High Order Explicit Lorentz Invariant Volume-preserving Algorithms for Relativistic Dynamics of Charged Particles

TL;DR

This paper develops high-order explicit Lorentz invariant volume-preserving algorithms for charged particle dynamics, ensuring long-term stability and Lorentz invariance in relativistic simulations.

Contribution

It introduces a novel Lorentz invariant splitting technique to construct explicit volume-preserving algorithms with high order accuracy for relativistic charged particle simulations.

Findings

Algorithms demonstrate long-term stability.

Algorithms preserve Lorentz invariance.

Performance analysis confirms effectiveness.

Abstract

Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct structure-preserving algorithms, but without exquisite considerations, it can easily break the Lorentz invariance of continuous systems. In this paper, we introduce a Lorentz invariant splitting technique to construct high order explicit Lorentz invariant volume-preserving algorithms (LIVPAs) for simulating charged particle dynamics. Using this method, long-term stable explicit LIVPAs with different orders are developed and their performances of Lorentz invariance and long-term stability are analyzed in detail.