A description and analysis of the solution of a twohyphen;dimensional model for a HV breakdown of a short gap is presented. The model consists of the electron, ion, and excitedhyphen;atom conservation and Poisson equations and is applied to a planehyphen;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 cmminus;1. Twohyphen;dimensional plots of the charged and excitedhyphen;particle densities and electric field components are presented and discussed. It is shown that in the first, diffusionhyphen;controlled, stage density profiles are close to a Gaussian distribution with an effective radius increasing in time. The subsequent stage is controlled by the spacehyphen;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 excitedhyphen;atom profiles as well, and the forming conductive chanel exhibits a tendency towards constriction. Calculations were conducted up to a maximum time oft=1139 ns, when maximum electron, ion, and excitedhyphen;atom densities reached values of 3.1times;1010, 3.7times;1011, and 2.5times;1012cmminus;3. Among the ionization processes the direct and Penning interactions are dominant, accounting at average for approximately 70percnt; and 30percnt; of the total at timet=1139 ns; ionization frequencies are substantially affected by spacehyphen;charge field and vary considerably in time and space near the end of calculations.
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