Proceedings of ITC/ISHW2007

On the zonal flows identification in the plasma edge of theTJ-II stellarator
M.A. Pedrosa, C. Silva(1), C. Hidalgo, R.O. Orozco, D. Carralero and the TJ-II team
EURATOM-CIEMAT, Spain,(1)

EURATOM-IST, Portugal

TJ-II has revealed to be an ideal laboratory to study the development of edge sheared flows that can be easily
driven and damped at the plasma edge changing the plasma density or during biasing experiments.
Cross-correlation between edge magnitudes (density and potential) simultaneously measured with Langmuir probes
located at two different positions approximately 180º toroidally apart, has been obtained in TJ-II. Results show along distance correlation between floating potential signals that increases when probes are approximately at thesame radial location, whereas there is no correlation between ion saturation current signals. Cross-correlation showsa maximum value when plasma density is close to the threshold for the development of spontaneous edge shearedflows with cross-phase close to zero. Furthermore, correlation between potential signals increases in the presence of
externally applied electric fields. These findings show for the first time that the development of fluctuating
perpendicular flows (with zonal flow-like structure) is the first step in the transition to improved confinement
regimes.
Keywords: Turbulence, zonal flows, plasma edge, correlation, electric fields, stellarators.

1. Introduction
It is well known and widely accepted the importanceof turbulent transport effects on plasma confinement infusion devices. In particular it is very important to develop
techniques to improve plasma confinement. Recently,
fusion community has focused its attention on turbulent
toroidally and azimuthally symmetric sheared flows(zonal flows) and the role that they can play in theturbulence regulation. It has been theoretically assessedthat zonal flows play a role in the dynamics of turbulence
and its self-regulation [ 1 , and references therein].
Experimental works in different magnetically confinedplasmas have been carried out to prove the existence of
these zonal flows and some fingerprints of their presence
have been found in different fusion devices [2, 3, 4, 5,6 , 7 ]. Zonal flows have also been suggested as animportant ingredient to explain the Low to Hightransition (L-H) in magnetic confinement devices [8].
Due to the recent development of two sets ofLangmuir probes located at two different toroidal positions,
TJ-II can be considered a good laboratory to study thepresence of zonal flows in the plasma edge region.
Moreover, it has been reported that sheared flows can beeasily driven and damped at the plasma edge by changing
the plasma density [9, 10] or during biasing experiments[11]. Toroidal cross-correlations between plasma edge

magnitudes have been studied in TJ-II in extremely
different plasma conditions and different magnetic
configurations providing valuable experimental data.
2. Experimental set-up
Experiments were carried out in the TJ-II stellarator
in Electron Cyclotron Resonance Heated plasmas(PECRH≤400 kW, BT = 1 T, <R> = 1.5 m, <a> ≤ 0.22 m,
ι(a)/2π ≈ 1.5 – 1.9). Different edge plasma parameters
were simultaneously characterized in two different
toroidal positions approximately 180º apart using two
similar multi-Langmuir probes, installed on fast
reciprocating drives (approximately 1 m/s) [12]. One ofthe probes is in the low field side (LFS) and the other inthe high field side (HFS) of the TJ-II as is schematicallyshown in figure 1.

Fig 1 Schematic view of the location of the probes (arrows)
at the high (a) and low (b) field sides in TJ-II.

author’s e-mail: angeles.pedrosa@ciemat.es

Proceedings of ITC/ISHW2007

0.08
0.04
040
0-40
-80
0.9 0.95

1 1.05 1.1 1.15
r/aFig. 2 Radial profiles of ion saturation current and floating
potential measured simultaneously at two toroidal
locations for plasma density above the threshold.
HFS Probe
LFS Probe

E !rms/B (m/s)

4000

3000

r/a!0.93

Perp. velocity (x 10 m/s)

2000
20-2
0.4
0.5
0.6
0.7
0.8
Line average density (x1019 m-3)

Fig. 3 Electric field fluctuations and perpendicularvelocity measured at HFS and LFS positions as afunction of plasma density at r/a≈0.9.

