Long-Range Time Correlations in Plasma Edge Turbulence

Carreras, B. A.; Milligen, B. Ph. van; Pedrosa, M. A.; Balbín, Rosa; Hidalgo, C.; Newman, D. E.; Sánchez, E.; Frances, Maria F.; Garcı́a-Cortés, I.; Bleuel, J.; Endler, M.; Davies, S.; Matthews, G. F.

doi:10.1103/physrevlett.80.4438

Cited by 155 publications

(121 citation statements)

References 15 publications

(15 reference statements)

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“…Various authors have found appealing the idea that in self-organized systems avalanches can be generated on all scales, leading to low-frequency, long-wavelength, selfsimilar correlations. This observation leads to a second thread relating to the possible significance of long-time correlations in certain experimentally observed time series, as reported for example by Carreras et al [10][11][12][13] Carreras 11 suggested that "the measurements [on long-time tails] are consistent with the SOC paradigm of turbulent transport." (He cautioned "However, it does not prove that this model offers the only explanation.…”

Section: Introductionmentioning

confidence: 82%

Self-organized criticality, long-time correlations, and the standard transport paradigm

Krommes

2000

Physics of Plasmas

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Some aspects of low-frequency, long-wavelength fluctuations are considered. A stochastic model is used to show that power-law time correlations need not arise from self-organized criticality. A formula for the frequency spectrum of uncorrelated, overlapping avalanches is shown to be a special case of the spectral balance equation of renormalized statistical turbulence theory. It is argued that there need be no contradiction between the presence of long-time correlations and the existence of local transport coefficients.

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Section: Introductionmentioning

confidence: 82%

Self-organized criticality, long-time correlations, and the standard transport paradigm

Krommes

2000

Physics of Plasmas

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“…Carreras et al (1998b) [see also Carreras et al (1998a)] attempted to answer that question by analyzing experimental data in search of long-time correlations-in particular, algebraic tails on two-time Eulerian correlation functions of the form C(τ ) ∼ |τ | −β (0 < β < 1). [Intuitively, one expects that long-ranged, scaleinvariant avalanches should give rise to long-lived, scale-invariant time correlations, as argued in the first paper by Bak et al (1987), although I will question the uniqueness of this interpretation shortly.]…”

Section: Long-time Tails and Socmentioning

confidence: 99%

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Krommes¹

2002

Physics Reports

261

397

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A pedagogical review of the historical development and current status (as of early 2000) of systematic statistical theories of plasma turbulence is undertaken. Emphasis is on conceptual foundations and methodology, not practical applications. Particular attention is paid to equations and formalism appropriate to strongly magnetized, fully ionized plasmas. Extensive reference to the literature on neutral-fluid turbulence is made, but the unique properties and problems of plasmas are emphasized throughout. Discussions are given of quasilinear theory, weak-turbulence theory, resonance-broadening theory, and the clump algorithm. Those are developed independently, then shown to be special cases of the direct-interaction approximation (DIA), which provides a central focus for the article. Various methods of renormalized perturbation theory are described, then unified with the aid of the generating-functional formalism of Martin, Siggia, and Rose. A general expression for the renormalized dielectric function is deduced and discussed in detail. Modern approaches such as decimation and PDF methods are described. Derivations of DIA-based Markovian closures are discussed. The eddy-damped quasinormal Markovian closure is shown to be nonrealizable in the presence of waves, and a new realizable Markovian closure is presented. The test-field model and a realizable modification thereof are also summarized. Numerical solutions of various closures for some plasmaphysics paradigms are reviewed. The variational approach to bounds on transport is developed. Miscellaneous topics include Onsager symmetries for turbulence, the interpretation of entropy balances for both kinetic and fluid descriptions, self-organized criticality, statistical interactions between disparate scales, and the roles of both mean and random shear. Appendices are provided on Fourier transform conventions, dimensional and scaling analysis, the derivations of nonlinear gyrokinetic and gyrofluid equations, stochasticity criteria for quasilinear theory, formal aspects of resonance-broadening theory, Novikov's theorem, the treatment of weak inhomogeneity, the derivation of the Vlasov weak-turbulence wave kinetic equation from a fully renormalized description, some features of a code for solving the direct-interaction approximation and related Markovian closures, the details of the solution of the EDQNM closure for a solvable three-wave model, and the notation used in the article.

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“…Similarities of these properties in different devices have been found through different kinds of numerical analyses. [4][5][6][7][8][9] Quantitative investigations of the electrostatic fluctuations using spectral approaches like Fourier and wavelet analysis show that drift waves are destabilized in the confining magnetic field so as to yield a turbulent spectrum. 1, [10][11][12] On the other hand, dynamical diagnostics used to describe fluid turbulence 13 have been applied to analyze the plasma edge turbulence, as the return-time statistics 8,14 and recurrence analyses.…”

Section: Introductionmentioning

confidence: 99%

Multifractality in plasma edge electrostatic turbulence

et al. 2008

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Plasma edge turbulence in Tokamak Chauffage Alfvén Brésilien (TCABR) [R. M. O. Galvão et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences.

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Long-Range Time Correlations in Plasma Edge Turbulence

Cited by 155 publications

References 15 publications

Self-organized criticality, long-time correlations, and the standard transport paradigm

Self-organized criticality, long-time correlations, and the standard transport paradigm

Fundamental statistical descriptions of plasma turbulence in magnetic fields

Multifractality in plasma edge electrostatic turbulence

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