Rigorous derivation of the Landau equation in the weak coupling limit

Abstract

We examine a family of microscopic models of plasmas, with a parameter [\alpha] comparing the typical distance between collisions to the strength of the grazing collisions. These microscopic models converge in distribution, in the weak coupling limit, to a velocity diffusion described by the linear Landau equation (also known as the Fokker-Planck equation). The present work extends and unifies previous results that handled the extremes of the parameter [alpha] to the whole range [(0,1 over 2]] ,by showing that clusters of overlapping obstacles are negligible in the limit. Additionally, we study the diffusion coefficient of the Landau equation and show it to be independent of the parameter.