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ETG Scale Turbulence and Transport in the DIII–D Tokamak EX/P4-37 T.L. Rhodes* Presented by E.J. Doyle* for W.A. Peebles, * M.A. Van Zeeland, J.S. deGrassie, R.V. Bravenec, K.H. Burrell, G.R. McKee, § J. Lohr, C.C. Petty, X.V. Nguyen, * E.J. Doyle, * C.M. Greenfield, L. Zeng, * and G. Wang * * University of California-Los Angeles, Los Angeles, California. General Atomics, San Diego, California. University of Texas, Austin, Texas. § University of Wisconsin. Madison, Wisconsin. Presented at the 21st IAEA Fusion Energy Conference Chengdu, China October 16–21, 2006
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Page 1: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

ETG Scale Turbulence and Transport in theDIII–D Tokamak EX/P4-37T.L. Rhodes*Presented by E.J. Doyle*forW.A. Peebles,* M.A. Van Zeeland,† J.S. deGrassie,†R.V. Bravenec,‡ K.H. Burrell,† G.R. McKee,§ J. Lohr,†C.C. Petty,† X.V. Nguyen,* E.J. Doyle,* C.M. Greenfield,†L. Zeng,* and G. Wang*

*University of California-Los Angeles, Los Angeles, California.†General Atomics, San Diego, California.‡University of Texas, Austin, Texas.§University of Wisconsin. Madison, Wisconsin.

Presented at the21st IAEA Fusion Energy ConferenceChengdu, China

October 16–21, 2006

Page 2: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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New results since FEC 2004

• Observed correlation of increased high k (~35 cm-1, k i=4-10) turbulence

with increased electron heat transport.

– Consistent with high k turbulence driving at least part of electron heat

transport.

• Determined that high k (~35 cm-1) is not a short remnant or tail of low k

(~1 cm-1) ITG/TEM type modes

• Differing effect of electric field shear on low and high k observed:

– Low k fluctuation behavior consistent with reduction due to Er shear

– High k apparently not affected by Er shear

• Relative levels of high and low k fluctuation levels comparable to non-

linear turbulence simulation (GYRO) results

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• Source of electron thermal transport often not well understood.

– Ion temperature gradient (ITG) (k i~0-1),

– Trapped electron drive (TEM) (k i~0-2)

– Electron temperature gradient (ETG) (k i >2)

• High frequency, high k modes predicted to drive varying levels of

electron heat transport.

– Dorland, et al., PRL (2000), Jenko and Dorland, PRL (2002), Labit and

Ottaviani, PoP (2003), Li and Kishimoto, PoP (2004), Horton, et al., PoP

(2004), Lin, et al., PoP(2005), Gürcan and Diamond, PoP (2004),

– Predictions range from small to significant depending upon

model and plasma.

– Motivates experimental measurements

• DIII-D, NSTX, FT-2, Tore-Supra

Recent theoretical work indicates high k turbulence maycontribute to anomalous electron heat transport

Page 4: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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• Ultimate goal: test and validate

turbulence simulations via

experimental comparison.

– Compare turbulence

behavior over large k range.

• BES, FIR, PCI, reflectometry,

magnetics, high k backscatter.

– Broad k range:

• ~ 0-40 cm-1, k i~0-10

• Important to measure broad k

range due to potential interaction

of various k ranges + allows

closer comparison to theory.

Broad Wavenumber (~0-35 cm-1) ñ Measurements Provide New,More Complete Picture of Turbulence Behavior on DIII-D

Page 5: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Can cover large range of k’sdepending upon geometry and probefrequency used.

Approach: Collective Thomson scattering is well-suited to study long-to-short wavelength turbulence

kw

ki

ks

kw

ki

ks

Momentum matching gives

ki+kw=ks

Energy conservation gives

i+ w= s i.e scatteredradiation Doppler shifted.

