Dynamics of steady and unsteady operation of inductive discharges with attaching gases

Relaxation oscillations in charged particle densities are seen in low-pressure inductive discharges, if attaching gases such as SF6 and Ar/SF6 mixtures are used, such that the plasma contains negative ions. These oscillations occur in the neighborhood of the transition between lower power capacitive operation and higher power inductive operation. An instability, which occurs around this transition, can be described by a global model, that consists of time-dependent equations for the electrons, ions, and electron temperature. The model qualitatively agrees with experimental observations, but leaves significant quantitative differences to be explained. To understand the reasons for the model’s inability to make quantitative predictions, the local conditions for instability are determined for a model somewhat simplified from the one that approximates the experiment, but retains most of the important physics. The simplified model allows explicit determination for the local transition to instability and identifies two parameters that govern the transition. The local criteria are related to the global criterion that all fixed points are unstable. The importance for the instability of the physical parameters of the ion wall loss and of the ratio of capacitive to inductive power transfer has led to a reexamination of the size of these factors, and gives better quantitative agreement of the model to experiments.