A scaling limit for Vlasov equations with electrostatic fluctuations

Abstract

We consider a Vlasov equation for a plasma with a given constant magnetic field, and introduce a white noise perturbation of the electric field in the electrostatic approximation, with a discussion of the motivations of such random perturbation. We prove that diffusion in velocity emerges in a suitable scaling limit of the noise, and also discuss the physical relevance of this result.