Proceedings of ITC/ISHW2007

Investigation of plasma turbulence in strongly sheared E × B flows
using multi-probe arrays
M. RAMISCH1) , F. GREINER2) , N. MAHDIZADEH1) , K. RAHBARNIA1) and U. STROTH1)
1)

2)

Institut für Plasmaforschung, University Stuttgart, 70569 Stuttgart, Germany
Institut für Experimentelle und Angewandte Physik, University Kiel, 24098 Kiel, Germany

Poloidal E × B shear flows can act on turbulent transport through the shear decorrelation mechanism, which
can reduce the radial size of turbulent structures [1] or change the phase relation between density and potentialfluctuations [2]. In this contribution, the influence of sheared E × B flows on the microscopic structure of turbulence is investigated in the toroidally confined plasma of the torsatron TJ-K. Multi-probe arrays are used todetect turbulent structures and study the dynamics perpendicular to the magnetic field. Sheared poloidal E × B
flows are generated by plasma biasing. It turns out that at strong flow shear, the fluctuations are dominated bylarge-scale coherent structures with increased correlation and poloidal wave lengths. Constant particle flux isrealised at steeper gradients due to modifications of the cross-phase, which relates the large-scale structures toinward transport.
Keywords: drift-wave turbulence, shear flows, turbulence suppression, biasing, probe array, torsatron TJ-K.

1 Introduction

2 Experimental setup

The understanding of the formation of transport barriers during transitions from low-confinement (L-mode) tohigh-confinement (H-mode) regimes is one of the key objectives in fusion research. Poloidal E × B shear flows arewidely accepted as a trigger mechanism of transport barriers in the edge of fusion plasmas [3]. This has been confirmed in experiments with spontaneously excited transportbarriers [2] and such triggered by external plasma biasing [4]. Strong E × B flows can act on turbulent transport through the shear decorrelation mechanism [1], which
can reduce the radial size of turbulent structures or change
the phase relation between density and potential fluctuations [2].
For interchange and ion-temperature-gradient driven
turbulence it was found that a transport reduction by
sheared flows is mostly due to a reduction of the fluctuation amplitudes [5]. Other analytical studies suggested,
however, that strong shear flows predominantly influence
the cross-phase leading to reduced or in case of collisional
drift-waves even locally inward directed transport [6]. In
fact, strong cross-phase modifications have already been
observed during spontaneous [7] as well as externally induced L-H transitions [8].
In this work, the influence of strong E × B shear flows
on the microscopic structure of turbulence is investigatedin high detail using multi-probe arrays inside the confinement region of a toroidal plasma. The experiments arecarried out on the low-temperature plasma of the torsatron
TJ-K, which is dimensionally similar to fusion edge plasmas [9]. E × B flows are generated by biasing an internal
flux surface.

The torsatron TJ-K [10] toroidally confines a lowtemperature plasma, which is dimensionally similar to fusion edge plasmas [9]. The major and the minor plasma
radius is R0 = 0.6 m and a = 0.1 m, respectively. The
confining magnetic field has a rotational transform ofabout 1/3 with low magnetic shear. TJ-K can be operated with nominal magnetic field strengths in the range
B = 70–100 mT when electron-cyclotron-resonance heating (ECRH) at 2.45 GHz is used for plasma generation.
In the present experiment, the working gas was hydrogen at a neutral gas pressure of p0 = 4 × 10−5 mbar, aheating power of PECRH = 1.8 kW and a magnetic fieldstrength of B = 72 mT. For these parameters, the typicalelectron temperature and maximum density is T e ≈ 7 eVand n ≈ 2 × 1017 m−3 , respectively. The ions are cold
(T i < 1 eV).
In order to generate the appropriate E × B flow, anelectrode consisting of a closed stainless steel wire in theshape of the poloidal cross-section of an inner flux surface
was used. The wire had a diameter of 3 mm. It was biased positively with respect to the grounded vacuum vessel via a single lead, which was insulated by a ceramics
tube. A grounded electrode will be referred to as unbiased. The electrode was introduced from a top port at a
toroidal angle of φ = 50◦ , where the flux surfaces are elliptical. Equilibrium-profile and fluctuation measurements
have been carried out at two outer ports at φ = 270◦ or330◦ and φ = 90◦ , respectively. At the positions of theouter ports, the flux-surface cross-sections are triangular.
In Fig. 1, the mapping of the electrode onto such a positionis shown.
For the measurements of turbulent structures in thedensity fluctuations, two diagnostics consisting of 64

