Propagation of ionizing electron shock waves in electrical breakdown

Abstract

A numerical solution of a hydrodynamic second-order model shows that the propagation of the first ionizing wave arises from an overgrowth of hot electrons in the wave front in a zone of a greatly disturbed electric field. This gives rise, in the electron shock zone ahead of the wave, to a precursor phenomenon, whose effect is to accelerate the channel propagation. Inside the shock zone, the electronic energy differs from the characteristic energy; the nonequilibrium between the electrons and the electric field, as a result of the electron pressure gradient, induces a heating of electrons in this zone. The space-charge electric field is calculated assuming that the discharge evolves in a variable ellipsoidal envelope with revolution symmetry around the propagation axis. The electron shock-wave structure is shown to maintain itself and to propagate during the evolution of the discharge. The results obtained from this second-order model are compared to those obtained from a classical first-order model in which the electron temperature is a function of the reduced electric field alone. This comparison allows us to define the concept of electron nonequilibrium in an electron shock wave and to show that it is the source of the high-speed propagation of the streamer. The close agreement of the results obtained from the second-order model with the experimental data justifies the formulation of the model, particularly that of the interaction operators of the energy equation.

High-order fluid model for streamer discharges: I. Derivation of model and transport data

“…To make contact with previous work [42,47,48,50], we here present different forms of equations (29)- (32). When we evaluate the averages over the velocities c in these equations and perform a considerable amount of algebra, we find…”

“…The first important steps beyond first order fluid models of streamer discharges, to our knowledge, were carried out by Abbas and Bayle [46,47], and by Bayle and Carenbois [48]. They employed a second order model which involves the energy balance equation to explore the zone at the streamer tip where the electron energy is not determined anymore by the local electric field only.…”

“…There are many examples which illustrate this issue and the reader is referred to [35,40,41] for a detailed discussion. In the context of streamer and breakdown studies beyond first order fluid models, it has become common practice to evaluate the collision terms and averages by assuming some particular form of the velocity distribution function, usually Maxwellian [48,49,52,53,54].…”

Generation of energetic He atom beams by a pulsed positive corona discharge

“…Within this time the voltage dropped at least 40% of the maximum value. The discharge voltage then remained at this low level for [10][11][12][13][14][15][16][17][18][19][20] s, before slowly rising back to the initial voltage. Measurements of the voltage divider signal indicated that despite the high source voltage ͑defined as the voltage at the power supply͒ in the range from 1 to 4.8 kV, the actual potential across the needle ranged approximately from 300 to 450 V. The average current through the source increased with the source voltage, and was in the range from 15 to 85 A.…”

“…On the other hand, many experiments concerning the properties of corona discharges have been conducted [13][14][15] ͑for an insightful overview on mechanisms of coronas see Loeb 16 ͒ and extensive theoretical literature exists regarding these discharges. 13,[17][18][19] However, the typical configuration for creating atom beams differs considerably from experiments on the properties of corona discharges. In the latter, discharges occur at high uniform pressures in ideal point-to-plane or point-to-cylinder electrode geometries.…”