Exact Energy Conservation Laws for Full and Truncated Nonlinear Gyrokinetic Equations

TL;DR

This paper derives exact energy conservation laws for full and truncated nonlinear electromagnetic gyrokinetic equations, highlighting the role of polarization, magnetization, and ponderomotive effects in magnetic geometries.

Contribution

It provides the first derivation of exact energy conservation laws for both full-$f$ and $ extdelta f$ gyrokinetic formulations in general magnetic geometry.

Findings

Energy conservation laws are explicitly formulated for full-$f$ and $ extdelta f$ gyrokinetics.

The relations between polarization, magnetization, and the gyrocenter Hamiltonian are clarified.

The results ensure consistent energy accounting in gyrokinetic simulations.

Abstract

The exact global energy conservation laws for the full-$f$ and $\delta f$ formulations of the nonlinear electromagnetic gyrokinetic equations in general magnetic geometry are presented. In both formulations, the relation between polarization and magnetization effects in the gyrokinetic Poisson and Amp\`{e}re equations and the quadratic ponderomotive gyrocenter Hamiltonian is emphasized.