Theoretical description of ac arcs in mercury and argon

Abstract

The energy balance and circuit equations, together with Ohm’s law, are solved numerically to obtain temperature profiles, current, and voltage as functions of time for wall−stabilized ac arcs. Experimental measurements of current and voltage oscillograms and also temperature profiles have been made for 1.5− and 7.5−A rms arcs in mercury vapor. Derived net emission coefficients of radiation as a function of temperature for the 1.5− and 7.5−A arcs are consistent with one another; furthermore, the experimental temperature profiles for both arcs are in good agreement with our theoretical predictions. Theoretical current and voltage waveforms and central temperatures for a 20−A rms arc in argon are in good agreement with the experimental results of Detloff and Uhlenbusch. Radial convection has little influence on these results. An approximate criterion for arc extinction or reignition at current zero is given in terms of the steady−state V−I characteristic and the arc time constant. By relating the present analysis to methods using the Cassie−Francis and the Mayr equations, expressions are derived for the undetermined constants used in these equations for arcs dominated by thermal conduction losses.