Theory of the constant property arc

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Abstract
The canal model for arc discharges is examined and shown to yield a unique consistent solution when the canal boundary temperature T* is specified as a gas property. Electrical and thermal conductivities are taken as constants appropriate to T*. Solutions are obtained for both cylindrical and planar arc columns. Both are qualitatively similar and show a distinct minimum in the current‐electric field characteristic. This is attributed to the competition between the growing arc diameter with current and the increasing conduction to the wall of the dissipated energy. Favorable comparison is shown between this simple model and more exact calculations for arc discharges.