions on the Development of Instabilities				209
7.3.4 The Case of Degenerate Plasma				209
7.4 The Plasma in a Superhigh-Frequency Electric Field				210
7.4.1 The Dispersion Equation for Oscillations in the Plasma in a SHF Field				213
7.4.2 High-Frequency Electro-Acoustic Oscillations				214
7.4.3 Ion Acoustic Oscillations of the Plasma in a SHF Field				215
7.4.4 Spectra of Oscillations of the Magneto-Active Plasma in a SHF Field				216
7.4.5 Oscillations of the Degenerate Plasma in a SHF Field				217
7.5 Paramagnetic Interaction of SHF Electric Fields with a Plasma				218
7.5.1 Resonant Parametric Excitation of the High-Frequency Longitudinal Oscillations of the Plasma by SHF Fields				219
7.5.2 The Effect of a Magnetic Field on the Development of the Parametric Instability of the Plasma in a SHF Field				221
7.5.3 The Ion-Acoustic Parametric Instability of the Nonisothermal Plasma				224
7.5.4 The Effect of the Magnetic Field on the Development of the Low-Frequency Parametric Instabilities				225
7.5.5 The Case of the Degenerate Plasma				225
7.6 Plasma Parametric Instability with Respect to Nonpotential Perturbations				226
7.7 Exercises				228
8. Electromagnetic Properties of Inhomogeneous Plasmas				243
8.1 Inhomogeneous Media Without Spatial Dispersion. Approximation of Geometrical Optics				243
8.1.1 Field Equations for an Inhomogeneous Medium Without Spatial Dispersion				244
8.1.2 The Method of Geometrical Optics and the WKB Method				245
8.1.3 The Bohr-Sommerfeld Quasiclassical Quantization Rules				249
8.2 Approximation of Geometrical Optics for Inhomogeneous Media with Spatial Dispersion				251
8.2.1 Eikonal Equation for an Inhomogeneous Medium with Spatial Dispersion				252
8.2.2 Quantization Rules				253
8.3 Dielectric Tensor of Weakly Inhomogenous Plasmas in the Approximation of Geometrical Optics				254
8.3.1 Distribution Function for the Equilibrium Inhomogeneous Plasma				254
8.3.2 Magnetic Confinement of the Inhomogeneous Plasma				256
8.3.3 The Dielectric Tensor of Weakly Inhomogeneous Plasma				257
8.3.4 The Larmor Drift Frequency				259
8.3.5 The Case of the Degenerate Plasma				260
8.4 Spectra of HF-Oscillations in Weakly Inhomogeneous Plasma				261
8.4.1 Transverse Oscillations of Weakly Inhomogeneous Isotropic Plasma				261
8.4.2 The Langmuir Oscillations. The Tonks-Dattner Resonances				263
8.4.3 Ion-Acoustic Oscillations of the Inhomogeneous Isotropic Plasma				264
8.4.4 The Case of the Degenerate Isotropic Plasma				265
8.4.5 Oscillations of the Weakly Inhomogeneous Magneto-Active Plasma				266
8.5 Drift Oscillations of a Weakly Inhomogeneous Collisionless Plasma				268
8.5.1 Larmor Drift in the Inhomogeneous Plasma				269
8.5.2 The Dispersion Equation for Drift Oscillations				271
8.5.3 Spectra of the Fast Long-Wavelength Drift Oscillations				272
8.5.4 Universal Instability of the Inhomogeneous Plasma				273
8.5.5 Spectra of the Slow Long-Wavelength Drift Oscillations				273
8.5.6 The Drift-Dissipative and Drift-Temperature Instabilities				274
8.6 Influence of Charged Particle Collisions on the Spectra of Drift Oscillations in Weakly Inhomogeneous Plasmas				275
8.6.1 Weakly Ionized Plasma				275
8.6.2 Completely Ionized Plasma				278
8.6.3 Spectra of the Hydrodynamic Drift-Dissipative Oscillations				281
8.6.4 The Effect of Ion Collisions on the Development of Drift Oscillations				283
8.7 Convective Instabilities of the Inhomogeneous Plasma				285
8.7.1 Inhomogeneous Plasma in a Curvilinear Magnetic Field				286
8.7.2 The Gravitational Drift of Plasma Particles				287
8.7.3 Dielectric Permittivity of the Inhomogeneous Plasma in a Curvilinear Magnetic Field				288
8.7.4 The Flute (Interchange) Instability				289
8.7.5 The Current-Convective Instability				290
8.7.6 The Effect of Particle Collisions on Convective Instabilities of the Plasma				291
8.8 Exercises				292
9. Linear Electromagnetic Phenomena in Bounded Plasmas				302
9.1 Surface Electromagnetic Waves in Semi-Bounded Plasmas				302
9.1.1 Solution of the Vlasov Equation for the Semi-Bounded Isotropic Plasma				303
9.1.2 Solution of Field Equations				305
9.1.3 Surface Impedance				308
9.1.4 Dispersion Equation for Surface Waves				308
9.1.5 Surface Waves in Cold Semi-Bounded Plasma				309
9.1.6 Cherenkov Damping of Surface Waves				310
9.1.7 Surface Ion-Acoustic Waves				311
9.2 Instability of the Boundary of Magnetically Confined Plasma				313
9.2.1 Poisson's Equation for the Magnetically Confined Inhomogeneous Plasma				314
9.2.2 Surface Oscillations of the Cold Magneto-Active Plasma with a Sharp Boundary				316
9.2.3 Instability of the Surface of the Magnetically Confined Plasma				318
9.3 Plasma Waveguide				321
