Resonant terms on gyrocenter coordinates introduced by resonant electromagnetic perturbations

TL;DR

This paper refines gyrokinetic theory by identifying and deriving physically meaningful resonant terms in gyrocenter trajectories affected by electromagnetic perturbations, revealing a frequency shift in particle gyration.

Contribution

It introduces a modified transform method to accurately extract resonant terms up to second harmonic resonance in gyrocenter equations, correcting nonphysical artifacts from previous approaches.

Findings

Resonant terms are explicitly derived for various resonant conditions.

The gyroangle frequency shifts from the cyclotron frequency under wave influence.

A simple example demonstrates the impact of the frequency shift on particle dynamics.

Abstract

It's pointed out that the treatment of the resonant electromagnetic perturbation with the Lie transform method adopted in the gyrokinetic theory generates some nonphysical terms in the trajectory equations. By utilizing a modified application of this transform method, the resonant terms in the trajectory equations satisfying each resonant condition are found out up to the second harmonic resonance. Through separating the fast-dynamic terms from the slow-dynamic ones, the slow-dynamic trajectory equations including the resonant terms are derived for various resonant conditions. The slow-dynamic evolution equation of gyroangle reveals that the real gyrating frequency of the charged particle around the magnetic field line under driving by the resonant wave has a shift from the cyclotron frequency without the wave driving. To study the effect caused by the frequency shift, a simple example for the fundamental-frequency cyclotron resonance is presented.