|approved||barham_sherwood_2022.pdf||2022-04-04 14:28:56||William Barham|
Author: William J. Barham
Requested Type: Poster
Submitted: 2022-03-05 15:23:06
Co-authors: Y. Güçlü, P. J. Morrison, E. Sonnendrücker
University of Texas at Austin
Austin, Texas 78712
The Hamiltonian formalism provides a coherent modeling framework which is advantageous, among other reasons, for discovering conserved quantities, for prescribing a meaningful notion of energy, and for clearly elucidating connections between the myriad models used in plasma physics. Hamiltonian structure has also been shown to be valuable in designing structure preserving discretizations in plasma physics. This work is motivated by the need to discretize Maxwell’s equations in a medium with nonlinear polarization and magnetization as frequently arises in gyrokinetic and drift kinetic models. We consider here only the Maxwell component in isolation. The primary concern of this work is furnishing a Hamiltonian structure preserving discretization of the macroscopic Maxwell equations. Maxwell’s equations are most naturally stated in terms of differential forms. It is helpful to distinguish between twisted and straight differential forms. We discretize Maxwell’s equations with a mimetic spectral element method interpolated over two staggered grids: the straight forms over a primal grid, and the twisted forms over a staggered grid. This approach yields two evolution equations (discretized Faraday’s and Ampère’s laws), and two constitutive relations relating the fields (D,B) with (E,H). The Gauss constraints are automatically enforced as Casimir invariants.