Finite element based hydrodynamic sheath model

In the present work, a finite element discretized one-dimensional formulation of plasma-sheath dynamics, using multi-fluid equations for a partially ionized plasma, is given. Based on the experimental data for multiple ionization of xenon 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 decrease in the plasma-sheath region as expected. The neutral number density decreases in the bulk plasma region and increases in the sheath region pointing to the dominant role of recombination near the wall. The ion velocity, sheath potential and electron temperature profiles exhibit the expected behavior.