A self-consistent Hamiltonian model of the ponderomotive force and its structure preserving discretization

TL;DR

This paper develops a Hamiltonian model for the ponderomotive force in plasmas and introduces structure-preserving discretizations that conserve key invariants with high accuracy.

Contribution

It presents a self-consistent Hamiltonian framework for the ponderomotive force and introduces novel discretization methods that preserve the model's geometric invariants.

Findings

Discretizations conserve Casimir invariants to machine precision.

Energy conservation is achieved to the order of the splitting method.

The model effectively couples electromagnetic fields with plasma dynamics.

Abstract

In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which self-consistently couples the electromagnetic field to a plasma which experiences the ponderomotive force. We derive a family of structure preserving discretizations of the model of varying order in space and time using conforming and broken finite element exterior calculus spectral element methods. In all variants of our discretization framework, the method is found to conserve the Casimir invariants of the continuous model to machine precision and the energy to the order of the splitting method used.