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This study presents the investigation of the connection between radial electric field, gradient of Reynolds stress and Long Range Correlation (LRC), as a proxy for Zonal Flows (ZF), in different plasma scenarios in the TJ-II stellarator. Monte Carlo simulations were made showing that radial electric fields in the range of those experimentally measured have an effect on the neoclassical orbit losses. The results indicate that, despite the order of magnitude of turbulent acceleration is comparable to the neoclassical damping of perpendicular flows, its dependence with radial electric field is not correlated with the evolution of LRC amplitude, indicating that turbulent acceleration alone cannot explain the dynamics of Zonal Flows. These results are in line with the expectation that the interplay between turbulent and neoclassical mechanisms is a crucial ingredient of the dynamics of edge Zonal Flows., Comment: 6 pages, 15 figures, results presented in 19th Coordinated working group meeting of IPP

The understanding of the outward radial transport of heat in magnetic confinement fusion devices is a priority for the development of economically viable fusion reactors. Here, we analyze the radial propagation of spontaneously generated electron temperature (T_e) fluctuations measured using the Electron Cyclotron Emission (ECE) diagnostic in Wendelstein 7-X, which disposes of 32 channels, covering a large part of the plasma minor radius. By applying a relatively new statistical analysis technique (the Transfer Entropy), the present work provides, for the first time, a view of the detailed mechanism of electron heat transport in fusion plasmas. It is shown that rational surfaces have a significant impact on radial heat transport and may in fact be essential in setting the global energy confinement. The reported observations provide support for various explanatory concepts suggested in literature: namely, critical gradients, non-locality, and self-organization., Comment: 10 pages, 3 figures

In this work, we study the outward propagation of temperature perturbations. For this purpose, we apply an advanced analysis technique, the Transfer Entropy, to ECE measurements performed in ECR heated discharges at the low-shear stellarator TJ-II. We observe that the propagation of these perturbations is not smooth, but is slowed down at specific radial positions, near 'trapping zones' characterized by long time lags with respect to the perturbation origin. We also detect instances of rapid or instantaneous (non-local) propagation, in which perturbations appear to 'jump over' specific radial regions. The analysis of perturbations introduced in a resistive Magneto-Hydrodynamic model of the plasma leads to similar results. The radial regions corresponding to slow radial transport are identified with maxima of the flow shear associated with rational surfaces (mini-transport barriers). The non-local interactions are ascribed to MHD mode coupling effects., Comment: 35 pages, 25 figures

Achieving impurity and helium ash control is a crucial issue in the path towards fusion-grade magnetic confinement devices, and this is particularly the case of helical reactors, whose low-collisionality ion-root operation scenarios usually display a negative radial electric field which is expected to cause inwards impurity pinch. In these work we discuss, based on experimental measurements and standard predictions of neoclassical theory, how plasmas of very low ion collisionality, similar to those observed in the impurity hole of the Large Helical Device, can be an exception to this general rule, and how a negative radial electric field can coexist with an outward impurity flux. This interpretation is supported by comparison with documented discharges available in the International Stellarator-Heliotron Profile Database, and it can be extrapolated to show that achievement of high ion temperature in the core of helical devices is not fundamentally incompatible with low core impurity content.

We review in a tutorial fashion some of the causes of impurity density variations along field lines and radial impurity transport in the moment approach framework. An explicit and compact form of the parallel inertia force valid for arbitrary toroidal geometry and magnetic coordinates is derived and shown to be non-negligible for typical TJ-II plasma conditions. In the second part of the article, we apply the fluid model including main ion-impurity friction and inertia to observations of asymmetric emissivity patterns in neutral beam heated plasmas of the TJ-II stellarator. The model is able to explain qualitatively several features of the radiation asymmetry, both in stationary and transient conditions, based on the calculated in-surface variations of the impurity density.

We study radial particle transport in stellarator plasmas using cryogenic pellet injection. By means of perturbative experiments, we estimate the experimental particle flux and compare it with neoclassical simulations. Experimental evidence is obtained of the fact that core depletion in helical devices can be slowed-down even by pellets that do not reach the core region. This phenomenon is well captured by neoclassical predictions with DKES and FORTEC-3D.

