Weak turbulence plasma induced by two-scale homogenization

This paper is devoted to the homogenization of the quasilinear theory of the plasma turbulence described by the Vlasov-Poisson system. It is shown that the homogenization limit, in the sense of two-scale limit, of the distribution function satisfies the linear Vlasov-Poisson equations. Moreover, the limit distribution function can be decomposed into the mean and the fluctuation parts and the mean part (the equilibrium distribution function) is shown to be the solution of the nonlocal quasilinear velocity-space diffusion equation. We also investigate the Landau damping from the point of view of homogenization through the two-scale limit.