Comparison of Conservation Behavior in Several Variationally Derived Implementations for Simulating Electromagnetic Plasmas

Variational techniques based on Low's Lagrangian formulation have demonstrated significant improvement in conservation properties as compared to traditional particle-in-cell (PIC) algorithms. Previous work showed that equations derived from a discretized Lagrangian preserve a discretized version of the connection between Lagrangian symmetries and conservation laws, i.e., Noether's theorem. Specifically, a thorough analysis of energy conservation within the new system explained the absence of “grid heating” phenomena. In the present work, variationally derived implementations in a gridded periodic domain were compared to analogous implementations using Fourier bases. Since the Fourier basis allows for exact momentum conservation, this approach enables us to compare the relative merits of exact and approximate momentum conservation. To establish a tangible comparison for numerical methods, we investigate two simple physical examples; (1) the coupling of an electrostatic and electromagnetic plasma wave and (2) an equilibrium supporting Weibel instability.