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TJ-II:Turbulence: Difference between revisions
→Self-similarity
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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. | 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 | In order to test this hypothesis, one can determine the shape of the autocorrelation function (ACF) of turbulent signals. | ||
<ref>[http://link.aip.org/link/?PHPAEN/3/2664/1 B.A. Carreras et al, ''Fluctuation-induced flux at the plasma edge in toroidal devices'', Phys. Plasmas '''3''' (7) (1996) 2664]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/3/2664/1 B.A. Carreras et al, ''Fluctuation-induced flux at the plasma edge in toroidal devices'', Phys. Plasmas '''3''' (7) (1996) 2664]</ref> | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.80.4438 B.A. Carreras et al, ''Long-range time correlations in plasma edge turbulence'', Phys. Rev. Lett. '''80''', (1998) 4438]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.80.4438 B.A. Carreras et al, ''Long-range time correlations in plasma edge turbulence'', Phys. Rev. Lett. '''80''', (1998) 4438]</ref> | ||
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<ref>[http://dx.doi.org/10.1088/0741-3335/44/8/309 C. Hidalgo et al, ''Empirical similarity in the probability density function of turbulent transport in the edge plasma region in fusion plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) 1557]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/44/8/309 C. Hidalgo et al, ''Empirical similarity in the probability density function of turbulent transport in the edge plasma region in fusion plasmas'', Plasma Phys. Control. Fusion '''44''' (2002) 1557]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/12/052507/1 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'', Phys. Plasmas '''12''' (2005) 052507]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/12/052507/1 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'', Phys. Plasmas '''12''' (2005) 052507]</ref> | ||
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. | 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. | 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. | ||