Kinetic Theory of Dawson Plasma Sheet Model

Abstract

A kinetic theory of one-dimensional plasma sheet model (Dawson model) is developed. The Vlasov equation, the Landau equation, and the Balescu–Lenard equation corresponding to this model are derived. For the Vlasov equation, it is shown that the linearized Vlasov equation exhibits a typical behavior of plasmas as in the three-dimensional space. The Landau collision term and the Balescu–Lenard collision term are identically zero. The fact of the vanishing collision term agrees with the behavior of generic one-dimesional systems. In an approximation that the system is in a thermal bath, the derived Landau equation and Balescu–Lenard equation are transformed into the Fokker–Planck equations. Some physical quantities such as thermal conductivity, relaxation rate, etc., are estimated. A discussion on physical meaning of these results, in particular, the zero collision terms, will be given.