The energetic interaction between drift-wave turbulence and zonal flows is studied experimentally in two-dimensional wave number space. The kinetic energy is found to be transferred nonlocally from the drift waves to the zonal flow. This confirms the theoretical prediction that the parametric-modulational instability is the driving mechanism of zonal flows. The physical mechanism of this nonlocal energetic interaction between and zonal flows and turbulent drift-wave eddies in relation to the suppression of turbulent transport is discussed.Turbulence is responsible for the major part of particle and energy losses in toroidal fusion plasmas. Since the discovery of a transport barrier in 1982 [1] the reduction of turbulent transport by sheared E Â B plasma flows has been intensively investigated. Of special interest is the spontaneous generation of transport barriers triggered by azimuthally symmetric, bandlike shear flows called zonal flows. In magnetized plasmas, zonal flows have the potential to improve confinement mainly due to two mechanisms: (i) the shear decorrelation mechanism [2,3] can reduce turbulent diffusive step width and (ii) the zonal flow is excited by the turbulence and thus is an energy sink for the fluctuations. Since it is impossible for zonal flows to drive radial E Â B flows and, hence, turbulent transport, for the turbulence this energy is lost [2]. Zonal flows as a universal feature are also found in planetary atmospheres and in the interior of the Sun [2]. Hence, the investigation of the generation of zonal flows is also of general interest in physics.The interaction between turbulence and zonal flows has been studied in many experiments ([4] and references therein). Especially, the nonlinear drive of shear flows by Reynolds stress has been demonstrated in the linear device CSDX [5] and the reversed field pinch RFX [6]. Theory predicts that zonal flows are driven nonlocally in k space by the parametric-modulational instability [2]. For an experimental verification of the modulational instability as the zonal-flow driving mechanism a scale resolved analysis is required. To achieve this, usually, a bicoherence analysis is carried out in frequency space. Thus, a nonlocal coupling between turbulence and zonal flows, including the geodesic acoustic mode (GAM), has been demonstrated, e.g., in Refs. [7][8][9][10][11][12]. The GAM is a finite frequency zonal flow. However, a bicoherence analysis yields information on the degree of phase locking of different modes only and, thus, identifies modes that can couple with each other. Driving or damping of zonal flows and the relative importance of the various interactions can only be estimated from an energy transfer analysis. Energy transfer studies of the turbulencezonal-flow interaction and the turbulent cascades have been carried out [13][14][15][16][17]. These studies were done in frequency space, too, using Taylor hypothesis to transform the fluctuations from frequency to k space. Furthermore, the analyses were done in one dimension only. The phys...

Abstract. The intermittent character of turbulent transport is investigated with Langmuir probes in the scrape-off layer (SOL) and across the separatrix of ASDEX Upgrade Ohmic discharges. Radial profiles of plasma parameters are in reasonable agreement with results from other diagnostics. The probability density functions of ion-saturation current fluctuations exhibit a parabolic relation between skewness and kurtosis. Intermittent blobs and holes are observed outside and inside the nominal separatrix, respectively. They seem to be born at the edge of the plasma and are not the foothills of avalanches launched in the plasma core. A strong shear flow was observed 1 cm radially outside the location where blobs and holes seem to be generated. Blobs and holes in ASDEX Upgrade

Comparative studies between a toroidal low-temperature plasma and drift-Alfvén-wave simulations were carried out in order to investigate the microscopic structure of turbulence. The dimensionless plasma parameters in the TJ-K torsatron [Krause 2002] are similar to those in the edge of a fusion plasma. At the same time the fluctuations can be fully diagnosed by probe arrays. Fluctuation spectra are analysed by wavelet techniques indicating a large amount of intermittency in both numerical and experimental data. Since in both cases no critical gradient is present, the intermittency is not due to a state in self-organised criticality (SOC). The spectral density P (ω, k) of the turbulence was measured with a 64-tip Langmuir probe array. A broad spectrum indicates fully developed turbulence. The wave-number spectrum of the density fluctuations decays with a power law with an exponent of −3. The experiments confirm predictions from the turbulence code. The cross-phase between potential and density fluctuations is close to zero on all scales and the spectra shift to smaller wave-numbers when the drift scale ρ s is increased by changing the ion mass from Hydrogen to Helium and Argon. The ρ s scaling is confirmed by correlation measurements within the tips of the poloidal array and an 8 × 8 probe matrix. The results point to the drift-wave mechanism being responsible for the drive of the turbulence in the low-β plasma of TJ-K.

In toroidally confined plasmas, background E × B flows, microturbulence and zonal flows constitute a tightly coupled dynamic system and the description of confinement transitions needs a self-consistent treatment of these players. The background radial electric field, linked to neoclassical ambipolar transport, has an impact on the interaction between zonal flows and turbulence by tilting and anisotropization of turbulent eddies. Zonal-flow drive is shown to be non-local in wavenumber space and is described as a straining-out process instead as a local inverse cascade. The straining-out process is also discussed as an option to explain turbulence suppression in sheared flows and could be the cause of predator-prey oscillations in the turbulence zonal-flow system.

Recently, a European transport project has been carried out among several fusion devices for studying the possible link between the mean radial electric field (E r ), long-range correlation (LRC) and edge bifurcations in fusion plasmas. The main results reported in this paper include: (i) the discovery of low-frequency LRCs in potential fluctuations which are amplified during the development of edge mean E r using electrode biasing and during the spontaneous development of edge sheared flows in stellarators and tokamaks. Evidence of nonlocal energy transfer and the geodesic acoustic mode modulation on local turbulent transport have also been observed. The observed LRCs are consistent with the theory of zonal flows described by a ‘predator–prey’ model. The results point to a significant link between the LRC and transport bifurcation. (ii) Comparative studies in tokamaks, stellarators and reversed field pinches have revealed significant differences in the level of the LRC. Whereas the LRCs are clearly observed in tokamaks and stellarators, no clear signature of LRCs was seen in the RFX-mod reversed field pinch experiments. These results suggest the possible influence of magnetic perturbations on the LRC, in agreement with recent observations in the resonant magnetic perturbation experiments at the TEXTOR tokamak. (iii) The degree of the LRCs is strongly reduced on approaching the plasma density-limit in tokamaks and stellarators, suggesting the possible role of collisionality or/and the impact of mean E r × B flow shear on zonal flows.