Drift approximation by the modified Boris algorithm of charged-particle dynamics in toroidal geometry

TL;DR

This paper analyzes the long-term drift behavior of charged particles in toroidal magnetic fields using Fourier expansions, and evaluates the accuracy of a modified Boris algorithm for large time steps.

Contribution

It introduces a drift approximation method for charged particles in toroidal geometry and provides error analysis for the modified Boris algorithm over long durations.

Findings

The drift motion can be accurately approximated using Fourier expansions.

The modified Boris algorithm maintains stability over large time steps.

Numerical results confirm the theoretical error estimates.

Abstract

In this paper, we study the charged-particle dynamics under strong magnetic field in a toroidal axi-symmetric geometry. Using modulated Fourier expansions of the exact and numerical solutions, the long-term drift motion of the exact solution in toroidal geometry is derived and the error analysis of the large-stepsize modified Boris algorithm over long time scales is provided. Numerical experiments illustrate the theoretical results.