Advanced numerical techniques for time integration of relativistic equations of motion for charged particles

Abstract

Abstract Advanced numerical techniques for solving the relativistic equations of motion for charged particles are provided. A new fourth-order integrator is developed by combining the Taylor series expansion of the numerical angle of relativistic gyration and the fourth-order Runge–Kutta method for integrating the Lorentz factor. The new integrator gives the exact relativistic E-cross-B drift velocity, but has a numerical accuracy much higher than the classic fourth-order Runge–Kutta integrator. Graphical Abstract