Collisionless Plasmas in Astrophysics -- Contents -- About the Authors -- 1 Introduction -- 1.1 Goals of the Book -- 1.2 Plasmas in Astrophysics -- 1.2.1 Plasmas Are Ubiquitous -- 1.2.2 The Magnetosphere of Stars -- 1.2.3 Shock Waves -- 1.2.4 Planetary Magnetospheres -- 1.3 Upstream of Plasma Physics: Electromagnetic Fields and Waves -- 1.3.1 Electromagnetic Fields -- 1.3.2 Transverse and Longitudinal Electromagnetic Field -- 1.3.3 Electromagnetic Fields in Vacuum -- 1.3.4 Plane Waves in a Plasma -- 1.3.5 Electromagnetic Components of Plane Plasma Waves -- 1.3.6 Some General Properties of Plane Wave Polarization and Dispersion -- 1.3.7 Electrostatic Waves -- 1.3.8 Wave Packets and Group Velocity -- 1.3.9 Propagation of Plane Waves in a Weakly Inhomogeneous Medium -- 1.3.10 Useful Approximations of the Maxwell Equations in Plasma Physics -- 1.4 Upstream of Plasma Physics: The Motion of Charged Particles -- 1.4.1 The Motion of the Guiding Center -- 1.4.2 Adiabatic Invariants -- 1.4.3 The Motion of a Particle in a Wave -- 2 Plasma Descriptions and Plasma Models -- 2.1 Distribution Function and Moments -- 2.1.1 From Individual Particles to Kinetic Description -- 2.1.2 Kinetic Description and First Order Moments -- 2.1.3 Higher-Order Moments -- 2.1.4 Moments for a Mixture of Populations -- 2.1.5 Nontrivial Generalization of the Fluid Concepts -- 2.1.6 Fluid vs. Kinetic Description: An Example -- 2.2 From Kinetic to Fluid Equations -- 2.2.1 Moment Equations -- 2.2.2 Lagrangian Form of the Moment Equations -- 2.2.3 Fluid Equations: Necessity of a Closure Equation -- 2.2.4 Collisional Limit: Fluid Dynamics and Thermodynamics -- 2.3 Numerical Methods -- 2.3.1 Vlasov Codes -- 2.3.2 Particle in Cell Codes (PIC) -- 2.3.3 Perturbative PIC Codes -- 2.4 Fluid Codes -- 2.5 Hybrid Codes -- 3 The Magnetized Plasmas -- 3.1 Ideal MHD -- 3.1.1 The Ideal MHD System.

3.1.2 The Ideal Ohm's Law -- 3.2 Establishing the MHD Model -- 3.2.1 Large-Scale Conditions of Validity -- 3.2.2 Departures from MHD: Multi-Fluid and Kinetic Effects -- 3.3 Dimensional Analysis and Plasma Characteristic Scales -- 3.3.1 Dimensional Analysis: The General Methods -- 3.3.2 Temporal and Spatial Scales, Adimensional Numbers -- 3.3.3 Dispersive and Dissipative Effects -- 3.3.4 Physical Importance of the Dimensionless Parameters -- 4 Collisional-Collisionless -- 4.1 Notion of Collisions in Plasma Physics -- 4.1.1 Coulomb Interaction: A Long Range Interaction -- 4.1.2 Mean Free Path -- 4.1.3 The Debye Length and the Notion of Debye "Screening" -- 4.1.4 Knudsen Number -- 4.1.5 Plasma Regimes -- 4.2 Notion of Dissipation -- 4.2.1 Transfers of Energy and Dissipation -- 4.2.2 The Concept of Dissipation in Collisional Fluids -- 4.2.3 Reversibility -- 4.2.4 Irreversibility and Damping -- 4.2.5 The Notion of Reversibility Depends on the Description -- 4.2.6 Entropy -- 5 Waves in Plasmas -- 5.1 MHD Waves -- 5.1.1 Polarization of the MHD Waves -- 5.1.2 Application: Alfvén and MHD Waves in the Earth's Magnetosphere -- 5.2 Transport Induced by Waves -- 5.2.1 Alfvén Wave Pressure -- 5.3 High-Frequency Waves -- 5.3.1 Cold Plasma Model -- 5.3.2 Parallel Propagation -- 5.3.3 Perpendicular Propagation: Ordinary and Extraordinary Waves -- 5.3.4 Application: Plasma Cut-offs and Limits to the Radio Astronomy -- 5.3.5 Application: The Dispersion of Radio Waves from Pulsars -- 5.3.6 Application: Faraday Rotation in the Interstellar Medium -- 5.4 Whistler Mode -- 5.5 Collisional Damping in Fluid Theories -- 5.5.1 Dissipative Effects and Entropy -- 5.5.2 Dissipation and Collisions -- 5.5.3 Strongly Collisional Systems -- 5.5.4 Heat Conduction: From Collisional to Collisionless.

