Multiple solutions in the theory of near-cathode layers and self-organization on DC glow cathodes

Summary form only given. It has been suggested long ago that a self-consistent theoretical model of a near-cathode region in a glow discharge admits multiple steady-state solutions describing different modes. A bifurcation analysis has shown that multiple steady-state solutions must exist even in the framework of the most basic self-consistent model of glow discharge. In the present work, such multiple solutions have been calculated for the first time. As an example, the figure shows the dependence of the discharge voltage drop U on the average current density j for a xenon 30 Torr discharge of 0.5 mm of radius and height. The 1D solution (which only varies along the axis) is similar to the well-known solution of von Engel and Steenbeck. The axially symmetric (2D) solution with s=2 describes the normal glow discharge and a mode with a ring spot at the edge of the cathode. The 2D solution with s=3 describes modes with a ring spot; and with a spot at the center and a ring spot at the edge. Calculated structures with ring spots are qualitatively similar to those observed in experiments.