Figure 2 shows profiles of the ion saturation current
and the floating potential measured simultaneously in thetwo mentioned toroidal positions in one shot. Profiles of

4. Toroidal cross-correlations
Floating potential signals measured at both toroidal
locations show a clear similarity mainly for low
frequencies components, contrary to that observed with
ion saturation current signals. Figure 4 shows the raw
data of the floating potential and ion saturation current
signals measured in both probes simultaneously atapproximately the same radial position. The similarity inthe floating potential signals is also observed in shortertime scales (lower than 1 ms), particularly in the fast
events related to the shear flow development [13]. Thismeans that the large amplitude floating potential
fluctuations observed during the shear flow formation aretoroidally symmetric.

Floating Potential (V)HFS Probe
LFS Probe

the ion saturation current are slightly different in bothprobes: gradient is steeper at the LFS for all the plasma
configurations studied up to now. Floating potential
profiles are similar in both probes inside the last closed
flux surface (LCFS) but they differ in the scrape-off layer(SOL) region probably due to the different particles losses
rate at both positions.
The perpendicular electric field fluctuations and thephase velocity measured with both probes simultaneously
and located both at r/a≈0.9 in different shots as a functionof density are shown in figure 3. The behaviour of thevelocity and fluctuations measured at the LFS is similar tothe one reported at the HFS and the effect of the thresholddensity can be as well clearly seen [10, 13]. These results
have been explained in TJ-II using a simple second orderphase transition model [14].

50HFS Probe
LFS Probe

0-50-100

Ion saturation current (A)0.12

Floating Potential (V)Ion sat. current (A)3. Plasma edge measurements comparisonsRadial profiles of different plasma parameters havebeen measured at two far away toroidal locations
simultaneously for the first time. Profiles were obtained
both shot to shot and in a single shot with both probes andin different plasma configurations.

0.14

r/a≈0.9

0.1
0.06
0.02
67

68
69
Time (ms)70Fig. 4 Raw data of the floating potential and ion
saturation current signals measured in bothprobes simultaneously.

Proceedings of ITC/ISHW2007
To quantify the similarity between signals thetoroidal cross-correlation has been computed in TJ-II inparticular. The cross-correlation functions is defined as" xy (# ) =E {[ x(t + # ) $ x ][ y(t) $ y ]}{2} {E [ x(t) $ x ] .E [ y(t) $ y ]2}!

for different plasma density values. As illustrated infigures 5 and 6, the ion saturation current signals
correlation is significantly smaller than that of floatingpotential signals particularly during bias where the ion
saturation current correlation is decreased and the floating
potential correlation increased Bias makes also thecross-correlation more concentrated around τ=0. The
maximum of the floating potential correlation (see figure7) is observed when probes are approximately at the sameradial location. The toroidal correlation shows amaximum in the region just inside the LCFS, being
negligible in the SOL.

Fig. 7 Cross-correlation of floating potential signals
Fig. 5 Cross-correlation function for floating potential

measured as a function of the radial position ofand ion saturation current signals measured atprobe at the HFS in plasmas without and withdifferent radial positions of probe at the HFS andbias. Vertical line indicates the position of thein ECRH plasmas without bias.

LFS probe.

Fig. 8 Cross-correlation function of floating potential
signals measured at approximately the same radial
positions of both probes as a function of plasma
density.
Fig. 6 Cross-correlation function for floating potential
and ion saturation current signals measured at
different radial positions of probe at the HFS andin ECRH plasmas with bias.

Cross-correlation of plasma edge magnitudes havebeen obtained from probe measurements, duringexperiments in TJ-II with and without electrode bias andFigure 8 illustrates the dependence of the toroidal
floating potential correlation on the line-averaged density(for the same pulses presented in figure 3). It is observedthat correlation depends on the density, being larger for n≈ (0. 5- 0.6)x1019 m-3, which corresponds to the thresholddensity for shear flow development. Note that thiscorrelation increase with density results mainly from therise in the correlation at low frequencies (below 20 kHz).