Bragg Law:

For ki ~ ks, can show that

kw = 2kisin( /2)

Where is scattering angle

ForwardScattering

180º Backscatter FIR scattering isdominantly kHigh k backscattering isdominantly kr

Page 6: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Simultaneous data from low to high k using FIR andmm wave scattering diagnostics

low k mixer

high k detector

intermediatek mixer

• Low-k FIR

– Poloidal k: kθ =0-2 cm-1, kρs=0-0.3

– Chord average

• Intermediate-k FIR

– Poloidal k: k = 8-15 cm-1, k s=2-5

– Spatial localization, ±15 cm at 15 cm-1

• High-k mm-wave backscatter

– Radial k: k =35-40 cm-1, k s =4-10

– Chord from r/a=1 to r/a=0.4

Page 7: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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• k is dominated by radial kr

with small poloidal k

component

– e.g., kr 34.95 cm-1 and

k 1.2 cm-1 for k=35 cm-1.

• Wavenumber resolution

k ±0.2 cm-1.

• Frequency is well above

cutoff

– Refraction small, <1º

• Refractive index reduces

probed k 35-40 cm-1 for

plasmas discussed here.

High k system measures kr along a chord

120325, efit=2000, ts=2000 ms, z=3cm

0.0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100

Fre

quen

cy (

GH

z)

EFIT01

radial coordinate ρ

1.0 1.5 2.0 2.5-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

High k signal fromchord, typically >0.4

fce

fRH

2fce

94 GHz

94 GHz, ECEresonance

Page 8: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Electron Cyclotron Heating (ECH) of plasmaprimarily modified Te and turbulence behavior

• Used ECH (~2.5

MW) to locally

heat plasma

– Ip=800kA, BT=2

T, ne=1.7x1013

cm-3

• Te increased, small

decrease in ne, no

effect on Ti

• Monitor fluctuation

levels, gradients,

etc. and compare

to theory.

120325

0.00.51.01.52.0

EC

H P

ower

(M

W)

0.00.20.40.60.81.0

Te

(keV

rho=0.58

rho=0.67

rho=0.76

0.0

0.5

1.0

1.5

2.0

Den

sity

(10^

13 c

m-3

)

2000 2500 3000 3500time (ms)

(a)

(b)

(c)Density

Ti

Ti (eV

)

0

400

800

Times used in analysis:

Ohmic, 1975 ms

ECH, 3100 ms

Page 9: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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ne

0.00.5

1.0

1.5

2.0

2.53.0

n_e

(10

^13

cm-3

)a/Lne

0.0 0.2 0.4 0.6 0.8 1.0r/a

0

2

4

6

8

10

a/L

n_e

Te (keV)

0.0

0.5

1.0

1.5

2.0

2.5

Te

(keV

)

a/L_Te

0.0 0.2 0.4 0.6 0.8 1.0r/a

0

2

4

6

8

10

a/L

_Te

Ti (keV)

0.00.2

0.4

0.6

0.8

1.01.2

Ti (

keV

)

a/L_Ti

0.0 0.2 0.4 0.6 0.8 1.0r/a

0

2

4

6

8

10

a/L

_Ti

Te increased with ECH, ne decreased, modifyingpotential instability drives

• Effect of ECH is observed most strongly on Te.

OhmicECH

ECH heating at r/a~0.6

Page 10: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Electron heat flux increased substantially with ECH

• Fluxes determined using power balance and ONETWO transport code.

• Ion heat flux not strongly modified.

Electron heat flux Ion heat flux

0.0 0.2 0.4 0.6 0.8 1.0r/a

0

2

4

6

8

heat

flux

(w

atts

/cm

2 )

qelec 1901 ms

1 /u/rhodes/analysis/120327_1905.nc

120327

ECH on

qelec 3101 ms

0.0 0.2 0.4 0.6 0.8 1.0r/a

0

2

4

6

8

heat

flux

(w

atts

/cm

2 )1 /u/rhodes/analysis/120327_1905.nc

120327

ECH on

qion 3101 msqion 1901 ms

ECH heating at r/a~0.6

Page 11: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Differing response to ECH indicates that high k (35 cm-1,k i=4-10) is not a remnant or tail of low k (~1 cm-1)

Low k FIR scattering, mainly k High k mm wave scattering , mainly kradial

• High k fluctuation level increases while low k ~constant.

– Low k reflectometry also shows no increase with ECH

– Important as this relates to origin of high k

• Note narrowing of low k frequency spectrum

– consistent with a change in the Doppler shift.

