Predictions of arc temperature profiles using approximate emission coefficients for radiation losses

TLDR: In this paper, the authors used the Elenbaas Heller equation to derive temperature profiles of wall stabilized arc plasmas with complex spectra and showed that the approximation using the net coefficients yields central arc temperatures and electric field strengths for a given arc current accurate to 10 per cent.

Abstract: Coefficients are calculated for the net emission of radiation per cc from the center of cylindrical isothermal plasmas of various temperatures and radii. Coefficients are given as a function of temperature and radius for the D lines of sodium vapor at 250 torr and for the continuum radiation of air at 1 and 30 atm. These coefficients are used in the Elenbaas Heller equation to derive temperature profiles of wall stabilized arcs e.g. for 4·5A with a radius of 0·35 cm in sodium vapor at 250 torr and 10,000 and 20,000A with a radius of 1 cm for air at 30 atm. Comparisons are made with calculated temperature profiles where self absorption effects and the radiation transfer are treated exactly, but still assuming thermodynamic equilibrium. It is found that the approximation using the net coefficients yields central arc temperatures and electric field strengths for a given arc current accurate to 10 per cent. Computation time for the approximate calculation is more than an order of magnitude less than for the calculation where radiation transfer is treated exactly. Thus the approximation facilitiates an account of line radiation for arc plasmas having complex spectra.