  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).
