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A theory for the cathode region of glow discharges is developed in which the major assumptions are: (a) electron emission from the cathode due to positive ion impact is the dominant secondary mechanism; (b) the probability of ionization by electrons occurring in the high-field cathode region is small, so that electrons carry a negligible portion of the total tube current there; and (c) in this region the positive ions drift towards the cathode with a velocity governed by a mobility law. This theory is found to agree well with measurements in abnormal discharges in various gases at pressures above about 0.1 mm Hg. For lower pressures, measurements indicate that a great number of electrons are present in the cathode-negative glow space, probably due to ionization by high-energy positive ions and molecules; and, that at high enough values of E/p, the application of a mobility theory becomes completely invalid.
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Roger W. Warren (1955) studied this question.
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