Gyrokinetic resonant theory of low frequency electromagnetic perturbation

TL;DR

This paper identifies a flaw in traditional gyrokinetic theory related to resonance conditions and proposes a modified approach that maintains the near identity transformation, demonstrated through a numerical example.

Contribution

It introduces a modified gyrokinetic theory that correctly handles resonances by relaxing certain conditions in the first order Lagrangian 1-form.

Findings

Traditional theory violates near identity transformation during resonance.

The modified theory overcomes this issue.

Numerical example validates the new approach.

Abstract

It's pointed out that the traditional gyrokinetic theory dealing with low frequency electromagnetic perturbation violates the near identity transformation, which is supposed to be obeyed by Lie perturbed transformation theory, if resonance happens between \omega and k\cdot v. A modification is given to overcome this problem by not requiring all components in the first order Lagrangian 1-form equaling zero. A numerical example is given as an application of the new theory.