A high-order Boris integrator
  This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in an electric and magnetic field. Boris-SDC relies on a combination of the Boris-integrator with spectral deferred corrections (SDC). SDC can be considered as preconditioned Picard iteration to compute the stages of a collocation method. In this interpretation, inverting the preconditioner corresponds to a sweep with a low-order method. In Boris-SDC, the Boris method, a second-order Lorentz force integrator based on velocity-Verlet, is used as a sweeper/preconditioner. The presented method provides a generic way to extend the classical Boris integrator, which is widely used in essentially all particle-based plasma physics simulations involving magnetic fields, to a high-order method. Stability, convergence order and conservation properties of the method are demonstrated for different simulation setups. Boris-SDC reproduces the expected high order of convergence for a single particle and for the center-of-mass of a particle cloud in a Penning trap and shows good long-term energy stability. 
Mathias Winkel, Robert Speck, Daniel Ruprecht
math.NA cs.NA