Nonsteady coaxial arcs in fully developed plasma flow.

A simplified analytical model representing arc operations under conditions of nonsteady electrical inputs is considered. The assumptions that Emmons applied to the steady-state case are imposed: discontinuous model for electrical conductivity, other gas properties constant, fully developed flow within a tube. Solution of the energy equation (uncoupled from the momentum equation) is obtained separately in each of two regions: the heated zone (wherein electrical conductivity differs from zero) and the unheated zone. The solutions are joined at the arc boundary (critical radius), resulting in a moving boundary problem. Using the Green's function method, an integral equation for the boundary motion and integral equations for the temperature profiles in the two regions are obtained. Approximate solutions of these equations are obtained for small times. The case of a step function pulse of the source was considered; numerical solutions of the integral equations were obtained over the complete time range. Solutions obtained according to the approximate method are in good agreement with the numerical calculations. Arc extinction was also studied using a negative pulse of sufficient strength.