Proceedings of ITC/ISHW2007

Experimental studies and modelling of edge shear flow
development in the TJ-II stellarator
M.A. Pedrosa(1), B.A. Carreras(1), C. Silva(2), C. Hidalgo(1), J.A. Alonso(1), L. García(3),I. Calvo(1), J.L. de Pablos(1), R.O. Orozco(1), D. Carralero(1) and the TJ-II team(1)EURATOM-CIEMAT, Spain, (2) EURATOM-IST, Portugal, (3) Universidad Carlos III, Spain

The universality of the characteristics of sheared flows points to a general ingredient to explain thedamping/driving mechanisms responsible for the development of these flows in the plasma boundary region offusion devices. Experiments in the TJ-II stellarator showing that the generation of spontaneous sheared flows at theplasma edge requires a minimum plasma density or density gradient, open a unique possibility to characterize thedynamics of sheared flow development in fusion plasmas.
The effective viscosity at the plasma edge can be deduced by the decay rate of the perpendicular flow
measurement once the driving force is removed. In TJ-II changes in the plasma rotation and turbulence have beenstudied when an electric field is externally applied. Measurements of the decay time suggest an increase in decay
times above the threshold gradient value to trigger the emergence of shear flow (i.e. once edge perpendicular
sheared flows are fully developed).
The emergence of the plasma edge sheared flow as a function of plasma density can be explained using a simple
second order phase transition model. This simple model reproduces many of the features of the TJ-II experimental
data and captures the qualitative features of the transition near the critical point.
Keywords: Turbulence, sheared flows, plasma edge, biasing, stellarators.

1. Introduction
The importance of the ExB shear in flows as astabilizing mechanism to control plasma fluctuations inmagnetically confined plasmas has been widely
established. In fact, both H-mode and core transportbarriers are related to a large increase in the ExB sheared
flow [ 1 , 2 , 3 ]. Clarifying the driving/damping
mechanisms of sheared flow remains a key issue for thedevelopment of fusion. Both neoclassical (e.g. ion orbit
losses [4]) and anomalous mechanisms (i.e. anomalous
stringer spin-up [5] and Reynolds stress [6, 7]) havebeen considered as candidates to explain the generationof sheared flows. Atomic physics via charge-exchange
momentum losses [8, 9], parallel viscosity (magneticpumping) [10] and turbulent viscosity are considered as
candidates to explain perpendicular flow damping
physics.
The role of neoclassical mechanisms to explain
poloidal flows is an open issue in the fusion community.
The result of the experiments carried out in TJ-II
stellarator can help to understand and quantify theimportance of anomalous versus neoclassical mechanisms
author’s e-mail: angeles.pedrosal@ciemat.es

on the damping physics of radial electric fields and flows
in fusion plasmas.

2. Experimental set-up
Experiments were carried out 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) obtained in
the TJ-II stellarator. The plasma density was modified in
the range (0.35 – 1) x 1019 m-3. Different edge plasma
parameters were characterized using two multi-Langmuirprobe systems, installed on similar fast reciprocating
drives (approximately 1 m/s) [11], that allows obtaining
radial profiles simultaneously in a single shot, in two
toroidal locations approximately 180º apart in high (HFS)
and low (LFS) field sides of TJ-II.
A Carbon composite mushroom-shaped electrode (12mm high with a diameter of 25 mm) was installed onanother fast reciprocating drive similar to the one usedwith probes. The electrode was inserted typically 2 cm
inside the last-closed flux surface (LCFS) and biased
positively (200-300 V) with respect to one of the twopoloidal limiters located in the scrape-off layer regionProceedings of ITC/ISHW2007(SOL) (about 0.5 cm beyond the LCFS). Measured
electrode currents were in the range of 30-50 A [12].

3. Development of sheared flows
It has been previously shown that the development of
the sheared flows at the plasma edge of the TJ-II requires
a critical value of the plasma density or density gradient[ 13 , 14 ] that depends on the plasma magnetic
configuration [15].
Radial profiles of plasma edge are strongly modified
as plasma density increases: Gradient of the ion
saturation current (i.e. local density) increases andfloating potential becomes more negative at the plasmaedge [13, 14]. Consistent with the changes in the floating
potential, above a threshold density value theperpendicular phase velocity reverses sign at the plasmaedge from positive to negative values due to thedevelopment of the natural shear layer, with a shearing
rate about 105 s-1 of the order of the inverse of thecorrelation time of fluctuations (dvθ/dr≈1/τ≈105 s-1) [16].
Figure 1 shows the perpendicular flows and thefluctuations of the perpendicular electric field (i.e. theturbulent radial velocity) deduced from measurements at
the plasma edge of the TJ-II (r/a≈0.9, where a is theaveraged minor radius of the plasma). Measurements
have been obtained simultaneously in two toroidal
locations and changing density from shot to shot. The
levels of turbulent transport and fluctuations increase as
density increases up to the critical value for which
sheared flow is developed. For densities above thethreshold fluctuations and turbulent transport slightly

