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 $\alpha$, for the whole range (0, 1/2], 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.Comment: 22 pages, 8 figures, accepted to Communications in Pure and Applied Analysi