A scaling limit for Vlasov equations with electrostatic fluctuations

TL;DR

This paper studies a plasma Vlasov equation with a magnetic field and introduces a white noise electric field perturbation, demonstrating that velocity diffusion emerges in a specific scaling limit, highlighting its physical significance.

Contribution

It establishes a scaling limit where electrostatic noise induces velocity diffusion in the Vlasov plasma model, connecting stochastic perturbations to physical diffusion phenomena.

Findings

Diffusion in velocity space emerges under a specific noise scaling.

The introduced stochastic model captures physically relevant diffusion effects.

The results provide insight into plasma behavior under 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.