An Introduction to Plasma Astrophysics and Magnetohydrodynamics

Content.- 1 Introduction.- 1.1 Plasma as the fourth state of matter.- 1.2 Plasmas and magnetic fields.- 1.3 Why plasma physics.- 1.4 Aim of the course.- 2 Basic plasma properties.- 2.1 Elements of plasma, kinetic theory.- 2.2 Plasma oscillations : the plasma frequency.- 2.3 The Debye shielding length.- 2.4 Charge neutrality again.- 2.5 Weakly coupled plasmas.- 2.6 Damping of plasma oscillations.- 2.7 Collisions.- 2.8 Larmor frequency and Larmor radius.- 2.9 Recapitulation.- 2.10 Problems.- 3 Fluid equations for mass, momentum and energy.- 3.1 Multi-fluid theory.- 3.2 Two-fluid theory.- 3.3 Single-fluid equations.- 3.4 Recapitulation.- 3.5 Problems.- 4 Magnetohydrodynamics.- 4.1 Generalized Ohm's law.- 4.2 The MHD approximation of Ohm's law.- 4.3 The pre-Maxwell equations.- 4.4 Equations of Ideal and resistive MHD.- 4.5 The induction equation and conservation of magnetic flux.- 4.6 The diffusive limit of the induction equation.- 4.7 Magnetic field lines.- 4.8 The Lorentz force.- 4.9 Recapitulation.- 4.10 Problems.- 5 Basic MHD dynamics.- 5.1 Linear motions superimposed on a static equilibrium.- 5.2 Waves of a uniform plasma of infinite extent.- 5.3 Sound waves.- 5.4 Alfvén waves.- 5.5 Alfvén waves and slow waves.- 5.6 Alfvén waves and magnetosonic waves.- 5.7 Recapitulation.- 5.8 Problems.- 6 The solar wind.- 6.1 Overview of observations.- 6.2 Alternatives to the energy equation.- 6.3 Static models.- 6.4 de Laval nozzle.- 6.5 Parker's isothermal solution for a thermally driven wind.- 6.6 Rotating thermally driven wind.- 6.7 Rotating magnetized thermally driven wind.- 6.8 Recapitulation.- 6.9 Problems.