This work focuses on the relationship between L-H (or L-I) transitions and MHD activity in the low magnetic shear TJ-II stellarator. It is shown that the presence of a low order rational surface in the plasma edge (gradient) region lowers the threshold density for H-mode access. MHD activity is systematically suppressed near the confinement transition. We apply a causality detection technique (based on the Transfer Entropy) to study the relation between magnetic oscillations and locally measured plasma rotation velocity (related to Zonal Flows). For this purpose, we study a large number of discharges in two magnetic configurations, corresponding to 'fast' and 'slow' transitions. With the 'slow' transitions, the developing Zonal Flow prior to the transition is associated with the gradual reduction of magnetic oscillations. The transition itself is marked by a strong spike of 'information transfer' from magnetic to velocity oscillations, suggesting that the magnetic drive may play a role in setting up the final sheared flow responsible for the H-mode transport barrier. Similar observations were made for the 'fast' transitions. Thus, it is shown that magnetic oscillations associated with rational surfaces play an important and active role in confinement transitions, so that electromagnetic effects should be included in any complete transition model., Comment: 38 pages, 15 figures

This work explores the relation between magnetic islands, long range temporal correlations and heat transport. A low order rational surface ($\iota/2\pi = 3/2$) was purposely scanned outward through an Electron Cyclotron Resonance Heated (ECRH) plasma in the TJ-II stellarator. Density turbulence and the poloidal flow velocity (or radial electric field) were characterized using a two channel Doppler Reflectometer. Simultaneously, the ECRH power was modulated to characterize heat transport, using measurements from a 12 channel Electron Cyclotron Emission diagnostic. A systematic variation of the poloidal velocity was found to be associated with the stationary $\iota/2\pi = 3/2$ magnetic island. Inside from the rational surface, the Hurst coefficient, quantifying the nature of long-range correlations, was found to be significantly enhanced. Simultaneously, heat transport was enhanced as well, establishing a clear link between density fluctuations and anomalous heat transport. The variation of the Hurst coefficient was consistent with a magnetohydrodynamic turbulence simulation., Comment: 38 pages, 18 figures

The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained with a variety of models. {We present and use a simplified numerical model which does not contain any turbulence, Taylor dispersion, or fractality. With it, we show that the non-linearity in the intermediate regime nevertheless occurs. Furthermore,} we show that that the intermediate regime can be regarded as a phase transition between random, diffusive transport at low flow velocity and ordered transport controlled by the geometry of the pore space at high flow velocities. This phase transition explains the first-order behavior in the intermediate regime. A new quantifier, the ratio of the amount of solute in dominantly advective versus dominantly diffusive pore channels, plays the role of `order parameter' of this phase transition. Taylor dispersion, often invoked to explain the supra-linear behavior of longitudinal dispersion in this regime, was found not to be of primary importance. The novel treatment of the intermediate regime paves the way for a more accurate description of dispersion as a function of flow velocity, spanning the whole range of P\'eclet numbers relevant to practical applications, such as ground water remediation., Comment: 40 pages, 15 figures

This work addresses the identification of zonal flows in fusion plasmas. Zonal flows are large scale phenomena, hence multipoint measurements taken at remote locations are required for their identification. Given such data, the Biorthogonal Decomposition (or Singular Value Decomposition) is capable of extracting the globally correlated component of the multipoint fluctuations. By using a novel quadrature technique based on the Hilbert transform, propagating global modes (such as MHD modes) can be distinguished from the non-propagating, synchronous (zonal flow-like) global component. The combination of these techniques with further information such as the spectrogram and the spatial structure then allows an unambiguous identification of the zonal flow component of the fluctuations. The technique is tested using gyro-kinetic simulations. The first unambiguous identification of a zonal flow at the TJ-II stellarator is presented, based on multipoint Langmuir probe measurements., Comment: 26 pages, 17 figures

