Rigorous derivation of the Landau equation in the weak coupling limit

Details Rigorous derivation of the Landau equation in the weak coupling limit Rigorous derivation of the Landau equation in the weak coupling limit

2009-05-05

arxiv.org/abs/0905.0649v1

Physics

Mathematical Physics

22 pages, 8 figures, accepted to Communications in Pure and Applied Analysis

Scientific paper

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.

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