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.