Analysis of Thermal Induction Plasmas Dominated by Radial Conduction Losses

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Abstract
The energy balance equation is applied to induction plasmas in thermal equilibrium. Approximate, iteration-type, solutions are obtained for cases where heat losses by radiation, axial conduction, and convection can be disregarded. It is assumed that the electric conductivity rises in proportion to the heat conduction potential and that the radial distribution of the induced electric field can be represented by a power law. Under these conditions, the equation can be transformed into Bessel's equation and solved for the heat conduction potential. With a uniform field, the solution reduces to that for a dc arc. The condition of vanishing temperature at the enclosing wall establishes an eigenvalue for the induced electric field at the circumference. Absolute temperature distributions can be calculated as a function of gas properties and applied conditions. It is shown that the latter are given by the time rate of change of primary magnetic flux through the discharge section. The method is applied to argon plasmas at atmospheric pressure. For these plasmas, optimum conversion of magnetic energy into heat should occur at a primary flux rate of 48 V. This value is lowered by the secondary current in the plasma to an actual burning voltage of 32 V. Both values are independent of driving frequency and plasma radius. Skin depth ratio and conversion efficiency at the optimum point agree closely with the values known from induction heating of metals. Experimental data indicate that the discharge has a tendency to operate near this point. Comparison of temperature distributions obtained by this method with exact computer solutions show that the axis temperature is over-estimated by about 15%, but the general shape of the profile is well approximated.