Abraham Kadish

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.

End shorting induced rotation in a ϑ pinch

A possible explanation for the observed rotation in open ended ϑ‐pinch devices is shown to result from the shorting out of electric field components at the insulating boundary. The propagation of rotation into the plasma is primarily via torsional Alfven waves preceded by dispersive precursors. The precursors have spatially and temporally modulated amplitudes. They are due to gyrofrequency oscillations of the plasma and are seen throughout the plasma immediately following the shorting out of the electric field components at the insulators.

Analysis and simulation of virtual cathode oscillations

A nonlinear mechanism for virtual cathode oscillations is derived from an analysis of a cold plasma fluid model. Frequency scalings and field wave shapes are predicted. These are compared with extensive numerical simulation studies of non‐neutral electron beams using both one‐ and two‐dimensional particle‐in‐cell codes.

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. >

Electromagnetic radiation from abrupt current changes in electrical discharges

We treat electromagnetic radiation from narrow electrical discharges, with particular emphasis on the asymptotic behavior at high frequencies f. We show that discontinuities in the discharge current and its derivatives dominate the high‐frequency part of the radiated spectrum. Specifically, when a current discontinuity is present, the envelope of the radiated fields falls off with large f as f −1 for almost all observation angles. If the current is continuous but has discontinuities in its first derivatives, then the envelope of the radiated field falls off as f −(1+1/n) at large f for a range of observation angles. If the discharge current and its first derivatives are continuous, then the radiated fields fall off at least as fast as f −2 at large f. The characteristic high‐frequency dependence associated with abrupt current change persists for some large range of f, even when current variation is not precisely abrupt. We illustrate the general results with radiation from AWA discharge models (previously...

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. >

A Generalization of the Child-Langmuir Relation for One-Dimensional Time-Dependent Diodes

The steady-state Child-Langmuir relation between current and applied voltage has been a basic principle upon which all modern diode physics has been based. With advances in pulsed power technology and diode design, new devices which operate in vastly different parameter regimes have recently become of interest. Many of these devices cannot be said to satisfy the strict requirements necessary for Child-Langmuir flow. For instance, in a recent pulsed electron device for use in high-current accelerators, the applied voltage is sinusoidal in time. In another case, development of sources for heavy ion fusion necessitates understanding of transient current oscillations when the voltage is applied abruptly. We derive the time-dependent relationship between the emitted current and time-dependent applied voltage in a nonrelativistic planar diode. The relationship is valid for arbitrary voltage shapes V(t) applied to the diode for times less than the beam-front transit time across the gap. Using this relationship, transient and time-dependent effects in the start-up phase of any nonrelativistic diode can be analyzed.