Proceedings of ITC/ISHW2007

Parametric dependence of the perpendicular velocity
shear layer formation in TJ-II plasmas
L. Guimaraisa, T. Estrada, E. Ascasíbar, M.E. Mansoa, L. Cupidoa, T. Happel, E. Blanco, R.
Jiménez-Gómez, M.A. Pedrosa, C. Hidalgo, I. Pastor, A. López-Fraguas and the TJ-II Team
Laboratorio Nacional de Fusión. As. Euratom-CIEMAT, Madrid, Spaina

As. Euratom-IST, CFN, Instituto Superior Técnico, Lisbon, Potugal

In TJ-II plasmas, the perpendicular rotation velocity of the turbulence changes from positive tonegative (from ion to electron diamagnetic direction) inside the LCMS when the line-averaged plasma
density exceeds some critical value, this change being dominated by the inversion in the radial electricfield. In this work we study the parameters that control the inversion in the perpendicular rotation. A
parametric dependence of the critical density has been obtained studying plasmas confined in different
magnetic configurations (different rotational transform and/or plasma volume) and heated with different
ECH power levels. The studied data set shows positive exponential dependence on heating power andnegative one on plasma radius, while the dependence on rotational transform has low statistical meaning.
Besides, analysis of local plasma parameters points to plasma collisionality as the parameter that controls
the inversion of the perpendicular rotation velocity of the turbulence.
Keywords: Stellarator, Reflectometry, Perpendicular Rotation, Collisionality

1. Introduction
In TJ-II ECH plasmas, a perpendicularvelocity shear layer develops spontaneously at theplasma edge, above a certain line-averaged density[1]. The transition for the shear layer formation has
been characterized using Langmuir probes [2],Ultra Fast Speed cameras [3] and microwave
reflectometry [4]. Langmuir probe measurements
indicate that below the critical density theperpendicular velocity of the turbulence is positive(in the ion diamagnetic direction) at both sides ofthe LCMS, while above this critical density, theperpendicular velocity remains positive outside theLCMS and it turns out to be negative inside.
Besides, probe measurements show that there is a
coupling between the development of the shearlayer and an increase in the turbulence level at theplasma edge; the experimental results being
consistent with the expectations of second-ordertransition models of turbulence-driven shearedflows [5]. In addition, HIBP measurements indicatethat the radial electric field at the plasma edge
reverses from positive to negative as the plasma
density exceeds the critical value, while it remains
positive in the plasma core [6]. These HIBP
measurements indicate that the inversion in theperpendicular rotation velocity of the turbulence isdominated by the radial electric field.

author’s e-mail: guimas@cfn.ist.utl.pt

In order to investigate the parameters that control
the radial electric field, we have studied thedependence of the critical line-density on the ECH
heating power and on the magnetic configuration:
rotational transform and plasma volume. Besides, tofurther investigate the physics behind it, we havestudied the behaviour of local plasma parameters:
density, temperature and pressure and their radialgradients.

2. Experimental Results
The discharges used in this work correspondto ECH heated plasmas at 53 GHz, second
harmonic and X-mode polarization. These
discharges belong to six magnetic configurations,heated with three power levels: 200, 300 and 400
kW and with line-averaged densities from 0.3 to 1.2
1019 m-3. The six magnetic configurations cover
three rotational transform values (1.4, 1.8 and 2.2)
and, for each rotational transform, two plasma
volumes (0.65 and 1.0 m3). The rotational transformprofiles are shown in figure 1, while figure 2 shows
the plasma volume as a function of the rotationaltransform at ρ = 2/3 for these configurations. Eachmagnetic configuration is labelled with threenumbers that refer to the currents in the circular,
helical and vertical coils of TJ-II; by changing thesecurrents, the ι-profile and/or the plasma volume canbe scanned. These magnetic configurations wereProceedings of ITC/ISHW2007
selected in order to have very low correlation
between both configuration parameters: rotationaltransform and plasma radius. The electron and ion
contributions to the plasma energy are calculatedusing the electron density and temperature profiles
measured by the Thomson Scattering diagnosticand the ion temperature measured by the chargeexchange spectrometer. This data set (155 plasmadischarges) reproduces the parametric dependenceof the energy confinement time reported in [7]: theconfinement improves with plasma density, plasma
radius and rotational transform and degrades withheating power.
V ! 1 m3
V ! 0.65 m 3

