Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

TL;DR

This paper develops geometric exponential energy-preserving integrators for charged-particle dynamics in magnetic fields, effective across normal to strong regimes, ensuring energy conservation and symmetry.

Contribution

It introduces new symmetric continuous-stage exponential integrators of order up to four for charged-particle systems in magnetic fields, extending to nonuniform fields.

Findings

Methods preserve energy and symmetry.

Numerical experiments show improved efficiency.

Applicable to both uniform and nonuniform magnetic fields.

Abstract

This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a uniform magnetic field by using the idea of continuous-stage methods, and then discuss its energy-preserving property. Moreover, symmetric conditions and order conditions are analysed. Based on those conditions, we propose two practical symmetric continuous-stage exponential energy-preserving integrators of order up to four. Then we extend the obtained methods to the system in a nonuniform magnetic field and derive their properties including the symmetry, convergence and energy conservation. Numerical experiments demonstrate the efficiency of the proposed methods in comparison with some existing schemes in the literature.