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

TL;DR

This paper extends a charge-conserving finite element solver for Maxwell-Vlasov equations to the relativistic regime, enabling accurate modeling of relativistic plasmas and particle accelerators on unstructured meshes.

Contribution

It introduces and compares three relativistic particle pushers within a charge-conserving FETD-PIC framework for the first time.

Findings

Validated the relativistic algorithm with particle cyclotron motion

Simulated harmonic oscillations in Lorentz-boosted frames

Analyzed relativistic Bernstein modes in pair plasmas

Abstract

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.