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

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.