This work explores the potential of an information-theoretical causality detection method for unraveling the relation between fluctuating variables in complex nonlinear systems. The method is tested on some simple though nonlinear models, and guidelines for the choice of analysis parameters are established. Then, measurements from magnetically confined fusion plasmas are analyzed. The selected data bear relevance to the all-important spontaneous confinement transitions often observed in fusion plasmas, fundamental for the design of an economically attractive fusion reactor. It is shown how the present method is capable of clarifying the interaction between fluctuating quantities such as the turbulence amplitude, turbulent flux, and Zonal Flow amplitude, and uncovers several interactions that were missed by traditional methods., Comment: 26 pages, 14 figures

Long range correlations were measured using two remote reciprocating Langmuir probe systems at TJ-II. The influence of the rotational transform on the correlation was studied by scanning the magnetic configuration. A simple drift wave correlation model, assuming an exponential decay of the correlation with different correlation lengths in the directions parallel and perpendicular to the field lines, was found to describe the observations well at low densities. The experiment was repeated at gradually higher densities, and an additional correlation was detected at a critical value of the density. In accordance with previous work, this additional correlation was ascribed to zonal flows associated with a confinement transition. Thus, the total long range correlation is found to be a sum of the drift wave and zonal flow contributions., Comment: 15 pages, 8 figures

Plasma turbulence is studied using Doppler reflectometry at the TJ-II stellarator. By scanning the tilt angle of the probing beam, different values of the perpendicular wave numbers are probed at the reflection layer. In this way, the interaction between zonal flows and turbulence is reported with (a) spatial, (b) temporal, and (c) wavenumber resolution for the first time in any magnetic confinement fusion device. We report measurements of the bicoherence across the Low to High (L--H) confinement transition at TJ-II. We examine both fast transitions and slow transitions characterized by an intermediate (I) phase. The bicoherence, understood to reflect the non-linear coupling between the perpendicular velocity (zonal flow) and turbulence amplitude, is significantly enhanced in a time window of several tens of ms around the time of the L--H transition. It is found to peak at a specific radial position (slightly inward from the radial electric field shear layer in H mode), and is associated with a specific perpendicular wave number ($k_\perp \simeq 6-12$ cm$^{-1}$, $k_\perp \rho_s \simeq 0.8-2$). In all cases, the bicoherence is due to the interaction between high frequencies ($\simeq 1$ MHz) and a rather low frequency ($\lesssim 50$ kHz), as expected for a zonal flow., Comment: 11 pages, 3 figures

The dynamics of fluctuating electric field structures in the edge of the TJ-II stellarator, that display zonal flow-like traits, is studied. These structures have been shown to be global and affect particle transport dynamically [J.A. Alonso et al., Nucl. Fus. 52 063010 (2012)]. In this article we discuss possible drive (Reynolds stress) and damping (Neoclassical viscosity, geodesic transfer) mechanisms for the associated ExB velocity. We show that: (a) while the observed turbulence-driven forces can provide the necessary perpendicular acceleration, a causal relation could not be firmly established, possibly because of the locality of the Reynolds stress measurements, (b) the calculated neoclassical viscosity and damping times are comparable to the observed zonal flow relaxation times, and (c) although an accompanying density modulation is observed to be associated to the zonal flow, it is not consistent with the excitation of pressure side-bands, like those present in geodesic acoustic oscillations, caused by the compression of the ExB flow field.

Recently, it has been proposed that the turbulent fluctuations measured in a linear plasma device could be described as a superposition of uncorrelated Lorentzian pulses with a narrow distribution of durations, which would provide an explanation for the reported quasi-exponential power spectra. Here, we study the applicability of this proposal to edge fluctuations in toroidal magnetic confinement fusion plasmas. For the purpose of this analysis, we introduce a novel wavelet-based pulse detection technique that offers important advantages over existing techniques. It allows extracting the properties of individual pulses from the experimental time series, and quantifying the distribution of pulse duration and energy, as well as temporal correlations. We apply the wavelet technique to edge turbulent fluctuation data from the W7-AS stellarator and the JET tokamak, and find that the pulses detected in the data do not have a narrow distribution of durations and are not uncorrelated. Instead, the distributions are of the power law type, exhibiting temporal correlations over scales much longer than the typical pulse duration. These results suggest that turbulence in open and closed field line systems may be distinct and cast doubt on the proposed ubiquity of exponential power spectra in this context., Comment: 10 pages, 4 figures

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions., Comment: 14 pages, 1 figure. References added. Published version