Principles of plasma electrodynamics

Rukhadze/Alexandrov/Bogdankevich

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Principles of plasma electrodynamics

Rukhadze/Alexandrov/Bogdankevich

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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 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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Índice

Part I. Electromagnetic Properties of a Plasma in Thermodynamic Equilibrium 1. Basic Concepts of Plasma Physics 1.1 Definition of a Plasma 1.1.1 Plasmas in Nature 1.2 Plasma Parameters 1.2.1 Plasmas in Thermodynamic Equilibrium and Quasiequilibrium. The Maxwell and Fermi Distribution Functions 1.2.2 Characteristic Values of Plasma Parameters 1.3 Quasi-Neutrality, Plasma Frequency and Debye Length 1.4 Gas Approximation and Plasma Parameter 1.5 Exercises 2. Principles of Eletrodynamics of Media with Dispersion in Space and Time 2.1 Equations of the Electromagnetic Field in the Medium and Boundary Conditions 2.1.1 Material Equations of Linear Electrodynamics 2.1.2 Derivation of Boundary Conditions 2.2 Tensor of Complex Conductivity and Dielectric Permittivity 2.2.1 Dispersion in Time and Space 2.2.2 The Case of the Isotropic Medium 2.2.3 The Kramers-Kronig Formulas 2.3 Energy of the Electromagnetic Field in the Medium 2.3.1 The Dispersion of the Dielectric Permittivity Tensor 2.3.2 Average Force Affecting the Plasma in the Inhomogeneous High-Frequency Field 2.4 Electromagnetic Waves in the Medium 2.4.1 The Case of the Isotropic Medium 2.4.2 Longitudinal Waves in an Anisotropic Medium 2.5 Initial Value Problem 2.6 Boundary Value Problem 2.6.1 The Phase and Group Velocities of Waves 2.6.2 Correlation Between the Initial and Boundary Value Problems 2.7 Electro- and Magnetostatics 2.8 Exercises 3. Equations of Plasma Dynamics 3.1 Simplest Plasma Models 3.1.1 The Model of Indepedent Particles 3.1.2 The Íódrodynamic Model 3.2 Kinetic Equation with a Self-Consistent Field 3.3 Boltzmann Kinetic Equation 3.3.1 The Fokker-Planck Equation 3.4 Collision Integral of Charged Particles 3.4.1 The Case of the Degenerate Plasma 3.5 Model Integral for Elastic Particle Collisions 3.5.1 The Case of the Degenerate Plasma 3.6 Discussion of the Simplest Plasma Models 3.6.1 Two-Fluid Hydrodynamics of a Cold Collisionless Plasma 3.6.2 One-Fluid Hydrodynamics of the Nonisothermal Plasma 3.6.3 The Íódrodynamic Description of a Degenerate Plasma 3.7 Exercises 4. Dielectric Permittivity and Oscillation Spectra of Unmagnetized Plasmas 4.1 Dielectric Permittivity of a Collisionless Homogeneous Isotropic Plasma 4.1.1 Cherenkov Absorption and Radiation Emission of Waves 4.1.2 The Longitudinal and Transverse Dielectric Permittivities of an Isotropic Plasma 4.1.3 The Dielectric Permittivity of a Degenerate Plasma 4.2 Longitudinal Oscillations of a Collisionless Nondegenerate Plasma 4.2.1 High-Frequency Plasma Waves 4.2.2 Landau Damping 4.2.3 Ion-Acoustic Waves in a Nonisothermal Plasma 4.2.4 The Low-Frequency Range, Debye Screening 4.3 Longitudinal Oscillations in the Collisionless Degenerate Plasma 4.3.1 High-Frequency Plasma Waves and Zero-Point Sound 4.3.2 Ion-Acoustic Waves in Degenerate Plasma 4.3.3 Debye Screening