Explicit non-canonical symplectic algorithms for charged particle dynamics

TL;DR

This paper develops explicit, stable non-canonical symplectic algorithms for charged particle dynamics, leveraging Hamiltonian splitting to ensure long-term accuracy and structure preservation.

Contribution

It introduces a novel splitting technique for non-canonical Hamiltonian systems, enabling explicit symplectic methods that are stable over long simulations.

Findings

Methods preserve K-symplectic structure over long-term simulations

Numerical experiments demonstrate stability and efficiency

Error analysis confirms convergence properties

Abstract

We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the long-term simulation. The key point of splitting is to decompose the Hamiltonian as four parts, so that the resulting four subsystems have the same structure and can be solved exactly. This guarantees the K-symplectic preservation of the numerical methods constructed by composing the exact solutions of the subsystems. The error convergency of numerical solutions is analyzed by means of the Darboux transformation. The numerical experiment display the long-term stability and efficiency for these methods.