Experimental studies and modelling ofedge shear flow developmentin the TJ-II stellarator
M.A. Pedrosa
B.A. Carreras, C. Silva, C. Hidalgo, J.A. Alonso, L. García,I. Calvo, J.L. de Pablos, R.O. Orozco, D. Carralero and the TJ-II team

EURATOM-CIEMAT, Spain
EURATOM-IST, Portugal
Carlos III University, Spain
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Introduction
Laboratorio Nacional de Fusión

 Plasma confinement is limited by the presence of turbulence and shear flows are
crucial elements in edge turbulence dynamics: ExB shear stabilization mechanisms
are an important element for the improvement of plasma confinement in fusion
devices. Clarifying the driving/damping mechanisms of sheared flow is a key issue forthe development of fusion.
 The universality of the sheared flows characteristics points to a unique and common
ingredient to explain the driving/damping mechanisms in the plasma boundary regionof fusion devices. The role of neoclassical mechanisms to explain poloidal flows has
been recently questioned. Turbulence is a candidate to explain experimental findings.
 Techniques for generation and control shear flow in the plasma are crucial tounderstanding and providing the plasma confinement needed in fusion devices. TJ-II
is a good laboratory to characterize the dynamics of sheared flow development infusion plasmas.
 The result of the present experiments can help to understand and quantify theimportance of anomalous versus neoclassical mechanisms on the damping physics
of radial electric fields and flows in fusion plasmas.
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Experimental set up
Laboratorio Nacional de Fusión

TJ-II Stellarator<R> = 1.5 m<a> ≤ 0.22 m
BT ≤1.2 T<ne> ≈ (0.35 - 1) x 1019 m-3
PECRH ≤ 400 kW
fECRH = 53.2 GHz

Langmuir/Mach Probes
180º toroidally apartIs ∝ nTe1/2
Vf ≈ Vp - αTe

HFSLFS

Fast Camera
Electrode2 cm inside the LCFS
V= 160 - 400 V
I ≈ 20 - 50 A

Poloidal limiter

CCD sensor (PSI-5)
Hα filter
250.000 frames/s

Field lines
View plane
View cone

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Spontaneously developed edge
shear layer in TJ-II

Laboratorio Nacional de Fusión• The existence of sheared flows in TJ-II requires a minimum plasma density (or gradient) that depends
on the plasma configuration.

Isv

VflC. Hidalgo, M.A. Pedrosa et al., Phys. Rev. E 70 (2004) 067402
M.A. Pedrosa, et al., Plasma Phys. Control. Fusion, 47 (2005) 777

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Spontaneously developed shear
layer in two toroidal positions

Laboratorio Nacional de FusiónIs

HFS Probe
LFS Probe

0.042v

0-2-4

0.9 0.95

0.06

1r/a

17th International Toki Conference 2007

1.05 1.1 1.15

Is

HFS Probe
LFS Probe0.04
0.02
04

3304

ne<necr

Perp. phase velocity (x 10 m/s)

0.08

Ion saturation current (A)ne>necr

Perp. phase velocity (x 10 m/s)

Ion saturation current (A)• Radial profiles have been simultaneously obtained in two toroidal positions approximately
180º apart for different plasma conditions.

2v

0-2-4

0.9 0.95

1r/a

1.05 1.1 1.15

16th International Stellarator/Heliotron Workshop 2007

Spontaneously developed shear
layer in two toroidal positions

Laboratorio Nacional de Fusión• Sheared flows and fluctuations appear to be organized near marginal stability.

6000

r/a≈0.8

Eθrms

5000
4000

3Perp. phase velocity (x 10 m/s)

E!

rms/B (m/s)• The universality of this property is easily understood assuming that edge sheared flows are controlled
by turbulence.

1v

0-1

-2
0.3
0.5
0.7
0.9
1.1
19 -3
Line average density (x 10 m )C. Hidalgo, et al., Plasma Phys. Control. Fusion 46 (2004) 287
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Spontaneously developed shearlayer in two toroidal positionsLaboratorio Nacional de Fusión• Edge sheared flows are developed at the same threshold density in the two toroidal

r/a≈0.8

Eθrms

5000

1v

0-1

-2
0.3
0.5
0.7
0.9
1.1
19 -3
Line average density (x 10 m )3

3

Perp. phase velocity (x 10 m/s)

4000

Perp. phase velocity (x 10 m/s)

3000

!

E

4000

HFS Probe
LFS Probe

E!rms /B (m/s)

6000

rms/B (m/s)

positions.

2

r/a!0.9r/a≈0.9

0-2
0.4
0.5
0.6
0.7 19 0.8
Line average density (x10 m-3)

C. Hidalgo, et al., Plasma Phys. Control. Fusion 46 (2004) 287
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Time scales for the spontaneous
shear layer development in TJ-II
Vflne

r/a≈0.9

Laboratorio Nacional de Fusión• Slow time scale, in the range of theparticle confinement time (tens ofmilliseconds)

that

evolves

withplasma density.
• Fasttime

scalewithtransient

events that take place in a timescale of the order of tens of µs (few
Floating potential (V)40turbulence correlation times).