0.014

0.0001

0

200

400

600

800

f (kH

z)

shot 120325, channel: mmspc4, log scale of (autopower)0.032

7.5e-05

50

100

150

f (kH

z)

shot 120325, channel: mmspc3, log scale of (autopower)

ECH power

0.8

1.0

1.2

RM

S le

vel (

a.u.

)

low-k FIR scattering high k mmwave backscatter

2000 2500 3000 3500

time (ms)

0.8

1.0

1.2

RM

S le

vel (

a.u.

)

(a)

(b)

(c)

(d)

2000 2500 3000 3500

time (ms)

ECH power

Page 12: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Increase in high k turbulence correlates withincreased electron heat flux

• Lack of change in ion heat flux consistent with lack of change in low

k turbulence

• Increased electron heat flux due solely to increased high k

fluctuations not measured, can be estimated to be as much as 30%

over base flux using

– Flux due to high k higher if include measured increase in Te

– Need more direct experimental tests plus non-linear simulations.

˜ q e = n ˜ T e

˜ E B nk Te2 ˜ n n( )

2B

Page 13: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Critical gradient analysis indicates plasma is unstable toelectron temperature gradient driven modes (ETG)

• Experimental Te scale length exceeds predicted critical scale length forelectron temperature gradient driven modes (ETG) over large region

• Critical scale length from Jenko, et al. PoP2001

0.0 0.2 0.4 0.6 0.8 1.0rho

0

10

20

30

40

50

R/L

Te

120327

0.0 0.2 0.4 0.6 0.8 1.0rho

0

10

20

30

40

50

120327

Experiment

Predicted criticalscale length

Experiment

R/L

Te

Predicted criticalscale length

Ohmic ECH

ECH heating at r/a~0.6

Page 14: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Linear gyrokinetic calculations (GKS code) showincreases in both low and high k growth rates with ECH

• Expect increases in both low and high k in outer plasma

regions - however, experimentally low k ñ is constant.

k = 1 cm-1 k = 35 cm-1

•GKS: linear

gyrokinetic code

calculates

growth rates and

frequencies for

toroidal drift

waves

• Calculations

are for k , high k

is principally kr.-20

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1

r/a

0

10

20

30

40

50

60

70

-200

0

200

400

600

800

1000

0 0.2 0.4 0.6 0.8 1

r/a

0

100

200

300

400

500

Ohmic

ECH

Gro

wth

Rate

(kra

d/s)

Fre

quency (

kra

d/s)

Gro

wth

Rate

(kra

d/s)

Fre

quency (

kra

d/s)

120327

120327

120327

120327 Ohmic

ECHOhmic

ECH

Ohmic

ECH

Page 15: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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-50

0

50

100

γ ExB

(100

0 1/

s)

0.0 0.2 0.4 0.6 0.8 1.0normalized rho

(b)OhmicECH

120327120327-2

0

2

4

6

8E

r (k

V/m

)(a)

OhmicECH

0.0 0.2 0.4 0.6 0.8 1.0normalized rho

Radial Er decreases with ECH however resulting Er

shear is increased

• Resulting decrease in VExB is consistent with observed

decrease in frequency width of low k fluctuations.

• ExB shearing rate is found to be a significant fraction of

calculated low k growth rates.

– Potential explanation for GKS prediction of increased low

k during ECH while experiment shows constant level

– Note that high k apparently unaffected by shear

ECH heating at r/a~0.6

Page 16: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Recent GYRO simulations find ETG scale turbulence

isotropic in kr-k

GYRO simulations:μ=(mi/me)1/2=30

• Non-linear turbulence GYRO simulations addressing realistic couplingITG/TEM/ETG simulations (From R. Waltz, et al., General Atomics)

• GYRO simulation conditions are close to but not same as experimentalplasma studied here and only one radial position.

– Experiment covers range in both r/a and in plasma parameters

– Need more simulation results to compare with !

