A theory of abrupt termination and spontaneous restart of electrical current in surface flashover arcs

The space-time dynamics of surface flashover discharges is studied using a nonlinear one-dimensional transmission line model. When the current I is not zero, the relation between the resistance per unit length, R̂, and I is assumed to be given by a local arc welder’s ansatz, R̂‖I‖=E*, where E* is a constant. The model predicts a threshold for discharge, and abrupt local termination and spontaneous restart of the discharge current. If at a place on the discharge path it happens that the charge gradient fails to exceed the threshold condition when the current vanishes, then the current will abruptly terminate there. However, if a discharge current flows in a region adjacent to one where the current has terminated, the edge of the current-free region can be ‘‘ignited,’’ resulting in the ‘‘active’’ region encroaching on the ‘‘quiet’’ one. A formula for the speed of encroachment is derived. Formulas are also derived for current pulse waveforms and the charge transported during the discharge.