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