Variational principle for the parallel-symplectic representation of electromagnetic gyrokinetic theory

Abstract

The nonlinear (full-$f$) electromagnetic gyrokinetic Vlasov-Maxwell equations are derived in the parallel-symplectic representation from an Eulerian gyrokinetic variational principle. The gyrokinetic Vlasov-Maxwell equations are shown to possess an exact energy conservation law, which is derived by Noether method from the gyrokinetic variational principle. Here, the gyrocenter Poisson bracket and the gyrocenter Jacobian contain contributions from the perturbed magnetic field. In the full-$f$ formulation of the gyrokinetic Vlasov-Maxwell theory presented here, the gyrocenter parallel-Ampère equation contains a second-order contribution to the gyrocenter current density that is derived from the second-order gyrocenter ponderomotive Hamiltonian.

15 pages. Revised manuscript submitted to the special issue of Physics of Plasmas in honor of W.W. Lee

References in corpus (2)

• Second order Gyrokinetic theory for Particle-In-Cell codes
• Variational principles for the guiding-center Vlasov-Maxwell equations

Cited by in corpus (3)

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• Discovering exact, gauge-invariant, local energy-momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds
• Gyrokinetic theory with polynomial transforms: a model for ions and electrons in maximal ordering