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An investigation of the electrode current oscillations caused by the potential relaxation instability in a weakly magnetized discharge plasma

Oscillations of the electrode current, plasma density and plasma potential, caused by the potential relaxation instability in a weakly magnetized discharge plasma are studied. The oscillations appear when the electrode bias exceeds the plasma potential. As long as the difference between the electrode bias and the plasma potential is below approximately 2 V, that is approximately kTe/e0 in our experiment, the oscillations are periodic. When the electrode bias is increased above this value, the oscillations become irregular. The limit cycle in the phase space disappears, the power spectrum becomes broader and the autocorrelation time shorter. Presence of f- alpha noise is observed in the power spectra. Distribution of Fourier phases for electrode current, plasma density and plasma potential oscillations is shown. Dimensional analysis of the signals is performed using the Grassberger-Procaccia algorithm. The correlation dimension is found to be between 1.2 and 2.0 for low electrode biases and no saturation of the In(C(r)) versus In(r/r0) plots is found for higher electrode biases. Entropy K2 is plotted versus r/r0. The largest Lyapunov exponent is calculated using two different methods, one developed by Rosenstein and co-workers and the second by Wolf and co-workers. It appears that the largest Lyapunov exponent is positive and close to zero. An attempt to calculate the complete Lyapunov spectrum with the method of Kruel and co-workers is also made.