High-Accuracy Numerical Integration of Charged Particle Motion – with Application to Ponderomotive Force

Abstract

A high-accuracy numerical integration algorithm for a charged particle motion is developed. The algorithm is based on the Hamiltonian mechanics and the operator decomposition. The algorithm is made to be time-reversal symmetric, and its order of accuracy can be increased to any order by using a recurrence formula. One of the advantages is that it is an explicit method. An effective way to decompose the time evolution operator is examined; the Poisson tensor is decomposed and non-canonical variables are adopted. The algorithm is extended to a time dependent fields' case by introducing the extended phase space. Numerical tests showing the performance of the algorithm are presented. One is the pure cyclotron motion for a long time period, and the other is a charged particle motion in a rapidly oscillating field.