Hyper Boris integrators for kinetic plasma simulations

TL;DR

This paper introduces hyper Boris integrators that extend the standard Boris method with subcycling and gyrophase corrections, achieving higher-order accuracy in kinetic plasma simulations efficiently.

Contribution

The paper develops a family of high-accuracy particle solvers, the hyper Boris integrators, combining subcycling and gyrophase corrections for improved precision.

Findings

Achieves higher-order accuracy with controlled computational cost.

Provides a formula for arbitrary subcycling number n.

Demonstrates improved numerical error scaling with order N.

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 $N$th-order solver gives a numerical error of $\sim (\Delta t/n)^{N}$ at affordable computational cost.