Breakdown model of a short plane-parallel gap

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Abstract
A two-dimensional model of the high-voltage breakdown has been developed, consisting of the Poisson equation and the conservation equations for electrons, ions, and excited particles. The model is based on the assumption of a low degree of ionization, so that the transport coefficients of the gas are uniquely determined by the local electric field, i.e., the model is limited to the initial stages of the channel formation. It is applied to a short plane-parallel gap in He at atmospheric pressure. The discharge is started by releasing the cloud of electrons near the cathode, and its sequence is followed up to 1.11 μs. Cathode emission is taken to include that due to ion and metastable impact and the photoeffect. The discharge develops from the initial Townsend-type discharge governed by cathode emission and the direct and Penning volume ionization, and progresses to the space-charge dominated stage. At the moment when the calculations are terminated, the maximum densities have already attained values of 1.6×1010, 2.5×1011, and 1.8×1012 cm−3 for the electrons, ions, and excited particles, respectively. The maximum axial component of the space-charge electric field is approximately 3.3 kV cm−1.