Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

TL;DR

This paper develops explicit symplectic algorithms of order 2 and 3 for simulating relativistic charged particles in time-dependent electromagnetic fields, enabling accurate long-term numerical simulations.

Contribution

It introduces the first explicit symplectic algorithms for relativistic particle dynamics using generating functions and sum-split techniques.

Findings

Algorithms of order 2 and 3 successfully constructed.

Enhanced accuracy for long-term simulations.

Applicable to complex, time-dependent electromagnetic fields.

Abstract

Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using symplectic integrators. For modern large-scale particle simulations in complex, time-dependent electromagnetic field, explicit symplectic algorithms are much more preferable. In this paper, we treat the relativistic dynamics of a particle as a Hamiltonian system on the cotangent space of the space-time, and construct for the first time explicit symplectic algorithms for relativistic charged particles of order 2 and 3 using the sum-split technique and generating functions.