author’s e-mail: ramisch@ipf.uni-stuttgart.deProceedings of ITC/ISHW2007

3 Perpendicular dynamics
strong E × B flow

without

In TJ-K, the turbulence drive is governed by drift waves.
Evidence for drift-wave signatures in the spectral crossphase between density and potential fluctuations and forthe parallel structure in toroidal geometry is provided inRef. [9] and [12], respectively.
In order to investigate the dynamics perpendicular to
the magnetic field, turbulent structures are used as tracersof the background flow. Therefor, cross-correlation analyses according to Eq. (1) are carried out on density fluctuations measured with the matrix. For consecutive time lags
∆t, the result is shown in Fig. 2. Quasi-coherent structures

Fig. 1 Photo of the poloidal 64-tip probe array (a) and the 8 × 8probe matrix (b). Position of the electrode inside the separatrix (c) and mapping onto the probe section (d). The
shaded area depicts the region covered by the probe matrix.

Langmuir probes were used. The first diagnostics is set up
on a two-dimensional grid of 8 × 8 points in the poloidal
cross-section on the low-field side and centered at thebiased surface as shown in Fig. 1. The spatial resolution is 1 cm in vertical and horizontal direction. At all
64 positions, the fluctuations in the ion-saturation current were simultaneously acquired with 16 bit accuracy
at a rate of 1 MHz within a time interval of 1 s. Crosscorrelation analyses carried out on these data reveal thespatio-temporal evolution of turbulent density structures.
The cross-correlation between each probe of the matrix at
a position (Ri , z j ) and one reference probe as a function ofa time lag ∆t is calculated according toCi, j (∆t) =Zni, j (t + ∆t)
enref (t) edt,
σref
σi, j(1)where each signal is normalised to its respective rms value
σ. In Ref. [11], the probe array and the analysis technique is introduced in more detail. In order to resolve thepoloidal structure of turbulence, the matrix has been replaced by a poloidal probe array. The probes are poloidallyarranged on a complete circumference of a flux surface
near the biased one with a poloidal resolution of 7 mm.
Both the poloidal and the two-dimensional probe array are
shown in Fig. 1.

Fig. 2 Contour plots of cross-correlations between matrix
probes with the reference probe located at (×). The ellipse at ∆t = 0 approximates the structure size at 87 %correlation.

are observed, which propagate clockwise with a speed ofabout 800 ms−1 . The direction corresponds to the direction of the electron-diamagnetic drift U dia . Since the radial electric field is weak, the poloidal E × B flow velocity
is negligible compared to U dia . Hence, the propagation isin agreement with expectations from the linear drift-wave
dispersion relation [13]ω ≈ Udia k⊥ /(1 + k⊥2 ρ2s ),(2)where k⊥ is the perpendicular wavenumber and ρ s =√T e Mi /eB the drift-scale with T e the electron temperature,
Mi the ion mass and B the magnetic field strength. For thedischarge presented in Fig. 2, the normalised wavenumberk⊥ ρ s is about 0.26 [14]. Therefore, the propagation velocity directly reflects the electron-diamagnetic drift velocity

Proceedings of ITC/ISHW2007
within a deviation of 6 %. In Fig. 2, the approximate structure size at 87 % correlation at ∆t = 0 is indicated by an ellipse and will be used below for comparison with the case,where strong flow shear is present.

