An Overview of Relativistic Particle Pushers and their Extension to Arbitrary Order Accuracy

TL;DR

This paper reviews and compares various relativistic particle pushers used in PIC simulations, highlighting the development of high-order schemes and their potential for improved accuracy in plasma physics modeling.

Contribution

It provides a comprehensive comparison of explicit relativistic particle pushers, emphasizing the generalizability of certain schemes to arbitrary high order accuracy and analyzing fourth order variants.

Findings

High-order relativistic particle pushers can be generalized from second order schemes.

Fourth order schemes show improved accuracy over second order counterparts.

The comparison guides the selection of integration schemes for precise plasma simulations.

Abstract

Particle in Cell (PIC) simulations have become a vital tool for the investigation of kinetic processes in plasma physics. Many of the systems investigated with PIC simulations contain particles with relativistic velocities. The correct integration and the knowledge of possible sources of errors in relativistic particle trajectories is of importance to accurately judge the validity of the simulation results. Over the past few decades, various new integration schemes for relativistic particle trajectories in PIC simulations have been proposed. These are aimed at improving numerical accuracy in specific scenarios. This article presents a comprehensive comparison of particle pushers with a focus on explicit schemes. An important class of these schemes is found to be generalisable to arbitrary high order. A comparison of the fourth order variants of these schemes with their second order counterpart is also presented.