Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves

TL;DR

This paper develops a Hamiltonian framework for modeling the self-consistent interaction between electromagnetic waves and charged particle beams, simplifying the complex Vlasov-Maxwell system into a one-dimensional Hamiltonian model using Lie algebraic methods.

Contribution

It introduces a novel Hamiltonian reduction of the Vlasov-Maxwell system to a one-dimensional model via Lie algebraic formalism, maintaining Hamiltonian structure throughout.

Findings

Derived a one-dimensional Hamiltonian model from Vlasov-Maxwell equations.

Maintained Hamiltonian structure using Lie algebraic formalism.

Provided a simplified yet rigorous framework for wave-particle interactions.

Abstract

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to remain Hamiltonian at each step of the derivation.