Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

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.

27 pages

References in corpus (3)

• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Gauge-free electromagnetic gyrokinetic theory
• Nonlinear finite-Larmor-radius effects in reduced fluid models

Cited by in corpus (5)

• Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
• Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
• Polarization and magnetization in collisional and turbulent transport processes
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations
• Gauge-invariant variational formulations of electromagnetic gyrokinetic theory