Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics

TL;DR

This paper introduces explicit high-order gauge-independent symplectic algorithms for relativistic charged particle dynamics, ensuring long-term accuracy and gauge invariance by employing a Hamiltonian splitting method and variational discretization.

Contribution

The paper develops the first explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic particles using Hamiltonian splitting and variational integrator techniques.

Findings

Algorithms exhibit excellent long-term stability.

Numerical tests confirm gauge independence.

Methods outperform traditional implicit schemes.

Abstract

Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic schemes to relativistic charged particle dynamics result in implicit and electromagnetic gauge-dependent algorithms. In the present study, we develop explicit high-order gauge-independent noncanonical symplectic algorithms for relativistic charged particle dynamics using a Hamiltonian splitting method in the 8D phase space. It also shown that the developed algorithms can be derived as variational integrators by appropriately discretizing the action of the dynamics. Numerical examples are presented to verify the excellent long-term behavior of the algorithms.