Phenomenological Theory of Townsend Breakdown in Dielectrics

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Abstract
The Townsend model of dielectric breakdown is discussed. The transient equations describing the behavior of the electron and positive ion current densities are solved rigorously with boundary conditions appropriate to a simplifed Townsend model employing photoelectron production at the cathode as the only secondary mechanism. The correct boundary condition is found to lead to a set of integro-difference equations. Solution of the integro-difference equations allows rigorous specification of the criterion for breakdown. This criterion is found to become equivalent to the familiar Townsend criterion in the asymptotic limit of large time intervals. The results of our development may be applied to the calculation of formative time lags and to the estimation of space-charge distortion effects.

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