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] [4]
Self-similarity
Important transport phenomena such as profile stiffness (consistency), [5] power degradation, the rapid propagation of perturbations, [6] 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.
In order to test this hypothesis, one could determine the shape of the autocorrelation function (ACF) of turbulent signals. [7] 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.
It is much more 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 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).
In this framework, an important technique is the quiet-time analysis. [8]
Turbulent structures
An important effort has also been made to classify and visualise turbulent structures. [9] [10] [11] [12]
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
- ↑ B.Ph. van Milligen et al, Bicoherence during confinement transitions in the TJ-II stellarator, Nucl. Fusion 48 (2008) 115003
- ↑ B.Ph. van Milligen et al, Quantifying profile stiffness, Plasma and Fusion Research, 3 (2008) S1070
- ↑ B.Ph. van Milligen et al, Pulse propagation in a simple probabilistic transport model, Nucl. Fusion 47 (2007) 189
- ↑ B.Ph. Van Milligen et al, Additional evidence for the universality of turbulent fluctuations and fluxes in the scrape-off layer region of fusion plasmas, Physics of Plasmas 12 (2005) 052507
- ↑ V.E. Lynch et al, Determination of long-range correlation by quiet-time statistics, Phys. Plasmas 12 (2005) 052304
- ↑ C. Hidalgo et al, Intermittency and structures in edge plasma turbulence, Comptes Rendus Physique 7, 6 (2006) 679
- ↑ J. A. Alonso et al, Two-Dimensional Turbulence Analysis Using High-Speed Visible Imaging in TJ-II Edge Plasmas, Fusion Science and Technology 50, 2 (2006) 301
- ↑ J.A. Alonso et al, Impact of different confinement regimes on the two-dimensional structure of edge turbulence, Plasma Phys. Control. Fusion 48 (2006) B465
- ↑ D. Carralero et al, Turbulence studies by fast camera imaging experiments in the TJII stellarator, J. Nucl. Mat. 390-391 (2009) 457