in Degenerate Plasma 4.4 Transverse Waves in Collisionless Isotropic Plasmas 4.4.1 Transverse Electromagnetic Waves 4.4.2 The Anomalous Skin-Effect 4.5 Dielectric Permittivity and Oscillation Spectra of Weakly Ionized Plasmas with Account of Particle Collisions 4.5.1 Collisional Damping of Longitudinal Waves 4.5.2 Damping of Transverse Waves 4.5.3 Degenerate Plasma 4.6 Dielectric Permittivity and Oscillation Spectra of Fully Ionized Plasmas Taking Account of Particle Collisions 4.6.1 Damping of Longitudinal High-Frequency Waves 4.6.2 Collisional Damping of Ion-Acoustic Waves 4.6.3 Damping of Transverse Waves 4.6.4 Degenerate Plasma 4.7 Exercises 5. Dielectric Permittivity and Oscillation Spectra of Homogeneous Magneto-Active Plasmas 5.1 Dielectric Tensor of the Homogeneous Collisionless Magneto-Active Plasma 5.1.1 Dielectric Tensor of the Quasi-Equilibrium Maxwellian Plasma 5.1.2 Dielectric Tensor of the Degenerate Plasma 5.2 Dielectric Permittivity and Oscillation Spectra of the Cold Collisionless Magneto-Active Plasma 5.2.1 Wave Propagation Along the Magnetic Field 5.2.2 Wave Propagation Across the Magnetic Field 5.2.3 An Arbitrary Direction of Wave Propagation 5.2.4 Longitudinal Oscillations of the Magneto-Active Plasma 5.3 Oscillations in Collisionless Magneto-Active Plasmas Taking Account of Thermal Effects 5.3.1 Collisionless Damping of Waves in the MagnetoActive Plasma 5.3.2 Spectra of Low-Frequency Slow Waves 5.3.3 Degenerate Plasma 5.4 Cyclotron Waves 5.4.1 Cyclotron Waves in the Nondegenerate Plasma . 5.4.2 Cyclotron Waves in the Degenerate Plasma 5.5 Dielectric Tensor of Weakly Ionized Magneto-Active Plasmas Taking Account of Particle Collisions 5.5.1 Dielectric Tensor of the Quasi-Equilibrium Maxwellian Plasma 5.5.2 Degenerate Plasma 5.6 Dielectric Tensor of Completely Ionized Magneto-Active Plasmas Taking Account of Particle Collisions 5.6.1 The High-Frequency Range 5.6.2 The Range of Slow Waves 5.6.3 Degenerate Plasma 5.7 Electromagnetic Waves in Magneto-Active Plasmas Taking Account of Particle Collisions 5.7.1 Damping of Waves in the Cold Magneto-Active Plasma 5.7.2 Collisional Damping of Low-Frequency Waves in the Hot Magneto-Active Plasma 5.8 Exercises Part II. Electromagnetic Properties of Nonequilibrium Plasmas 6 Interaction of Charged Beams with the Plasma 6.1 Dielectric Tensor of the Homogeneous Anisotropic Nonequilibrium Plasma 6.1.1 The Lorentz Transform of the Dielectric Tensor . 6.2 Instability of the Plasma with Anisotropic Temperature of the Particle Components 6.2.1 Plasma Instability with Anisotropic Temperature in the Absence of Magnetic Field 6.2.2 Instability of the Magneto-Active Plasma with Anisotropic Temperature 6.3 Interaction of a Straight Electron Beam with the Plasma. The Cherenkov Instability 6.3.1 Interaction of a Straight Electron Beam with Cold Isotropic Plasma 6.3.2 Cherenkov Instability of the Electron Beam in the Cold Magneto-Active Plasma 6.3.3 The Resonance Cherenkov Amplification of Waves 6.3.4 The Effect of Thermal Motion on the Cherenkov Instability of the Electron Beam 6.4 Interaction of a Rotating Electron Beam (Beam of Oscillators) with the Plasma. Cyclotron Instability 6.4.1 Conditions for Resonance Cyclotron Interaction of a Rotating