Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory

Abstract

This letter reports on a metriplectic formulation of collisional, nonlinear full-$f$ electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell-Ampère equation and the gyrokinetic charge conservation law, is discovered.

5 pages

References in corpus (12)

• Linearized model Fokker-Planck collision operators for gyrokinetic simulations. I. Theory
• A general theory for gauge-free lifting
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Gauge-free electromagnetic gyrokinetic theory
• Some observations regarding brackets and dissipation
• Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
• Development of Advanced Linearized Gyrokinetic Collision Operators Using a Moment Approach
• Differential formulation of the gyrokinetic Landau operator
• Exact conservation laws for gauge-free electromagnetic gyrokinetic equations
• Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold
• Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
• The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates