Exact Energy Conservation Laws for Full and Truncated Nonlinear Gyrokinetic Equations

The exact global energy conservation laws for the full-$f$ and $δf$ 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 Ampère equations and the quadratic ponderomotive gyrocenter Hamiltonian is emphasized.

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