The Vlasov model under large magnetic fields in the low-Mach number regime

TL;DR

This paper derives a hybrid kinetic-fluid model for charged particles in strong magnetic fields under low-Mach number conditions, capturing microscopic gyration and macroscopic plasma behavior as the cyclotron period tends to zero.

Contribution

It introduces a new asymptotic model coupling kinetic and fluid descriptions for plasma under large magnetic fields in the low-Mach regime.

Findings

The model couples microscopic particle motion with macroscopic plasma flow.

Perpendicular velocity follows classical drift relations.

Parallel velocity satisfies an elliptic equation along magnetic field lines.

Abstract

This article is concerned with the kinetic modeling, by means of the Vlasov equation, of charged particles under the influence of a strong external electromagnetic field, i.e. when epsilon^2, the dimensionless cyclotron period, tends to zero. This leads us to split the velocity variable in the Vlasov equation into fluid and random components. The latter is supposed to have a large magnitude of order 1/epsilon (which corresponds to the low Mach number regime). In the limit epsilon -> 0, the resulting model is a hybrid model which couples a kinetic description of the microscopic random motion of the particles to a fluid description of the macroscopic behavior of the plasma. The microscopic model is a first-order partial differential system for the distribution function, which is averaged over the ultra-fast Larmor gyration and the fast parallel motion along the magnetic field lines. The perpendicular component (with respect to the magnetic field lines) of the bulk velocity is governed by the classical relations describing the E X B and diamagnetic drifts, while its parallel component satisfies an elliptic equation along the magnetic field lines.