IAEA San Diego Oct. 9, 2012

EX/2-2

Non-Local Heat Transport, Core Rotation Reversals and Energy Con�nement Saturation in Alcator C-Mod Ohmic Plasmas

with thanks to

M.L.Reinke, C.Gao, N.T.Howard, Y.A.Podpaly, M.J.Greenwald, J.L.Terry, M.Chilenski, P.C.Ennever, D.Ernst, C.L.Fiore, R.S.Granetz, A.E.Hubbard, J.W.Hughes, J.H.Irby, Y.Ma, E.S.Marmar, M.Porkolab, N.Tsujii, A.E.White, S.M.Wolfe, C-Mod Team H.J.Sun SWIP

P.H.Diamond, I.Cziegler CMTFO UCSD

R.M.McDermott, C.L.Angioni IPP Garching

L.Delgado-Aparicio, D.Mikkelsen PPPL

W.L.Rowan IFS UT

B.P.Duval, A. Bortolon EPFL

Plasma Science and Fusion Center, MIT

J.E.Rice

Longstanding mysteries in tokamak Ohmic plasmas:

Up/down impurity density asymmetries Con�nement saturationJ.L.Terry et al., Phys. Rev. Lett. 39 (1977) 1615. A.Gondhalekar et al., 7th IAEA (1978) Vol.I 199.

Non-local heat transport Rotation reversalsK.Gentle et al., Phys. Rev. Lett. 74 (1995) 3620. A.Bortolon et al., Phys. Rev. Lett. 97 (2006) 235003.

Rotation reversals, the LOC/SOC transition, non-local heat transport and up/down impurity density asymmetries are related.

0.0 0.5 1.0 1.5 2.0n

e (1020/m3)

0

10

20

30

40

50

τ E (ms)

5.2 T 0.81 MA

neo-Alcator

τ89-P

LOC SOC

Alcator APDXAlcator CTEXTCOMPASS-CC-Mod

TEXTTFTRRTPAUGHL-2AC-Mod

0. 20. 40. 60. 8

1 Electron and carbon temperature (KeV)

TC

Te

(b)

0 0. 2 0. 4 0.6 0.8 1

−20−10

01020

ρ

Carbon toroidal rotation ωφ (krad/s)

(c) TCV #28355

2

4

6

8 t=0.96 st=1.23 s

Electron density ne

(10 19 m−3)

(a) ← q=1

TCVC-ModAUG

LOC = linear Ohmic confinement SOC = saturated Ohmic confinement

nomenclature:

OutlineCold pulse propagation and connection to rotation reversalsRelation with LOC/SOC transition, up/down impurity asymmetriesAssociated turbulence changes during reversalsModeling and discussion, role of ν*

Alcator C-Mod Fusion Sci. Technol. 51 (2007) R = 0.67 m r ~ 0.2 m κ < 1.8

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

ne = 0.1-10 x1020/m3 Te~Ti = 1-8 keV

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

Rotation velocities and Ti from imaging x-ray spectrometers A.Ince-Cushman et al., Rev. Sci. Instrum. 79 (2008) 10E302.

Cold pulse from LBO CaF2 injection

No external momentum sources Ohmic plasmas only

Edge X-ray Spectra Show Up/Down Emissivity Asymmetry at High Density (J.E.Rice et al., Nucl. Fusion 37 (1997) 241., M.L.Reinke, Ph.D. thesis M.I.T. 2011)

Ar16+ x-ray spectra exhibit recombination population at r/a~0.9. Up/down symmetric in LOC Up/down asymmetric in SOC (0.6x1020/m3) (1.4x1020/m3)

3940 3960 3980 4000wavelength (mA)

0

1000

2000

3000

4000

5000

brig

htne

ss (a

rb)

top

w

x

y

z

bottom

3940 3960 3980 4000wavelength (mA)

0

50

100

150

200

250

300

brig

htne

ss (a

rb)

top

bottom

In LOC, the core electron and iontemperatures increase following edgecooling. Non-local, non-di�usive.

In SOC, the heat transport is di�usive. τE ~ 30 ms.

Cold Pulse Propagation Comparison in SOC and LOC Plasmas

LOC

0.00.5

1.0

1.5

(1020

/m3 )

electron density

SOCLOC

1.92.0

2.1

2.2

2.3

(keV

)

Te core

0.050.100.150.200.250.300.35

(keV

)

Te edge

1.151.201.251.301.351.40

(keV

)

Ti core

0.96 0.98 1.00 1.02 1.04 1.06 1.08 1.10t (s)

0.450.50

0.55

0.60

0.65

(keV

)

Ti edge

SOC

0.00.5

1.0

1.5

(1020

/m3 )

electron density

SOCLOC

1.25

1.30

1.35

(keV

)

Te core

0.100.120.140.160.180.200.220.24

(keV

)

Te edge

1.161.181.201.221.241.261.28

(keV

)

Ti core

0.76 0.78 0.80 0.82 0.84 0.86 0.88t (s)

0.400.45

0.50

0.55

0.60

(keV

)

Ti edge

Temperature Flex Point and Rotation Reversal Anchor Point Similar

LOC temperature pro�les before andduring cold pulse. R/LTe changes from11.5 to 14.0. R/LTi changes from 5.9 to 8.2. Ti pro�le develops more slowly.