E!rms /B (m/s)

4000

HFS ProbeLFS Probe

3

Perp. phase velocity (x 10 m/s)

3000

Fig. 1

2

r/a!0.9

0-2
0.4
0.5
0.6
0.7
0.8
Line average density (x1019 m-3)
Perpendicularflows

andfluctuationsof

theperpendicular electric field measured for different
plasma densities at the TJ-II plasma edge (r/a≈0.9).

decrease although edge gradients become steeper. Edge
sheared flows are developed at the same threshold density
in the two toroidal positions [17].
Sheared flows have been also developed in TJ-II
using an electrode that externally imposed a radialelectric field at the plasma edge. The modifications in theplasma properties induced by electrode biasing depend on
several parameters such as the biasing voltage, theelectrode location and the plasma density. The latter isvery important on TJ-II as the edge parameters and global
plasma confinement depend strongly on it. The responseof the plasma to bias is, therefore, different at densities
below and above the threshold value to trigger thespontaneous development of ExB sheared flows [12].
The results of the TJ-II biasing experiments presented
in this paper correspond to positive applied bias in theplasma edge of TJ-II. The changes observed in the edge
profiles, edge electric fields and fluctuation levels show
evidence of biasing induced improved confinement as
was observed in previous limiter biasing experiments inTJ-II [ 18 ]. The floating potential profile is strongly
modified by the electrode bias in the region r/a < 0.9,
leading to the formation of a strong positive radial
electric field (up to 10 kV/m) and as a consequence theperpendicular phase velocity is also modified.
As in the spontaneous development of the shear [19],two different time scales arise in the relaxation of
externally induced electric fields in TJ-II: a slow timescale, in the range of the particle confinement time (tensof milliseconds) that evolves with plasma density, and afast time scale in the range of few turbulence correlation
times (10 – 100 µs). The fast time evolution of floating
potential signals (Vfl), when biasing is switched off, canbe fitted to an exponential function using the expression
Vfl(t) = Vmax exp(-t/τ) + Vmin
(1)from which the exponential relaxation time τ is deduced.
This fitting procedure has been done for floating potential
signals measured at different densities and at different
radial and toroidal locations. Experimental results showthat the characteristic time decay obtained for the fast
decay is in the range of 10 - 100 µs for different values ofmean plasma density (in the range 0.4 – 1 x 1019 m-3).
Figure 2a shows the two time evolution scales of thefloating potential signal measured inside the LCFS (r/a ≈0.77) in TJ-II together with the evolution of plasma
density with biasing and in Fig 2b the fast decay scale isshown together with the fitting.
Figure 3 shows the behaviour of the fitting of the fast
relaxation time at the TJ-II plasma edge (0.75<r/a<0.92)
after switch-off the biasing as a function of the averageion saturation current, measured when switching off thebiasing and normalized to its value at the critical point(i.e. when shear flow develops). Results suggest an4)sProceedings of ITC/ISHW2007

increase in decay times above the critical value of thecontrol parameter (i.e. once edge perpendicular shearedflows are fully developed).

a)fl00.6-3BIASING

10040140
Time (ms)19V (V)

Slow time scale

Fast time scale-10060V (V)0.7

Density (10 m )# 16014100 r/a!0.77

1800.5b)!!24 µs

0fl-40
-80

-120
-0.05

Fig 2

00.05 0.1
Time (ms)

0.15

0.2

for short time scales, in the order of few turbulencecorrelation times (typically τc≈10 µs), this being
consistent with experimental time decay findings.

4. Model coupling shear flow and turbulence
A simple model to explain the generation of thesheared electric field has been used [20, 21]. This model,
as the pressure increases, predicts two successivetransitions. The first one is a second-order transition
controlled by the poloidal shear flow that leads to areduction of the turbulence level. The second, that
describes the H-mode, is a first-order transition controlled
by the pressure gradient that leads to the suppression ofturbulence. The first transition model (the second-orderone), that has the characteristic properties of theemergence of the sheared flow layer, has been used tocompare the theoretical predictions with the experimental
results of the formation of the sheared flow layer in TJ-II.
In order to do that, we normalize all the physicalmagnitudes to their values at the critical point so we canwrite the solutions of the model in terms of measurable
quantities [22].

a) Time scales of the floating potential measured
at r/a≈0.8 and plasma density evolution withbiasing. b) Fast decay of the floating potential at
the bias switch off (time =0).

Fig. 4 Comparison between the velocity shear obtained by
the model and from the experimental data.

Fig. 3 Relaxation time measured at the TJ-II plasma edgein both probes, as a function of normalized ion

saturation current measured after switch off thebiasing.

