Hopf bifurcations in balance equations of glow discharges

Starting from the hydrodynamic equations describing the positive column of glow discharges in inert gases. the instability of the axially homogeneous state is investigated. Dirichlet boundary conditions at the ends of the positive column are chosen. Stimulated by experiments, the influence of metastable atoms and of the outer circuit is taken into consideration by additional equations. Center manifold and normal form theories arc used to characterize the codimension-one bifurcations. Depending on the current, the length of the positive column and the resistance of the outer circuit supercritical and subcritical Hopf bifurcations are found. The importance of the results with respect to the experiments on the ionization instability in a neon discharge is discussed.