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TJ-II:Turbulence: Difference between revisions
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Turbulence is essentially non-linear. | 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. | 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. | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.74.395 B.Ph. van Milligen et al, Nonlinear phenomena and intermittency in plasma turbulence, Phys. Rev. Lett. '''74''', 3 (1995) 395]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.74.395 B.Ph. van Milligen et al, ''Nonlinear phenomena and intermittency in plasma turbulence'', Phys. Rev. Lett. '''74''', 3 (1995) 395]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, Wavelet bicoherence: a new turbulence analysis tool, Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, ''Wavelet bicoherence: a new turbulence analysis tool'', Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | ||
<ref>[http://link.aip.org/link/?RSINAK/68/967/1 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]</ref> | <ref>[http://link.aip.org/link/?RSINAK/68/967/1 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]</ref> | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.84.4842 P.H. Diamond et al, In search of the elusive zonal flow using cross-bicoherence analysis, Phys. Rev. Lett. '''84''', 12 (2000) 4842]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.84.4842 P.H. Diamond et al, ''In search of the elusive zonal flow using cross-bicoherence analysis'', Phys. Rev. Lett. '''84''', 12 (2000) 4842]</ref> | ||
A relation was found between confinement transitions and an increase of the bicoherence, as expected in the framework of shear flow models for turbulence stabilisation. | A relation was found between confinement transitions and an increase of the bicoherence, as expected in the framework of shear flow models for turbulence stabilisation. | ||
<ref>[http://dx.doi.org/10.1088/0029-5515/48/11/115003 B.Ph. van Milligen et al, Bicoherence during confinement transitions in the TJ-II stellarator, Nucl. Fusion '''48''' (2008) 115003]</ref> | <ref>[http://dx.doi.org/10.1088/0029-5515/48/11/115003 B.Ph. van Milligen et al, ''Bicoherence during confinement transitions in the TJ-II stellarator'', Nucl. Fusion '''48''' (2008) 115003]</ref> | ||
=== Self-similarity === | === Self-similarity === | ||
Important transport phenomena such as profile stiffness (consistency), | Important transport phenomena such as profile stiffness (consistency), | ||
<ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, Quantifying profile stiffness, Plasma and Fusion Research, '''3''' (2008) S1070]</ref> | <ref>[http://www.jspf.or.jp/PFR/PFR_articles/pfr2008S1/pfr2008_03-S1070.html B.Ph. van Milligen et al, ''Quantifying profile stiffness'', Plasma and Fusion Research, '''3''' (2008) S1070]</ref> | ||
power degradation, the rapid propagation of perturbations, | power degradation, the rapid propagation of perturbations, | ||
<ref>[http://dx.doi.org/10.1088/0029-5515/47/3/004 B.Ph. van Milligen et al, Pulse propagation in a simple probabilistic transport model, Nucl. Fusion '''47''' (2007) 189]</ref> | <ref>[http://dx.doi.org/10.1088/0029-5515/47/3/004 B.Ph. van Milligen et al, ''Pulse propagation in a simple probabilistic transport model'', Nucl. Fusion '''47''' (2007) 189]</ref> | ||
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 could determine the shape of the autocorrelation function (ACF) of turbulent signals. | In order to test this hypothesis, one could 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> | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.83.3653 B.A. Carreras et al, Self-similarity properties of the probability distribution function of turbulence-induced particle fluxes at the plasma edge, Phys. Rev. Lett. '''83''' (1999) 3653]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.83.3653 B.A. Carreras et al, ''Self-similarity properties of the probability distribution function of turbulence-induced particle fluxes at the plasma edge'', Phys. Rev. Lett. '''83''' (1999) 3653]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/7/3278/1 B.A. Carreras, Intermittency of plasma edge fluctuation data: Multifractal analysis, Phys. Plasmas, '''7''', 8 (2000) 3278]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/7/3278/1 B.A. Carreras, ''Intermittency of plasma edge fluctuation data: Multifractal analysis'', Phys. Plasmas, '''7''', 8 (2000) 3278]</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://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. | ||
