Analysis of the cathodic region of atmospheric pressure discharges

The cathodic region of atmospheric pressure arcs is dominated by a number of different mechanisms. This makes a theoretical model extremely difficult. A description of this region based on fundamental physical principles is given. Using a previously published model of the inhomogeneous boundary layer of a Saha plasma (Schmitz H and Riemann K-U 2001 J. Phys. D: Appl. Phys. 34 1193), the description is set on a firm theoretical basis. A number of equations including the energy balances of plasma boundary and cathode body lead to a maximum closure of the system. The values for the boundary conditions toward the plasma column could be motivated by a simple minimum principle argument thus eliminating all arbitrary fitting parameters. Results are given for a variety of external parameters and three different discharge gases. The comparison with experimental results shows excellent agreement.