Numerical thermalization in 2D PIC simulations: Practical estimates for low temperature plasma simulations

TL;DR

This paper provides practical estimates and analysis of numerical thermalization effects in 2D PIC simulations, especially for low temperature plasmas, offering guidance on mitigation strategies and impact assessment.

Contribution

It introduces a practical tutorial with numerical coefficients and timescales for understanding and estimating numerical thermalization in 2D PIC simulations of low temperature plasmas.

Findings

Numerical thermalization can significantly modify electron velocity distributions in 2D PIC simulations.

Comparison of analytical relaxation timescales with simulation results helps assess thermalization impact.

Strategies for mitigating numerical relaxation effects are discussed for various plasma applications.

Abstract

The process of numerical thermalization in particle-in-cell (PIC) simulations has been studied extensively. It is analogous to Coulomb collisions in real plasmas, causing particle velocity distributions (VDFs) to evolve towards a Maxwellian as macroparticles experience polarization drag and resonantly interact with the fluctuation spectrum. This paper presents a practical tutorial on the effects of numerical thermalization in 2D PIC applications. Scenarios of interest include simulations which must be run for many thousands of plasma periods and contain a population of cold electrons that leave the simulation space very slowly. This is particularly relevant to many low temperature plasma discharges and materials processing applications. We present numerical drag and diffusion coefficients and their associated timescales for a variety of grid resolutions, discussing the circumstances under which the electron VDF is modified by numerical thermalization. Though the effects described here have been known for many decades, direct comparison of analytically derived, velocity-dependent numerical relaxation timescales to those of other relevant processes has not often been applied in practice due to complications that arise in calculating thermalization rates in 1D simulations. Using these comparisons, we estimate the impact of numerical thermalization in several example low temperature plasma applications including capacitively coupled plasma (CCP) discharges, inductively coupled plasma (ICP) discharges, beam plasmas, and hollow cathode discharges. Finally, we discuss possible strategies for mitigating numerical relaxation effects in 2D PIC simulations.