The transition corona effect arc, in atmospheric air, for inter-electrode distances less than a few centimetres in point-to-plane geometry (the high DC positive voltage being applied to the point with the plane at earth potential) is dependent on the existence of a cathode zone and a 'cathode canal'. A sufficient reserve of energy (internal capacity in parallel with the spark gap) permits the 'cathode canal' to develop into a transient arc which is extinguished when the capacity has discharged itself. However, the increasing duration of the cathode zone, with increasing total current, leads to a continuous luminous discharge (named a 'silent' arc) which then evolves into an arc for high currents.
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Bertault et al. (1977) studied this question.