IAEA Lyon, Oct. 17, 2002

Spontaneous Toroidal Rotation in Alcator C-Mod Plasmas

with thanks to

A.Ince-Cushman, M.J.Greenwald, A.E.Hubbard, J.W.Hughes, J.Irby, B.LaBombard, Y.Lin, E.S.Marmar, R.R.Parker, Y.Podpaly, M.L.Reinke, G.Wallace, S.M.Wolfe, S.J.Wukitch, C-Mod Team

M.Bitter, K.Hill, S.Scott, PPPL

Plasma Science and Fusion Center, MIT

35th EPS Crete June 12, 2008

J.E.Rice

Motivation:

Rotation and velocity shear play important roles in the H-mode transition, ITB formation and RWM stabilization.

Usually provided by strong momentum input from NBI, which will not be available in ITER and future reactors.

Widely observed spontaneous/intrinsic rotation may provide the solution.

Comprehensive study may provide guidance to theorists for explanation.

Database of spontaneous rotation from various machines allows extrapolation to ITER.

Profile control desirable.

Understanding of rotation in L-mode plasmas is necessary for comprehensive H-mode transition models.

Relatively little study of momentum transport until recently.

Outline

Brief description of C-Mod and rotation diagnostics

Rotation in Ohmic L-mode plasmas

dependence on density, magnetic configuration, magnetic field rotation inversion relation to H-mode power threshold

Rotation in H-mode and improved confinement regimes

parameter scalings, profile evolution and transport multi-machine scalings and extrapolation to ITER ICRF mode conversion induced flowRotation in ITB plasmas

barriers formed with off-axis ICRF barriers formed with LHCD

Summary and Conclusions

Alcator C-Mod R = 0.67 m r ~ 0.21 m κ < 1.8

BT = 2-8 T IP = 0.3-2.0 MA

ne = 0.1-10 x1020/m3 Te~Ti = 1-6 keV

βN = 0.2-1.8 ν* = 0.01-20 1/ρ* = 170-500

ICRF 3 MW 80 MHz 2 strap 3 MW 40-80 MHz 4 strap 0-π phasing

LHCD ~1 MW 4.6 GHz 96 waveguide array npar = 1.5-3.0

(no core particle or momentum sources)

X-ray Spectrometers

3 tangentially viewing von Hamos type and imaging Johann type

EF-1EF-2

Ldc =125cm Lcp = 306cm

Lcf=190cm

hp = ~70cmhd=23cm

Side View

Ro = 67cm

DetectorsCrystal

A B C

Top View8.0

H-like CrystalHe-like Crystal

He-like Detectors

H-like Detector

C

B

A 100 cm

3725 3730 3735 3740 3745Wavelength (mA)

0

2.0

4.0

6.0

8.0

10.0

12.0

Brig

htne

ss (

arb

scal

e)

sightline CCW

IP CW

IP CCW

Ar17+

Ar17+

Mo32+

Doppler shifted H-like argon, from trace injection

o

rest wavelength

A.Ince-Cushman et al., submitted to Rev. Sci. Instrum. (2008)

L-mode 5.4 T 0.8 MA q~4.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0n

e (1020/m3)

-60

-40

-20

0

20

40

60

VTo

r(0)

(km

/s)

grad B Drift Up

grad B Drift Down

USN

LSN

LSN

USN

Core Ohmic L-mode Toroidal Rotation Complicated dependence on electron density, magnetic configuration and q.

SSEP is the distance between the primaryand secondary separatrices in near DN

-1.0 -0.5 0.0 0.5 1.0SSEP (cm)

-40

-30

-20

-10

0

10

VTo

r (km

/s)

1.4-1.6

1.3

1.1-1.2

1.0

0.8

density (1020/m3)

near DN q=4.8

~LSN ~USN

0.6 0.7 0.8 0.9 1.0 1.1 1.20.0

0.5

1.0

1.5

(1020

/m3 )

electron density

0.6 0.7 0.8 0.9 1.0 1.1 1.2

-0.5

0.0

0.5

(cm

)

SSEP

0.6 0.7 0.8 0.9 1.0 1.1 1.2t (s)

-30-25

-20

-15

-10

-5

(km

/s)

VTor

(0)

L-mode Momentum Transport Following Fast SSEP Sweeps

0.65 0.70 0.75 0.80 0.85t (s)

-35

-30

-25

-20

-15

-10

-5

VTo

r (km

/s)

0.53

0.0

r/a

SSEP jogged in 10 ms from LSNto USN at 0.7 s, and back at 1.0 s

Rotation change propagates infrom the edge. τφ ~ τE ~ 40 ms, anomalous.

