A new integrator for relativistic E-cross-B motion of charged particles

A new explicit numerical scheme for integrating the relativistic equations of motion for electrically charged particles is proposed as an alternative to the Boris integrator. It has been known that the original Boris integrator includes a large numerical error in the relativistic motion, although the integrator has been used in particle-in-cell simulations of plasma for a half century. The present integrator approximates the theoretical trajectory of the relativistic E-cross-B motion for a charged particle more accurately than the previous explicit integrators such as the Boris, Vay, and Higuera-Cary ones.