Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

TL;DR

This paper derives exact energy and angular-momentum conservation laws for gauge-free electromagnetic gyrokinetic equations, clarifying energy and momentum transfer mechanisms in turbulent magnetized plasmas.

Contribution

It provides the first explicit derivation of exact conservation laws for gauge-free electromagnetic gyrokinetics using Noether's theorem.

Findings

Derived exact energy and angular-momentum conservation laws.

Highlighted the roles of gyrocenter polarization and magnetization.

Presented a momentum transport equation applicable to various magnetic geometries.

Abstract

The exact energy and angular-momentum conservation laws are derived by Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov-Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocenters and the perturbed electromagnetic fields, in which the crucial roles played by gyrocenter polarization and magnetization effects are highlighted. In addition to yielding an exact angular-momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries.