Plasma walls beyond the perfect absorber approximation for electrons

TL;DR

This paper investigates the limitations of the perfect absorber model for electrons at plasma walls, calculating specific sticking coefficients and desorption times, and finds that real walls are less absorbing than the idealized model suggests.

Contribution

It introduces a detailed calculation of electron sticking coefficients and desorption times for dielectric walls, challenging the perfect absorber approximation in plasma wall models.

Findings

Electron sticking coefficient $s_e \,\ll\, 1$ for uncharged walls.

Electron desorption time $\tau_e \approx 10^{-4}$ s for uncharged walls.

Self-consistent wall potential is about 30% of the perfect absorber value.

Abstract

Plasma walls accumulate electrons more efficiently than ions leading to wall potentials which are negative with respect to the plasma potential. Theoretically, walls are usually treated as perfect absorber for electrons and ions implying perfect sticking of the particles to the wall and infinitely long desorption times for particles stuck to the wall. For electrons we question the perfect absorber model and calculate, specifically for a planar dielectric wall, the electron sticking coefficient $s_e$ and the electron desorption time $\tau_e$. For the uncharged wall we find $s_e\ll 1$ and $\tau_e\approx 10^{-4}s$. Thus, in the early stage of the build-up of the wall potential, when the wall is essentially uncharged, the wall is not a perfect absorber for electrons. For the charged wall we find $\tau_e^{-1}\approx 0$. Thus, $\tau_e$ approaches the perfect absorber value. But $s_e$ is still only of the order of $10^{-1}$. Calculating $s_e$ as a function of the wall potential and combining this expression with the quasi-stationary balance equations for the electron and ion surface densities we find the selfconsistent wall potential, including surface effects, to be 30% of the perfect absorber value.