HFS Probe
LFS Probe

0-40-80676869Time (ms)70

M.A. Pedrosa, et al., 15th Stell. Workshop (2005)
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Toroidal correlation
Laboratorio Nacional de Fusión• Significant toroidal correlation for low frequency potential fluctuations, but not for density.

M.A. Pedrosa, et al., P2-012 16th Stell. Workshop (2007)
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Toroidal correlation
Laboratorio Nacional de Fusión• Significant toroidal correlation for low frequency potential fluctuations, but not for density.
• Maximum correlation at the threshold density.

M.A. Pedrosa, et al., P2-012 16th Stell. Workshop (2007)
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

2-D visualization of edge shear layer
in TJ-IILaboratorio Nacional de Fusión• The reversal in the ExB rotation has been 2-D visualized using Ultra Fast Speed cameras.
• Edge sheared flows can be developed on a time scale of few tens of µs.

n < ncrn > ncrn ≈ ncr

J.A. Alonso, et al., Plasma Phys. Controll. Fusion 48 (2006) B465
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Effect of externally induced electricfields in TJ-II• Gradient increase in edge density profiles• Development of positive electric fields• Reduction of edge turbulenceElectrode r/a ≈0.9 Vbias= 300 V
3.5#14892
0.9
0.7

2.5

0.5
0.3

Vfl

100

0.14
sat

flV (V)

50

I (A)

Hα

150

r/a!0.8Isat

H! (a.u.)ne

Density (1019 m-3)

Biasing induced improved confinement

Laboratorio Nacional de Fusión

00.1-503v (x10 m/s)

7000r/a!0.8

E"rms/B (m/s)

v

4-100

BIASING

0.06

5000

03000

-440~
Eθ

80

BIASING

120160Time (ms)1000200

C. Silva, et al., Czech. J. Phys. 55 (2005) 1589
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Toroidal correlation in presence of
externally induced electric fields

Laboratorio Nacional de Fusión• Correlation between potential signals increases in the presence of
externally applied electric fields.

M.A. Pedrosa, et al., P2-012 16th Stell. Workshop (2007)
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Toroidal correlation in presence of
externally induced electric fields

Laboratorio Nacional de Fusión• Correlation between potential signals increases in the presence of
externally applied electric fields.

M.A. Pedrosa, et al., P2-012 16th Stell. Workshop (2007)
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Time scales for the externallyinduced shear flow damping
Vflne

Laboratorio Nacional de Fusión

Two time scales for shear flow
relaxation:• slow time scale, of the order of theparticle confinement time (10 ms)• fast time scale of the order ofcharacteristic
turbulencetimescales (10 – 90 µs)$ t'
V fl (t) = Vmax exp &" ) + Vmin
% #(
τ is the exponential relaxation time

Time decay rate of the flow, once the driving
force is switched off, can be a!
measure of the shear flow damping time.
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Fast time scale for the externallyinduced shear flow damping

Laboratorio Nacional de Fusión• Turbulence damping mechanisms are likely to apply for short time scales.
• Results suggest an increase in decay times above the critical value of the control
parameter (i.e. the local density gradient), that is, once edge perpendicular shear flow
is fully developed.

Decay time90
HFS Probe (0.75<r/a<0.85)
LFS Probe (0.88<r/a<0.92)! (µs)

70
50
30
100.9
17th International Toki Conference 2007

1.1

1.3
1.5
Isat/I sat|cr

1.7
16th International Stellarator/Heliotron Workshop 2007

Comparison between relaxation timescales in different devices

Laboratorio Nacional de Fusión

This result can help to quantify the importance of anomalous versusneoclassical mechanisms on the damping physics of radial electric fields andflows in fusion plasmas.

TJ-II

CASTOR

HSX

Stellarator(1)Tokamak(1,2)

Stellarator(3)Major radius (m)

1.5

0.4

1.2

Magnetic field (T)

11

0.5

Line Average Density (m-3)(0.4 - 1) x 1019

1 x 1018

0.5 x 1018

Relaxation time (µs)

10 - 90

10 - 30

15 - 50

DEVICE(1) M.A. Pedrosa et al., Plasma Phys. Controll. Fusion (2007)(2) M. Hron et al.,30th EPS Conference 2003
(3) S.P. Gerhardt, J.N. Talmadge, et al., Phys. Rev. Lett. 94 (2005) 015002, Phys. Plasmas 12 (2005) 056116.
17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields in• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión

Model for L to H-mode transition:
ELECTRIC FIELD

FLUCTUATIONS
Second-orderphase transition

ωExB/γ1

Controlled by shear
flow amplified via
Reynolds stress

CHARACTERISTICS:• Continuous transition• Symmetry breaking• Critical slowing down

FluctuationsFirst-order phasetransition

Pressure
Gradient

Control parameter(Particle Flux)
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Describes H-mode

Suppression ofturbulence byPressure gradient
16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión• The emergence of the plasma edge shear flow layer in TJ-II as density increases can be
described by a simple second-order phase transition model.

