Current interruption limit and resistance of the self-similar electric arc

A model for the axially blown cylindrical arc is derived. In contrast to earlier theories, the model is gauge invariant with respect to energy, which is crucial for investigating current interruption. We determine from our model the dependence of the maximum interruptible current rate, (dI∕dt)L, on the pressure, on the parallel capacitance, and on the line impedance for an SF6 arc. (dI∕dt)L scales, approximately independent of the gas type, with the square root of the pressure. The arc resistance, at current zero with current rate equal to (dI∕dt)L, is pressure independent. As a consequence, the arc resistance at current zero can serve as a figure of merit for the interruption performance of gas circuit breakers.