Exploring exponential time integration for strongly magnetized charged particle motion

TL;DR

This paper investigates exponential integration methods for simulating charged particle motion in strongly magnetized plasmas, demonstrating improved performance over traditional schemes especially in linear cases.

Contribution

It introduces exponential integrators as an effective alternative to finite difference schemes for stiff plasma simulations with strong magnetic fields.

Findings

Exponential integrators outperform finite difference schemes in linear plasma problems.

They are competitive with traditional methods in nonlinear cases with cubic and quartic potentials.

The approach reduces numerical stiffness issues in strongly magnetized plasma simulations.

Abstract

A fundamental task in particle-in-cell (PIC) simulations of plasma physics is solving for charged particle motion in electromagnetic fields. This problem is especially challenging when the plasma is strongly magnetized due to numerical stiffness arising from the wide separation in time scales between highly oscillatory gyromotion and overall macroscopic behavior of the system. In contrast to conventional finite difference schemes, we investigated exponential integration techniques to numerically simulate strongly magnetized charged particle motion. Numerical experiments with a uniform magnetic field show that exponential integrators yield superior performance for linear problems (i.e. configurations with an electric field given by a quadratic electric scalar potential) and are competitive with conventional methods for nonlinear problems with cubic and quartic electric scalar potentials.