New applications for the Boris Spectral Deferred Correction algorithm for plasma simulations

TL;DR

This paper explores two novel applications of the Boris Spectral Deferred Corrections (Boris-SDC) algorithm in plasma simulations, demonstrating improved accuracy and high-order convergence in both electrostatic and relativistic regimes.

Contribution

It introduces Boris-SDC as a particle pusher in PIC codes and modifies it for relativistic regimes, showing enhanced accuracy and convergence in plasma simulations.

Findings

Boris-SDC improves accuracy over standard Boris in linear electrostatic PIC.

Boris-SDC allows larger time steps, reducing computational cost.

Boris-SDC maintains high-order convergence at relativistic velocities.

Abstract

The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a particle pusher in an electrostatic particle-in-cell (PIC) code can, at least in the linear regime, improve simulation accuracy compared with the standard second order Boris method. In some instances, the higher order of Boris-SDC even allows a much larger time step, leading to modest computational gains. Second, we propose a modification of Boris-SDC for the relativistic regime. Based on an implementation of Boris-SDC in the \textsc{runko} PIC code, we demonstrate for a relativistic Penning trap that Boris-SDC retains its high order of convergence for velocities ranging from $0.5c$ to $>0.99c$. We also show that for the force-free case where acceleration from electric and magnetic field cancel, Boris-SDC produces less numerical drift than Boris.