A Comparative Analysis of Relativistic Particle Pushers vis-à-vis Computation Time & Accuracy

Abstract

The performance of relativistic particle pushers has long been a topic of interest in the field of computational plasma physics, particularly from the point of view of the particle-in-cell approach. Previous works undertaken to compare such integrators have predominantly targeted the ultra-relativistic regime. In this paper, we utilize a custom-built code to study the core run-times of the Boris, the Vay, and the Higuera-Cary particle pushers for low-, high-, and ultra-relativistic particles. This is followed by a comparison of the three integrators in terms of accuracy and error. A fitness parameter is then proposed that can serve as a one-stop value to determine which method is more suitable for a particular simulation setup. It is hoped that through knowledge of such intricacies, the choice for the integrator will be easier to make depending on the problem at hand.

Figures (19)

• Figure 1: Demonstrative graphics for the staggered updates followed by leapfrog integrators.
• Figure 2: Core runtimes (s) of Boris, Vay, and Higuera-Cary integrators. Solid lines correspond to average run-time, while faint dotted lines show the individual runs. The reader is advised to refer to the online version of this text for improved visibility.
• Figure 3: Configuration space plots in microns for the uniform magnetic field in the LR regime.
• Figure 4: Relative Gamma and absolute phase errors (rad) for magnetic gyration in the LR regime. The slight wave in HC phase error stems out of the sinusoidal nature of the trajectory.
• Figure 5: Gyroradius errors ($\times 10^{-3}$) for the uniform magnetic field in the LR regime.