BIFURCATION AND CHAOTIC TRANSITION TO RELAXATION OSCILLATIONS IN AN INDUCTIVELY DRIVEN ELECTRONEGATIVE PLASMA

Regular and chaotic relaxation oscillations in charged particle densities, light and floating potential are seen in low-pressure inductive discharges, in the transition between lower power capacitive operation and higher power inductive operation, if the plasma is electronegative, i.e. contains negative ions. As pressure or power is varied to cross a threshold, either from stable capacitive or stable inductive operation, the instability goes through a series of oscillatory, sometimes chaotic, states to large scale relaxation oscillations between higher and lower densities. A volume-averaged model, to describe the instability, contains time varying densities of charged species and temperature, indicating that the separation of the time scales of electron and negative ion motion is the driver of the complicated dynamics. The particle and energy balance equations are integrated to produce the dynamical behavior. A phase plane description of negative ions versus electrons is used to gain understanding of the instability. The theory shows that, depending on specific choices of parameters, as power is increased, the oscillations, born at Hopf bifurcation, can grow to a large amplitude relaxation oscillations, sometimes traversing chaotically between basins of attraction. The model qualitatively agrees with experimental observations which show the same range of behaviors, but with quantitative differences to be explained.