An Introduction to Plasma Astrophysics and Magnetohydrodynamics

Most of the visible matter in the universe exists in the plasma state. Plasmas are of major importance for space physics, solar physics, and astrophysics. On Earth they are essential for magnetic controlled thermonuclear fusion.

This textbook collects lecture notes from a one-semester course taught at the K.U. Leuven to advanced undergraduate students in applied mathematics and physics. A particular strength of this book is that it provides a low threshold introduction to plasmas with an emphasis on first principles and fundamental concepts and properties.

The discussion of plasma models is to a large extent limited to Magnetohydrodynamics (MHD) with its merits and limitations clearly explained. MHD provides the students on their first encounter with plasmas, with a powerful plasma model that they can link to familiar classic fluid dynamics. The solar wind is studied as an example of hydrodynamics and MHD at work in solar physics and astrophysics.

Inhalt
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.