High Order Numerical Integrators for Relativistic Charged Particle Tracking

Abstract

In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth order algorithm is given explicitly and tested with numerical examples. Such high order numerical integrators can significantly save the computational cost by using a larger step size in comparison to the second order integrators.