Basic Principles of Kinetic Equations for Particles, Waves, and Magnetic Field Lines

In this overview, the main arguments for a kinetic description of a classical, non-relativistic many-body system are reviewed. The need and strategy for a kinetic description of plasma particles are discussed. The Vlasov, the Landau-Fokker-Planck, and the Balescu-Lenard equations are presented as the most useful kinetic equations for the particle distribution functions. In the second part, some simple applications are discussed. First, collision frequencies are derived. Second, it is shown that in the mean field approximation a linearization of the initial value problem can already give interesting insights into the (collective) dynamic behaviors. Third, quasi-linear and weak turbulence theories are discussed. Fourth, it is argued why in many cases a reduction to a plasmadynamic (fluid) description is appropriate, and popular truncations are summarized. Finally, the generality of the statistical methods is demonstrated on the example of magnetic field line diffusion.