Symplectic gyrokinetic Vlasov-Maxwell theory

TL;DR

This paper introduces a new symplectic formulation of electromagnetic gyrokinetic Vlasov-Maxwell theory that expresses equations solely in terms of perturbed fields, ensuring exact conservation laws and improved theoretical consistency.

Contribution

It presents a novel symplectic gyrokinetic formulation based on a variational principle, explicitly including polarization and magnetization effects in the equations.

Findings

Derived self-consistent gyrokinetic equations with explicit polarization drift.

Established exact energy-momentum conservation laws.

Proved toroidal angular momentum conservation in axisymmetric fields.

Abstract

A new representation of electromagnetic gyrokinetic Vlasov-Maxwell theory is presented in which the gyrocenter equations of motion are expressed solely in terms of the perturbed electric and magnetic fields. In this representation, the gyrocenter symplectic (Poisson-bracket) structure and the gyrocenter Jacobian contain electric and magnetic perturbation terms associated with the standard first-order gyrocenter polarization and magnetization terms that traditionally appear in the gyrokinetic Maxwell equations. In addition, the gyrocenter polarization drift (which includes perturbed magnetic-field corrections) now appears explicitly in the gyrocenter velocity. The symplectic gyrokinetic Vlasov-Maxwell equations are self-consistently derived from a constrained Eulerian variational principle, which yields exact energy-momentum conservation laws (through the Noether method) that are verified explicitly. An exact toroidal canonical angular momentum conservation law is also derived explicitly under the assumption of an axisymmetric background magnetic field.