Fundamentals of Cosmic Electrodynamics

1 Charged Particles in the Electromagnetic Field.- 1.1 Initial equations and their properties.- 1.2 Liouville’s theorem and the exact distribution function.- 2 The Motion of a Charged Particle in Given Fields.- 2.1 A particle in constant homogeneous fields.- 2.2 Weakly inhomogeneous slowly changing fields.- 2.3 Adiabatic invariants.- 2.4 Reconnection and particle acceleration.- 3 Coulomb Collisions of Particles.- 3.1 Close and distant collisions.- 3.2 Debye shielding.- 3.3 Times of collisional relaxations.- 4 Statistical Description of a Plasma.- 4.1 The averaging of Liouville’s equation.- 4.2 Collisional integral and correlation functions.- 4.3 Equations for correlation functions.- 4.4 Approximations for binary collisions.- 4.5 Correlation function and Debye shielding.- 5 Hydrodynamic Description of a Plasma.- 5.1 Transition to macroscopic transfer equations.- 5.2 Hydrodynamic equations for plasma.- 5.3 Generalized Ohm’s law.- 6 Magnetohydrodynamics.- 6.1 Basic assumptions and the MHD equations.- 6.2 Magnetic flux conservation. Ideal MHD.- 6.3 The main approximations in ideal MHD.- 7 Plasma Flows in a Strong Magnetic Field.- 7.1 General formulation of the problem.- 7.2 The formalism of two-dimensional problems.- 7.3 On the existence of continuous flows.- 7.4 Plasma flows in the field of a time-dependent magnetic dipole.- 8 Waves and Discontinuous Flows in a MHD Medium.- 8.1 Small-amplitude waves.- 8.2 Discontinuity surfaces in hydrodynamics.- 8.3 Magnetohydrodynamic discontinuities.- 8.4 Continuous transitions between discontinuous solutions.- 9 Evolutionarity of MHD discontinuities.- 9.1 Conditions for evolutionarity.- 9.2 Consequences of evolutionarity conditions.- 10 Plasma Equilibrium in a Magnetic Field.- 10.1 The virial theorem in MHD.- 10.2 Force-freefields and Shafranov’s theorem.- 10.3 Properties of equilibrium configurations.- 10.4 Archimedean force in MHD.- 11 Stationary Plasma Flows in a Magnetic Field.- 11.1 Ideal plasma flows.- 11.2 Flows at small magnetic Reynolds numbers.- 11.3 Expulsion force and vortex flows.- 11.4 Expulsion force for large magnetic Reynolds numbers.- 12 Magnetic Reconnection in Current Sheets.- 12.1 Small perturbations near a neutral line.- 12.2 Field line deformation due to current displacement.- 12.3 Dynamic dissipation of a magnetic field.- 12.4 Particle acceleration into current sheets.- 12.5 Regular Versus Chaotic Acceleration.- 13 Evolutionarity of current sheets.- 13.1 Properties of reconnecting current sheets.- 13.2 Small perturbations outside the RCS.- 13.3 Small perturbations inside the RCS.- 13.4 Solution on the boundary of the RCS.- 13.5 Criterion of evolutionarity.- 14 Tearing Instability of the Reconnecting Current Sheet.- 14.1 Origin of tearing instability.- 14.2 Formulation of the problem and its analytic solution.- 14.3 Physical interpretation of the instability.- 14.4 Stabilizing effect of the transverse field.- 14.5 Compressibility and a longitudinal field.- 14.6 Kinetic approach.- 15 Selected Trends in Cosmic Electrodynamics.- 15.1 Reconnection and magnetic helicity.- 15.2 Reconnection in low-temperature plasma.- 16 Reconnection of Electric Currents.- 16.1 Models for flare energy storage and release.- 16.2 Current sheet formation mechanisms.- 16.3 Shear and reconnection of currents.- Appendix 1. Notation.- Appendix 2. Useful Expressions.- Appendix 3. Constants.