From charge motion in general magnetic fields to the non perturbative gyrokinetic equation

TL;DR

This paper derives a non perturbative, exact analytical description of non relativistic charge motion in general magnetic fields, leading to a new gyrokinetic equation applicable at all orders of gyro-center transformation.

Contribution

It introduces a non perturbative approach to derive the gyrokinetic equation, providing exact solutions for charge motion in arbitrary magnetic fields.

Findings

Exact guiding center coordinates are obtained.

The gyrokinetic equation is solved at marginal stability.

New solutions for particle motion in complex magnetic fields.

Abstract

The exact analytical description of non relativistic charge motion in general magnetic fields is, apparently, a simple problem but, it has not been solved up to now apart for rare cases. The key feature of the present derivation is to adopt a non perturbative magnetic field description to find new solutions of motion. Among all solutions, two are particularly important: guiding particle and gyro-particle solutions. The guiding particle has been characterized to be minimally coupled to the magnetic field, the gyro-particle has been defined to be maximally coupled to the magnetic field and, also, to move on a closed orbit. The generic charged particle motion is shown to be expressed as the sum of such particular solutions. This non perturbative approach corresponds to the description of the particle motion in the gyro-center and/or guiding center reference frame obtained at all the orders of the modern gyro-center transformation. The Boltzmann equation is analyzed with the described exact guiding center coordinates. The obtained gyrokinetic equation is solved for the Boltzmann equation at marginal stability conditions.