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

Abstract

This paper proposes a model that expands Godyak's collisional sheath model to the case of hot electrodes (anode or cathode) with thermionic electron emission. In the model, the electrodes are assumed to be made from refractory metals and, consequently, the erosion of the electrodes is small and can be neglected. In the frame of two temperature thermal plasma modeling, this model allows self-consistent calculation of the sheath potential drop, the Schottky correction factor for the work function of the wall material, the thermionic electron current density, and the heat fluxes of the charged particles from the plasma to the wall. The model is applied to the cathode spot at the tungsten cathode in argon. It is shown that the Shottky correction factor plays a crucial role in modeling high-intensity arcs. It is demonstrated that a virtual cathode can be formed in the atmospheric pressure argon plasma at the cathode surface temperature of 4785 K 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 model can be reduced to the case of cold walls where the thermionic electron emission and the wall erosion processes are small and can be neglected. 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).