Amplitude equation at ionization instability and the onset of turbulence in a neon glow discharge

We investigate the bifurcations of ionization waves from the homogeneous stationary state of the positive column in a neon glow discharge. In the weak nonlinear region the wave dynamics is approximated by an amplitude equation of the Ginzburg-Landau type with complex coefficients and an additional integral term. This nonlocal term describes the influence of the external circuit on the ionization waves. Conditions are derived for the band of Eckhaus stable wave solutions. The dependence of the complex coefficients on the plasma parameters is discussed and used to classify the solution manifold of the amplitude equation. Raising the gas pressure from 139 Pa up to 720 Pa, the intermittency, bichaos, and amplitude turbulence regions are visited successively. Some of these theoretical results are supported by numerical calculations for selected parameter values.