comparison of experimental measurements and gyrokinetic turbulent … · 2011-04-20 · pci b i+...

Comparison of experimental measurements and gyrokinetic turbulent electron transport models in Alcator C-Mod plasmas

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��51st Annual Meeting of the Division of Plasma Physics

November 2 - 6, 2009, Atlanta, Georgia

L. Lin†, M. Porkolab, E.M. Edlund, J.C. Rost, C.L. Fiore, M. Greenwald, A. Hubbard, Y. Ma, and N. TsujiiPlasma Science and Fusion Center, MIT, Cambridge, MA 02139J. Candy and R. E. WaltzGeneral Atomics, PO Box 85608, San Diego, CA 92186D. R. MikkelsenPrinceton Plasma Physics Laboratory, Princeton, NJ 08543W. M. NevinsLawrence Livermore National Laboratory, Livermore, CA 94550

†Present address: University of California, Los Angeles, Los Angeles, CA 90095

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��Outline

• Introduction• Phase contrast imaging (PCI) diagnostic • TRANSP, GYRO and synthetic PCI• Turbulence• Thermal Transport• Impact of ohmic drift velocity • Summary

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��Introduction

• The experiments were carried out over the range of densities covering the "neo-Alcator" ( ) to the "saturated ohmic" regime.

Linear regime

Saturatedregime

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

[m

sec]

0

10

20

30

40

50

e [1020m-3]n_

BT=5.2 TIp=0.8 MA

• Low density ohmic plasma in the neo-Alcator regime, where the thermal energy is mainly lost through the electron channel, is an excellent candidate to unambiguously investigate electron transport.

E eτ n

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��Approaches

GYRO

en

e,i,eff TRANSP

Phase Contrast Imaging

en dl

e,i,eff

Synthetic Diagnostic

Turbulence

Thermal Transport

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• PCI measures density fluctuations along 32 vertical chords.

• The localization upgrade allows PCI to resolve the direction of propagation of the measured turbulence in ITG and TEM range.

• The improved calibration also allows for the intensity of the observed fluctuations to be determined absolutely.

• It is almost impossible to directly infer from .

Wavenumber Range:0.5cm-1<|kR|< 55 cm-1

Frequency Range:2kHz~5MHz

PCI

k<0k>0

R [m]0.4 0.6 0.8 1.0

0.0

-0.2

-0.4

-0.6

0.2

0.4

0.6

z [m

]

B

i+

e-

A phase contrast imaging (PCI) diagnostic is used to measure turbulence.

/n n en dl

��

��GYRO* is used to predict fluctuations and associated transport.

• GYRO is an initial value Eulerian (continuum) 5D gyrokinetic code

• GYRO contains the following ingredients for quantitatively accurate transport predictions

– takes measured experimental profiles as inputs– local and global– realistic geometry (Miller formulation)– trapped and passing electrons – finite beta (magnetic fluctuations)– equilibrium sheared ExB

*http://fusion.gat.com/theory/Gyro

• GYRO is well-documented and user-friendly.

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��TRANSP is used to calculate thermal diffusivities χ

• TRANSP calculates thermal diffusivities from energy balance equation

3 :2

jj j j j j E

dTn Q S

dt=-⋅ + - +q P u

: heat flux

: energy exchange due to collisions

: pressure tensor

: fluid velocity

: external source of energy

j

j

j

j

E

Q

S

q

P

u

0r

j j condjj

j j surface j j surface j j

dV Pn T A n T A n T

cò ⋅

= = =

q q

e e e i i ieff

e e i i

n T n Tn T n Tc c

c +

= +

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��A synthetic PCI diagnostic is used for quantitative code-experiment comparisons

• A synthetic PCI diagnostic has been developed to post-analyze GYRO output and emulate the PCI instrumental response.

• The same data analysis package is used to process the experimental and emulated PCI signals.

