Proceedings of ITC/ISHW2007

Overview of Edge Turbulence and Zonal Flow Studies on TEXTOR
Y. Xu1, A. Krämer-Flecken2, D. Reiser2, M. Vergote1, S. Jachmich1, M. Van Schoor1,M. W. Jakubowski3, M. Lehnen2, Y. Liang2, M. Mitri2, S. Soldatov2, B. Unterberg2,
D. Reiter2, U. Samm2, R. R. Weynants1 and the TEXTOR team* Partners in the Trilateral Euregio Cluster (TEC):
Laboratory for Plasma Physics, Ecole Royale Militaire/Koninklijke Militaire School,
Euratom-Belgian State Association, Avenue de la Renaissance 30, B-1000 Brussels, Belgium*
1

2

Institute für Energieforschung-Plasmaphysik, Forschungszentrum Jülich, Association Euratom,
D-52425 Juelich, Germany*3
Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Greifswald, Germany

In the TEXTOR tokamak, the edge turbulence properties and turbulence-associated zonal flows have beensystematically investigated both experimentally and theoretically. The experimental results include the investigationof self-organized criticality (SOC) behavior, the intermittent blob transport and the geodesic acoustic mode (GAM)
zonal flows. During the Dynamic Ergodic Divertor (DED) operation in TEXTOR, the impact of an ergodized
plasma boundary on edge turbulence, turbulent transport and the fluctuation propagation has also been studied indetail. The results show substantial influence by the DED on edge turbulence. The theoretical simulations for
TEXTOR parameters show characteristic features of the GAM flows and strong reduction of the blob transport by
the DED at the plasma periphery. Moreover, the modelling reveals the importance of the Reynolds stress in driving
mean (or zonal) flows at the plasma edge in the ohmic discharge phase in TEXTOR.
Keywords: Tokamak, edge turbulence, self-organized criticality, blob transport, zonal flows, Dynamic Ergodic
Divertor, Reynolds stress.

1. Inroduction
In the TEXTOR tokamak, the edge turbulence
properties and turbulence-associated zonal flows havebeen systematically investigated experimentally by fast
reciprocating Langmuir probe and correlationreflectometry measurements, and theoretically by
three-dimensional (3D) non-linear electromagnetic
drift-turbulence simulations. The role of theReynolds-stress in driving mean plasma flows has also
been studied by fluid modelling. In this paper, anoverview of the recent work is given.

2. Experimental results
First, we report on some fundamental features of theedge turbulence observed on TEXTOR. These include: (i)the self-organized criticality (SOC) behavior andself-similar characters in the fluctuation data [1]; (ii) theturbulence intermittency and blob transport in the plasmaboundary [2]; (iii) identification of geodesic acoustic
mode (GAM) zonal flows in density and velocity
fluctuations by poloidal correlation reflectometry [3].
(i) For the SOC studies, we have measured both thepotential and density fluctuations by the Langmuir probes
and analyzed the data using various methods [1]. The
results show a lot of characteristics associated with theE-mail: y.xu@fz-juelich.de

SOC dynamics, including similar frequency spectra to the“running sandpile” modelling and f -1 dependence in thespectrum as an indication of avalanche overlapping, aslowly decaying long tail in the autocorrelation function,a long-range radial propagation of avalanche-like eventsin the edge plasma region, and values of Hurst parameterslarger than 0.5 at all detected radial locations, as shown inFig. 1(a).
(ii) The intermittent convective transport has also
been investigated by Langmuir probes in the plasma edge
and in the scrape-off layer (SOL) [2]. It has been
observed that the probability distribution function (PDF)of the density fluctuations are positively skewed, while aGaussian shape is recorded for the negative values [seeFig. 1(b)]. The deviation of the signals from Gaussianstatistics increases from the plasma edge to the SOL.
Conditional averaging reveals that in the SOL the wave
form of blobs is asymmetric in time and the blobs move
radially outwards at velocities of 0.5~1 km/s. The largebursts (≥ 2.5×rms) account for ~ 40% of the totaltransport. Statistics of the waiting-time indicate that thePDF of the time interval follows a Poisson-distribution
for small duration events and changes into a power-law
form for larger ones. Moreover, the turbulenceintermittency shows self-similar characters in thefluctuation data.

φ [rad] Amplitude a.u.

Proceedings of ITC/ISHW2007#98648: 2.0134−2.0953s; r/a =0.87

300200GAMaCoherence

100010Ω = 12800 rad/sb∂ φ/∂ f ≈ 0−11c0.50−50 −40 −30 −20 −10 0 10 20 30 40 50Frequency [kHz]Fig. 2Spectra of (a) amplitude, (b)cross-phase and (c) coherence of density
fluctuations measured by the top antenna arrayof a correlation reflectometer [3].

