Breakdown of a wire-to-plane discharge: Transient effects

A wire-to-plane discharge during the early phases of breakdown has been studied. The discharge has been modeled in a prolate spheroidal coordinate system with the wire shape taken as a hyperboloid of revolution. Four simultaneous coupled, time-dependent, nonlinear partial differential equations describe the electrical discharge. These are the conservation equations for ion and electron densities, the energy equation for electron temperature, and Poisson’s equation for the self-consistent electric field. By solving this formulation subject to appropriate initial and boundary conditions, charged particle densities and temperature variations have been obtained as the ionization progresses in the discharge. The results show that both the electron temperature and the charged particle densities increase with the progress of ionization. The effect of different wire polarities is also examined. With a positive wire polarity, the increases in electron temperature and charged particle densities are confined to regions of the discharge in the vicinity of the wire tip. With a negative wire polarity, the breakdown occurs in the entire gap at a faster rate than with a positive wire polarity. The wire polarity affects the magnitude of energy transfer between the particles.