Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations

TL;DR

This paper establishes the Hamiltonian framework for gauge-free gyrokinetic Vlasov-Maxwell equations, demonstrating their conservation laws and mathematical properties like the Jacobi identity.

Contribution

It introduces the Hamiltonian structure and bracket formulation for gauge-free gyrokinetic Vlasov-Maxwell equations, including conservation laws and mathematical consistency.

Findings

Hamiltonian functional and bracket formulation developed

Gyrokinetic angular-momentum conservation expressed in Hamiltonian form

Jacobi property of the bracket explicitly verified

Abstract

The Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations is presented in terms of a Hamiltonian functional and a gyrokinetic Vlasov-Maxwell bracket. The bracket is used to show that the gyrokinetic angular-momentum conservation law can also be expressed in Hamiltonian form. The Jacobi property of the gyrokinetic Vlasov-Maxwell bracket is also demonstrated explicitly.