Two-dimensional simulation of inductive-capacitive transition instability in an electronegative plasma

Plasma instabilities are observed in low-pressure inductive discharges in the transition between low density capacitively driven and high density inductively driven discharges when attaching gases are used. A two-dimensional hybrid fluid-analytic simulation is used to determine the space- and time-varying densities of electrons, positive and negative ions, and neutral species, and electron and neutral gas temperatures. The simulation includes both the capacitive and inductive coupling of the source coils to the plasma and the neutral gas dissociation and heating. The plasma is described using the time-dependent fluid equations, along with an analytical sheath model. The simulation is applied to an experiment in Cl ₂, in which gaps in the electron and positive ion densities versus power curves were observed, with our numerical results indicating the existence of an inductive-capacitive transition instability, corresponding approximately to the observed gaps. The fluid calculation captures various features that are not included in previous global instability models. A method is developed to match the numerical results to the global model formalism, which predicts the existence of the unstable mode, as numerically found. The time and space variations can be used to improve the global model formalism.