Reduced Descriptions for Complex Plasmas: Simple Examples, Plasma Kinetics, and Transport Truncations

The statistical description of a hot, magnetized, and classical plasma is reviewed. The latter represents the appropriate model for a fusion plasma in magnetic confinement. Various approaches for (reduced) kinetic descriptions are presented. We first discuss the problems related with reduction of information by investigating extremely simple mathematical models and reviewing standard projection techniques. The famous Boltzmann equation for dilute gases is then presented (without a systematic derivation), and the differences between the kinetic and the hydrodynamic regimes are worked out. In the main part, the consequences of long-range Coulomb interactions are demonstrated. Several plasma-kinetic equations, like for instance the Balescu-Lenard equation, are are systematically presented. Physical consequences from the linearization of the kinetic equations, e.g. collision frequencies and Landau damping, are elucidated. In the final part of the paper the specific re-formulations in magnetized plasmas are investigated. The drift-kinetic and the gyrokinetic approaches are presented. The paper is concluded by an outlook on often used truncations.