Time-dependent current leading to a spark

The Schade and the Kachickas and Fischer theories for the time-dependent current leading to a spark consider secondary ionisation by positive ions and photons, respectively; they are adapted here for photon and positive-ion secondary ionisation at the cathode. The theories are then extended to include simultaneous secondary ionisation by positive ions and photons. It is shown that, for small overvoltages, the extended Schade theory is reduced to the more accurate Davidson theory. However, no such reduction appears possible for the Kachickas and Fischer theory. The advantage of the Schade theory is that it gives a better engineering insight into the development of the time-dependent current leading to a spark than does the mathematical derivation by Davidson; also, no. subsidiary experiment is required to derive the current-growth constant.