Charged particle motion in a strong magnetic field: The first order expansion

TL;DR

This paper rigorously derives the first order expansion of charged particle motion in a strong magnetic field, avoiding common assumptions and justifying the guiding centre approximation even at bounce points.

Contribution

It provides a mathematically rigorous derivation of the first order expansion without structural assumptions, validating the guiding centre approximation in more general settings.

Findings

Rigorous derivation of particle motion expansion

Validation of guiding centre approximation at bounce points

No structural assumptions on gyroradius required

Abstract

We provide a mathematically rigorous derivation of the first order expansion of the motion of a charged particle in a strong magnetic field. In contrast to the derivations that can be found in the physics literature we solely assume throughout that the magnetic field is strong. In particular we do not need to make any structural assumptions on the particle motion, such as the gyroradius being small in comparison to the magnetic length scale. Instead, some of the additional assumptions which are usually made in the physics literature turn out to be an a posteriori consequence in our approach. Our approach further justifies the utilisation of the guiding centre approximation at "bounce points" within magnetic mirrors, a situation which violates the usual assumptions which are made in the physics literature when deriving the guiding centre approximation.