(Ed Synakowski)

Limited

0.4 0.6 0.8 1.0 1.2

3.23.43.63.84.04.2

q

0.4 0.6 0.8 1.0 1.2

0.60.70.80.91.0

n e (10

20/m

3 ) <ne>

0.4 0.6 0.8 1.0 1.2t (s)

-30-20

-10

0

10

20

(km

/s)

VTor

(0)

0.4 0.6 0.8 1.0 1.2 1.4 1.60.8

1.0

1.2

1.4

1.6

1.8

n e (10

20/m

3 )

<ne>

ne(0)

0.4 0.6 0.8 1.0 1.2 1.4 1.6t (s)

-40

-20

0

20

40

(km

/s)

VTor

(0)

USN q95=3.5

Rotation Inversion/Reversal Can be induced by density ramping in L-mode plasmas. Other factors at work, such as plasma current, q.

J.E.Rice et al., Nucl. Fusion 45 (2005) 251.A.Bortolon et al., Phys. Rev. Lett. 97 (2006) 235003.B.P.Duval et al., Plasma Phys. Control. Fusion 49 (2007) B195.

L-mode USN grad B Drift Down

0.0 0.5 1.0 1.5 2.0 2.5n

e (1020/m3)

-50

-40

-30

-20

-10

0

10

20

VTo

r(0)

(km

/s)

USN with B. Duval, ITPA

0.8 MA L-mode

3.0 3.5 4.0 4.5B

T (T)

-30

-20

-10

0

10

VTo

r (km

/s)

Counter-current rotation in Ohmic L-mode decreases as BT is lowered.Rotation approaches 0 for q95 ~ 2.8. H-mode transition occurs near V=0.

Consistent with H-mode power threshold scaling: ~B.8 see J.Snipes et al., this meeting. J.A.Snipes et al., Plasma Phys. Contr. Fusion 42 (2000) A299. F.Ryter et al., Plasma Phys. Contr. Fusion 44 (2002) A415.

Ohmic H-mode

0.4 0.6 0.8 1.0 1.201020304050

(kJ)

WP

0.4 0.6 0.8 1.0 1.20.00.51.01.5

n e (10

20/m

3 )

ne

0.4 0.6 0.8 1.0 1.201234

(arb

) Dα

0.4 0.6 0.8 1.0 1.22.53.03.54.04.5

B (T)T

q95

0.4 0.6 0.8 1.0 1.2t (s)

-30

-20

-10

0

10

20

( km

/s) V

Tor(0)

-2 -1 0 1 2-50

-40

-30

-20

-10

0

VTo

r (k

m/s

)

LSN DN

USN

5.4 T0.8 MA1.4 x 1020/m3

L-mode

-2 -1 0 1 2SSEP (cm)

0

1

2

3

4

(MW

)

ICRF H-mode Power Threshold

Application of ICRF power increments the rotation in the co-current direction. The H-mode transition occurs when V~0, for certain conditions.

J.E.Rice et al., Nucl. Fusion 45 (2005) 251.LSN DN USN

ne

PICRF

Te(95)

Vφ (0)

grad Te (95)

t - t L-H

(km

/s)

(keV

/m)

(eV

)(M

W)

(1020

/m3 )

improvedL-mode

0.70 0.75 0.80 0.85R (m)

-20

0

20

40

60

80

100

VTo

r (km

/s)

L-mode

H-mode

transition

Velocity Profile Evolution Following H-mode Transition

Velocity propagates in from the outsidefollowing the H-mode transition, indicating an edge source.

Peaked profile suggests the workingsof a momentum pinch.

0.9 1.0 1.1 1.20.0

0.5

1.0

1.5

2.0

2.5

(1020

/m3 )

electron density

0.9 1.0 1.1 1.20.00.20.40.60.8

(MW

)

ICRF

0.9 1.0 1.1 1.2t (s)

-20

-10

0

10

20

30

(km

/s)

normalized velocity

r/a = 0.7

r/a = 0.0

E r [k

v/m

]Mechanism for Spontaneous Rotation Unknown

Turbulent momentum transport fairly well studied: A.G.Peeters et al., Phys. Plasmas 12 (2005) 072515. linear gyrokinetic, ITG driven A.G.Peeters et al., Phys. Rev. Lett. 98 (2007) 265003. Coriolis drift pinch O.D.Gurcan et al., Phys. Plasmas 14 (2007) 042306. symmetry breaking by sheared ExB flows T.S.Hahm et al., Phys. Plasmas 14 (2007) 072302. nonlinear gyrokinetic pinch P.H.Diamond et al., Phys. Plasmas 15 (2008) 012303. collisionless drift wave drive T.S.Hahm et al., Phys. Plasmas 18 (2008) 055902. turbulent equipartition pinch

but edge drive mechanism unknown.