PCI beam path

0.03

0.00

-0.03

n/n~

0.0

-0.2

-0.4

0.2

0.4

z [m

]

R [m]0.4 0.5 0.6 0.7 0.8 0.9

C. Rost, to be submitted (2009).

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GYRO enPhase

Contrast Imaging

en dl Synthetic Diagnostic

Turbulence

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��

-5-10 5 10010

50

100

150

200

250Shot: 1070713009

Freq

uenc

y [k

Hz]

Wavenumber [cm-1]

[1032

m- 4

/cm

-1/H

z] 10-4

10-6

10-8Positive kNegative k

BPCI

i+

20 3Saturated ohmic 0.93 10en m-= ´

PCI has established the fluctuations above ~80 kHz are dominated by the mode propagating in the ion diamagnetic direction and from r/a<0.85

• Available Er measurements indicate that the background Doppler rotation is not enough to reverse the mode propagating direction of the turbulence with the wavenumbers in the ITG and TEM regime.

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��

-5-10 5 10010

50

100

150

200

250Shot: 1070713009

Freq

uenc

y [k

Hz]

Wavenumber [cm-1]

[1032

m- 4

/cm

-1/H

z] 10-4

10-6

10-8Positive kNegative k

BPCI

i+


PCI has established the fluctuations above ~80 kHz are dominated by the mode propagating in the ion diamagnetic direction and from r/a<0.85

Localization depends on the magnitude of the magnetic pitch angle ζ

z [m

]

0.0

-0.2

-0.40 10

5

• Available Er measurements indicate that the background Doppler rotation is not enough to reverse the mode propagating direction of the turbulence with the wavenumbers in the ITG and TEM regime.

��

��Nonlinear GYRO simulation shows that the ITG mode is the dominant turbulence.

0, direction 0, direction.f if e

+

-

<

>

A separate global simulation shows no significant density fluctuation (ñe/ne<0.3%) in r/a<0.35.


r/a0.5 0.6 0.7

1.0

0.5

0.0

1.5

2.0

2.5n_n~

(%)ee

Flux-tubeSimulation

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��

Experimental PCI Synthetic PCI

Assuming vE×B~ 2 km/sec for the Doppler shift, the synthetic and experimental spectra are similar.


• Simulations cover and with .0 1.5skqr£ £ 0.4 / 0.8r a< <

/ 3600i em m =

• Turbulence below 80 kHz might be localized at the plasma edge, where the turbulence propagating in the ion and electron diamagnetic directions may be comparable.

Shot: 1070713009

[1032

m- 4

/cm

- 1/H

z] 10-4

10-6

10-8

-5-10 5 10010

50

100

150

200

250

Freq

uenc

y [k

Hz]

Wavenumber [cm-1]-5-10 5 100

10

50

100

150

200

250Shot: 1070713009

Freq

uenc

y [k

Hz]

Wavenumber [cm-1]

[1032

m- 4

/cm

- 1/H

z] 10-4

10-6

10-8

��

��


GYRO Simulation:

PCI Measurement:

Nn: 16; n:10

(a)

-5-10 5 100Wavenumber [cm-1]

0.00

0.05

0.10

0.15

0.20

0.25

Aut

opow

er [1

032m

- 4/c

m-1]

Shot: 1070713009[80, 250] kHz

Nn: 10; n:12 Nn: 20; n:10

Ti = Ti (Transp)

GYRO Simulation:

PCI Measurement:

Ti = 0.8 TeTi = Te

-5-10 5 100Wavenumber [cm-1]

0.00

0.05

0.10

0.15

0.20

0.25

Aut

opow

er [1

032m

- 4/c

m-1]

Shot: 1070713009[80, 250] kHz

(Nn: 16; n: 10)

(b)Convergence Studies Different Ti Profiles

The wavenumber spectrum of density fluctuations in the frequency range of 80-250 kHz quantitatively agrees with GYRO simulation.

• The uncertainties are mainly from the absolute calibration ~50 %.

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��

GYRO Simulation:PCI Measurement:

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

e [1020m-3]n_

Fluc

tuat

ion

Inte

nsity

[1032

m- 4

]

0.01

0.10

1.00

10.0[ 80, 250] kHz

Density fluctuation intensities in the 80-250 kHz frequency range quantitatively agree with GYRO for a range of densities

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Thermal Transport

GYRO e,i,eff TRANSPe,i,eff

��

��In the linear ohmic regime, χi is much smaller than χe.

20 3

Saturated ohmic0.93 10en m-= ´20 3

Transition0.62 10en m-= ´20 3

Linear ohmic0.34 10en m-= ´

increasesen

• As ne increases, χe decreases, but χi increases slowly, χeff also decreases.• In the saturated ohmic regime, χi becomes comparable to χe.

