Dispersion and the Speed-Limited Particle-in-Cell Algorithm

TL;DR

This paper analyzes the dispersion relation of the speed-limited particle-in-cell (SLPIC) method, showing it reduces electron plasma oscillation frequencies while maintaining key plasma physics, enabling larger timesteps and faster plasma simulations.

Contribution

It provides a detailed dispersion analysis of the SLPIC method, demonstrating its ability to relax timestep constraints while accurately modeling plasma dynamics.

Findings

Reduces fast electron plasma oscillation frequencies

Preserves ion acoustic wave physics

Enables larger timesteps in simulations

Abstract

This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and damping). We then demonstrate how the timestep constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger timesteps and faster simulations. These results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.