**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** |