Beam with Electromagnetic Waves in the Plasma 6.4.2 Convective and Absolute Cyclotron Instabilities 6.4.3 Screening of the Cyclotron Radiation in the Plasma 6.5 Exercises 7. Plasmas in an External Homogeneous Electric Field 7.1 The Distribution Function of the Charged Particles in an External Electric Field 7.1.1 Plasmas in a Strong Constant Electric Field 7.1.2 Runaway Electrons 7.1.3 The Stationary Distribution Function of Electrons in a Weak Constant Electric Field 7.1.4 Plasma in a High-Frequency Electric Field 7.2 Stability of the Nonmagnetized Plasma in an External Constant Electric Field 7.2.1 Buneman Instability of Nonmagnetized Plasma in Strong Electric Field 7.2.2 Ion-Acoustic Instability of Plasma with a Current 7.2.3 The Critical Velocity 7.2.4 The Effect of Collisions on the Development of Instabilities 7.2.5 The Case of the Degenerate Plasma 7.3 Stability of the Magnetized Plasma in an External Constant Electric Field 7.3.1 The Buneman Instability of the Magneto-Active Plasma 7.3.2 The Ion-Acoustic Instability of Plasma with a Current in a Magnetic Field 7.3.3 Effect of Collisions on the Development of Instabilities 7.3.4 The Case of Degenerate Plasma 7.4 The Plasma in a Superhigh-Frequency Electric Field 7.4.1 The Dispersion Equation for Oscillations in the Plasma in a SHF Field 7.4.2 High-Frequency Electro-Acoustic Oscillations . 7.4.3 Ion Acoustic Oscillations of the Plasma in a SHF Field 7.4.4 Spectra of Oscillations of the Magneto-Active Plasma in a SHF Field 7.4.5 Oscillations of the Degenerate Plasma in a SHF Field 7.5 Paramagnetic Interaction of SHF Electric Fields with a Plasma 7.5.1 Resonant Parametric Excitation of the High-Frequency Longitudinal Oscillations of the Plasma by SHF Fields 7.5.2 The Effect of a Magnetic Field on the Development of the Parametric Instability of the Plasma in a SHF Field 7.5.3 The Ion-Acoustic Parametric Instability of the Nonisothermal Plasma 7.5.4 The Effect of the Magnetic Field on the Development of the Low-Frequency Parametric Instabilities 7.5.5 The Case of the Degenerate Plasma 7.6 Plasma Parametric Instability with Respect to Nonpotential Perturbations 7.7 Exercises 8. Electromagnetic Properties of Inhomogeneous Plasmas 8.1 Inhomogeneous Media Without Spatial Dispersion. Approximation of Geometrical Optics 8.1.1 Field Equations for an Inhomogeneous Medium Without Spatial Dispersion 8.1.2 The Method of Geometrical Optics and the WKB Method 8.1.3 The Bohr-Sommerfeld Quasiclassical Quantization Rules 8.2 Approximation of Geometrical Optics for Inhomogeneous Media with Spatial Dispersion 8.2.1 Eikonal Equation for an Inhomogeneous Medium with Spatial Dispersion 8.2.2 Quantization Rules 8.3 Dielectric Tensor of Weakly Inhomogenous Plasmas in the Approximation of Geometrical Optics 8.3.1 Distribution Function for the Equilibrium Inhomogeneous Plasma 8.3.2 Magnetic Confinement of the Inhomogeneous Plasma 8.3.3 The Dielectric Tensor of Weakly Inhomogeneous Plasma 8.3.4 The Larmor Drift Frequency 8.3.5 The Case of the Degenerate Plasma 8.4 Spectra of HF-Oscillations in Weakly Inhomogeneous Plasma 8.4.1 Transverse Oscillations of Weakly Inhomogeneous Isotropic Plasma 8.4.2 The Langmuir Oscillations. The Tonks-Dattner Resonances 8.4.3 Ion-Acoustic Oscillations of the Inhomogeneous Isotropic Plasma 8.4.4 The Case of the Degenerate Isotropic Plasma 8.4.5 Oscillations of the Weakly Inhomogeneous MagnetoActive Plasma 8.5 Drift Oscillations of a Weakly Inhomogeneous Collisionless Plasma 8.5.1 Larmor Drift in the Inhomogeneous Plasma 8.5.2 The Dispersion Equation for Drift Oscillations . 