Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory

TL;DR

This paper develops a metriplectic framework for electromagnetic gyrokinetic theory that ensures energy conservation, entropy production, and angular momentum conservation, introducing a new collisional current in the process.

Contribution

It introduces a novel metriplectic formulation of gyrokinetic theory that maintains key physical conservation laws and identifies a new collisional current.

Findings

Energy conservation and entropy production are achieved.

A new collisional current is identified in the gyrokinetic equations.

Toroidal angular momentum conservation is demonstrated.

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-Amp\`ere equation and the gyrokinetic charge conservation law, is discovered.