Relativistic Extension of a Charge-Conservative Finite Element Solver for Time-Dependent Maxwell-Vlasov Equations

In many problems involving particle accelerators and relativistic plasmas, the accurate modeling of relativistic particle motion is essential for accurate physical predictions. Here, we extend a charge-conserving finite element time-domain (FETD) particle-in-cell (PIC) algorithm for the time-dependent Maxwell-Vlasov equations on irregular (unstructured) meshes to the relativistic regime by implementing and comparing three particle pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.