8.5.3 Spectra of the Fast Long-Wavelength Drift Oscillations 8.5.4 Universal Instability of the Inhomogeneous Plasma 8.5.5 Spectra of the Slow Long-Wavelength Drift Oscillations 8.5.6 The Drift-Dissipative and Drift-Temperature Instabilities 8.6 Influence of Charged Particle Collisions on the Spectra of Drift Oscillations in Weakly Inhomogeneous Plasmas 8.6.1 Weakly Ionized Plasma 8.6.2 Completely Ionized Plasma 8.6.3 Spectra of the Íódrodynamic Drift-Dissipative Oscillations 8.6.4 The Effect of Ion Collisions on the Development of Drift Oscillations 8.7 Convective Instabilities of the Inhomogeneous Plasma . 8.7.1 Inhomogeneous Plasma in a Curvilinear Magnetic Field 8.7.2 The Gravitational Drift of Plasma Particles 8.7.3 Dielectric Permittivity of the Inhomogeneous Plasma in a Curvilinear Magnetic Field 8.7.4 The Flute (Interchange) Instability 8.7.5 The Current-Convective Instability 8.7.6 The Effect of Particle Collisions on Convective Instabilities of the Plasma 8.8 Exercises 9. Linear Electromagnetic Phenomena in Bounded Plasmas 9.1 Surface Electromagnetic Waves in Semi-Bounded Plasmas 9.1.1 Solution of the Vlasov Equation for the SemiBounded Isotropic Plasma 9.1.2 Solution of Field Equations 9.1.3 Surface Impedance 9.1.4 Dispersion Equation for Surface Waves 9.1.5 Surface Waves in Cold Semi-Bounded Plasma 9.1.6 Cherenkov Damping of Surface Waves 9.1.7 Surface Ion-Acoustic Waves 9.2 Instability of the Boundary of Magnetically Confined Plasma 9.2.1 Poisson's Equation for the Magnetically Confined Inhomogeneous Plasma 9.2.2 Surface Oscillations of the Cold Magneto-Active Plasma with a Sharp Boundary 9.2.3 Instability of the Surface of the Magnetically Confined Plasma 9.3 Plasma Waveguide 9.3.1 Field Equation for the Cylindrical Plasma Waveguide 9.3.2 Spectrum of Oscillations of the Isotropic Plasma Waveguide 9.3.3. Spectrum of Oscillations of the Magnetized Plasma Waveguide 9.4 Stability of Spatially Bounded Nonequilibrium Plasma . 9.4.1 Buneman Instability in the Plasma Waveguide . 9.4.2 Pierce Instability of the Plasma with a Current in Longitudinally Bounded Systems 9.4.3 Ion-Acoustic Instability of the Bounded Plasma with a Current 9.5 Excitation of a Plasma Resonator by Relativistic Electron Beam 9.5.1 Cherenkov Wave Excitation 9.5.2 Cyclotron Wave Excitation 9.6 Exercises Part III. Principles of Nonlinear Electrodynamics of Plasma 10. Electromagnetic Fluctuations in Plasma and Wave Scattering . 10.1 Correlation Functions of the System of Charged Particles. General Analysis 10.1.1 Fluctuations of Charge und Current Densities in the System of Noninteracting Particles 10.1.2 Plasma Fluctuations in the First-Order Approximation of Interparticle Interactions 10.2 Fluctuations in Equilibrium Plasma. Fluctuation-Dissipation Theorem 10.2.1 Fluctuation-Dissipation Theorem for the Thermodynamically Equilibrium Isotropic Plasma 10.2.2 The Case of the Anisotropic Plasma 10.3 Spectra Distribution of Fluctuations in Equilibrium Collisionless Plasma 10.3.1 Fluctuations of Charge Densities and Longitudinal Electric Field 10.3.2 Fluctuations in the Degenerate Electron Plasma . 