Hamiltonian Structure of the Guiding-center Vlasov-Maxwell Equations with Polarization and Magnetization

TL;DR

This paper develops a Hamiltonian framework for guiding-center Vlasov-Maxwell equations incorporating polarization and magnetization, ensuring exact conservation laws and a consistent energy structure.

Contribution

It introduces a Hamiltonian functional and antisymmetric bracket for guiding-center Vlasov-Maxwell equations with dipole effects, satisfying the Jacobi property.

Findings

Derived a guiding-center Hamiltonian functional from energy conservation

Established an antisymmetric bracket satisfying Jacobi property

Demonstrated exact energy-momentum and angular momentum conservation

Abstract

The Hamiltonian formulation of guiding-center Vlasov-Maxwell equations, which contain dipole contributions to the guiding-center polarization and magnetization, is presented in terms of a guiding-center Hamiltonian functional that is derived from the exact guiding-center Vlasov-Maxwell energy conservation law, and an antisymmetric functional bracket that satisfies the Jacobi property. Exact energy-momentum and angular momentum conservation laws are expressed in Hamiltonian form and the guiding-center Vlasov-Maxwell entropy functional is shown to be a Casimir functional.