Fig. 1 (a) The radial dependence of Hurst exponent(H) estimated by rescaled range (open circles) andstructure function (solid triangles) analysis ofpotential fluctuations. The dotted line marks thelimiter position [1]. (b) Semi-log plot of the PDFof the density (∝ Is) fluctuations normalized by thestandard deviation, measured in the SOL. The Sand K denote skewness and kurtosis. The dottedline is the best Gaussian fit [2].
(iii) In TEXTOR, the GAMs have been measured byan O-mode correlation reflectometer system [3]. Figure 2
shows the amplitude, cross phase φ, and coherence
spectrum of density fluctuations measured by the top
antenna array. The GAMs appears around 17 kHz for thereflection layer detected. The ∂φ/∂f ≅ 0 at the GAM
frequency implies a poloidal homogenous structure of theGAM zonal flows. The frequency dependence of theGAMs on the acoustic speed has been verified underdifferent discharge conditions. The poloidal asymmetric(m=1) feature of density fluctuations of GAMs has also
been identified by the cross-correlation of the top andmidplane antennas. The influence of the GAMs on theambient turbulence level has been observed from themodulation of the GAM flows on the fluctuation
amplitudes of ambient turbulence. More recently, thedirect evidence of the GAMs on the poloidal velocity
fluctuations has been observed.
Secondly, we investigated the influence of DED(Dynamic Ergodic Divertor) on edge turbulence. During

the DED operation in TEXTOR, the magnetic
perturbation creates a chaotic behavior of the field lines atthe plasma boundary, including an ergodic zone with long
and a laminar zone with short connection lengths,
respectively [4]. The impact of the static DED (dc DEDcurrent) on edge equilibrium profiles, turbulence
properties, turbulent transport, plasma rotations,
Reynolds stress profiles and the blob transport has been
investigated in detail [5]. Common features have beenfound among different DED configurations (m/n =12/4,6/2 and 3/1). At the plasma edge, the density andtemperature profiles are steepened or flattened by theDED, depending on discharge conditions [5, 6]. During
the DED, a typical behavior is the increase of the floating
potential in the perturbation area, leading to a reversal of
the radial electric filed Er from the negative to positive inmost of the laminar and the ergodic zone, as can be seenin Fig. 3(a). A possible interpretation is that during DED
the electrons mover faster than massive ions along the field
line to the wall so that a positive Er must be brought
about to restore the ambipolarity [7]. The influence of theDED on turbulence mainly occurs in the ergodic region.
With DED, the fluctuation amplitudes in potential andpoloidal electric field fluctuations are largely reduced,
whereas for density fluctuations the modification is small.
In the DED phase, it has been generally observed that thelocal turbulent flux reverses direction from radiallyoutwards to inwards in the ergodic area, as illustrated inFig. 3(b). Meanwhile, the turbulence itself is profoundly
modified by energy re-distribution in frequency spectra,
suppression of large-scale structures and reduction of theradial and poloidal correlation lengths at all frequencies[7]. With DED, the poloidal propagation of fluctuations
changes direction from the electron diamagnetic drift toProceedings of ITC/ISHW2007
ion drift direction in the perturbation region, consistent
with the observed reversal of the Er×B flow [5, 8].
Moreover, in the plasma boundary the size of the blobs
and the blob transport are significantly reduced by theDED [9]. In the ohmic discharge phase before the DED
the Reynolds stress displays a radial gradient at theplasma edge while during DED the profile is suppressed,
suggesting a rearrangement by the DED on the flow
momentum profile [7, 10].

velocity) have been performed [11, 12]. The simulations
show a lot of results consistent with the experimental
observations in TEXTOR-DED, for instance, thesuppression of blob amplitudes by magnetic perturbationat the plasma boundary, as shown in Fig. 4. The
simulations also show characteristic features of the GAM
flows before the DED and the suppression of GAMs at
the resonances during the DED.

1050048121620time [ms]Fig. 4 Time trace of density fluctuations
simulated before (red color) and during (bluecolor) the magnetic perturbation in the SOL.
The blob amplitudes are suppressed by themagnetic perturbation.
In addition, starting from renewed 2D HasegawaWakatani equations to explore the poloidally geometricaldependence of the Reynolds stress (RS), another fluid
modeling (with flux-surface averaging in toroidalgeometry) reveals the importance of the Reynolds stressin driving mean (or zonal) flows at the plasma edge in theabsence of magnetic perturbation [13, 14]. To illustrate
the role of RS in driving the mean poloidal flow andtherefore the development of edge radial electric field Er,
the modeled Er without RS (dotted blue line) and with RS

Fig. 3 (a) The radial dependence of radial electricfield Er measured by fast reciprocating probes
before (black curve) and during (red curve) a static
6/2 DED [5]. (b) The radial dependence offluctuation-induced flux, <Γfl>, measured by fast
reciprocating probes before (crosses) and during(circles) a static 6/2 DED [5]. The vertical solidline denotes the limiter position. The dashed line
separates the ergodic (left side) and laminar (rightside) zones.

3. Theoretical modelling and simulations
For the study of the impact of the resonant magnetic
perturbation fields on turbulence, three-dimensional
numerical simulations of drift fluid turbulence for 4 fields(potential, density, magnetic potential and parallel ion

Fig. 5 Comparison of the simulated Er (dottedblue curve without RS contribution and solid
curve with RS contribution) and theexperimentally measured one (red points).

Proceedings of ITC/ISHW2007(solid blue line) are depicted in Fig. 5 in comparison withthe experimentally measured one (red points). It can beseen that with the contribution of RS, the solid blue curveis much closer to the measured Er in the plasma edge.

4. Conclusions
In this paper, the recent experimental andtheoretical work on the study of the edge turbulence andzonal flows on TEXTOR tokamak has been briefly
summarized. The experimental observation of the basic
features of edge turbulence, like SOC behavior, blobtransport and GAM zonal flows, and the influence of theDED on turbulence properties have been presented. The
simulation results show a lot of characteristics ofturbulence, in agreement with the experimental
observations.

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