Empirical Similarity of Frequency Spectra of the Edge-Plasma Fluctuations in Toroidal Magnetic-Confinement Systems (original) (raw)
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Magnetic and electrostatic fluctuations in RFX exhibit bursty behavior as commonly observed in other fusion experiments. A detailed investigation of the statistical properties of these fluctuations has revealed that their Probability Distribution Function (PDF) is not self-similar at the different scales [1,2], developing non-gaussian tails at the smaller scales. This property allow bursts in RFX to be named 'intermittent events' according to the definition of intermittency as departure from pure self similarity [3]. Owing to the relationship between magnetic and electrostatic turbulence and anomalous particle and energy fluxes, the statistical properties of the fluctuations of the primary quantities (namely magnetic fields, density, temperature and plasma potential) and derived fluxes, are expected to be related to the fundamental processes underlying the anomalous transport. In order to identify this processes the statistical properties of the particle flux have been compared with the predictions of Self Organized Criticality (SOC) models. These models have been proposed to describe the transport processes in plasmas for thermonuclear fusion research, owing to some properties [4] like density and temperature profile resilience and power law decay in fluctuation spectra. Among the different SOC models discussed in literature, [see [5] for a review, the running sand pile model developed by Hwa and Kardar [6],appears particularly suitable to better mimic a magnetically confined plasma continuously powered and refueled with particles. So that in this contribution the comparison will be made with this model. The experimental data have been collected in the edge region of the Reversed Field Pinch (RFP) experiment RFX (R = 2 m, a = 0.46 m) operated at low plasma current (300-400 kA) and with electron density ~ 3.5 10 19 m -3 . The electrostatic fluctuations have been measured by a set of Langmuir probes described elsewhere [7] and the data have been sampled at 1 MHz. The instantaneous radial particle flux induced by the electrostatic turbulence ¡ es has been evaluated from two-point measurements as ¡ es =/B¢ where B¢ is the mean magnetic field (which is mainly poloidal at the edge) and E and n are the electric field and density signals. In this case temperature fluctuations have been neglected, so that E and n have been approximated by ion saturation current and floating potential signals . It has been found that the particle flux is mostly concentrated in the range 30-250 kHz [7] which corresponds to time scales approximately in the range 4 -30 £ s. The power spectrum of particle flux, as previously observed for the primary quantities (i.e. plasma density and potential), decays with a power law behavior, as shown in , in the frequency range relevant for transport processes.
Long-Range Time Correlations in Plasma Edge Turbulence
Physical Review Letters, 1998
Analysis of the edge plasma fluctuation in several confinement devices reveals the self-similar character of the fluctuations through the presence of long-range time correlations. These results show that the tail of the autocorrelation function decays as a power law for time lags longer than the decorrelation time and as long as times on the order of the particle diffusion time. The algebraic decay of the longrange time correlations is consistent with plasma transport characterized by self-organized criticality.
Experimental evidence of long-range correlations and self-similarity in plasma fluctuations
Physics of Plasmas, 1999
To better understand long time transport dynamics, techniques to investigate long-range dependences in plasma fluctuations have been applied to data from several confinement devices including tokamaks, stellarators, and reversed field pinch. The results reveal the self-similar character of the edge plasma fluctuations. This implies that the tail of the autocorrelation function decays as a power law and suggests that there is a superdiffusive component of the anomalous transport. Rescaled fluctuation and turbulent flux spectra from different devices also show a strong similarity. For a range of parameters corresponding to the tokamak ohmic regime and equivalent power for other devices, the spectral decay index may show a universal character.
Intermittency and extended self-similarity in space and fusion plasma: boundary effects
Plasma Physics and Controlled Fusion, 2008
A comparative study of fluctuation features in the edge plasma of fusion devices and in turbulent boundary layers (TBLs) of the Earth's magnetosphere has demonstrated similar statistical characteristics including scalings of structure functions and multifractal spectra. The detected intermittency and anomalous transport of mass and momentum is carried by sporadic plasma flux bursts with nonGaussian probability of flux magnitude. The turbulence exhibits a generalized (extended) self-similarity in an extended scale range. The experimental scalings of the structure functions are rather well fitted by the log-Poisson model considering quasi-1D singular dissipative structures. It appears that the turbulence in the edge plasma of fusion devices and in the TBL of the Earth's magnetosphere is governed by cross-field motions similar to hydrodynamic turbulence. Here the experimental scalings from the plasma are available for a comparison with experimental results from neutral fluids. The plasma scalings display universal properties of intermittent turbulence. A statistical approach permits us to evaluate turbulent transport scalings. The time dependence of an average squared particle displacements δx 2 ∝ τ α infers superdiffusion with α ≈ 1.4-1.
