Hamiltonian formulation of reduced Vlasov-Maxwell equations

TL;DR

This paper develops a Hamiltonian framework for reduced Vlasov-Maxwell equations using macroscopic fields D and H, expressing polarization and magnetization in terms of a generating functional S and Poisson brackets.

Contribution

It introduces a Hamiltonian formulation of reduced Vlasov-Maxwell equations with macroscopic fields and defines polarization and magnetization via a functional Lie-derivative approach.

Findings

Expresses D and H in terms of functional Lie-derivative and Poisson brackets.

Defines polarization and magnetization vectors in terms of the generating functional S.

Provides lowest-order dipole contributions for polarization and magnetization.

Abstract

The Hamiltonian formulation of the reduced Vlasov-Maxwell equations is expressed in terms of the macroscopic fields D and H. These macroscopic fields are themselves expressed in terms of the functional Lie-derivative generated by the functional S with the Poisson bracket [.,.] for the exact Vlasov-Maxwell equations. Hence, the polarization vector P= (D-E)/(4pi) and the magnetization vector M=(B-H)/(4pi) are defined in terms of the expressions 4pi P=[S,E]+... and 4pi M =-[S,B]+..., where lowest-order terms yield dipole contributions.