2.5

To monitor the inversion in the perpendicularrotation velocity we have used microwave
reflectometry. The sign of the perpendicularrotation velocity of the turbulence can be resolvedby the asymmetry of the turbulence spectra
measured using the reflectometer [4, 8]. We haveclassified the discharges in three groups attending
to the perpendicular rotation velocity in the plasmaedge region (ρ ≥ 0.6). The first and second set ofdischarges includes plasmas with positive andnegative
perpendicularrotation
velocity,
respectively. The third set of discharges includes
plasmas in which the inversion in the perpendicularrotation velocity is detected during the discharge;
the corresponding critical line-density is obtained as
the line-averaged density measured by themicrowave interferometer at the inversion time.
The obtained critical line-density values vary withina rather broad range, from 0.5 to 1 1019 m-3,depending on magnetic configuration and ECH
heating power. From this last set of discharges (44discharges) we have extracted the parameter
dependence of the critical line-density on ECH
power, plasma radius and rotational transform,
assuming a factorial dependence:

31_92_53
47_96_69

2!/2"

78_66_63
55_55_50

103_30_61

1.5

101_26_43#< n cr >" P# P a# a ($ / 2 % ) $10.2

0.4

0.60.8The best fit that results from the regression analysisis shown in figure 3 and is given by:!
+0.09±0.05< n cr >" P +0.34±0.03a #1±0.1($ / 2 % )1#Figure 1: Rotational transform profiles for the six
selected magnetic configurations.
1.2
78_66_63
47_96_69

103_30_61

0.8

0.6

0.4
1.2

-0.05
-0.1
-0.15

cr3

V (m )

10!
log <n > measured

0-0.2555_55_50
101_26_43-0.2

31_92_53-0.3-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0

1.4

1.6 1.8
2!/2" at #=2/3

2.2

2.4

Figure 2: Plasma volume as a function of therotational transform at ρ = 2/3 for themagnetic configurations shown in figure 1.

log <n > predicted
crFigure 3: Critical line-density values obtained
experimentally versus the best fit found in
the regression analysis, represented in a loglog scale.

Proceedings of ITC/ISHW2007

PECH contribution to log <n cr>-0.8
y = -1.7 + 0.34x R= 0.87
-0.85
-0.9
-0.95
-1-1.05-1.1a)-1.15

a contribution to log <ncr>

22.1

2.2
2.3
log P ECH

2.4

2.5

y = -1.7 - 1x R= 0.86

-0.8
-0.85
-0.9-0.95-1b)

-1.05
-0.92

-0.88

-0.84

-0.8

-0.76

!/2" contribution to log <n cr>

log ay = -1.7 + 0.092x R= 0.26
-1.65

-1.7

-1.75

-1.8c)
0.15

0.2

0.25
log !/2"

0.3

0.35

Figure 4: ECH power (a), plasma radius (b) androtational transform (c) contribution to thecritical line-density, represented in a log-log
scale. The linear fits reproduce theregression coefficients.

