  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.
