Guiding-center recursive Vlasov and Lie-transform methods in plasma physics

TL;DR

This paper clarifies the connection between recursive Vlasov methods and Lie-transform techniques in deriving gyrocenter phase-space coordinates for nonlinear gyrokinetic plasma theory.

Contribution

It demonstrates the equivalence of recursive Vlasov and Lie-transform methods in guiding-center transformations within plasma physics.

Findings

Unified framework for gyrocenter coordinate derivation

Clarification of recursive and Lie-transform method relations

Enhanced understanding of nonlinear gyrokinetic theory

Abstract

The gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.