Codimension-two bifurcations and ionization instability in a glow discharge

We investigate the bifurcations of ionization waves from the homogeneous stationary state of the positive column in a neon glow discharge. The underlying physical model is based on a hydrodynamic description which takes into account the external current circuit and the influence of metastable atoms. Periodic boundary conditions are chosen and by performing a linear stability analysis, we identify the instability boundaries in parameter space and compare the properties of the critical modes with corresponding experimental data. The normal form constants of a codimension-two bifurcation are determined and their dependence upon the plasma parameters is discussed. The calculated bifurcation phenomena show that the nonlinear properties of ionization waves depend not only on the plasma of the positive column but also on the external circuit. Copyright (C) 1998 Elsevier Science B.V.