A Self-Consistent Model of the Ponderomotive Force in a Hydrodynamic Plasma and its Hamiltonian Structure Preserving Discretization

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.