Transport in fusion-grade plasmas is often dominated by turbulent transport. In contrast with Neoclassical transport, turbulent transport (assumed to be the cause of the experimental so-called "anomalous" component of transport) is not well understood. As a consequence, predictions of machine performance generally rely on rather crude scaling law techniques, rather than first-principles calculations. Improving our understanding of turbulence is hard, due to (1) the complexity of fusion-grade plasmas (the presence of charged particles and magnetic fields make this into a much harder topic than fluid turbulence), (2) the enormous variety of plasma instabilities, and (3) the difficulty of diagnosing the plasma due to the hostile conditions inside the plasma.
Our work on turbulence has focussed mainly on the analysis of edge Langmuir probe data, although some analysis was done on other types of data (e.g., reflectometry signals). Much effort was devoted to the development of new data analysis techniques.
Bicoherence and wavelets
Turbulence is essentially non-linear. Non-linear interactions can be detected by means of higher-order spectra (e.g. quadratic interactions can be detected through the bi-spectrum). With Fourier analysis, however, in order to achieve statistically significant values for the bi-spectrum, very long time series are necessary. This fact has mostly precluded its use in fields like plasma turbulence, since long steady-state data series are not generally available. In our work, for the first time, the bicoherence was calculated using wavelet transforms, thus making the detection of non-linear interactions with time resolution possible.     A relation was found between confinement transitions and an increase of the bicoherence, as expected in the framework of shear/zonal flow models for turbulence stabilisation. 
Important transport phenomena such as profile stiffness (consistency),  power degradation, the rapid propagation of perturbations,  and the Bohm scaling of plasma confinement might be explained on the basis of profile self-regulation in the framework of the Self-Organised Criticality paradigm. This paradigm predicts that transport is regulated by avalanches, which would generate self-similar behaviour in space and time of the turbulent data.
Unfortunately, the most revealing information is present in the tail of the distribution (i.e., well beyond the correlation time), where statistics are generally poor. Therefore, it is convenient to resort to the Rescaled-Range analysis technique and the determination of the Hurst exponent. We have shown that this type of analysis is far more robust with respect to random noise perturbations than the direct determination of the ACF or the Probability of Return.
The analysis of data from Langmuir probes taken at the plasma edge in a wide variety of fusion devices reveals the existence of self-similar behaviour or long-range correlations in all devices studied. The observed variation of the Hurst exponent in the plasma edge, 0.62 < H < 0.75, is small in spite of the variety of devices.  On the other hand, the variation of H in the Scrape-Off Layer (SOL) is much larger. In Wendelstein VII-AS, a slight decrease in H at the sheared flow layer was observed, possibly corresponding to a local decorrelation effect.
The repeated occurrence of values of H differing significantly from the value corresponding to random noise (H = 0.5) in all machines points to a universal aspect of the underlying turbulence. Further, the degree of self-similarity detected implies the existence of long-range correlations (with respect to the correlation time).  
An important effort has also been made to identify and classify turbulence,    to analyse its spectra,    and to determine its relation with local plasma parameters (rational surfaces, gradients, electric fields).   
Recently, much effort is being dedicated to the visualization of turbulent structures, and to the corresponding analysis techniques for extracting quantitative information from the images.    See also: TJ-II:Fast camera.
To disentangle the complex relation between fluctuating variables, a technique for Causality detection has been used.  It has revealed that magnetic fluctuations may play an important role in the L-H transition. 
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