Two electrostatic gyrokinetic models derived by two different perturbative methods

TL;DR

This paper derives two electrostatic gyrokinetic models using different perturbative methods, one conventional with a correction, and a new simplified model that removes finite Larmor radius terms for easier numerical application.

Contribution

It introduces a novel perturbative approach based on covariant transform formulas, simplifying gyrokinetic models by eliminating finite Larmor radius terms.

Findings

The new model simplifies numerical implementation.

Finite Larmor radius terms are fully removed in the new model.

The conventional model's derivation is corrected with a Lie transform.

Abstract

This paper presents two different electrostatic gyrokinetic models derived through two different perturbative methods. One of the two models is just the conventional electrostatic gyrokinetic model, the derivation of which is repeated using the Lie transform perturbative method. One term is rectified in the derivation of the conventional model. To derive the other model, we use a new method, which is based on the covariant transform formula of the differential 1-form. The new method doesn't split the coordinate transform into the guiding-center transform and the gyrocenter transform. It carries out the coordinate transform up to the order equaling that of the amplitude of the perturbative wave. Compared with the conventional model, the finite Larmor radius terms are completely removed from the orbit equations of the new one, making it simpler for the numerical application.