Basic Principles for a Kinetic Description of Particles and Waves

In this overview, the main arguments for a kinetic description of a classical non-relativistic many particle system are reviewed. First, the need and strategy for a kinetic description of plasma particles is 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. It is shown that a linearization of the initial value problem can already give interesting insights into the dynamic behaviors. In many cases a reduction to a plasmadynamic (fluid) description is appropriate, and popular truncations are summarized. Finally, the basic methods for a kinetic description of waves are presented. When some wave excitations are driven unstable and the collective motion of particles dominates, the wave-kinetic equations will be the appropriate dynamical equations. It is shown that spectra of the Kolmogorov-Obukhov type are exact stationary solutions of the latter.