Comparison of LOC and SOC velocitypro�les. Anchor point close to Te

�ex point in LOC.

0.70 0.75 0.80 0.85R (m)

0

1

2

3

(keV

)

0.2 0.4 0.6 0.8r/a

Te

Ti

1.011 s

0.999 s

1.03 s

1.01 s

0.99 s

0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84R (m)

-20

-10

0

10

20

(km

/s)

0.1 0.2 0.3 0.4 0.5 0.6 0.7r/a

VTor

SOC

LOCcold pulse at 1.000 s

0.7x1020/m3

0.9x1020/m3

Rotation Reversal, LOC/SOC Transition, Non-Local Heat Transport and Up/Down Impurity Density Asymmetry All Related

At LOC/SOC transition, Te/Ti ~ 1.2for 0.8 MA.

0.80 MA

05

1015202530

(ms)

τI

01

2

3

(keV

)

Te

Ti

0.81.01.21.41.61.8

Te/T

i

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4n

e (1020/m3)

123456

Zeff

For 0.8 MA, reversal and non-localtransition at exact same density.

-20-10

0

10

(km

/s)

VTor

(0)

010203040

(ms) τ

e

LOC SOC

-10-5

0

5

(%)

Te change at R = 0.78 m

2.53.03.54.04.55.0 R/L

n (0.79 m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4n

e (1020/m3)

0.51.0

1.5

2.0 up/down edge z brightness ratio

non-local local

Critical Density for Rotation Reversal, LOC/SOC Transition, Non-Local Cut-O� and Up/Down Impurity Density Asymmetry Scales with Current

-20

-10

0

10

(km

/s)

VTor

(0)

0.55 MA

010203040

(ms)

τe

LOC SOC

-10-5

0

5

(%)

Te change at R = 0.77 m

1.01.52.02.53.03.5

R/Ln (0.77 m)

0.0 0.2 0.4 0.6 0.8 1.0n

e (1020/m3)

0.51.0

1.5

2.0 up/down edge z brightness ratio

-20-10

01020

(km

/s)

VTor

(0)

1.1 MA

010203040

(ms)

τe

LOC SOC

-10-5

0

5

(%)

Te change at R = 0.81 m

1.01.52.02.53.03.5

R/Ln (0.81 m)

0.0 0.5 1.0 1.5 2.0n

e (1020/m3)

0.51.0

1.5

2.0 up/down edge z brightness ratio

non-local local non-local local

0.15 0.20 0.25 0.30 0.351/q

95

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

(1020

/m3 )

up-down asymmetry

rot rev

Te inv

LOC/SOC

Scalings of Critical Densities and Characteristic Radii with Plasma Current

Rotation reversal anchor points and temperature�ex points located inside of q =3/2.

Critical densities for temperature inversion,rotation reversal, LOC/SOC transition andup/down impurity asymmetries scale similarly with plasma current.

0.15 0.20 0.25 0.30 0.351/q

95

0.74

0.76

0.78

0.80

0.82

R (m

)

0.3

0.4

0.5

0.6

0.7

r/a

q=3/2 (EFIT)

q=1 (EFIT)

rot rev

Te inv

s.t. inv

0.81.01.21.41.61.82.0

T e/Ti

0.55 MA0.8 MA

1.1 MA

1234567

Z eff

0.0 0.5 1.0 1.5 2.0n

e (1020/m3)

0.00.2

0.4

0.6

0.8

1.0

Z eff/T

e2 (keV

-2)

(0.55 MA) (0.8 MA) (1.1 MA)

Values of Z/T2 and Collisionality at LOC/SOC Transition Fixed

Values at LOC/SOC transition Scalings with density

Transition occurs at �xed Z/T2 but not Te/Ti.

0.15 0.20 0.25 0.30 0.351/q

95

0

1

2

3

4Z

eff

Te/T

i

Z/T2 (keV-2)

ν*x10

Turbulence Characteristics Very Di�erent in LOC and SOC Core density �uctuations from PCI.J.E.Rice et al., Phys. Rev. Lett. 107 (2011) 265001.

Edge density �uctuations from GPI.

LOC

-10 -5 0 5 10kR (cm-1)

100

200

300

400

500

Freq

uenc

y (k

Hz)

SOC 1.05x1020/m3

-10 -5 0 5 10k

R (cm-1)

0

200

400

600

Freq

uenc

y (k

Hz)

TEM?kθρs<1

-10 -5 0 5 10kR (cm-1)

100

200

300

400

500

Freq

uenc

y (k

Hz)

LOC 0.99x1020/m3

- =

SOC Edge turbulence propagationdirection reverses atLOC/SOC transition.

LOC ne = 1.03x1020/m3

1.5 2.0 2.5 3.0a/LTi

0.8

1.0

1.2

1.4

1.6

1.8

2.0

a/L n

0.261

0.326

0.391 0.4570.522

0.587Electron

Ion

SOC ne = 1.16x1020/m3

1.5 2.0 2.5 3.0 3.5 4.0a/LTi

0.8

1.0

1.2

1.4

1.6

1.8

2.0

a/L n

0.314

0.377

0.439

0.439

0.502

0.502

Electron

Ion

Linear GYRO Simulations Indicate Dominance of TEMs at Low Collisionality, ITG Modes at High Collisionality (for non-linear simulations see M.Porkolab et al., EX/P3-13 Wed. AM)

Contour plots of the linear growth rate (cs/a) of the most unstable mode with 0.1 < kθρs < 0.75

Rotation Reversals, LOC/SOC Transition, Non-Local Heat Transport, Density Pro�le Peaking and Up/Down Impurity Density Asymmetries CorrelatedPieces of the puzzle have been around for many years:

LOC/SOC transition occurs at a critical density A.Gondalekar et al., Proc. 7th IAEA Conf., Innsbruck (1978)

which depends on current Y.Shimomura et al., JAERI-M Report 87-080 (1987)

and is correlated with turbulence changes. R.L.Watterson et al., Phys. Fluids 28 (1985) 2857.

Non-local heat transport K.W.Gentle et al., Phys. Rev. Lett. 74 (1995) 3620.

occurs below a critical density. P.Mantica et al., Phys. Rev. Lett. 82 (1999) 5048.

Density pro�le peaking saturates at LOC/SOC transition. C. Angioni et al., Phys. Plasmas 12 (2005) 040701.

Up/down impurity density asymmetries seen in SOC. J.L.Terry et al., Phys. Rev. Lett. 39 (1977) 1615.

Rotation reversal is the most sensitive indicator of the LOC/SOC transition:

Rotation reversals occur at a critical density A.Bortolon et al., Phys. Rev. Lett. 97 (2006) 235003.

which depends on q95 and is associated J.E.Rice et al., Nucl. Fusion 51 (2011) 083005.

with turbulence changes and the LOC/SOC transition. J.E.Rice et al., Phys. Rev. Lett. 107 (2011) 265001.

Momentum �ux is proportional to the Reynolds stress: -χφ dvφ /dr + V vφ + Πres

χφ is positive de�nite, quasi-linear V can change sign if dn/dr changes sign

Πres can change sign if mode propagation direction changes.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5R (m)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

dens

ity a

t con

�nem

ent s

atur

atio

n (1

020/m

3 )

2.8 < q < 3.8

1/R

C-Mod

FT

TCV

TEXT

JFT-2M

ASDEX

AUG

Tore Supra

JET

JT-60

Machine Size Scaling of LOC/SOC Density

ν* = 0.018 neq R Ze� / Te

2 ε3/2 ~ nqR = const. J.E.Rice et al., Phys. Plasmas 19 (2012) 056106.

Unifying ansatz:

low collsionality, LOC, co- rotation, TEM turbulence, non-local heat transport, peaking density pro�les

high collisionality, SOC, counter- rotation, ITG turbulence, di�usive heat transport, stable density pro�les

at q=3/2 surface

.

-20

-10

0

10

(km

/s)

0.62 MA

VTor

(0)

0.0 0.2 0.4 0.6 0.8 1.0 1.2ν

*

-20

-10

0

10

(km

/s)

1.0 MA

VTor

(0)

Is Collisionality ν* the Determining Parameter?

Conclusions and DiscussionNon-di�usive, non-local heat transport has been observed below a critical density.

Te pro�le �ex point coincides with the rotation reversal anchor point, inside of the q = 3/2 surface.

Critical densities for Te inversion, rotation reversal and LOC/SOC transition are very close.

Radii of Te pro�le �ex point and rotation reversal anchor point scale with 1/q.

Critical densities for Te inversion, rotation reversal, LOC/SOC transition and up/down impurity density asymmetries scale with 1/q.

Reversals from the co- to counter-current direction are correlated with a sharp decrease in core density �uctuations with 2 cm-1< kθ < 11 cm-1 and frequencies above 70 kHz. Propagation direction of edge turbulence switches at LOC/SOC transition.

Linear GYRO simulations indicate TEM domination in LOC, ITG mode prevalence in SOC.

Unifying ansatz:

At low collisionality, in the LOC regime, the rotation is co-current, TEMs dominate, heat transport is non-local, density pro�les peak and impurity density pro�les are up/down symmetric.

At high collisionality, in the SOC regime, the rotation is counter-current, ITG modes dominate, heat transport is di�usive, density pro�le peaking saturates and impurity density pro�les are up/down asymmetric.

The transition occurs at a particular collisionality, near ν* ~ 0.4.