4 Influence of shear flows on the perpendicular dynamics
In order to generate a strong E × B shear flow, the electrodewas biased to 100 V. In Fig. 3, the effect on the potential
profile is shown. The potential inside the biased surface isFig. 4 Contour plots of cross-correlations between matrix
probes with the reference probe in the same representation as in Fig. 2 (but note the different time windows inboth cases). Here, the dashed line marks the biased flux
surface.

Fig. 3 Radial profile of the floating potential for the unbiased (•)
and the biased case (◦). Vertical lines mark the positionof the biased flux surface.

strongly increased leading to enhanced radial electric fields
outside. The potential drops by about 80 V over a distanceof 7 cm. The resulting radial electric field of 1100 Vm−1
corresponds to a poloidal E × B velocity of U E×B = 16
kms−1 . The shearing rate of the generated flow with values
between 100 and 400 kHz in almost the entire radial range
becomes larger than the decorrelation rate of about 50 kHz
in the unbiased case. At the same time, the density gradientis steepened by a factor of five [15].
In the biased state, turbulent structures have beenmeasured with the probe matrix and detected by crosscorrelation analyses. The result is shown in Fig. 4. Incomparison with the unbiased state (see Fig. 2), the propagation points into the opposite direction, i.e., in the direction of the E × B drift. The propagation speed is increased
by a factor of 15 from 0.8 to about 12 kms−1 . This can beunderstood directly by taking into account the changes inthe equilibrium profiles. For the unbiased case, the potential profile in Fig. 3 does not show steep gradients, which
would lead to substantial radial electric fields and, thus,poloidal E × B rotation. The propagation of the structures is governed by the electron-diamagnetic drift velocity. During biasing, the density gradient and, therefore,
Udia increased by a factor of five to 4 kms−1 (k⊥ ρ s reduces

to 0.2, see below). But now, U E×B = 16 kms−1 dominates
the poloidal flow resulting in a poloidal propagation speedof 12 kms−1 .
Strong flow shear as in the biased case with shearing
rates larger than the turbulence decorrelation rate in the absence of shear is expected to reduce the radial correlation
length of turbulent structures [1]. However, instead of a reduction an increase in the structure size is observed, whenfigures 2 and 4 are compared. The structure becomes morecircular and essentially exceeds the matrix dimensions.

5 Poloidal mode structure under strongshear
For a proper statement on the change in the mode structure,
the comparative biasing studies have been repeated withthe poloidal probe array. Density fluctuations have beenrecorded under the same conditions and cross-correlation
analyses have been carried out on the data. The mode
structure as a function of the poloidal coordinate ∆s withrespect to the reference probe is represented by the crosscorrelation function at ∆t = 0. The calculation was donewith all 64 probes one by one taken as reference probe.
Then the 64 correlation functions have been averaged. For
the unbiased and biased case, the result is shown in Fig. 5.
It can be seen that the poloidal mode structure changes
from m = 4 to m = 3 during biasing. With a safety factor of about q ≈ 3, this corresponds to a single helicalProceedings of ITC/ISHW2007

Fig. 5 Average spatial poloidal mode structure in the unbiased(solid) and the biased case (dashed line). The mode structure changes from m = 4 to m = 3 during biasing.

