Theory of the cathode sheath in a vacuum arc

A previous theory of the plasma sheath transition starting from the charge exchange model for ion collisions is extended to account for ionization and recombination. It is applied to the quasi-neutral boundary layer (presheath) in front of the cathode sheath of a vacuum arc. An essential potential and density difference between the sheath edge and cathodic plasma ball is found. This difference is accounted for in a unified theory of the arc cathode based on G. Ecker´s (1971) existence diagram method, which indicates possible areas of arc operation in the T_cj plane, where T_c is the spot temperature and j is the current density. A numerical evaluation for Cu gives the results which are qualitatively similar to Ecker´s theory. The existence areas are quantitatively enlarged and shifted to lower current densities