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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. | ||
<ref>[http://link.aip.org/link/?PHPAEN/5/3632/1 B.A. Carreras et al, Self-similarity of the plasma edge fluctuations, Phys. Plasmas '''5''', 10 (1998) 3632]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/5/3632/1 B.A. Carreras et al, ''Self-similarity of the plasma edge fluctuations'', Phys. Plasmas '''5''', 10 (1998) 3632]</ref> | ||
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. | 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). | 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). | ||
<ref>[http://link.aip.org/link/?PHPAEN/6/485/1 B.A. Carreras et al, Long-range time dependence in the cross-correlation function, Phys. Plasmas '''6''', 2 (1999) 485]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/6/485/1 B.A. Carreras et al, ''Long-range time dependence in the cross-correlation function'', Phys. Plasmas '''6''', 2 (1999) 485]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/6/1885/1 B.A. Carreras et al, Experimental evidence of long-range correlation and self-similarity in plasma fluctuations, Phys. Plasmas '''6''', 5 (1999) 1885]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/6/1885/1 B.A. Carreras et al, ''Experimental evidence of long-range correlation and self-similarity in plasma fluctuations'', Phys. Plasmas '''6''', 5 (1999) 1885]</ref> | ||
In this framework, an important technique is the quiet-time analysis. | In this framework, an important technique is the quiet-time analysis. | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevE.66.036124 R. Sánchez et al, Quiet-time statistics: A tool to probe the dynamics of self-organized-criticality systems from within the strong overlapping regime, Phys. Rev. E, '''66''' (2002) 036124]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevE.66.036124 R. Sánchez et al, ''Quiet-time statistics: A tool to probe the dynamics of self-organized-criticality systems from within the strong overlapping regime'', Phys. Rev. E, '''66''' (2002) 036124]</ref> | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.90.185005 R. Sánchez et al, Quiet-time statistics of electrostatic turbulent fluxes from the JET tokamak and the W7-AS and TJ-II stellarators, Phys. Rev. Lett. '''90''', 185005 (2003)]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.90.185005 R. Sánchez et al, ''Quiet-time statistics of electrostatic turbulent fluxes from the JET tokamak and the W7-AS and TJ-II stellarators'', Phys. Rev. Lett. '''90''', 185005 (2003)]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/12/052304/1 V.E. Lynch et al, Determination of long-range correlation by quiet-time statistics, Phys. Plasmas '''12''' (2005) 052304]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/12/052304/1 V.E. Lynch et al, ''Determination of long-range correlation by quiet-time statistics'', Phys. Plasmas '''12''' (2005) 052304]</ref> | ||
=== Turbulence classification === | === Turbulence classification === | ||
An important effort has also been made to identify and classify turbulence, | An important effort has also been made to identify and classify turbulence, | ||
<ref>[http://link.aip.org/link/?PHPAEN/7/1408/1 E. Sánchez et al, Statistical characterization of fluctuation waveforms in the boundary region of fusion and non-fusion plasmas, Phys. Plasmas '''7''', 5 (2000) 1408]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/7/1408/1 E. Sánchez et al, ''Statistical characterization of fluctuation waveforms in the boundary region of fusion and non-fusion plasmas'', Phys. Plasmas '''7''', 5 (2000) 1408]</ref> | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/42/4/302 I. García-Cortés et al, Turbulent transport studies in the JET edge plasmas in limiter configuration, Plasma Phys. Control. Fusion '''42''' (2000) 389]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/42/4/302 I. García-Cortés et al, ''Turbulent transport studies in the JET edge plasmas in limiter configuration'', Plasma Phys. Control. Fusion '''42''' (2000) 389]</ref> | ||
