Comment on "Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field''

TL;DR

This paper defends the standard Lie-transform perturbation theory against recent criticisms, arguing that it remains valid and does not require modifications when applied to guiding-center theory in charged-particle motion.

Contribution

It provides a rebuttal to claims that the standard Lie-transform perturbation theory has ordering inconsistencies, affirming its correctness in guiding-center applications.

Findings

Standard Lie-transform theory remains valid for guiding-center problems.

Criticism of ordering inconsistencies is unfounded.

No modifications to the theory are necessary.

Abstract

A recent paper by L.~Zheng [Phys. Plasmas, 30, 042515 (2023)] presented a critical analysis of standard Lie-transform perturbation theory and suggested that its application to the problem of charged-particle motion in a magnetic field suffered from ordering inconsistencies. In the present Comment, we suggest that this criticism is unjustified and that standard Lie-transform perturbation theory does not need to be modified in its application to guiding-center theory.