H-mode rotation not ICRF wave or fast particle effect, since also observed in Ohmic plasmas.

For H-mode, with positive core Er, need inward shift of ions or outward electrons.

Role of SOL flows:B.LaBombard et al., Phys. Plasmas 15 (2008) 056106.

Recent measurements of pedestal flows:R.McDermott et al., TTF Boulder (2008).

Do blobs leave the edge in apreferential direction?J.R.Myra et al., Phys. Plasmas 15 (2008) 032304.

see P.Molchanov et al., this meetingfor MAST edge flows.

0 50 100 150∆W

P/I

P (kJ/MA)

0

20

40

60

80

100

120

∆V

Tor (

km/s

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2∆β

N

0.0

0.1

0.2

0.3

∆M

i

Rotation Scaling in H-mode and Improved L-mode

The change in the rotation velocity scales as the change in the stored energy normalized to the plasma current.

dimensional

The change in ion thermal Mach numberscales as the change in the normalizedpressure.

dimensionless

J.E.Rice et al., Nucl. Fusion 39 (1999) 1175.

binned binned

-20 0 20 40 60 80 100 120V

Tor (km/s)

0.8

1.0

1.2

1.4

1.6

H89

0.0 0.5 1.0 1.5 2.0 2.5change in average density (1020/m3)

0

20

40

60

80

100

120

∆V

Tor (

km/s

)Rotation Scaling in H-mode and Enhanced L-mode

Very weak dependence on electron density,ICRF power or electron temperature.

The fastest rotating plasmas have the best confinement properties.(not implying causality)(link through the pedestal)

J.E.Rice et al., Nucl. Fusion 38 (1998) 75.

Dimensionless Parameter Scaling Regression Analysis of MA

MA = Vφ/CA CA2=B2/µ0nemave β = 2µ0<P>/B2 q* = 2πκa2B/µ0RIp

MA M

easu

red

MA Scaling

C-ModDIII-DTore Supra

JT-60UTCV

ITER InductiveITER Non-Inductive

JET

MA = 0.65β1.4q*2.3

J.E.Rice et al., Nucl. Fusion 47 (2007) 1618.ITPA

∆V Scaling [km/s]

∆V M

easu

red

[km

/s]

∆V = C Bo1.1 ∆<p>1.0 Ip

-1.9 R2.2

C-ModDIII-DTore Supra

JT-60UTCV

ITER InductiveITER Non-Inductive

JET

Dimensional Parameter Scaling Regression Analysis of ∆V

J.E.Rice et al., Nucl. Fusion 47 (2007) 1618. ITPA

ICRF Mode Conversion Induced Rotation

Rotation exceeds nominal scaling by about a factor of 2.

80 MHz D(H) 50 MHz D(He3)Very strong core rotation.Impurity temperature exceeds Te.

0.6 0.8 1.0 1.2 1.4 1.6020406080

100

(kJ) W

P

0.6 0.8 1.0 1.2 1.4 1.60.00.5

1.0

1.5

n e (10

20/m

3 )

<ne>

0.6 0.8 1.0 1.2 1.4 1.60123

(MW

)

ICRF

Mode ConversionMinority Heating

0.6 0.8 1.0 1.2 1.4 1.60.00.51.01.52.02.5

(keV

)

TI

0.6 0.8 1.0 1.2 1.4 1.60.00.51.01.52.02.53.0

(keV

)

Te

0.6 0.8 1.0 1.2 1.4 1.6t (s)

-200

20406080

(km

/s)

VTor

0 50 100 150∆W

P/I

P (kJ/MA)

0

20

40

60

80

100

120

∆V

Tor (

km/s

)

0.6 0.8 1.0 1.2 1.4 1.6020406080

(kJ) W

P

0.6 0.8 1.0 1.2 1.4 1.601234

n e (10

20/m

3 )

ne(0.7)

ne(0)