(a) (b) (c)

[m

2 /sec

]

2.0

1.5

1.0

0.5

0.00.2 0.4 0.6 0.8

r/a

2.0

1.5

1.0

0.5

0.00.2 0.4 0.6 0.8

r/a

2.0

1.5

1.0

0.5

0.00.2 0.4 0.6 0.8

r/a

e

[m

2 /sec

]

[m

2 /sec

]

i

eff

eieff

eieff

eieffe

i

eff

e

i

eff

��

��

• Simulation covers

with

• Diffusivities are averaged over

• The estimated uncertainty of a/LTi is as much as 30% in ohmic plasmas

• ε is the reduction factor of a/LTi

• Simulated fluctuation intensities still agree with experiments within the experimental uncertainty after the a/LTi reduction

( )sim

1i i

i i

T Ta aT r T r

eæ ö¶ ¶÷ç ÷ = -ç ÷ç ÷ç ¶ ¶è ø

Agreement between experiment and theory in χeff is obtained after reducing a/LTi by 20%

0.0 1.5skqr< <

0.4 / 0.8r a< <

/ 3600i em m =

ef

f [m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

0.2 0.4 0.6 0.8 1.0e [1020m-3]n

_

EXP: SIM: =0.0

=0.1=0.2=0.3

(a) Effective Thermal DiffusivityFl

uctu

atio

n In

tens

ity [1

032m

- 4]

0.01

0.10

1.00

10.0

[ 80, 250] kHz

(b) Fluctuation Intensity

EXP: SIM: =0.0

=0.1=0.2=0.3

0.2 0.4 0.6 0.8 1.0e [1020m-3]n

_

��

��

At higher densities, agreement between experiment and code predictions of χe and χi is obtained after the a/LTi reduction; however, at the lowest density, the experimental values of χe and χi disagree with code results.

( )sim

1i i

i i

T Ta aT r T r

eæ ö¶ ¶÷ç ÷ = -ç ÷ç ÷ç ¶ ¶è ø

• ε is the reduction factor of a/LTi :

Electron Thermal Diffusivity Ion Thermal Diffusivity

e[m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

0.2 0.4 0.6 0.8 1.0

e [1020m-3]n_

3.0

3.5EXP: SIM: =0.0

=0.1 =0.3=0.2

i[m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

0.2 0.4 0.6 0.8 1.0

e [1020m-3]n_

3.0

3.5

=0.0=0.1 =0.3

=0.2EXP: SIM:

��

��

To further explore the discrepancy in thermal diffusivity between experiments and simulations in the linear ohmic regime, we have investigated the impact of

• ExB shear suppression• trapped electron mode• collisionality• finite-β• high-k turbulence

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��

The simulated χ i can be reduced to the experimental level by further reducing a/LTi and/or adding E×B shear, but by doing so the simulated χe is further reduced below the experimental level.

(b) Ion Thermal Diffusivity

Exp.

Lev

el

=0.0

=0.4=0.2

e[m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5(a) Electron Thermal Diffusivity

ExB Shear Rate [Cs/a]0.0 0.1 0.30.2

Exp.

Lev

elExB Shear Rate [Cs/a]

0.0 0.1 0.30.2

=0.0

=0.4=0.2

i[m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5Electron Thermal Diffusivity Ion Thermal Diffusivity

( )sim

1i i

i i

T Ta aT r T r

eæ ö¶ ¶÷ç ÷ = -ç ÷ç ÷ç ¶ ¶è ø


��

�� e

[m2 /s

ec]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

a/Lne @ r/a=0.630.5 1.0 2.01.5 2.5 3.0

Base x2 x3

=0.0

=0.4=0.2

Exp.

Lev

el(a)

i[m

2 /sec

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

a/Lne @ r/a=0.630.5 1.0 2.01.5 2.5 3.0

Base x2 x3

=0.0

=0.4=0.2

Exp.

Lev

el

(b) Electron Thermal Diffusivity Ion Thermal Diffusivity

Significant transport contribution from the TEM turbulence is not likely for the measured temperature and density profiles.

( )sim

1i i

i i

T Ta aT r T r

eæ ö¶ ¶÷ç ÷ = -ç ÷ç ÷ç ¶ ¶è ø


• The simulated χe can only be raised to the experimental level after increasing a/Lne by a factor of two where the TEM turbulence becomes significant.

