The time series analysis method for chaotic attractor dimension by Grassberger and Procaccia [P. Grassberger and I. Procaccia, Physica D 9, 189 (1983)] was applied to fluctuations due to an E×B rotational flute mode in the Columbia Linear Machine (CLM) [G. A. Navratil, J. Slough, and A. K. Sen, Plasma Phys. 24, 184 (1982)]. After frequency domain filtering, the results show that the fluctuations carry a dimension close to three. A dimension of three supports a possible three-wave mode coupling process revealed in bi-coherence studies. The Grassberger Procaccia method was also performed on cases where partial feedback suppression was applied to the instability. It is shown that feedback does not alter the attractor dimension of the instability, supporting previous findings that the linear feedback only affects the linear drive of the instability, and not its non-linear saturation mechanism.
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Chiu et al. (2000) studied this question.