Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.

Figure 1

Experimental setup for two coupled plasma sources.

Figure 2

Experimental observations of frequency pulling, frequency synchronization, phase-flip bifurcations, and hysteresis phenomenon between two inductively coupled plasma sources. The synchronization region is enlarged in (b) due to stronger coupling between the sources when the inductive coil is placed at 6 cm from the cathode and is hence closer to the plasma column. In (a) only the fundamental frequencies of the two sources have been plotted.

Figure 3

Phase-flip transition from an in-phase state to an antiphase state occurring within a 1 V increase in the voltage of chamber 2.

Figure 4

Phase-flip transition from an antiphase state to an in-phase state occurring within a 1 V decrease in the voltage of chamber 2.

Figure 5

Numerical observations of frequency pulling, frequency synchronization, phase-flip bifurcations, and hysteresis phenomenon between two bath coupled van der Pol equations. Coupling parameters are (a) $M=0.06$ and (b) $M=0.1$.