BACKGROUND:Endocardial mapping of sustained arrhythmias has traditionally been performed with a roving diagnostic catheter. Although this approach is adequate for many tachyarrhythmias, it has limitations. The purpose of this study was to evaluate a novel noncontact mapping system for assessing atrial tachyarrhythmias.METHODS AND RESULTS:The mapping system consists of a 9F multielectrode-array balloon catheter that has 64 active electrodes and ring electrodes for emitting a locator signal. The locator signal was used to construct a 3-dimensional right atrial map; it was independently validated and was highly accurate. Virtual electrograms were calculated at 3360 endocardial sites in the right atrium. We evaluated right atrial activation by positioning the balloon catheter in the mid right atrium via a femoral venous approach. Experiments were performed on 12 normal mongrel dogs. The mean correlation coefficient between contact and virtual electrograms was 0.80+/-0.12 during sinus rhythm. Fifty episodes of atrial flutter induced in 11 animals were evaluated. In the majority of experiments, complete or almost complete reentrant circuits could be identified within the right atrium. Mean correlation coefficient between virtual and contact electrograms was 0.85+/-0.17 in atrial flutter. One hundred fifty-six episodes of pacing-induced atrial fibrillation were evaluated in 11 animals. Several distinct patterns of right atrial activation were seen, including single-activation wave fronts and multiple simultaneous-activation wave fronts. Mean correlation coefficient between virtual and contact electrograms during atrial fibrillation was 0.81+/-0.18. The accuracy of electrogram reconstruction was lower at sites >4.0 cm from the balloon center and at sites with a high spatial complexity of electrical activation.CONCLUSIONS:This novel noncontact mapping system can evaluate conduction patterns during sinus rhythm, demonstrate reentry during atrial flutter, and describe right atrial activation during atrial fibrillation. The accuracy of electrogram reconstruction was good at sites <4.0 cm from the balloon center, and thus the system has the ability to perform high-resolution multisite mapping of atrial tachyarrhythmias in vivo.

The relationship between mathematical models of active parameters for transmission lines is studied. Treating transmission lines as a series of differential lumped circuits, we show that pairs of line parameters for inductance and capacitance per unit length must satisfy one of two constraints. One of these is a symmetry condition, which is satisfied by passive (i.e. constant) parameters. If a parameter pair satisfies either of these constraints, the energy per unit length and power loss in the line may be written as integrals of known functions, no matter what the pair's dependence on line current and voltage may be. Potential applications of these results to other subject areas are discussed.

Formative times in electrical discharges in overvoltaged gaps are analyzed with a model having no spatial dependence and with simple assumptions about discharge channel temperature T and discharge voltage. The model treats the early temporal evolution of the discharge. Specifically, the dissipative voltage drop, V*, across the discharge is taken to be a step function of T. Thermal quasi-equilibrium is assumed in the discharge medium, and it is shown that d(In t/sub d/)//sub d/(In theta )=-1, i.e., theta t/sub d/=constant, where theta is the fractional overvoltage and t/sub d/ is the formative time lag, in agreement with measured values of t/sub d/ for much of the experimentally explored range of theta . Highly-time-resolved ( approximately 92 ps) experimental data are presented for the first 10 ns of electrical discharge initiation; these data suggest that the authors' model should provide a reasonable representation of t/sub d/ when t/sub d/>10-100 ns. >

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 referred to as arc welder’s ansatz models) featuring a constant electric field associated with dissipative discharge processes.

Electromagnetic radiation from narrow-bore electrical discharges is analyzed with emphasis on the asymptotic behavior at high frequencies, f. This part of the radiated spectrum is dominated by discontinuities in the discharge current and its derivatives. When a discontinuity in the current is present, the envelope of the radiated field falls off with large f as f -1 for almost all observation angles. If the current is continuous but has discontinuities in its first time derivative, the envelope falls off like f - (1 + 1/n) (where n is an integer ≥ 2) for a range of observation angles. If the current and its derivatives are continuous, then the fields fall off at least as fast as f -2 . To some extent, the presence of discontinuities is model-dependent. However, the above frequency dependencies persist over a large range of high frequency even when current variations are rapid but not precisely abrupt.

