On a large-stepsize integrator for charged-particle dynamics

TL;DR

This paper analyzes a large-stepsize modification of the Boris algorithm for charged-particle dynamics, providing error bounds and numerical validation in non-uniform magnetic fields.

Contribution

It offers the first rigorous error analysis of the large-stepsize Boris method in complex magnetic field settings, extending previous numerical evidence.

Findings

Error bounds are established for the modified Boris method.

Numerical experiments confirm the theoretical error estimates.

The method performs well with larger step sizes in non-uniform magnetic fields.

Abstract

Xiao and Qin [Computer Physics Comm., 265:107981, 2021] recently proposed a remarkably simple modification of the Boris algorithm to compute the guiding centre of the highly oscillatory motion of a charged particle with step sizes that are much larger than the period of gyrorotations. They gave strong numerical evidence but no error analysis. This paper provides an analysis of the large-stepsize modified Boris method in a setting that has a strong non-uniform magnetic field and moderately bounded velocities, considered over a fixed finite time interval. The error analysis is based on comparing the modulated Fourier expansions of the exact and numerical solutions, for which the differential equations of the dominant terms are derived explicitly. Numerical experiments illustrate and complement the theoretical results.