Bifurcations of current transfer through a collisional sheath with ionization and self-organization on glow cathodes

A bifurcation analysis is performed of a dc glow discharge between parallel electrodes and of a dc near-cathode space-charge sheath bordering a uniform plasma column. A model of plasma is considered with a single ion species and motion of the charged particles dominated by drift. Bifurcation points are found at which steady-state modes with spots on the cathode branch off from the abnormal mode or from the mode corresponding to the falling section of the current-density-voltage characteristic. In both discharge configurations, bifurcations in the abnormal mode have been detected; an unexpected result given that loss of stability and pattern appearance in dc gas discharges are usually associated with a negative differential resistance of the discharge. The conclusion is drawn that the two most important mechanisms governing appearance of patterns on glow cathodes, which are electrostatic mechanism and diffusion, produce competing effects: the former favors appearance of modes with multiple spots, while the latter favors appearance of a mode with one spot. This may explain the appearance in experiments of a normal spot or, alternatively, of patterns with multiple spots.