Multidimensional hydrodynamic plasma-wall model for collisional plasma discharges with and without magnetic-field effects

A numerical model for two-species plasma involving electrons and ions at pressure of 0.1 torr is presented here. The plasma-wall problem is modeled using one- and two-dimensional hydrodynamic equations coupled with Poisson equation. The model utilizes a finite-element algorithm to overcome the stiffness of the resulting plasma-wall equations. The one-dimensional result gives insight into the discharge characteristics including net charge density, electric field, and temporal space-charge sheath evolution. In two dimensions, the plasma formation over a flat plate is investigated for three different cases. The numerical algorithm is first benchmarked with published literature for plasma formed between symmetric electrodes in nitrogen gas. The characteristics of plasma are then analyzed for an infinitesimally thin electrode under dc and rf potentials in the presence of applied magnetic field using argon as a working gas. The magnetic field distorts the streamwise distribution because of a large y-momentum V×B coupling. Finally, the shape effects of the insulator-conductor edge for an electrode with finite thickness have been compared using a 90° shoulder and a 45° chamfer. The 90° chamfer displays a stronger body force created due to plasma in the downward and forward directions.