Abstract Details
Abstracts
Author: William Barham
Requested Type: Poster
Submitted: 2023-03-31 16:53:19
Co-authors: Y. Güçlü, P. J. Morrison, E. Sonnendrücker
Contact Info:
University of Texas at Austin
2515 Speedway
Austin, Texas 78712
Travis
Abstract Text:
A simple model is derived from the two-fluid equations in which the ponderomotive force drives a current source for Maxwell’s equations. This model is shown to come from an asymptotic treatment of an electron fluid model and possess Hamiltonian structure. The net result of the WKB ansatz, which underlies the derivation of the ponderomotive force, is that the electromagnetic fields evolve in a nonlinearly polarized (field dependent) medium. The model is closely related to existing fluid models of the ponderomotive force, but, due to its Hamiltonian structure, is shown to conserve energy and Gauss’s laws through its temporal evolution. The Poisson bracket is a direct sum of the Poisson brackets for the Maxwell and acoustic wave equations and an additional coupling bracket. As these brackets are field-free, a structure preserving spatial discretization is easily accomplished using finite element exterior calculus (FEEC). Moreover, the Hamiltonian splits in a manner which allows exact time integration of each subsystem. Hence, a structure preserving time integration is possible. By utilizing a new broken-FEEC method, all nonlinear solves are localized to each finite element yielding a scalable algorithm. Moreover, because many models in nonlinear optics feature structurally similar Hamiltonian models, similar discretization methods may be derived for a broad class of models.
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