Approximate Fokker–Planck collision operator for transport theory applications

TLDR: In this paper, an analytically tractable approximation for the linearized Fokker-Planck collision operator describing a plasma nearly in thermal equilibrium was developed, which preserves the symmetry properties of the exact collision integral which imply the physical conservation laws, selfadjointness, and the H theorem.

Abstract: An analytically tractable approximation is developed for the linearized Fokker–Planck collision operator describing a plasma nearly in thermal equilibrium. This approximate operator preserves the symmetry properties of the exact collision integral which imply the physical conservation laws, self‐adjointness, and the H theorem. A renormalization procedure is developed to accurately treat collisions between particles of arbitrary masses. For large or small mass ratios, the approximate operator reduces to the standard expansions of the exact operator. In the case of identical particle collisions, the present approximation provides a significant improvement over the ’’model operator’’ previously given in the literature, yet retains the simplicity of former operators necessary for analytic work. The recalculation of the classical transport coefficients with this operator reduces to the solution of a coupled set of algebraic equations and indicates its reliability for use in complex neoclassical transport situations. The neoclassical electrical conductivity calculation demonstrates the new physical features of the approximate operator.