Similarity for downscaled kinetic simulations of electrostatic plasmas: reconciling the large system size with small Debye length

TL;DR

This paper introduces a similarity scaling method for kinetic plasma simulations that allows large system sizes to be modeled while maintaining the microscopic physics at the Debye length scale, enabling more efficient and accurate simulations.

Contribution

The paper proposes a novel similarity transformation for particle-in-cell plasma simulations that preserves macroscopic physics while scaling microscopic parameters, facilitating large-scale plasma modeling.

Findings

The similarity transformation effectively preserves transport physics.

Scaling Coulomb logarithm enables control over microscopic physics.

Demonstrated with 1D plasma transport simulations in VPIC.

Abstract

A simple similarity has been proposed for kinetic (e.g., particle-in-cell) simulations of plasma transport that can effectively address the longstanding challenge of reconciling the tiny Debye length with the vast system size. This applies to both transport in unmagnetized plasma and parallel transport in magnetized plasmas, where the characteristics length scales are given by the Debye length, collisional mean free paths, and the system or gradient lengths. The controlled scaled variables are the configuration space, $\mathbf{x}/\mathscr{L},$ and artificial collisional rates, $\mathscr{L}\mu$, which is realized through scaling the Coulomb Logarithm in the simulations, $\mathscr{L}\ln \Lambda.$ Whereas, the scaled time, $t/\mathscr{L}$, and electric field, $\mathscr{L}\mathbf{E}$, are automatic outcomes. The similarity properties are examined, demonstrating that the macroscopic transport physics is preserved through a similarity transformation while keeping the microscopic physics at its original scale of Debye length. To showcase the utility of this approach, two examples of 1D plasma transport problems were simulated using the VPIC code: the plasma thermal quench in tokamaks [J. Li, et al., Nuclear Fusion \textbf{63}, 066030 (2023)] and the plasma sheath in the high-recycling regime [Y. Li, et al., Physics of Plasmas \textbf{30}, 063505 (2023)].