TJ-II:Turbulence
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 so-called experimental "anomalous" component of transport) is not well understood.
Our work on turbulence has focussed mainly on the analysis of edge probe data, although some analysis was done on reflectometry signals. A large effort was devoted to the development of new 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. [1] [2] [3]
Self-similarity
The shape of the autocorrelation function (ACF) of turbulent signals reveals some of the properties of the underlying mechanisms of generation of the turbulence. 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.
In particular, the ability to discern between an algebraic or exponential decay of the ACF at large lags would provide an indication whether recently proposed Self-Organized Criticality (SOC) models could be appropriate descriptions of the turbulence. These models predict transport by avalanches, which would generate self-similar behaviour in space and time of the turbulent data and thus lead to the mentioned algebraic decay.
Such possible self-similarity can be quantified by the Rescaled-Range analysis technique and the Hurst exponent. We show that this type of analysis is far more robust against 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 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). This may either be due to a response of the system to perturbations that is much slower than the turbulence autocorrelation time, or to long-range correlations generated by some mechanism, for which the avalanches of SOC models are a good candidate
References
- ↑ B.Ph. van Milligen et al, Nonlinear phenomena and intermittency in plasma turbulence, Phys. Rev. Lett. 74, 3 (1995) 395
- ↑ B.Ph. van Milligen et al, Wavelet bicoherence: a new turbulence analysis tool, Phys. Plasmas 2, 8 (1995) 3017
- ↑ B.Ph. van Milligen et al, Statistically robust linear and non-linear wavelet analysis applied to plasma edge turbulence, Rev. Sci. Instrum. 68 (1997) 967