9.3.1 Field Equation for the Cylindrical Plasma Waveguide				323
9.3.2 Spectrum of Oscillations of the Isotropic Plasma Waveguide				324
9.3.3. Spectrum of Oscillations of the Magnetized Plasma Waveguide				327
9.4 Stability of Spatially Bounded Nonequilibrium Plasma				330
9.4.1 Buneman Instability in the Plasma Waveguide				330
9.4.2 Pierce Instability of the Plasma with a Current in Longitudinally Bounded Systems				332
9.4.3 Ion-Acoustic Instability of the Bounded Plasma with a Current				333
9.5 Excitation of a Plasma Resonator by Relativistic Electron Beam				334
9.5.1 Cherenkov Wave Excitation				334
9.5.2 Cyclotron Wave Excitation				339
9.6 Exercises				341
Part III Principles of Nonlinear Electrodynamics of Plasma				363
10. Electromagnetic Fluctuations in Plasma and Wave Scattering				363
10.1 Correlation Functions of the System of Charged Particles. General Analysis				363
10.1.1 Fluctuations of Charge und Current Densities in the System of Noninteracting Particles				366
10.1.2 Plasma Fluctuations in the First-Order Approximation of Interparticle Interactions				368
10.2 Fluctuations in Equilibrium Plasma. Fluctuation-Dissipation Theorem				370
10.2.1 Fluctuation-Dissipation Theorem for the Thermo-dynamically Equilibrium Isotropic Plasma				370
10.2.2 The Case of the Anisotropic Plasma				371
10.3 Spectra Distribution of Fluctuations in Equilibrium Collisionless Plasma				373
10.3.1 Fluctuations of Charge Densities and Longitudinal Electric Field				373
10.3.2 Fluctuations in the Degenerate Electron Plasma				377
10.3.3 Fluctuations in the Equilibrium Magneto-Active Plasma				378
10.4 Fluctuations in Nonequilibrium Plasmas. Nonisothermal Plasma and Plasma with a Beam				380
10.4.1 Fluctuations in the Quasi-Equilibrium Nonisothermal Plasma				381
10.4.2 Fluctuations in the Plasma with an Electron Beam				383
10.5 Fluctuations and Interparticle Collisions in Plasma				385
10.5.1 Fokker-Planck Equation				386
10.5.2 Correlation Coefficients of the Dynamic Friction and Diffusion with Plasma Fluctuation Fields				388
10.6 Scattering of Electromagnetic Waves in a Plasma				390
10.6.1 Differential Cross Section of Scattering of Transverse Electromagnetic Waves in the Nonisothermal Plasma				395
10.6.2 Effect of Collisions on Scattering				398
10.7 Wave Transformation in Plasmas				400
10.7.1 Transformation of Transverse into Longitudinal Wave in an Isotropic Plasma				400
10.7.2 Transformation of Longitudinal into Transverse Wave				401
10.8 Exercises				402
11. Principles of the Quasilinear Theory of Plasma Oscillations				408
11.1 Basic Equations				408
11.1.1 Quasilinear Equations for the Isotropic Plasma				409
11.1.2 Conservation Laws of the Quasilinear Theory				412
11.1.3 Quasilinear Equations for Magnetized Plasma				413
11.2 Quasilinear Relaxation of Plasma Oscillations				415
11.2.1 Relaxation of the Distribution Function				415
11.2.2 Plateau Creation				416
11.2.3 Time of Quasilinear Relaxation				418
11.3 Quasilinear Relaxation of the Beam Instability				419
11.3.1 Quasilinear Dynamics of the Hydrodynamical Beam Instability				420
11.3.2 Relaxation of the Beam in the Kinetic Stage				421
11.4 Exercises				424
12. Nonlinear Interaction of Waves in a Plasma				431
12.1 Principles of Nonlinear Electrodynamics of Material Media				431
12.1.1 Multi-Index Dielectric Tensors				432
12.1.2 Averaged Equation of Nonlinear Electrodynamics				433
12.1.3 Shortened Equation for Waves with Chaotic Phases				435
12.2 Multi-Index Dielectric Tensors of Homogeneous Plasmas				438
12.2.1 Solution of the Vlasov Equation				438
12.2.2 Three- and Four-Index Tensors of the Isotropic Plasma				440
12.2.3 Nonlinear Solution of the Vlasov Equation for the Magneto-Active Plasma				442
12.2.4 Three- and Four-Index Tensors of the Magneto-Active Plasma				444
12.3 Nonlinear Interaction of Waves in Isotropic Plasmas				445
12.3.1 Induced Scattering of Plasma Waves in the Isotropic Plasma				447
12.3.2 Nonlinear Coalescence of Plasma Waves				450
12.3.3 Electromagnetic Scattering of Plasma Waves				451
12.4 Nonlinear Three-Wave Interaction in a Plasma in the Field of Strong Electromagnetic Waves				452
12.4.1 Equilibrium Distribution Function in the Field of Strong Electromagnetic Waves				453
12.4.2 Dispersion Equation for Small Oscillations				454
12.4.3 Induced Raman Scattering of Electromagnetic Waves in the Isotropic Plasma				457
12.4.4 Mandelstam-Brillouin Scattering in the Nonisothermal Plasma				458
12.5 Exercises				459
Appendix A. The Main Operators of Field Theory in Orthogonal Curvilinear Coordinate System				467
A. l Exercises				469
Appendix B. Elements of Tensor Calculus				470
B. l Exercises				476
References				479
Subject Index				485