structure.
During biasing, the local value of ρ s at the centre position of the structure stays constant, while the poloidal
wavelength increases by a factor of 4/3, which reducesk⊥ ρ s from 0.26 to about 0.2. Hence, the contribution of
the diamagnetic drift to the total propagation velocity of
the large-scale structure is still consistent with the linear
dispersion relation of drift waves given by Eq. (2).
In the unbiased case, m = 3 with U dia = 800 ms−1 corresponds to a frequency of about 5 kHz. An increase of thepoloidal rotation by a factor of 15 would lead to a shift ofthis mode to about 75 kHz. In fact, the large-scale structure is related to a dominant peak at 72 kHz in the powerspectrum. Modes m ≥ 4 were found to be suppressed. The
m = 3 mode was shown to be related to local turbulent
inward transport due to a modification of the cross-phasebetween density and potential fluctuations [15]. The total
particle flux, thus, remains unchanged compared to the unbiased case, i.e., the same flux is realised at steeper density
gradients, which implies an improvement of the particle
confinement.
In H-mode fusion plasmas, reduced radial correlation
lengths were found in the shear layer [16]. However, theresults presented here rather point to the importance ofthe phase relation between density and potential fluctuations for confinement improvement. Significant crossphase modifications have been predicted for systems with aquasi-coherent fluctuation spectrum [6] under the influenceof very strong shear like in the present case and such modifications have also been found during H-mode discharges
in several devices (see, e.g., Refs. [7, 8, 17]).

6 Summary
The influence of strong E × B shear flows on the microscopic structure of drift-wave turbulence has been investigated by means of multi-probe arrays. Turbulent densitystructures were detected with an 8 × 8-probe array perpendicular to the magnetic field inside the confinement regionof the torsatron TJ-K. The poloidal mode structure wasmeasured with a 64-tip poloidal probe array. The E × B
flow was generated by biasing an internal flux surface.
This way, a poloidal E × B flow with a velocity of about
16 kms−1 and a shearing rate larger than 100 kHz with amaximum value of about 400 kHz has been achieved. At
the same time, the density gradient steepened by a factorof 5. In both the unbiased and biased case, the propagation of turbulent structures, which were used as tracersof the background flow, was due to poloidal E × B andelectron-diamagnetic drift velocities in agreement with thelinear drift-wave dispersion relation. During biasing, theturbulence suppression criterion [1] was well fulfilled inalmost the entire radial range. However, the fluctuations
were found to be dominated by large-scale structures. The
characteristic poloidal mode structure changed from m = 4
to m = 3. Hence, it has been demonstrated that strong
shear can change the spatial structure of drift-wave turbulence in toroidal geometry in favour of coherent structureswith larger correlation lengths. In Ref. [15], these structures were shown to be associated with local turbulent inward transport due to modifications in the phase relation
between density and potential fluctuations.

References[1] H. Biglari, P. H. Diamond, and P. W. Terry, Phys. Fluids, B
2, 1 (1990).
[2] K. H. Burrell, Phys. Plasmas 4, 1499 (1997).
[3] K. Itoh and I. Sanae-I, Plasma Phys. Controll. Fusion 38, 1(1996).
[4] R. J. Taylor et al., Phys. Rev. Lett. 63, 2365 (1989).
[5] E.-J. Kim, P. H. Diamond, and T. S. Hahm, Phys. Plasmas
11, 4554 (2004).
[6] P. W. Terry, D. E. Newman, and A. S. Ware, Phys. Plasmas
10, 1066 (2003).
[7] R. A. Moyer et al., Phys. Plasmas 2, 2397 (1995).
[8] J. A. Boedo et al., Phys. Rev. Lett. 84, 2630 (2000).
[9] U. Stroth et al., Phys. Plasmas 11, 2558 (2004).
[10] N. Krause et al., Rev. Sci. Instrum. 73, 3474 (2002).
[11] M. Ramisch et al., Phys. Plasmas 12, 032504 (2005).
[12] N. Mahdizadeh et al., Plasma Phys. Controll. Fusion 49,1005 (2007).
[13] M. Wakatani and A. Hasegawa, Phys. Fluids 27, 611(1984).
[14] M. Ramisch, E. Häberle, N. Mahdizadeh, and U. Stroth,submitted to Plasma Sources Sci. Technol. (2007).
[15] M. Ramisch et al., Plasma Phys. Controll. Fusion 49, 777(2007).
[16] J. Schirmer et al., Plasma Phys. Controll. Fusion 49, 1019
(2007).
[17] M. G. Shats et al., Phys. Rev. Lett. 84, 6042 (2000).