R. T. Robiscoe

A lumped circuit model for transient arc discharges

Electrical breakdown of highly charged insulating systems can result in an arc discharge, i.e., a sudden, intense pulse of current. We model such arcs by a simple circuit: the discharge of a capacitor C (related to the initial charge reservoir) through a series inductor L and resistor R. For R=V*/‖Ia‖, where V* is a positive constant and Ia is the arc current, an essentially arbitrary dependence for L=L(Ia), a constant capacitance, and a circuit starting voltage V0, we establish four remarkable results for the subsequent arc discharge: (1) no discharge occurs at all unless ‖V0‖>V*; (2) if n is the largest non‐negative integer for which ‖V0‖≥(2n+1)V*, then the arc current will reverse sign precisely n times and will decline in amplitude by 2V* at each extreme; (3) the discharge stops abruptly at a final voltage Vf=(−1)n+1[V0−(n+1)2V* sgn V0]; (4) maxima and minima in Ia occur at voltages V=±V*. Results (1) and (3) provide the threshold condition and finite final potential necessary for any realistic arc di...

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, R, and I is assumed to be given by a local arc welder’s ansatz, R‖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.

A distributed parameter wire model for transient electrical discharges

A model for freely propagating transient electrical discharges, such as lightning and punch‐through arcs, is developed in this paper. We describe the electromagnetic fields by Maxwell’s equations and we represent the interaction of electric fields with the medium to produce current by ∂J/∂t=ω2(E−E*J)/4π, where ω and E* are parameters characteristic of the medium, J≡current density, and J≡J/‖J‖. We illustrate the properties of this model for small‐diameter, guided, cylindrically symmetric discharges. Analytic, numerical, and approximate solutions are given for special cases. The model describes, in a new and comprehensive fashion, certain macroscopic discharge properties, such as threshold behavior, quenching and reignition, path tortuosity, discharge termination with nonzero charge density remaining along the discharge path, and other experimentally observed discharge phenomena. Fields, current densities, and charge densities are quantitatively determined from given boundary and initial conditions. We s...

Overdamped arc discharge data and an AWA model

Experimental data on overdamped arc discharges are compared with a lumped-circuit discharge mode employing the arc welders ansatz (AWA). The AWA prescribes that the arc resistance-varies time as R/sub a/(t)=V*/ mod I(t) mod , 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/sub a/ and a small arc inductance L/sub a/, there are an external time-dependent series resistance R/sub o/, inductance L/sub o/, and source capacitance C, the values of which are given. The AWA theory is compared with an observed arc current pulse I(t) by using these given values and normalizing the theory to one point on the data curve; an adequate fit to the data is obtained. Data for the dynamic arc resistance R/sub a/(t) are also compared with the AWA prescription and with other available theories for R/sub a/, which also use a one-point normalization. The AWA form for R/sub a/ compares favorably with the other theories. >

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

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, R, and the current, I, is assumed to be given by the local arc‐welder’s ansatz, R‖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 tha...

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. >

Detection of radio‐frequency signals emitted by an arc discharge

We analyze the nature of radiation signals detected from electrical arcing events originating on highly charged dielectric surfaces. Starting from a simple model of the arc current pulse, we calculate the electromagnetic radiation signal incident on a distant radio‐frequency receiver. The receiver is tuned to some central frequency and operates in a given bandwidth. Because the receiver responds to the arc current derivative rather than the arc current itself, the detected radiation pulse profile can differ substantially from the current pulse profile, even when the receiver bandwidth is large compared to the reciprocal pulse width. This signal distortion significantly affects the interpretation of arc radiation data. To illustrate the point, we show that at high frequencies the detected pulse width carries very little information on the arc itself, and that even a scan of pulse width versus frequency may provide a misleading picture of possible arc dynamics. Finally, we argue that arc radiation data from...

A theory of weak transient electrical discharges on dielectric surfaces

The nonlinear evolution of transient electrical discharges initiated from a small charge spot on dielectric surfaces is analyzed with a transmission line model. The relation between the resistance per unit length, R, and the current, I, is assumed to be given by a local Arc Welder’s Ansatz: R‖I‖=E*, where E* is a positive constant. Comparison is made with a similar study of discharges initiated from a large charge spot. While both studies predict conditions under which charge is, or is not, transported to a dielectric edge, significant differences in the two cases are revealed. For example, if charge is not transported to an edge, current reversal is possible if the charge spot is small, but can only be unidirectional if the spot is large.

Circuit model of surface arcing

An electrical breakdown on a highly charged dielectric surface can result in a discharge along the surface, i.e., a flashover arc. We construct a simple circuit model for such an arc: the discharge of a capacitor C (related to the initial charged area) through a series inductor L and resistor R (related to the arc considered as a plasma). The arc current assumes a very simple form over most of its dynamic range, and such measured arc quantities as total charge transport, pulse width, peak current, and rise time are easily calculated. Moreover, straightforward a priori estimates of C, L, and R values give calculated arc quantities in good agreement with observation, for both typical magnitudes and areal scaling. We also analyze the effect on areal scaling of allowing the arc resistance R to ‘‘switch’’ during the evolution of the arc, from a small value characteristic of the arc plasma to a large value characteristic of the dielectric surface. Finally, we consider some aspects of the electromagnetic radiati...

Shape‐dependent effects on an electromagnetic pulse propagating in a lossy plasma

We develop a theory describing the propagation of an electromagnetic pulse propagating in one dimension through a medium of essentially arbitrary conductivity and polarizability. An integral solution for the pulse amplitude is obtained by means of the slowly varying envelope approximation. Within the limits of this approximation (which requires linear coupling of the pulse to the medium, smooth variation of the pulse envelope, and pulse widths large enough to contain many cycles of the pulse carrier frequency), our solution is quite general, and it allows relatively easy comparison of the evolution of various pulse shapes as they travel through the medium. We apply the theory to an analysis of a pulse propagating in a lossy plasma, and show that among pulses with similar initial widths and energies, the initial pulse shape can have significant effects on the subsequent pulse distortion, broadening, and energy transport. Specifically, for a lossy plasma, we find that the pulse energy transport is enhanced ...