These time decays have been compared with the ones
obtained in similar experiments in other devices withdifferent characteristics [19] being the values in the samerange (tens of µs) in all of them. As a consequence and in
spite of another mechanisms (i.e. magnetic pumping,charge exchange) turbulence can be considered as animportant element in the physics of flows and electricfields. Turbulent damping mechanisms are likely to apply

Comparisons between the model and experimental
data show that in spite of the simplicity of the model, it
captures the qualitative features of the transition near thecritical point as can be seen in Fig 4, that shows acomparison between the velocity shear obtained by themodel and the deduced from the experimental data as afunction of the control parameter defined in the previoussection. Note that the model has no free parameters oncethe position of the critical point is determined. Resultsfrom plasmas with more complicated density evolutions
than a simple ramp are also in good agreement withexperiments [22].

Proceedings of ITC/ISHW2007
Apart from the problem of interpreting the decay rate
in terms of viscosity, an effective viscosity at the plasmaedge can be determined by measuring the decay rate of
the perpendicular flow once the driving force has beenremoved. The properties of the damping rate of the flow
in TJ-II have been investigated in the framework of amodel based in the previously described with an external
drive added: the applied bias. Fig 5 shows the short timescale decay after switching off the bias potential deducedby the model showing an increase of the decay time close
to the critical point as has been observed experimentally(Fig 3). The exponential decay of the flow is also
reproduced, giving the model a qualitative description of
the behaviour of the decay time obtained experimentally.

confinement time) plasma potential modifications arelinked to the evolution of the plasma density.
Measurements of the fast decay time suggest an
increase in decay times above the threshold gradientvalue to trigger the emergence of shear flow (i.e. onceedge perpendicular sheared flows are fully developed).
The emergence of the plasma edge shear flow as afunction of the plasma density can be explained using asecond-order phase transition model that reproduces
many of the features of the TJ-II experimental data and of
the transition near the critical point. The properties of thedamping rate of the flow in TJ-II have also been
described by means of the model adding a driving force.
[1] P. W. Terry, Reviews of Modern Physics, 72, 109 (2000).
[2] K. Burrel, Phys. Plasmas 6 (1999) 4418
[3] B.A. Carreras, IEEE Trans. Plasma Sci. 25 (1997) 1281
[4] K.C. Shaing and E.C. Crume, Phys. Rev. Lett. 63 (1989)
2369.
[5] A.B. Hassam and T.M. Antonsen, Phys. Plasmas 1 (1994)
337.
[6] P.H. Diamond and Y.B. Kim, Phys. Fluids 3 (1991) 1626.
[7] B.A. Carreras, V.E. Lynch and L. García, Phys. Fluids B 3(1991) 1438.
[8] P. Monier-Garbet, K.H. Burrel, et al., Nuclear Fusion 37(1997) 403.
[9] M.A. Mahdavi, N. Brooks, et al., J. Nuclear Mater
176&177 (1990) 32.

Fig. 5 Decay time obtained by the model as a function of[10] S.P. Hirsman, Nuclear Fusion 18 (1987) 917.

the local average ion saturation current normalized at[11] M.A. Pedrosa, et al., Rev. Sci. Instrum. 70 (1999) 415.

the corresponding critical point (development of[12] C. Silva et al., Czech. J. Phys. 55 (2005) 1589.

shear flow).

[13] C. Hidalgo et al., Phys. Rev. E, 70 (2004) 067402.
[14] M.A. Pedrosa et al., Plasma Phys. Control. Fusion 47

5. Summary and conclusions
The generation of the shear layer depends in TJ-II on
the plasma density gradient, being necessary a thresholdvalue for its development. These sheared flows appear to
be organized near marginal stability with fluctuations inTJ-II. The universality of this property is easily
understood assuming that edge sheared flows arecontrolled by turbulence. These results can shed light inthe understanding of the physics responsible for thegeneration of critical sheared flows, pointing to theimportant role of turbulence as a driving mechanism.
Two time scales have been found for edge plasma
potential decay measured in the TJ-II edge plasma region
when electrode applied potential is turned off. The fastscale decay times are in the range of few turbulencecorrelation times, suggesting the important effect ofanomalous (turbulent) mechanisms in the damping rate ofsheared flows in the plasma boundary of fusion devices.
In the slow time scale (comparable to the particle(2005) 777.
[15] M.A. Pedrosa, C. Hidalgo, et al., Czech. J. Phys. 55 (2005)
1579[16] C. Hidalgo, M.A. Pedrosa and B. Gonçalves, New J. Phys.
4 (2002) 51.1
17M.A. Pedrosa et al.,Procceedings 16th Stell. Workshop(2007)[18] C. Hidalgo, M.A. Pedrosa et al., Plasma Phys. Control.
Fusion 46 (2004) 287[19] M. A. Pedrosa, B.A. Carreras et al. Plasma Phys. Control.
Fusion To be published[20] P. H. Diamond, Y. M. Liang, B. A. Carreras, and P. W.
Terry, Phys. Rev. Lett. 72, 2565 (1994).
[21] B. A. Carreras, D. E. Newman, P. H. Diamond, and Y.-M.
Liang, Phys. Plasmas 1, 4014 (1994).
[22] B.A. Carreras, L. García et al., Phys. Plasmas 13 (2006)
122509