Splitting methods for time integration of trajectories in combined electric and magnetic fields

TL;DR

This paper introduces a second-order splitting method for integrating particle trajectories in combined electric and magnetic fields, preserving the Poisson structure and demonstrating superior long-term stability compared to traditional methods.

Contribution

The paper develops a novel second-order Poisson-preserving splitting method for particle trajectory integration in combined fields, with a comprehensive framework and efficient implementation techniques.

Findings

The new method maintains excellent long-term stability.

Compared to the Boris scheme, it offers improved structure preservation.

Numerical experiments validate the method's effectiveness.

Abstract

The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called $\phi$ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical experiments show an excellent long term stability for the new method considered.