A finite element procedure for time-dependent radio-frequency sheaths based on a two-dimensional microscale fluid model

Abstract

In this paper, we present a finite element scheme for the analysis of time-dependent radio-frequency (RF) sheath behavior in a plasma-filled domain bounded by periodically curved plates. This numerical scheme is based on a two-dimensional (2D) microscale model in which the time-dependent cold-ion fluid equations, the Maxwell–Boltzmann relation for electrons, and Poisson's equation are solved subject to periodic boundary conditions (BCs) and conducting-wall BCs. The continuity of the total current is employed in localized regions to provide a constraint on the reference sheath potential. The primary purpose of this work is to understand 2D dynamic sheath behavior in order to improve predictive capabilities for RF wave interactions in magnetic fusion experiments. In particular, this work treats cases where the local radius of curvature of the wall surface is comparable to the non-neutral sheath width. Using the developed numerical code, the dependences of the ion, electron, and displacement admittances on the wall bump height, ion magnetization, ion mobility, and the magnetic field angle are investigated. It is shown that the ion and electron admittances are nearly unchanged over wide ranges of the bump height and ion magnetization. In addition, the 2D sheath effects are assessed through the spatial distributions of various quantities such as the electron density, electrostatic potential, ion velocity, and surface wall current.