RESUMO
We report the first experimental observations of phase switching in a system of three coupled plasma sources. Two of the plasma sources are inductively coupled to each other while the third one is directly coupled to one of them. The coupled system acquires a frequency pulling synchronized state following which a transition occurs to a frequency entrainment state with an increase in the frequency of the directly coupled system. We also observe a sudden jump from a lower to a higher frequency entrainment state and a concomitant phase switching between the oscillations of the two directly coupled sources while the phase difference between the inductively coupled sources remains constant. These experimental findings are established using various diagnostic tools, such as the Fourier spectra, frequency bifurcation plots, Lissajous plots, and Hilbert transforms of the data. The experimental results are qualitatively modeled using three coupled van der Pol equations, in which two of them are environmentally coupled while the third one is directly coupled with one of them.
RESUMO
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.