Pressure
Gradient (N)Particle
Flux

Shear Flow (U)Anomalous
diffusivity
Reynolds
stressInstability
Shear flow
stabilization

Turbulent fluctuations (E)
B.A. Carreras, L. García et al., Phys. Plasmas 13 (2006) 122509
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16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión• The emergence of the plasma edge shear flow layer in TJ-II as density increases can be
described by a simple second-order phase transition model.

"N= # $ DEN"tNeoclassicaldamping

Particle
Flux"U= #N 1/ 3UE $ µU"t!

Anomalous
diffusivity
Reynolds
stressInstability!

Shear flow
stabilization

Drive
Damping"E= N 2 / 3 E # N #1/ 2 E 2 # N #1/ 3U 2 E"tB.A. Carreras, L. García et al., Phys. Plasmas 13 (2006) 122509
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16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión• Normalizing to the values at the critical point the model gives twosolutions with no free parameters:without Barrier (NB)U NB = 0!

Shear Flowwith Edge Barrier (EB) that exists
when density gradient is above acritical value. Above this value there
are two possible states (NB and EB).

U EB " N 1/c 2

1/ 2$'NN#& )Nc % Nc (17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Comparison with experimental
results

Laboratorio Nacional de Fusión• This model captures the qualitative features of the transition near the critical point for
density ramp experiments.
• Ion saturation current normalized to the value for critical density has been considered
as a control parameter and phase velocity as the order parameter.

Density fluctuations

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Velocity shear

16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión• The properties of the damping rate of flow in TJ-II have been investigated in theframework of the previously shown model with the addition of an external drive.

Pressure
Gradient (N)Particle
FluxShear Flow (U)Anomalous
diffusivity
Reynolds
stressInstability
Shear flow
stabilization

External
TorqueTurbulent fluctuations (E)17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Model coupling shear flow andturbulence

Laboratorio Nacional de Fusión• The properties of the damping rate of flow in TJ-II have been investigated in theframework of the previously shown model with the addition of an external drive.

"N= # $ DEN"tNeoclassicaldamping

Particle
Flux

"U"U
1/ 3
==
#N
$ µ$Uµ+U% ext#1/N3UE
UE" t"t!

Anomalousdiffusivity
Reynolds
stressInstability!
!

Shear flow
stabilization

DriveDamping

External
Torque"E= N 2 / 3 E # N #1/ 2 E 2 # N #1/ 3U 2 E"t
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16th International Stellarator/Heliotron Workshop 2007

Comparison with experimental
results

Laboratorio Nacional de Fusión• The results of the fast decay time from the model equations show exponential
behaviour and are also consistent with the experimental data.
• The time decay as a function of the input flux show a sharp peak near the critical point.

Decay time

17th International Toki Conference 200716th International Stellarator/Heliotron Workshop 2007

Comparison with experimental
results

Laboratorio Nacional de Fusión• The results of the fast decay time from the model equations show exponential
behaviour and are also consistent with the experimental data.
• The time decay function of the input flux show a sharp peak near the critical point.

Decay time90
HFS Probe (0.75<r/a<0.85)
LFS Probe (0.88<r/a<0.92)! (µs)

70
50
30
100.9

17th International Toki Conference 2007

1.1

1.3
1.5
Isat/I sat|cr

1.7

16th International Stellarator/Heliotron Workshop 2007

Outline
Laboratorio Nacional de Fusión• Introduction• Experimental set-up• Sheared flows development in TJ-II• Spontaneously developed edge shear layer• Effect of externally induced electric fields• Relaxation time scales measurements for electric fields• Model coupling shear flow and turbulence• Comparison with experimental results• Summary and conclusions

17th International Toki Conference 2007

16th International Stellarator/Heliotron Workshop 2007

Summary and Conclusions
Laboratorio Nacional de Fusión

 The development of the naturally occurring velocity shear layer in TJ-II requires aminimum plasma density / gradient. Sheared flow and fluctuations appear to beorganized near marginal stability in TJ-II.
 The decay time scale of plasma potential measured in TJ-II when the external torqueis switched off, is (as in other devices) in the range of the turbulence characteristictimes. Results in TJ-II suggest an increase in decay times once edge perpendicular
shear flow is fully developed.
 Significant correlation has been found between potential signals 180º toroidally
apart. Correlation is maxima for plasma density close to the threshold for shear flow
development and increases with externally applied electric fields.
 The emergence of the plasma edge sheared flow as a function of plasma density canbe explained using a simple second-order phase transition model, that reproduces
well experimental data and the qualitative characteristics of the transition near thecritical point. Adding an external torque in the model the main features of the flow
decay rate can be also reproduce.
 These results can help to understand the physics responsible for the generation ofshear flow, pointing out the important role of turbulence on the driving/damping
physics of the radial electric fields and flows in fusion plasmas.
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Thank you very much

ありがとう ございます“Naruto rapids at Awa”
Hiroshige Utagawa (歌川広重)