Nystr\"om Type Exponential Integrators for Strongly Magnetized Charged Particle Dynamics

Abstract

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nystr\"om-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nystr\"om-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nystr\"om-type exponential integators exhibit significant improvement in computation speed over the standard exponential integrators.