Experimental data for three 1.7-m-long transient discharges are compared with an AWA lumped-circuit discharge model developed earlier by the authors (R.T. Robiscoe, A. Kadish, and W.B. Maier, III, J. Appl. Phys. vol.64, 1988) in which the arc resistance is taken from the 'arc welder's ansatz', R/sub a/=V*/ mod I mod , where V* is a positive constant and I is the discharge current. In addition to the arc resistance, a small series resistance R is present in the external circuit. A single value for each R and V* is deduced from the data, and these values are used to characterize all three discharges. Adequate agreement of the experimental data with the model is obtained; for example, it is possible to predict the proper number of current reversals for each discharge and abrupt termination of current flow after a finite time. It is suggested that the AWA lumped-circuit model provides a better representation of the data than a standard lumped-circuit RLC model and hence is more useful as a tool for prediction and interpretation of discharge.< >

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*Ĵ)/4π, where ω and E* are parameters characteristic of the medium, J≡current density, and Ĵ≡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 suggest that many macroscopic discharge properties are properly explained by the model as electromagnetic phenomena, and we discuss extensions of the model to include chemistry, principally ionization and recombination.

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, R̂, and the current, I, is assumed to be given by a local Arc Welder’s Ansatz: R̂‖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.

In this paper we calculate the nonlocal growth rate of gradient drift plasma waves under conditions where the electron density gradient scale length changes with altitude. The results are compared with the local growth rate and discussed in the context of the kilometer‐scale waves which have been observed in the vicinity of mid‐latitude sporadic E layers. These large‐scale waves drastically violate the local approximation, kLm»1, where k is the irregularity wave number and Lm is the minimum gradient scale length on the edge of a layer. The first step in the analysis is to derive a general eigenmode equation, starting with the same assumptions usually used in the derivation of the local dispersion relation for long wavelength waves. Modeling a sporadic E layer as a slab, the nonlocal growth rate spectrum is found by solving the eigenmode equation for this profile. The solution is an algebraic dispersion relation with a growth rate spectrum which is roughly proportional to k, rather than the k2 dependence predicted by conventional local theory at long wavelengths. At short wavelengths the nonlocal growth rate determined with the slab is unbounded, in disagreement with local theory. The slab is an inadequate model for short wavelength waves and a bound on the growth rate is instead derived from a theory which can be applied to any realistic profile with nonzero Lm. At short wavelengths this bound is identical to the local growth rate expression, while at long wavelengths the bound remains proportional to k and thus is consistent with the dispersion relation for a slab. Nonlocal effects alone do not explain the dominance of kilometer scales, but they do tend to favor the excitation of long wavelengths.

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, R̂, and the current, I, is assumed to be given by the local arc-welder’s ansatz, R̂‖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 than the critical voltage, we obtain upper and lower bounds for both the arc duration time and amount of charge removed from the charge spot.

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

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 discharge theory, while result (2) suggests an experiment to look for a finite number of current oscillations in a highly driven arc. Result (4) suggests an experimental method for determining V*. Finally, the empirical areal scaling laws for arcs are reproduced with this model. The usual phenomenological treatments of arc start and stop voltages, current ringing, and areal scaling are thus modeled by a single parameter, V*. These results are generalized to voltage-dependent capacitance, C(V).

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.

A simple time-dependent relation between the current and voltage pulse in a one-dimensional diode has been obtained. The relation is applicable to diodes in which the voltage or current pulse changes appreciably during the beam transit time across the diode gap. A simple application of the results to eliminating current transients in ion diodes is presented.

A new high-voltage scaling based on Kilpatrick's criterion is presented that suggests that voltages more than twice the Kilpatrick limit can be obtained with identical initial conditions of vacuum and surface cleanliness. The calculations are based on the experimentally observed decrease in secondary electron emission with increasing ion impact energy above 100 keV. A generalized secondary-emission package has been developed to simulate actual cavity dynamics in conjunction with our 2½-dimensional fully electromagnetic particle-in-cell code CEMIT. The results are discussed with application to the suppression of vacuum breakdown in rf accelerator devices.