A self-consistent model for the cathode fall region of an electric arc

A one-dimensional model of the non-equilibrium plasma region adjacent to an electric are cathode is developed. The collisionless space-charge zone (sheath) and the hydrodynamically described ionization zone (pre-sheath) are connected to a unified model. In the pre-sheath, ionization, diffusion and decoupling of electron and heavy-particle temperature are considered. The voltage drop in the space-charge zone is computed self-consistently including thermionic electron emission at the cathode surface. This unified model yields the overall cathode potential drop (cathode fall), the extent of the non-equilibrium region and the net energy flux towards the cathode surface. In this paper, the model is applied to an argon are plasma at atmospheric pressure with a thoriated tungsten cathode, as is typically used for welding of stainless steel materials.