Rigorous derivation of the Landau equation in the weak coupling limit

Plasmas (high-temperature, highly charged gases) arise in important applications like rocket exhaust and space-vehicle re-entry. Microscopically, a plasma consists of particles grazing each other, and the goal has been to arrive at the linear Landau equation (which describes it macroscopically) via the weak coupling limit.; Previous work in this field has dealt with two extremes of a parameter, alpha, which compares the typical distance between collisions to the strength of each grazing. For the upper extreme, alpha = 1/2, Kesten and Papanicolaou (1980) and Durr, Goldstein, and Lebowitz (1987) showed that the microscopic processes converge in distribution to the velocity diffusion described by the linear Landau equation. At the other extreme, Desvillettes and Ricci (2001) proved a weaker result for 0 < alpha < 1/8.; In the present work, it is shown that the microscopic processes converge in distribution to the Landau diffusion process for the entire range of alpha. Additionally, the diffusion constant is studied and shown to be independent of alpha, that is, there is agreement between the previous formulas for the extreme values of the parameter.