Early stages of channel formation in a short-gap breakdown

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A description and analysis of the solution of a two-dimensional model for a HV breakdown of a short gap is presented. The model consists of the electron, ion, and excited-atom conservation and Poisson equations and is applied to a plane-parallel gap with an electrode separation of 0.48 mm in helium gas at atmospheric pressure and a temperature of 293 K subjected to an electrical field of 10 kV cm−1. Two-dimensional plots of the charged and excited-particle densities and electric field components are presented and discussed. It is shown that in the first, diffusion-controlled, stage density profiles are close to a Gaussian distribution with an effective radius increasing in time. The subsequent stage is controlled by the space-charge field, causing prominent constriction of the electron density channel. In consequence, a high ionization near the discharge axis results in a virtual narrowing of the ion and excited-atom profiles as well, and the forming conductive chanel exhibits a tendency towards constriction. Calculations were conducted up to a maximum time of t=1139 ns, when maximum electron, ion, and excited-atom densities reached values of 3.1×1010, 3.7×1011, and 2.5×1012 cm−3. Among the ionization processes the direct and Penning interactions are dominant, accounting at average for approximately 70% and 30% of the total at time t=1139 ns; ionization frequencies are substantially affected by space-charge field and vary considerably in time and space near the end of calculations.