ASYMPTOTIC BEHAVIOR OF THE TWO-DIMENSIONAL VLASOV-POISSON-FOKKER-PLANCK EQUATION WITH A STRONG EXTERNAL MAGNETIC FIELD

Abstract

The subject matter of the paper is concerned with the Vlasov-Poisson-Fokker-Planck (VPFP) equations in the context of magnetic confinement. We study the long-term behavior of a VPFP system with an intense external magnetic field, neglecting the curvature of the magnetic lines. When the intensity of the magnetic field tends to infinity, the long-term behavior of the particle concentration is described by a first-order nonlinear hyperbolic equation of the Euler type for fluid mechanics. More exactly, when the magnetic field is uniform, we find the vorticity formulation of the incompressible Euler equations in two-dimensional space. Our proofs rely on the modulated energy method.