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. (Specific functions would be determined by configuration-specific self-consistent variations of the current channel with fields.) The resistance per unit length is taken to vary inversely with current, thereby assuring dynamical properties common to transient electrical discharges, i.e., 1) thresholds to be exceeded by local voltage gradients for discharge current initiation, 2) locally abrupt current termination with the possibility of later self-generated current restart, and 3) residual charge gradients in the current channel at discharge termination. (This model of the resistance describes the ''glow region'' of 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.

We compare experimental data on overdamped arc discharges with a lumped-circuit discharge model employing the Arc Welder's Ansatz (AWA). The AWA prescribes that the arc resistance varies in time as R-alpha (t) = V*/\I(t)\, where V* is a positive constant and I (t) is the discharge current. In the circuit, in addition to the time-dependent arc resistance R-alpha and a small arc inductance L-alpha, there is an external time-dependent series resistance R(o), inductance L(o), and source capacitance C; the values of R(o), L(o), and C are given. We compare the AWA theory with an observed arc current pulse I (t) by using the given values of R(o), L(o), and C and normalizing the theory to one point on the data curve; an adequate fit to the data is obtained. We also compare data for the dynamic arc resistance R-alpha (t) with the AWA prescription and with other available theories for R-alpha, which also use a one-point normalization. The AWA form for R-alpha compares favorably with the other theories. Next, we show that many theories for the arc resistance near threshold (where the current I --> 0+ as t --> 0+) can be reduced to the form R-alpha is-proportional-to 1/I(P), p > 0, and we argue that for proper threshold behavior, one must have p = 1. The AWA theory meets this criterion; most other theories do not. Although all theories of R-alpha are subject to questions regarding the onset of the arc, we conclude that our AWA theory-in its present form-accounts for overdamped arc discharge data after onset at least as well as other existing theories.

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. >

Summary Form only given, as follows. Charge transport in a surface flashover arc has been analyzed using a transmission line model. The generator is a charge spot whose capacitance is taken to be large compared to the capacitance of the charge path. Resistance per unit length, R, is assumed to satisfy a local arc welder's ansatz, R mod I mod =E.*, where I is the local current and E* is a constant with the dimensions volts per meter. If charge flow is in the interval 0or=E(1+x/sub 1//L)/2, charge will not arrive at the far end of the line. The current will first abruptly terminate everywhere on the line. For configurations of different lengths but fixed x/sub 1/, the inequality shows that, for a flashover to occur, the minimum value of V/sub 0//L is a decreasing function of the path length, L. The inequality can also be used to show that if the initial charge on the line is localized near the generator, then, for a flashover to occur, the initial potential gradients must be very large compared to E*.<>

Summary Form only given, as follows. The dynamics of flashover arc discharges is studied using a transmission line model in which the resistance per unit length, R, and the current, I, are assumed to satisfy the local arc welder's ansatz R mod I mod =E*, where E* is a constant that has the dimensions of an electronic field. The model predicts a local threshold condition for onset of current flow: mod delta V/ delta x mod >E*, where V(x,t) is the electric potential across the transmission line at position x and time t. This condition can be interpreted as a condition for stripping of charge by electric fields parallel to the arc path. The model also predicts abrupt termination of arc current in some parts of the transmission line, while other parts remain active. In general, passive regions where current flow has terminated remain electrically charged. Current in the active regions can either quench or generate restart of current in a neighboring passive region.<>