10.3.3 Fluctuations in the Equilibrium Magneto-Active Plasma 10.4 Fluctuations in Nonequilibrium Plasmas. Nonisothermal Plasma and Plasma with a Beam 10.4.1 Fluctuations in the Quasi-Equilibrium Nonisothermal Plasma 10.4.2 Fluctuations in the Plasma with an Electron Beam 10.5 Fluctuations and Interparticle Collisions in Plasma 10.5.1 Fokker-Planck Equation 10.5.2 Correlation Coefficients of the Dynamic Friction and Diffusion with Plasma Fluctuation Fields 10.6 Scattering of Electromagnetic Waves in a Plasma 10.6.1 Differential Cross Section of Scattering of Transverse Electromagnetic Waves in the Nonisothermal Plasma 10.6.2 Effect of Collisions on Scattering 10.7 Wave Transformation in Plasmas 10.7.1 Transformation of Transverse into Longitudinal Wave in an Isotropic Plasma 10.7.2 Transformation of Longitudinal into Transverse Wave 10.8 Exercises 11. Principles of the Quasilinear Theory of Plasma Oscillations 11.1 Basic Equations 11.1.1 Quasilinear Equations for the Isotropic Plasma . 11.1.2 Conservation Laws of the Quasilinear Theory 11.1.3 Quasilinear Equations for Magnetized Plasma 11.2 Quasilinear Relaxation of Plasma Oscillations 11.2.1 Relaxation of the Distribution Function 11.2.2 Plateau Creation 11.2.3 Time of Quasilinear Relaxation 11.3 Quasilinear Relaxation of the Beam Instability 11.3.1 Quasilinear Dynamics of the Hydrodynamical Beam Instability 11.3.2 Relaxation of the Beam in the Kinetic Stage 11.4 Exercises 12. Nonlinear Interaction of Waves in a Plasma 12.1 Principles of Nonlinear Electrodynamics of Material Media 12.1.1 Multi-Index Dielectric Tensors 12.1.2 Averaged Equation of Nonlinear Electrodynamics 12.1.3 Shortened Equation for Waves with Chaotic Phases 12.2 Multi-Index Dielectric Tensors of Homogeneous Plasmas 12.2.1 Solution of the Vlasov Equation 12.2.2 Three- and Four-Index Tensors of the Isotropic Plasma 12.2.3 Nonlinear Solution of the Vlasov Equation for the Magneto-Active Plasma 12.2.4 Three- and Four-Index Tensors of the MagnetoActive Plasma 12.3 Nonlinear Interaction of Waves in Isotropic Plasmas 12.3.1 Induced Scattering of Plasma Waves in the Isotropic Plasma 12.3.2 Nonlinear Coalescence of Plasma Waves 12.3.3 Electromagnetic Scattering of Plasma Waves 12.4 Nonlinear Three-Wave Interaction in a Plasma in the Field of Strong Electromagnetic Waves 12.4.1 Equilibrium Distribution Function in the Field of Strong Electromagnetic Waves 12.4.2 Dispersion Equation for Small Oscillations 12.4.3 Induced Raman Scattering of Electromagnetic Waves in the Isotropic Plasma 12.4.4 Mandelstam-Brillouin Scattering in the Nonisothermal Plasma 12.5 Exercises Appendix A. The Main Operators of Field Theory in Orthogonal Curvilinear Coordinate System Appendix B. Elements of Tensor Calculus References Subject Index

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Principles of plasma electrodynamics

Rukhadze/Alexandrov/Bogdankevich

Principles of plasma electrodynamics

Rukhadze/Alexandrov/Bogdankevich

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