0.6 0.8 1.0 1.2 1.4 1.60.00.51.01.52.0

(MW

)

ICRF

0.6 0.8 1.0 1.2 1.4 1.60.00.51.01.5

(keV

)

Te

Ti

0.6 0.8 1.0 1.2 1.4 1.6t (s)

-10

0

10

20

30

(km

/s)

V (0)Tor

0.70 0.75 0.80 0.8501

2

3

45

(1020

/m3 )

electron density

0.70 0.75 0.80 0.85

-10

0

10

20

30

(km

/s) V

Tor

0.70 0.75 0.80 0.85R (m)

0.0

0.5

1.0

1.5

(keV

)

ion temperature

0.8 s

1.1 s

1.4 s

ITB Formation with Off-Axis ICRF

Following the H-mode transition, core densityand temperature peak up while the rotationfalls, on a time scale >> τE ~ 40 ms.

The ITB foot is near r/a = 0.5. Thesebarriers are characterized by strongcore density peaking.

J.E.Rice et al., Nucl. Fusion 41 (2001) 277.J.E.Rice et al., Nucl. Fusion 42 (2002) 510.J.E.Rice et al., Nucl. Fusion 43 (2003) 781.

0.6 0.8 1.0 1.2 1.4 1.60.550.600.650.700.75

1020

/m3

<ne>

0.6 0.8 1.0 1.2 1.4 1.61.301.35

1.40

1.45li

0.6 0.8 1.0 1.2 1.4 1.6

2.22.42.62.83.0

keV T

e(0)

0.6 0.8 1.0 1.2 1.4 1.60.00.20.40.60.8

MW

LH

0.6 0.8 1.0 1.2 1.4 1.6t (s)

-40-30-20-10

0

km/s

VTor

(0)

0.70 0.75 0.80 0.850.0

0.2

0.4

0.6

0.8

1.0

n e (10

20/m

3 )0.70 0.75 0.80 0.85

-30

-20

-10

0

VTo

r (km

/s)

0.70 0.75 0.80 0.85R (m)

0.00.51.01.52.02.53.0

T (

eV)

Te

Ti

0.7 s

1.2 s

Counter-current Rotation and ITB Formation with LHCD

With application of LHCD power, core density and temperature increase while internal inductance drops and core rotation increments in the counter-current direction. Time scale >> τE.

Transport barriers in particle, momentum and energy channels.ITB foot near r/a=0.4.

LHCD Power Scan

0 200 400 600 800 10001.4

1.5

1.6

1.7

1.8

1.9

density peaking

0 200 400 600 800 10000

50

100

150

200

∆T

i (eV

)

0 200 400 600 800 1000LHCD Power (kW)

0

10

20

30

−∆V

Tor (

km/s

)

Strong correlation between rotation and internal inductance. Higher rotation seenfor lower index of refraction.

0.0 0.1 0.2 0.3-∆ l

i

0

20

40

60

-∆V

Tor (

km/s

)

60 75 90105120-60-90

phase

Rotation Scaling in LHCD Plasmas

Strength of ITB and magnitude of rotationdrop increases with LHCD power anddecreasing electron density.

u Ohmic L-mode complicated dependence on ne, Ip, magnetic configuration rotation reversals/inversions observed intimately related to H-mode power threshold transport is anomalous

u H-mode and enhanced L-mode direction mostly co-current magnitude scales with stored energy/plasma current or βN evidence for ICRF mode conversion induced rotation transport is anomalous, momentum pinch observed

u ITB plasmas rotation trends in the counter-current direction as ITB builds slow evolution, >>τφ observed with ICRF (in H-mode) and LHCD (in L-mode) for LHCD, change in rotation scales with change in li

Summary of Spontaneous Rotation in C-Mod Plasmas

u Need to understand edge rotation, since core responds to edge symmetry breaking mechanism required blobs leaving in preferential direction? several models for transport exist

u L-mode understanding of H-mode power threshold must include L-mode rotation mechanism for rotation inversion?

u H-mode and enhanced L-mode highly rotating plasmas have best confinement properties RWM suppression without NBI possible in ITER momentum pinch observed, can test models

u Rotation and profile control without beams co-current with ICRF minority heating and mode conversion, flat to peaked counter-current with LHCD, peaked hollow with ICRF + LHCD hollow with ECH (DIII-D, J.S.deGrassie et al., Phys. Plasmas 14 (2007) 056115)

Discussion