Macroscopic models of internal dynamics of electrical discharges

The existence of thresholds for electrical discharge onset suggests a functional relation between macroscopic resistivity and current. At low current, the resistivity should be inversely proportional to the magnitude of the current. Macroscopic models which employ this scaling predict many empirically observed properties of transient electrical discharges such as: (i) thresholds for the onset of current, (ii) the abrupt termination of current in active regions of a current channel, (iii) current restart in passive regions of current channels, (iv) leaders, and (v) residual charge, both in channels and at sources when current terminates. An overview of research with these models is presented and examples are used to illustrate the results that have been obtained. These models are shown to predict current channel formation and describe results of efforts to benchmark theory with experimental data