Transient Analysis of the Townsend Discharge

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Abstract
The transient growth of currents in a one-dimensional Townsend gas discharge system under uniform dc field conditions is examined. It is shown that a general solution for arbitrary external conditions can be given in terms of a "unit pulse" solution. Two cases are examined in detail; in one case the discharge is initiated by a single pulse from the cathode, in the second case the discharge develops under constant external illumination of the cathode. Expressions are derived which permit reasonably rapid calculation of quantities pertinent to the transient characterization of the discharge. For the two cases considered in detail, numerical illustrations are given and comparison is made with the results of other investigators.