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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>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>B.Ph. van Milligen et al, Wavelet bicoherence: a new turbulence analysis tool, Phys. Plasmas '''2''', 8 (1995) 3017</ref> | <ref>B.Ph. van Milligen et al, Wavelet bicoherence: a new turbulence analysis tool, Phys. Plasmas '''2''', 8 (1995) 3017</ref> | ||
<ref>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>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>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> | ||
<ref>B.Ph. van Milligen et al, Bicoherence during confinement transitions in the TJ-II stellarator, Nucl. Fusion '''48''' (2008) 115003</ref> | <ref>B.Ph. van Milligen et al, Bicoherence during confinement transitions in the TJ-II stellarator, Nucl. Fusion '''48''' (2008) 115003</ref> | ||
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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>B.A. Carreras et al, Fluctuation-induced flux at the plasma edge in toroidal devices, Plasma Physics '''3''' (7) (1996) 2664</ref> | <ref>B.A. Carreras et al, Fluctuation-induced flux at the plasma edge in toroidal devices, Plasma Physics '''3''' (7) (1996) 2664</ref> | ||
<ref>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.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>B.A. Carreras, Intermittency of plasma edge fluctuation data: Multifractal analysis, Phys. Plasmas, '''7''', 8 (2000) 3278</ref> | <ref>B.A. Carreras, Intermittency of plasma edge fluctuation data: Multifractal analysis, Phys. Plasmas, '''7''', 8 (2000) 3278</ref> | ||
<ref>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>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> | ||
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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>B.A. Carreras et al, Self-similarity of the plasma edge fluctuations, Phys. Plasmas '''5''', 10 (1998) 3632</ref> | <ref>B.A. Carreras et al, Self-similarity of the plasma edge fluctuations, Phys. Plasmas '''5''', 10 (1998) 3632</ref> | ||
<ref>B.A. Carreras et al, Long-range time dependence in the cross-correlation function, Phys. Plasmas '''6''', 2 (1999) 485</ref> | <ref>B.A. Carreras et al, Long-range time dependence in the cross-correlation function, Phys. Plasmas '''6''', 2 (1999) 485</ref> | ||
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In this framework, an important technique is the quiet-time analysis. | In this framework, an important technique is the quiet-time analysis. | ||
<ref>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>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''', | <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>V.E. Lynch et al, Determination of long-range correlation by quiet-time statistics, Phys. Plasmas '''12''' (2005) 052304</ref> | <ref>V.E. Lynch et al, Determination of long-range correlation by quiet-time statistics, Phys. Plasmas '''12''' (2005) 052304</ref> | ||
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<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>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>B.A. Carreras et al, Characterization of the frequency ranges of the plasma edge fluctuation spectra, Phys. Plasmas '''6''', 12 (1999) 4615</ref> | <ref>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> | ||