Nonlinear discharge dynamics in small bore current channels

General properties of current and voltage dynamics for discharges having narrow current channels are studied using a generic transmission-line model with active parameters. The line parameters for the inductance and capacitance per unit length are, except for positivity and some physically motivated monotonicity conditions, left as unspecified functions of local line current and voltage. The resistance per unit length is taken to vary inversely with current, thereby assuring dynamical properties common to transient electrical discharges. Emphasis is placed on determining global properties of current front dynamics, i.e., the speed and direction of motion of the free boundary interfaces between instantaneously active (current-carrying) and passive (current-free) regions of the discharge current channel, and the space-time paths across which current reversal occurs. The results are applied to surface electrical discharges initiated at a charge spot