Two-dimensional analysis of thermal induction plasmas in finite cylinders

Abstract

The temperature field of a static thermal induction plasma, enclosed in a cylindrical container, is calculated from an approximate closed-form solution of the Elenbaas-Heller equation without radiation term. By the assumption that the induced electric field has only a radial dependence, the heat conduction potential can be separated into its radial and axial dependences. Integration of the latter yields a cosine function; solution of the former is obtained by Picard’s iteration method with a previously obtained Bessel-function solution for the infinite cylinder serving as zeroth approximation. The two integration constants are determined by the conditions of zero wall temperature and equality between dissipated rf power and heat conduction losses at the side and end walls. The method is applied to an argon plasma at atmospheric pressure. It is then shown how the results can be refined by including the quartz walls into the heat conduction system, so that the temperature variation along the plasma-wall interface is obtained.