5.5.5 The Thermoelectric Field: Another Consequence of Collisions between Ions and Electrons -- 5.6 Collisionless Damping -- 5.6.1 Number of Eigenmodes: Fluid vs. Kinetic -- 5.6.2 A Simple Example: The Langmuir Wave, from Fluid to Kinetic -- 5.6.3 Fluid Treatment of the Langmuir Wave: Choice of a Closure -- 5.6.4 Kinetic Treatment of the Langmuir Wave: Landau Damping -- 5.6.5 Other Types of Kinetic Damping -- 5.7 Instabilities -- 5.7.1 Real Space Instabilities: Fluid Treatment -- 5.7.2 Velocity Space Instabilities: Kinetic Treatment -- 5.7.3 Weak Kinetic Effects -- 5.7.4 An Example: The Two-Stream Instability -- 6 Nonlinear Effects, Shocks, and Turbulence -- 6.1 Collisionless Shocks and Discontinuities -- 6.1.1 Nonlinear Propagation, Discontinuities, Jumps -- 6.1.2 Shocks and Other Discontinuities in a Magnetized Plasma -- 6.1.3 The Unmagnetized Shock Wave -- 6.1.4 A Particular Case: The Tangential Discontinuity -- 6.1.5 Example: The Terrestrial Bow Shock, the Foreshocks -- 6.2 Turbulence (Mainly MHD) -- 6.2.1 Hydrodynamics: Equations, Shocks -- 6.2.2 Hydrodynamics: 3D Incompressible Turbulence -- 6.2.3 MHD Turbulence - Introduction -- 6.2.4 Weak Isotropic (IK) Regime -- 6.2.5 Anisotropic Regimes -- 6.2.6 Discussion -- 6.3 Nonlinear Kinetic Physics -- 6.3.1 Nonlinear Electrostatic Waves -- 6.3.2 Particle Trapping -- 6.3.3 The Nonlinear Interaction of Many Electrostatic Waves of Low Amplitude -- 6.3.4 Quasi-Linear Theory -- 6.3.5 Trapping versus Quasi-Linear Diffusion -- 7 Flow and Particle Acceleration Processes -- 7.1 Flow Acceleration and Heating in a Collisional Fluid -- 7.1.1 Basic Equations -- 7.1.2 Expressions for the Polytropic Fluids -- 7.1.3 Bernoulli's Principle -- 7.1.4 Venturi Effect -- 7.1.5 De Laval Nozzle -- 7.1.6 Stellar Winds -- 7.1.7 Possible Routes to Turbulence in Stellar Winds -- 7.1.8 Accretion -- 7.2 Magnetic Reconnection.

7.2.1 Conservation of Connections vs. Reconnection -- 7.2.2 Departure from the Ideal Ohm's Law: Microscopic Mechanisms and Macroscopic Consequences -- 7.2.3 Flow Acceleration by Reconnection -- 7.2.4 Tearing Instability -- 7.2.5 3D Reconnection -- 7.3 Kinetic Acceleration Processes in Magnetospheres -- 7.3.1 Substorms and Auroras in the Earth's Magnetosphere -- 7.3.2 Fermi Acceleration in the Magnetosphere -- 7.3.3 Acceleration by a Forced Current Forced along Convergent Magnetic Field Lines -- 7.3.4 Acceleration by an Electric Current Forced by a Wave -- 7.3.5 Acceleration by an Alfvén Wave (NonMHD) Parallel Electric Field -- 7.3.6 Resonant Acceleration by a Wave -- 7.3.7 Acceleration by a Wave of Short Length -- 7.3.8 Application: Acceleration in the Earth's Magnetosphere -- 8 Transport and Acceleration of Cosmic Rays -- 8.1 The Problem of Transport -- 8.1.1 The Magnetic Field: Obstruction to Transport -- 8.1.2 Magnetic Irregularities: Transport Agent -- 8.1.3 Other Diffusion Coefficients -- 8.1.4 Transport Equation of Cosmic Rays -- 8.1.5 Distribution of Suprathermal Particles Crossing a Shock -- 8.1.6 From Transport to Acceleration -- 8.2 Fermi Acceleration of Cosmic Rays -- 8.2.1 The Basic Fermi Process -- 8.2.2 Fermi Process at a Nonrelativistic Shock -- 8.2.3 Astrophysical Application: Cosmic Rays and Supernovae -- 8.2.4 Astrophysical Application: Synchrotron Sources -- 8.2.5 Generation of Magnetic Turbulence -- 8.2.6 Why Are Fermi Processes Favored at Shocks? -- 8.2.7 What about the Relativistic Regime of Fermi Acceleration? -- 9 The Kinetic-Fluid Duality -- 9.1 Toy Models -- 9.1.1 Small Amplitude Ballistic Fluctuations -- 9.1.2 Large-Amplitude Ballistic Fluctuations -- 9.1.3 Quasi-Fluid Behavior of a Collisionless Plasma: Launching a 2D Plasma Bullet -- 9.2 Solar and Stellar Wind Expansion -- 9.2.1 A Simple Noncollisional Wind.

9.2.2 More Sophisticated Noncollisional Wind Models -- 9.2.3 Charge Neutralizing Field for a Plasma in a Gravitational Field -- 9.2.4 Qualitative Radial Profile of the Total Proton Potential -- 9.2.5 Charge Neutralizing Electric Field and Dreicer Field -- 9.2.6 Electric Field Intensity at the Sonic Radius rs -- 9.2.7 Effective Closure for the Solar Wind -- Appendix -- A.1 Notation -- A.1.1 Vectors and Tensors -- A.1.2 Derivatives -- A.1.3 List of Notation -- A.2 Asymptotic Expansions and Adiabatic Invariants -- A.2.1 Multiscale Expansion -- A.2.2 The Adiabatic Invariants -- A.2.3 Derivation of the Guiding Center Equations -- A.3 Fokker-Planck Equation, First Order Term -- References -- Index.