Abstract
Abstract The transient electron avalanche which constitutes the primary pro-breakdown event of a gas medium is examined in a one-dimensional uniform field Townsend gas discharge system that is initiated by a single pulse of electrons at the cathode. Analytic solutions of other investigators which yield to stable numerical evaluation are presented. A convergent and stable finite-difference technique for systems of quasi-linear first-order hyperbolic partial differential equations is adapted to the Townsend system for two separate secondary electron emission mechanisms, due to either ion impact or incident photons. Numerical illustrations are given comparing the results of the finite-difference technique to the numerical evaluation of the given analytic solutions for the cathode electron current density, illustrating convergence of the numerical method with suggestion of adaptation of finite-difference techniques to more complicated discharge models. The total external current density is also computed for photon secondary emission with applied fields below, equal to, and above the breakdown threshold.
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