The critical line-density shows opposite
exponential dependences as compared with theenergy confinement time: positive exponential
dependence on the heating power and negative oneon the plasma radius, while the dependence on therotational transform has low statistical meaning.
These dependences are shown in figures 4.a to 4.c.
The contribution from each parameter to the criticalline-density is obtained subtracting the contribution
from the other parameters. These results partiallyconfirm some preliminary results reported in [9].
The opposite exponential dependences as comparedwith the energy confinement time may reflect theinfluence of the radial electric field profile on theconfinement. Moreover, particle transport analysisof TJ-II plasmas indicates that above the thresholddensity the particle confinement time improves
considerably [10].
So far we have considered the line-density as theexternal knob to control the perpendicular rotation
velocity; however, the large variation of the criticalline-density with the ECH power and with theplasma volume indicates that line-density may not
be the relevant parameter. To investigate thephysics behind the radial electric field inversion wehave studied the behaviour of local plasma
parameters: electron density, temperature andpressure. These local values are obtained from theradial profiles measured using the Thomson
scattering diagnostic in the three sets of discharges.
Experimentally it is observed that, in a given
magnetic configuration and at fixed ECH power,
the inversion in the radial electric field (frompositive to negative) takes place by increasing theplasma density; however, local values of plasma
density or plasma pressure do not show any clear
trend when data measured in plasmas with different
ECH power and in different magnetic
configurations are merged. The same result is found
for the local values of density or pressure gradients.
On the other hand, ECH power modulation
experiments indicate that the inversion in the radial
electric field (from positive to negative) occurs as
the electron temperature decreases. Theseobservations point to plasma collisionality as alikely candidate to control the sign of the radial
electric field. In fact, experiments performed inLHD show that the sign of the radial electric field iscontrolled by the plasma collisionality [11]. Thisconclusion is supported by the plasma discharges
analysed in this work. Local values of plasma
collisionality measured in plasmas with different
ECH power and in the six magnetic configurations

Proceedings of ITC/ISHW2007
are shown in figure 5. Plasma collisionality is
calculated as the average of the local values
measured within the radial range 0.5<ρ<0.7.
Plasmas with negative radial electric field are foundto have higher collisionality than those having
positive radial electric field. The plasma
collisionality measured at the inversion time iscomparable to that measured for Er < 0. This result
explains the dependence of the critical line-density
on the ECH power (shown in figure 4.a): as theECH power is increased the electron temperaturerises (the collisionality decreases) and a higher
plasma density is required to increase thecollisionality to the critical value that triggers theradial electric field inversion.

Er >0transition
Er < 0e

1 / (n /T3/2

0.3e)

0.4

0.2

0.1

00.4

0.5

0.6

0.7

0.8
19

0.9

1

1.1

-3

<n > (10 m )eFigure 5: Plasma collisionality as a function of theline-density for plasmas heated withdifferent ECH power and in the six different
magnetic configurations. Plasmas withpositive and negative radial electric field arerepresented in red and blue, respectively,
while those in which the radial electric fieldtransition is detected are shown in black.
The dependence of the critical density on the ECH
heating power allows the study of the plasma
response time during ECH power modulation
experiments [12]. In these ECH power modulation
experiments the temperature profile follows thepower modulation frequency (360 Hz) while thedensity profile remains constant. The perpendicularvelocity reverses following the ECH modulation ina time scale faster than 200 µs and in a wide plasma
region, from the plasma edge up to ρ ≈ 0.6.

3. Conclusion
The behaviour of the perpendicular rotation
velocity in the edge region of TJ-II plasmas has
been studied in six different magnetic
configurations, scanning both ECH power level andplasma density. The inversion in the perpendicularrotation velocity occurs when the line-averaged
density reaches a certain critical value that depends
on plasma conditions. The parametric dependenceof the critical line-density on ECH power level andmagnetic configuration characteristics shows apositive exponential dependence on EC heating
power and a negative one on plasma radius; thedependence on rotational transform is weak and has
low statistical meaning. Besides, analysis of local
plasma parameters points to plasma collisionality as
the parameter that controls the inversion of theperpendicular rotation velocity of the turbulence.
This result explains the positive exponential
dependence of the critical line-density on the ECHpower. Further studies are needed to understand thedependence on the plasma radius.

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