A Sheath Collision Model with Thermionic Electron Emission and the Schottky Correction Factor for Work Function of Wall Material

This paper is a further development of the collisional sheath model at the thermionic cathode for two temperature modeling of thermal arcs that was recently suggested by Pekker and Hussary. In the present work, the Schottky correction factor to the work function of the electrode material is calculated taking into account the friction of ions in the sheath, while in the model of Pekker and Hussary it was calculated neglecting this friction. The model is applied to the cathode spot at the tungsten cathode in argon. It is demonstrated that a virtual cathode can be formed in the atmospheric pressure argon plasma at the cathode surface if the cathode current density is sufficiently small. The heat flux to the thermionic cathode due to charged particles and the heat flux to the plasma due to thermionic electrons are calculated. The obtained results are compared with the model of Pekker and Hussary. The sheath potential drop and the heat fluxes calculated by this model can be used as boundary conditions at the wall for the electric potential and for the energy equations for the electrons and heavy particles (ions and neutrals) in two temperature modeling of thermal plasma.