High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

TL;DR

This paper develops high order symmetric volume-preserving algorithms for relativistic charged particles in electromagnetic fields, offering improved accuracy, efficiency, and stability for long-term simulations.

Contribution

It introduces explicit high order volume-preserving methods using splitting and processing techniques applicable to time-dependent electromagnetic systems.

Findings

Methods achieve good accuracy and conservative properties.

High order methods allow larger time steps.

Numerical experiments verify efficiency and stability.

Abstract

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. Via expanding the phase space to include time $t$, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of processing technique the high order methods are explicit, and cost less than the methods derived from standard compositions, thus are more efficient. The results are verified by the numerical experiments. Linear stability analysis of the methods show that the high order processed method allows larger time step size during integration.