Diffusion and guiding center approximation for particle transport in strong magnetic fields

TL;DR

This paper derives a diffusion equation for particle transport in strong magnetic fields, combining diffusion in the parallel direction with guiding center motion in the orthogonal direction, based on asymptotic analysis of the Boltzmann equation.

Contribution

It introduces a new collision operator and provides a correction to guiding center motion in the context of strong magnetic fields.

Findings

Diffusion limit in the parallel direction is characterized.

Guiding center motion is explicitly derived.

A new averaged collision operator is developed.

Abstract

The diffusion limit of the linear Boltzmann equation with a strong magnetic field is performed. The giration period of particles around the magnetic field is assumed to be much smaller than the collision relaxation time which is supposed to be much smaller than the macroscopic time. The limiting equation is shown to be a diffusion equation in the parallel direction while in the orthogonal direction, the guiding center motion is obtained. The diffusion constant in the parallel direction is obtained through the study of a new collision operator obtained by averaging the original one. Moreover, a correction to the guiding center motion is derived.