Beyond linear gyrocenter polarization in gyrokinetic theory

TL;DR

This paper clarifies and extends the concept of polarization in gyrokinetic theory by including guiding-center and nonlinear gyrocenter contributions, derived through variational and transformation methods.

Contribution

It introduces a generalized polarization model in gyrokinetics that incorporates both zeroth-order guiding-center and second-order nonlinear gyrocenter effects.

Findings

Guiding-center polarization derived from a modified transformation.

Nonlinear gyrocenter polarization obtained variationally and via push-forward.

Enhanced understanding of polarization contributions in gyrokinetic theory.

Abstract

The concept of polarization in gyrokinetic theory is clarified and generalized to include contributions from the guiding-center (zeroth-order) polarization as well as the nonlinear (second-order) gyrocenter polarization. The guiding-center polarization, which appears as the antecedent (zeroth-order) of the standard linear (first-order) gyrocenter polarization, is obtained from a modified guiding-center transformation. The nonlinear gyrocenter polarization is derived either variationally from the third-order gyrocenter Hamiltonian or directly by gyrocenter push-forward method.