Effective field formulation of plasma kinetic theory

Abstract

The kinetic theory of classical Coulomb plasmas is formulated in terms of an effective electric field representing the response of the plasma medium to a set of fluctuating particles. The diffusion and friction coefficients of the particle kinetic equation are written explicitly in terms of this effective field. For wavevectors of the order of the Debye wavevector the effective field can be computed from a linearized Vlassov equation and yields the first order in the plasma parameter kinetic equations. For small wavevectors of the order of the inverse of the 90° deflection mean free path the effective field can be computed from an inhomogeneous Balescu-Guernsey-Lenard (BGL) equation containing a nonlinear Vlassov term and a BGL-like collision term. Retaining only the lowest-order nonlinear corrections the kinetic equations recently derived by Rogister and Oberman are recovered while some collisional damping contributions missing in the latter kinetic equations are included. Finally we briefly discuss the contribution from collision-dominated waves as well as the close encounter contributions to the effective electric field.