A simple model for high-current arcs stabilized by forced convection

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Abstract
Using a one-dimensional analysis investigations are made of properties of arcs stabilized by forced convection in a nozzle. For the current regime where arc diameters are large enough so that conduction and turbulence losses can be neglected at the arc center, yet small enough so that axial pressure and velocity distributions are determined by the nozzle shape, a simple model yields the following analytic properties: (i) Electric field E (z) and temperature distributions T (z) are independent of current, I; (ii) arc area is proportional to arc current and is given approximately by a simple formula; (iii) T (z) is approximately independent of p0, but E (z) ∝p01/2 and arc area ∝1/p01/2, where p0 is the tank pressure; and (iv) the Cassie equation for the time variation of arc conductance is valid. It is assumed that the effective radiation-emission coefficient U (T) is independent of arc radius. We have made measurments of arc area as a function of current in sulfur hexafluoride. These results, together with similar measurements of other investigators using also air and nitrogen, are in good agreement with the theoretical predictions.

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