About the Authors

Rukhadze Anri Amvros’evich

Professor of Lomonosov Moscow State University, Principal Researcher of the Prokhorov Institute of General Physics of the Russian Academy of Sciences He is an eminent theoretical physicist and specialist in plasma physics. A. A. Rukhadze was awarded twice the USSR State Prize; also, has obtained the First-Degree Lomonosov Prize, the Order of the Badge of Honour and the Order of the Red Banner of Labour, as well as the title of Honored Scientist of the Russian Federation. He is an academician of the National Academy of Sciences of Georgia, the Russian Academy of Natural Sciences and the Prokhorov Engineering Academy. Also, he is a Honoris Causa Doctor of both the University of Sofia (Bulgaria) and the Bogolubov Institute of Theoretical Physics (Ukraine). His professional activity is indissolubly connected with the electrodynamics of media, plasma physics and plasma relativistic electronics. A. A. Rukhadze is the author of more than 600 scientific works, including 60 reviews and 16 monographs. He is the founder of a world-famous school on relativistic microwave electronics, which has brought up 68 Candidates of Sciences and 32 Doctors of Sciences.

Aleksandrov Andrey Fedorovich

Professor of Lomonosov Moscow State University, head of the physical electronics chair, head of the radiophysics and electronics branch of the Physics Department, Honored Professor of Lomonosov Moscow State University, Academician of the Russian Academy of Natural Sciences. He was awarded the Lomonosov Prize (1989, 1997) and the USSR State Prize (1981, 1991). Areas of scientific interest: plasma physics, relativistic microwave electronics, physical electronics. His researches deal with the physical bases of thin film production, and film structures for tasks of micro- and nanoelectronics, materials science and medicine. His team has created hydrocarbon carbonlike covers for medical implants possessing a unique biocompatibility and thrombus resistance, microporous carbon adsorbents, and others. He has assisted 26 Candidates of Sciences and 6 Doctors of Sciences. He is the author of more than 250 scientific papers and works, 10 monographs and scientific textbooks, including «Principles of Plasma Electrodynamics» (Springer Verlag, Berlin, 1984).

Bogdankevich Larisa Semeonovna

Senior Researcher of the Prokhorov Institute of General Physics of the Russian Academy of Sciences. She was an outstanding scientist in plasma physics and plasma relativistic electronics. She was awarded the USSR State Prize. Her professional activity was dedicated to the plasma physics and plasma electronics. L. S. Bogdankevich published more than 100 scientific works, including 5 reviews and 3 monographs.

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