Current limitation in mercury vapour discharges. I. Theory

A theoretical description of the current limit phenomenon based on the limited ionizing ability of the electrons has been obtained. The current limit is found to be a double-valued function of pressure. This limited ionizing ability implies that positive column existence is only possible when the product of the gas density and column radius is greater than a critical value. High currents reduce the gas density to the critical value causing current limitation. Assumptions of the form of the electron velocity distribution at current limit are avoided by working with the mean free path of the neutral for ionization, lambda , as a parameter. Both the ion wall current and the neutral depletion are calculated in terms of lambda and, by relating ion wall current and arc current, gas density is related to arc current. Low currents reduce the plasma radius until the critical value is reached causing current limitation.