Self-sustained oscillations in a low-current discharge with a semiconductor serving as a cathode and ballast resistor: II. Theory

Current self-sustained oscillations in a Townsend discharge are studied analytically. The proposed method for solving simple equations is applicable even when the Townsend coefficient of electron reproduction g (the main factor governing the oscillations) cannot be determined theoretically. The coefficient g is related to the discharge current-voltage characteristic, which can be obtained experimentally or from numerical simulations. Self-oscillating solutions (limit cycles) are found under various conditions. The mechanisms governing the excitation and stabilization of the solutions obtained are interpreted. It is shown that the waveform of the undamped oscillations may change significantly (the current peaks are smoothed, and the oscillation period decreases) when a weak constant cathode current, which is presumably related to the emission caused by slowly diffusing metastable molecules, is included in the equations.