An asymptotic treatment of the Elenbaas–Heller equation for a radiating wall-stabilized high-pressure gas-discharge arc

An asymptotic analysis of the Elenbaas–Heller equation for a radiating wall-stabilized high-pressure gas-discharge arc is given. This analysis applies when the operating temperatures within the arc are lower than the ionization temperature by an order of magnitude. It is shown that for arcs that are radiating highly efficiently a further asymptotic treatment can be given. It is shown under what conditions, governed by a dimensionless parameter M, this limiting case prevails. Comparison with earlier results put forward by Zollweg [J. Appl. Phys. 49, 1077 (1978)] shows satisfactory agreement.