A novel treatment of Trichel-type phenomena with possible application to stepped-leader phenomena

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Abstract
A simple theory for Trichel discharges in gases is proposed, in which the corona region is assumed to be describable in terms of a Townsend generation-recombination mechanism, while the outer drift region is deemed subject to photoionisation-attachment processes, together with displacement current effects. The pair of first-order nonlinear differential equations is examined with a linearising 'small signal' procedure, yielding stability limits, frequency and damping coefficients. A numerical treatment of the full equations gives the development of pulse shapes, as well as large-signal modifications of the stability limits. Good qualitative agreement with observation is established, especially with the well-known proportionality between average current and pulse frequency. An extension of the theory to stepped-leader phenomena is proposed and it is shown that the agreement with observation is quite acceptable, even though the parameters involved here are of a different order of magnitude when compared with Trichel discharges.

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