Nonlinear phenomena and intermittency in plasma turbulence.

A new technique combining wavelet analysis and bispectral analysis has been developed. This analysis tool permits the detection of structure in turbulent or chaotic data with time resolution, even in the presence of a significant noise contribution. Application of this technique to data obtained in fusion plasmas with Langmuir probes demonstrates its possibilities by detecting short-lived intermittent nonlinear coupling. Its application in the field of chaos analysis is indicated. PACS numbers: 52.35.Mw, 02.70.Hm, 52.35.Ra, 52.55.Hc The purpose of this Letter is to introduce a new analysis tool for turbulent or chaotic data to the physics community. It allows detection and characterization of short-lived structures in turbulence. The characterization and understanding of strong turbulence is especially urgent in the field of thermonuclear plasma physics, where the so-called anomalous transport which deteriorates the energy confinement due to turbulence is an important phenomenon that is far from understood. Apart from the difficulty of obtaining local measurements of turbulent quantities in the hostile plasma environment, the main obstacle to analysis is the high fractal dimension of between 5 and 9 of the turbulence [1]. Most traditional methods for determining the nature of the turbulence rely to a large degree on correlation techniques, probability distributions, and spectral analyses, all involving long time averages [2]. Similar techniques supplemented with two-dimensional visualization have been reported in [3]. The wavelet bicoherence technique presented here detects phase coupling while reducing time averages to a minimum, thus permitting short-lived events, pulses, and intermittency to be resolved. Its use is especially indicated for signals contaminated with noise, although its application to data from numeric models without noise has also been highly successful. Wavelet bicoherence is based on two existing techniques: wavelet analysis and bispectral analysis. Wavelet analysis is a relatively recent technique [4 ‐ 7] that has enjoyed increasing popularity in the field of chaos and turbulence. Rather than giving time-averaged estimates of the frequency contributions to a signal, as are provided by the traditional Fourier decomposition, the wavelet analysis decomposes a signal into wavelet components that depend on both scale (which under some conditions is equivalent to frequency) and time. The use of wavelet analysis is recommended in the analysis of data records containing pulses or short-lived events in order to avoid averaging out these temporally localized occurrences by examining large sections of the data record. Whereas the Fourier decomposition is based on the harmonic wave e ivt , the wavelet analysis is based on an ana