Numerical challenges in the simulation of 1D bounded low-temperature plasmas with charge separation in various collisional regimes

TL;DR

This paper investigates numerical challenges in simulating 1D low-temperature plasmas with charge separation, proposing a new scheme with controlled diffusion and boundary conditions to improve accuracy across collisional regimes.

Contribution

It introduces a novel numerical scheme with controlled diffusion and boundary conditions tailored for simulating 1D bounded low-temperature plasmas with charge separation.

Findings

Identified key numerical challenges in plasma boundary layer simulations.

Proposed a scheme with controlled diffusion to improve accuracy.

Developed new discrete boundary conditions for better boundary layer modeling.

Abstract

We study a 1D geometry of a plasma confined between two conducting floating walls with applications to laboratory plasmas. These plasmas are characterized by a quasi-neutral bulk that is joined to the wall by a thin boundary layer called sheath that is positively charged. Although analytical solutions are available in the sheath and the pre-sheath, joining the two areas by one analytical solution is still an open problem which requires the numerical resolution of the fluid equations coupled to Poisson equation. Current numerical schemes use high-order discretizations to correctly capture the electron current in the sheath, presenting unsatisfactory results in the boundary layer and they are not adapted to all the possible collisional regimes. In this work, we identify the main numerical challenges that arise when attempting the simulations of such configuration and we propose explanations for the observed phenomena via numerical analysis. We propose a numerical scheme with controlled diffusion as well as new discrete boundary conditions that address the identified issues.