Plasma Sheath Modeling in the Presence of Collisions

The present work develops a finite element discretized one-dimensional formulation for plasma-sheath dynamics, using multi-fluid equations. The applications include dc and rf sheath inside a glow discharge tube and a partially ionized plasma sheath inside a electric propulsion thruster channel. Based on the experimental data for multiple ionization of a noble gas, a third order polynomial has been used as a fit to describe ionization processes. Such a polynomial has been used to self-consistently calculate the rate of ionization in the plasma dynamic equations. The electron and ion number densities of the numerical solution decrease in the plasma-sheath region as expected. The ion velocity, sheath potential and electron temperature profiles also exhibit the expected behavior. The computed sheath potential compares well with the available experimental data. The model needs to be generalized in the near future for potential application to the high-speed air vehicles.