Full-fluid modelling of rotating plasma instabilities in Penning-like configurations

Abstract A novel time-dependent full-fluid 2D model of E × B discharges is presented. The model is based on the finite volume method with the addition of a threshold-based vacuum tracking algorithm. These tracking capabilities enable unprecedented fluid simulations of E × B plasma instabilities with near-vacuum regions. Two test cases are presented: the plasma layer (a semi-periodic domain resembling a hollow beam) and a square cross-section Penning-like discharge. In the two cases, an electron beam is injected into a background of neutrals, and ions are solely produced by impact ionisation. In both geometries, the simulations are performed from the limit of a pure electron plasma to a quasineutral plasma by increasing the background neutral density, showing a distinct transition from diocotron modes at low pressures to rotating spokes at high pressures. In line with theoretical and experimental results, the saturated regime of the diocotron mode results in the formation of electron vortices. The structure of the discharge in the different regimes is analysed, and the main spoke characteristics are assessed. In the square Penning configuration, the discharge transitions from vortices to the long-wavelength m = 1 rotating spoke. Finally, a variation of the square configuration is used to demonstrate the onset of the short-wavelength spiral structure observed in particle-in-cell simulations.