Theory of electrical discharges initiated from a large charge spot on dielectric surfaces

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Abstract
The nonlinear dynamics of charge transport due to an electric discharge on a dielectric surface is analyzed using a transmission line model. The relation between the resistance per unit length, R̂, and the current, I, is assumed to be given by the local arc-welder’s ansatz, R̂‖I‖=E*, where E* is a positive constant. The model predicts that a discharge initiated in the vicinity of a charge spot can propagate partway down a current channel and abruptly terminate before transporting charge to the dielectric edge. This behavior is similar to leader phenomena observed in lightning and other electrical discharges. We show that the direction of the current along the current channel is constant throughout such a discharge. The minimum voltage at the charge spot that allows charge to be transported to the dielectric edge is determined. This critical voltage Vl depends on the length l of the current channel. We show that the ‘‘average field,’’ Vl/l, decreases as l increases. When the charge spot voltage is less than the critical voltage, we obtain upper and lower bounds for both the arc duration time and amount of charge removed from the charge spot.

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