Hyper Boris integrators for kinetic plasma simulations

Abstract

We propose a family of numerical solvers for the nonrelativistic Newton–Lorentz equation in kinetic plasma simulations. The new solvers extend the standard 4-step Boris procedure, which has second-order accuracy in time, in three ways. First, we repeat the 4-step procedure multiple times, using an n-times smaller timestep ($\Delta t/n$). We derive a formula for the arbitrary subcycling number n, so that we obtain the result without repeating the same calculations. Second, prior to the 4-step procedure, we apply Boris-type gyrophase corrections to the electromagnetic field. In addition to a well-known correction to the magnetic field, we correct the electric field in an anisotropic manner to achieve higher-order ($N=2,4,6\dots$th order) accuracy. Third, combining these two methods, we propose a family of high-accuracy particle solvers, the hyper Boris solvers, which have two hyperparameters of the subcycling number n and the order of accuracy, N. The n-cycle Nth-order solver gives a numerical error of $\sim {(\Delta t/n)}^N$ at affordable computational cost.