Explicit high-order symplectic integrators for charged particles in general electromagnetic fields

TL;DR

This paper introduces explicit high-order symplectic integrators for simulating non-relativistic charged particles in complex electromagnetic fields, improving accuracy and efficiency over traditional methods.

Contribution

It presents the first construction of explicit high-order symplectic integrators for nonseparable, time-dependent Hamiltonian systems in electromagnetic fields.

Findings

Superior performance over Runge-Kutta methods in simulations

Effective in modeling particle confinement in tokamaks

Demonstrates energy injection via parametric resonance

Abstract

This article considers non-relativistic charged particle dynamics in both static and non-static electromagnetic fields, which are governed by nonseparable, possibly time-dependent Hamiltonians. For the first time, explicit symplectic integrators of arbitrary high-orders are constructed for accurate and efficient simulations of such mechanical systems. Performances superior to the standard non-symplectic method of Runge-Kutta are demonstrated on two examples: the first is on the confined motion of a particle in a static toroidal magnetic field used in tokamak; the second is on how time-periodic perturbations to a magnetic field inject energy into a particle via parametric resonance at a specific frequency.