Plasma Instabilities and Nonlinear Effects

1. Introduction to Plasma Instabilities.- 1.1 Introduction.- 1.2 Basic Equations.- 1.3 Dispersion Relations.- 1.4 Analysis of Instability.- References for Chapter 1.- 2. Microinstabilities-Instabilities Due to Velocity Space Nonequilibrium.- 2.1 Introduction.- 2.2 Instabilities Due to Two Humped Velocity Distributions..- 2.2a Electrostatic Instabilities.- 2.2b Electromagnetic Instabilities.- 2.2c Effect of Magnetic Mirror.- 2.2d Application to the Field Aligned Current-Anomalous Resistivity.- 2.3 Instabilities Due to Anisotropic Velocity Distributions.- 2.3a Electrostatic Instabilities.- 2.3b Electromagnetic Instabilities.- 2.3c Effect of Nonuniformity on Anisotropic Distributions.- 2.3d Quasi-Linear Diffusion in Velocity Space.- 2.4 Hydromagnetic Instabilities.- 2.4a Introduction.- 2.4b Mirror Instability.- 2.4c.- 2.5 Instabilities in Partially Ionized Plasmas.- 2.5a Introduction.- 2.5b General Properties of Instabilities.- 2.5c Application to Ionospheric Plasma Instabilities.- References for Chapter 2.- 3. Macroinstabilities-Instabilities Due to Coordinate Space Nonequilibrium.- 3.1 Introduction.- 3.2 Drift Wave Instabilities.- 3.2a Low ? Case.- 3.2b Medium ? Case.- 3.2c High ? Case.- 3.2d Notes on the Application of Drift Wave Instabilities.- 3.3 Rayleigh-Taylor Instability.- 3.4 Kelvin-Helmholtz Instability.- 3.4a Hydromagnetic Instability.- 3.4b Electrostatic Instability.- 3.5 Current Pinch Instabilities.- 3.5a Instability of Cylindrical Current with Infinite Conductivity.- 3.5b Instability of a Current with Finite Resistivity: Tearing Mode Instability.- References for Chapter 3.- 4. Nonlinear Effects Associated with Plasma Instabilities.- 4.1a Introduction.- 4.1b Methods of Approach.- 4.2 Nonlinear Effects on Particles.- 4.2a Introduction.- 4.2b Quasilinear Theory.- 4.2c Resonance Broadening.- 4.2d Particle Trapping and Wave Overtaking.- 4.3 Nonlinear Effects on Waves.- 4.3a Introduction.- 4.3b Coherent Three-Wave Interactions.- 4.3c Three Wave Interactions with Random Phase.- 4.3d Nonlinear Two Wave Interactions Due to Scattering by Particles-Nonlinear Landau Damping.- 4.4 Nonlinear Waves and Envelopes.- 4.4a Introduction.- 4.4b Nonlinear Waves-Solitons and Shocks.- 4.4c Nonlinear Envelopes-Envelope Solitons, Envelope Shocks, and Envelope Holes.- 4.4d Modulational Instability.- References for Chapter 4.- General References.- List of Symbols.