Characterization of the frequency ranges of the plasma edge fluctuation spectra
Physics of Plasmas, 1999
Frequency spectra of fluctuations for the ion saturation current, floating potential, and turbulent transport measured in the plasma edge of plasma confinement experiments ͑tokamaks and stellarators͒ have been analyzed to identify the frequency ranges characterized by a power dependence. Three main regions can be identified. For the intermediate frequency region, the decay of the spectra is close to 1/f , as is expected in self-organized criticality systems. This region is particularly important for the role that it plays in plasma transport and the self-similarity of the fluctuations and fluxes. The effect of plasma rotation on the decay indices has also been studied.
Self-similarity of the plasma edge fluctuations
Physics of Plasmas, 1998
The rescaled range analysis techniques are used to investigate long-range dependence in plasma edge fluctuations ͓Mandelbrot and Wallis, Water Resources Res. 4, 909 ͑1969͔͒. This technology has been applied to data from several confinement devices such as tokamaks, stellarators, and reversed-field pinch. The results reveal the self-similar character of the electrostatic fluctuations at the plasma edge with self-similarity parameters ranging from 0.62 to 0.72. These results show that the tail of the autocorrelation function decays as a power law for time lags longer than the decorrelation time and as long as times of the order of the confinement time. In cold plasma devices (T e Ͻ1 eV at the core͒, there is no evidence of algebraic tails in the autocorrelation function. Some other characteristic features of the autocorrelation function and power spectrum have been investigated. All of these features are consistent with plasma transport as characterized by self-organized criticality.
Phys. Plasmas 8, 2107 ͑2001͔͒, the Wendelstein 7-Advanced Stellarator ͓H. Renner, E. Anabitarte, E. Ascasibar et al., Plasma Phys. Controlled Fusion 31, 1579 ͑1989͔͒, and the TJ-II stellarator ͓C. Alejaldre, J. Alonso, J. Botija et al., Fusion Technol. 17, 131
Fusion plasma turbulence described by modified sandpile dynamics
The European Physical Journal E, 2014
Transport in fusion plasmas is investigated with modified sandpile models. Based on results from more complete simulations the sandpile model is modified in steps. Models with a constant source are obtained and decoupling the meanfield from the bursts allows one develop a reduced model which captures some of the evidence from flux driven simulations. In such a model where turbulent transport is mediated by the burst field one investigate spreading and transport barriers. These are found to exhibit intermittent behaviors when switching between different transport regimes. Finally, one couples to the sandpile algorithm a species evolution algorithm that assigns a quality factor to each site. The latter allows one to self-generate corrugations, or micro-barriers and investigate their evolution. These are found to naturally cluster radially in structures that are large enough to impact confinement. The mechanisms introduced to alleviate the clustering, either destabilization of the corrugation by overloading and by secondary instabilities at critical radial extents are shown to generate long range relaxation events in space in time with quasiperiodic reorganization of the corrugation pattern.
Recurrence Analysis of Turbulent Fluctuations in Magnetically Confined Plasmas
2016
Recurrence plots and their quantification became a modern tool in nonlinear data analysis, currently being used in a myriad of scientific disciplines, a diversity that characterizes the Recurrence Plot Workshop since its beginning. In this work we review some applications of recurrence quantification analysis to data analysis in a fusion plasma, namely turbulent fluctuations in the plasma edge of Tokamak Chauffage Alfven Bresilien tokamak, which is a magnetic confinement plasma machine. A similar analysis was performed in a low-density plasma device called Texas Helimak (University of Texas at Austin). Our results point out that the deterministic content of the fluctuations tends to increase as we approach the plasma edge, indicating a concentration of the recurrences therein. This favours the use of fluid models to describe the physics of the plasma edge turbulence.