<ref>C. Hidalgo et al, Intermittency and structures in edge plasma turbulence, Comptes Rendus Physique '''7''', 6 (2006) 679</ref> | <ref>C. Hidalgo et al, ''Intermittency and structures in edge plasma turbulence'', Comptes Rendus Physique '''7''', 6 (2006) 679</ref> | ||
to analyse its spectra, | to analyse its spectra, | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.82.3621 M. A. Pedrosa et al, Empirical similarity of frequency spectra of the edge plasma fluctuations in toroidal magnetic confinement systems, Phys. Rev. Lett. '''82''' (1999) 3621]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.82.3621 M. A. Pedrosa et al, ''Empirical similarity of frequency spectra of the edge plasma fluctuations in toroidal magnetic confinement systems'', Phys. Rev. Lett. '''82''' (1999) 3621]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/6/4615/1 B.A. Carreras et al, Characterization of the frequency ranges of the plasma edge fluctuation spectra, Phys. Plasmas '''6''', 12 (1999) 4615]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/6/4615/1 B.A. Carreras et al, ''Characterization of the frequency ranges of the plasma edge fluctuation spectra'', Phys. Plasmas '''6''', 12 (1999) 4615]</ref> | ||
<ref>M. A. Pedrosa et al, Studies of spectra of the edge plasma fluctuations in toroidal magnetic confinement systems, J. Plasma Fusion. Res. SERIES, '''2''' (1999) 77</ref> | <ref>M. A. Pedrosa et al, ''Studies of spectra of the edge plasma fluctuations in toroidal magnetic confinement systems'', J. Plasma Fusion. Res. SERIES, '''2''' (1999) 77</ref> | ||
to determine its relation with local plasma parameters (rational surfaces, gradients, electric fields), | to determine its relation with local plasma parameters (rational surfaces, gradients, electric fields), | ||
<ref>M.A. Pedrosa et al, Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator, Czechoslovak Journal of Physics, '''50''', 12 (2000) 1463</ref> | <ref>M.A. Pedrosa et al, ''Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator'', Czechoslovak Journal of Physics, '''50''', 12 (2000) 1463</ref> | ||
<ref>[http://dx.doi.org/10.1088/0029-5515/42/10/305 B. Gonçalves et al, Experimental investigation of dynamical coupling between density gradients, radial electric fields and turbulent transport in the JET plasma boundary region, Nucl. Fusion '''42''' (2002) 1205]</ref> | <ref>[http://dx.doi.org/10.1088/0029-5515/42/10/305 B. Gonçalves et al, ''Experimental investigation of dynamical coupling between density gradients, radial electric fields and turbulent transport in the JET plasma boundary region'', Nucl. Fusion '''42''' (2002) 1205]</ref> | ||
<ref>M.A. Pedrosa et al, Edge turbulence during limiter biasing experiments in the TJ-II stellarator, Czechoslovak Journal of Physics, '''53''' (2003) 877</ref> | <ref>M.A. Pedrosa et al, ''Edge turbulence during limiter biasing experiments in the TJ-II stellarator'', Czechoslovak Journal of Physics, '''53''' (2003) 877</ref> | ||
and to visualise turbulent structures. | and to visualise turbulent structures. | ||
<ref>[http://www.new.ans.org/pubs/journals/fst/a_1250 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]</ref> | <ref>[http://www.new.ans.org/pubs/journals/fst/a_1250 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]</ref> | ||
<ref>[http://dx.doi.org/10.1088/0741-3335/48/12B/S44 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]</ref> | <ref>[http://dx.doi.org/10.1088/0741-3335/48/12B/S44 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]</ref> | ||
<ref>[http://dx.doi.org/10.1016/j.jnucmat.2009.01.140 D. Carralero et al, Turbulence studies by fast camera imaging experiments in the TJII stellarator, J. Nucl. Mat. '''390-391''' (2009) 457]</ref> | <ref>[http://dx.doi.org/10.1016/j.jnucmat.2009.01.140 D. Carralero et al, ''Turbulence studies by fast camera imaging experiments in the TJII stellarator'', J. Nucl. Mat. '''390-391''' (2009) 457]</ref> | ||
== References == | == References == | ||
<references /> | <references /> | ||