Mostafa Hemmati

Electric breakdown waves: Exact numerical solutions. Part I

Electrical breakdown is generally a progressive wave phenomenon governed by fluid dynamical equations relating chiefly to the electron gas. Computer solution of these equations is investigated extensively, resulting in improvements in their formulation, and in the understanding of the conditions under which solution is possible. The most significant new discovery is the importance of heat conduction, especially at the shock front of the wave.

Electric breakdown waves: Exact solutions. Part II

The methods of numerical solution of the electron fluid dynamical equations that govern wave breakdown, and were described in a previous paper, are applied here to the various situations under which these waves have been observed. Samples of the detailed structures of the waves are presented. Solutions have been investigated for both negatively and positively driven waves, into both ionized and nonionized media, and for waves followed by a large current as in a lightning return stroke.

Antiforce Current Bearing Waves

In the case of breakdown waves in a long discharge tube, near the electrode where the potential gradient in the gas is greatest, small quantity of gas is ionized. Analysis of the spectrum of radiation emitted from electric breakdown of a gas reveals no Doppler shift, indicating that the ions have negligible motion. The large difference in mobilities of positive ions and electrons causes establishment of a space charge and consequently a space charge field. The electric field accelerates the free electrons until they aquire enough of energy for collisional ionization of the gas. Since the ionized gas is a conductor and it can not hold internal electric filed, the electric field which has its maximum value at the interface between the ionized gas and the neutral gas has to reduce to a negligible value at the trailing edge of the wave.

Electron shock waves moving into an ionized medium

The propagation of electron driven shock waves has been investigated by employing a one-dimensional, three-component fluid model. In the fluid model, the basic set of equations consists of equations of conservation of mass, momentum, and energy, plus Poissons equation. The wave is assumed to be a shock front followed by a dynamical transition region. Following Fowlers (1976) categorization of breakdown waves, the waves propagating into a preionized medium will be referred to as Class II Waves. To describe the breakdown waves, Shelton and Fowler (1968) used the terms proforce and antiforce waves, depending on whether the applied electric field force on electrons was with or against the direction of wave propagation. Breakdown waves, i.e., return strokes of lightning flashes, therefore, will be referred to as Antiforce Class II waves. The shock boundary conditions and Poissons equation for Antiforce Class II waves are different from those for Antiforce Waves. The use of a newly derived set of boundary conditions and Poissons equation for Antiforce Class II waves allows for a successful integration of the set of fluid equations through the dynamical transition region. The wave structure, i.e., electric field, electron concentration, electron temperature, and electron velocity, are very sensitive to the ion concentration ahead of the wave.

Wave Profile and Current Limits for Lightning Return Stroke

The propagation characteristics of breakdown waves propagating in the opposite direction of the electric field force on electrons and with a significant current behind the wave front have been studied. Breakdown waves for which the net electric field force on electrons is in the opposite direction of the wave propagation are referred to as anti-force waves (lightning return strokes); however, the electron gas temperature, and therefore the electron gas partial pressure, is assumed to be large enough to provide the driving force, causing the wave to propagate down the tube with observed velocities. Breakdown waves, for which the electric field force on electrons is in the same direction of the wave propagation, are referred to as pro-force waves. Waves propagating in the opposite direction of the electric field force on electrons will possess variance in structure from those moving in the same direction as the direction of the electric field force on electrons. Anti-force waves seem to be slightly faster than the pro-force waves, which agree fairly well with the experimental results.

Return Stroke with Current behind the Shock Front

Electrical breakdown of a gas in a strong electric field is carried out by a wave with a strong discontinuity at the wave front, traveling with speed comparable to the speed of light. For theoretical investigation of electrical breakdown of a gas, we apply a one-dimensional, steady profile, constant velocity, three component fluid model, and assume that the electrons are the main element in the propagation of the wave.

Electron Driven Shock Waves: Antiforce Class II Waves

The propagation of electrical breakdown waves in a gas has been investigated by applying a set of three-component fluid equations. The basic set consists of equations of conservation of mass, momentum, and energy, plus Poisson’s equation. In the fluid model, the wave front is assumed to be an electron shock wave followed by a transition region. The transition region in which the electron drift velocity and electric field go to zero is referred to as the sheath region. The sheath is very thin, being roughly a few mean free path long. Following the sheath region lies a comparatively thick region, in which the electron gas by means of further ionization cools to room temperature. This is referred to as the Quasi-Neutral Region. In a 1991 article (Proc. 18th ISSW), the solutions to different categories of breakdown waves for Quasi-Neutral Region, using the fluid model were reported. Now the boundary conditions and solutions to the Antiforce Class II Waves will be discussed.