Proceedings of ITC/ISHW2007
Figure 9 shows the cross-power spectrum and thephase between the floating potential signals of the twoprobes. It is clear that the toroidal correlation isdominated by low frequencies (below 20 kHz) and thatthe phase between the two signals is close to zero for thewhole frequency range. Electrode bias reduces the edge
fluctuations and therefore the cross-power spectrum( Sxy ( f ) ) is also reduced. Note however that thecoherence!

Sxy ( f )increases during bias inSx ( f ) Sy ( f )agreement with the results presented in figures 5-7.

!

5. Interpretation of the experimental results
The toroidal coupling of density and potential
fluctuations has been investigated, for the first time,
during the transition to improved confinement regimes in
the TJ-II stellarator. It has been observed highcross-correlation at the plasma edge between floating
potential signals measured approximately at the sameradial location but toroidally apart. As the probes are notin the same filed line, this effect is compatible with thepresence of zonal flows at the plasma edge. Moreover thephase between both signals is around zero indicating a
toroidally symmetric structure, as is characteristic of thezonal flows. This fact is also demonstrated observing thesimilar waveforms of the raw data when probes arelocated radially closed. Besides that, the spectra aredominated by low frequency fluctuations as expected forzonal flows.
The observation of a maximum in thecross-correlation for a plasma density around thethreshold value for shear flow development suggests arelationship between the generation of zonal flows andthe improvement of confinement, being possible toconsider the zonal flows generation as a trigger forplasma confinement improvement.
TJ-II experimental results are consistent with modelfor L-H transition based on the generation of zonal flows.
New experiments are going to be done in TJ-II
looking for the presence of zonal flows and theirrelationship with confinement.
References

Fig. 9Cross-correlation

spectrumandcross-correlation phase spectrum between twofloating potential signals toroidally apart.

[1] P.H. Diamond et al., Plasma Phys. Control. Fusion 47(2005) R35[2] S. Coda et al., Phys. Rev Lett. 86 (2001) 4835

Previous measurements of the parallel correlation in
the SOL have shown an increase of correlation only whenprobes were located at the same field line [15, 16]. Other
measurements have been performed more recently withthe aim of identifying zonal flows [3, 4, 5, 6, 7],
Measurements in TJ-II allows to compute thecross-correlation both in the SOL and in the edge plasmaregions with the probes not located in the same field line
being results compatible with those previously obtained[15, 16].
Experiments with fast visible cameras haveinvestigated with 2-D resolution the development of edge
sheared flows, showing a dithering phase at the thresholddensity with fluctuating perpendicular flows consistentpoloidal symmetric structure.

[3] M.G. Shats and W.M. Solomon, New Journal of Phys. 4(2002) 30.1
[4] G.S. Xu et al., Phys. Rev Lett. 91 (2003) 125001[5] G.D. Conway et al., 31st EPS Conference P-4.124 (2004)[6] Y. Nagashima et al., Phys. Rev. Lett. 95 (2005) 095002[7] A. Fujisawa et al., Phys. Rev Lett. 93 (2004) 165002[8] P.N. Guzdar et al., Phys. REv. Lett. 87 (2001) 015001.
[9] C. Hidalgo et al., Phys. Rev. E, 70 (2004) 067402[10] M.A. Pedrosa et al., Plasma Phys. Control. Fusion 47(2005) 777[11] C. Silva et al., Czech. J. Phys. 55 (2005) 1589
[12] M.A. Pedrosa, et al., Rev. Sci. Instrum. 70 (1999) 415.
[13] M.A. Pedrosa et al., 34th EPS Conference I2-020 (2007)[14] B.A. Carreras et al., Phys. Plasmas 13 (2006) 122509[15] Ch. P. Ritz et al., Rev. Sci. Instruí. 59 (1988) 1739
[16] H. Thomsen et al., Phys. Plasmas 9 (2002) 1233