Page 17: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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• GYRO simulation parameters (so-called “GA standard conditions”)

– s =1, q=2, r/a=0.5, R/a=3, a/LT=3, a/Ln=1, Te/Ti=1

• “Cyclone conditions” are similar:

– s =0.8, q=1.4, r/a=0.54, R/a=3, a/LT=2.3, a/Ln=0.73, Te/Ti=1

• In simulation only one radial position documented, r/a~0.5

GYRO simulation parameters are close to experiment

0

1

2

3

ne (

10^1

9 m

-3)

0

1

2

3

Te

(keV

)

0.00.20.40.60.81.01.2

Ti (

keV

)

0 .2 .4 .6 .8 1.r/a

0.00.51.01.52.0

Zef

f

02468

10

q

02468

10

s

02468

10

a/Ln

05

101520

a/L_

Te

02468

a/L_

Ti

0 .2 .4 .6 .8 1.r/a

0 .2 .4 .6 .8 1.r/a

^

^

^

Experiment, OhmicExperiment, ECH"CYCLONE" conditions"GA standard" conditions

Page 18: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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• Perturbed Ohmic plasma with short

NBI blips (Pinj~2.5 MW)

– Ip=800kA, BT=2 T, ne=1.7x1013 cm-3

• Te, Ti increased but no significant

change in ne

• Fluctuation levels increase with NBI

over broad range in k

– As opposed to only the high k

increasing with ECH

– Example shown is high k, 35 cm-1.

– Next compare theoretical and

experimental response of different

wavenumbers

Broadband turbulence response to short NBI blipssomewhat different from ECH response

Page 19: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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GKS predicts plasma unstable over broad rangein k: 1-35 cm-1, k i~0-10

• Good counterpoint to ECH

data.

• Range of instabilities

corresponds to ITG, TEM,

ETG type instabilities.

• Note that with exception of

high k the growth rates do

not change strongly with

the NBI

OhmicNBI

Growth rates Frequency

1 cm-1

k i~0.2

7 cm-1

k i~1-2

35 cm-1

k i=4-10

Page 20: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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• Fluctuation magnitude increases

and broadens with NBI

• Ohmic fluctuation levels ñ/n:

– Low k: ñ/n ~ 8x10-3

• =0.7, k i~0.2-0.4, BES

– High k: ñ/n ~ 3x10-6

• =0.4-1.0, k i=4-10 high k

– ñ/n increases ~25% with NBI

Quantitative comparison of high k and low k fluctuationlevels reveals large difference in magnitude

10-9

10-7

P(f

) (a

.u.)

0 50 100 150 200 250 300f (kHz)

10-8

10-7

P(f

) (a

.u.)

120876

120883

10-6

10-5

120884

0 200 400 600 800 1000f (kHz)

10-8

10-7

10-6

120873

P(f

) (a

.u.)

P(f

) (a

.u.)

OhmicNBI

BES0-3 cm-1

FIR0-2 cm-1

FIR5-9 cm-1

Backscatter35-40 cm-1

Page 21: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Ratio of high to low k fluctuation levels comparereasonably well with non-linear GYRO simulation

• Simulation:

– (ñ/n)high k/(ñ/n)low k ~ 10-3

• Ratio compares reasonably

well with experimental ratio

– (ñ/n)high k/(ñ/n)low k ~ .4x10-3

• Simulation shown is at r/a=0.5

and for conditions which are

close to but not same as

experimental plasma

GYRO simulation

High k range

Low k range

Page 22: ETG Scale Turbulence and Transport in the DIII–D … · ETG Scale Turbulence and Transport in the ... 0 20 40 60 80 100 ... (ETG) over large region • Critical scale length from

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Summary

• DIII-D has a comprehensive set of turbulence diagnostics spanning a

wide range in k: ITG, TEM, ETG relevant

• Observed correlation of increased high k (~35 cm-1, k i=4-10) turbulence

with increased electron heat transport.

– Consistent with high k turbulence driving at least part of electron heat

transport.

• Determined that high k (~35 cm-1) is not a short remnant or tail of low k

(~1 cm-1) ITG/TEM type modes

• Differing effect of electric field shear on low and high k observed:

– Low k fluctuation behavior consistent with reduction due to Er shear

– High k apparently not affected by Er shear

• Relative levels of high and low k fluctuation levels comparable to non-

linear turbulence simulation (GYRO) results


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