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��Nonlinear flux-tube simulations show that the impact of varying νei on turbulent transport is very weak.

2.320.480.102.670.560.052.970.670.01

χi [m2/sec]χe [m2/sec]νei/(cs/a)

• νei/(cs/a)=0.05 corresponds to the experimental measurement.

• The other plasma parameters are taken from r/a=0.63 at the lowest density plasma with . 20 30.34 10 men

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��

GYRO shows that the contribution from the electromagnetic fluctuations are negligible in the low-β C-Mod Plasmas.

2.6730.5770.14%2.6710.5640.07%2.6700.5600.00%

χi [m2/sec]χe [m2/sec]β

• β=0.07% corresponds to the experimental measurement.

• Electromagnetic fluctuations contribute less than 3% of the total simulated electron thermal transport even after doubling the experimental measured β.

• The other plasma parameters are taken from r/a=0.63 at the lowest density plasma with . 20 30.34 10 men

��

��

• After adding E×B shear suppression and/or reducing ▽Ti, to match χ i, the electron transport from high-k turbulence is not significantly affected.

• Measurements to date by PCI indicate very low levels of high-k turbulence, falling into the background noise level.

20 3Linear ohmic 0.35 10en m-= ´

At the lowest density, inclusion of high-k turbulence in the ETG range kθρs=2-8 accounts for less than 5% of total simulated electron transport; it is not known if including even higher values of kθρs would significantly change this result.

Electron Energy Diffusion

frac

tion

cont

ribut

ion

per m

ode

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8kθρs

x20

Contribution from kθρs<1 : 95.2%kθρs>1 : 4.8%kθρs>2 : 3.1%

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��

Ohmic Drift Velocity

One piece of physics that is omitted in gyrokinetic codes is the potential importance of electron drift velocity:

eju

ne

��

��

•(Goldston, PPCF, 1984)

The electron drift velocity is up to 6 times the ion acoustic speed in the linear ohmic regime.

• A correlation exists between the energy confinement timeand the ohmic drift velocity.

τ Ε[m

sec]

20

30

40

50

1 2 3 4 5 6 7

5.2 T; 0.8 MA: 5.2 T; 0.6 MA:5.2 T; 0.4 MA:

ue||/cs

q95ne [1020m-3]0 1 2 3 4 5 6

5.2 T; 0.8 MA: 5.2 T; 0.6 MA:5.2 T; 0.4 MA:

1

2

3

4

5

6

7

u e||/c

sτ Ε

[mse

c]

20

30

40

50

0 1 2 3 4 5 6

5.2 T; 0.8 MA: 5.2 T; 0.6 MA:5.2 T; 0.4 MA:

q95ne [1020m-3]

2 0.5E nqR a

��

��

The electron thermal diffusivity from the TRANSP analysis shows a dependence on ue||/cs.

χ e[m

2 /sec

]

1 2 3 4 5 6 7ue||/cs

2.0

3.0

4.0

1.0

0.5

1.5

2.5

3.55.2 T; 0.8 MA: 5.2 T; 0.6 MA:5.2 T; 0.4 MA:

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��Summary• The key role played by the ITG turbulence in the saturated ohmic and H-mode

plasmas has been verified.-Propagation of turbulence is found to be dominantly in the ion diamagnetic direction. -Intensity of the ITG turbulence increases with density, in agreement between simulation and experiments. -The absolute fluctuation intensity agrees with simulation within experimental error. -Simulated χeff, χe, and χi agree with experiments after varying a/LTi within 20%.

• At the low densities in the linear ohmic regime, where the electron transport dominates (χe >> χi), GYRO shows χi > χe .-TEM is unlikely to be important for the measured density and temperature profiles.-Inclusion of high-k (kθρs≤ 8) turbulence does not raise χe to the experimental level.-GYRO shows that the contributions from the electromagnetic fluctuations are negligible in the low-β C-Mod Plasmas.

• Electron drift velocity (ue||/cs≥1) associated with the ohmic toroidal plasma current may play an important role.

• Future GYRO and TGLF work will look into turbulent exchange (Waltz-Stabler, PoP, 2008) as another possible remedy.

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Appendix

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��

ITG ITG

Freq

: [kH

z]

ExpExp

-120

120

0

(a)

TEMTEM

Stable Stable

a/LTi

0 1 2 3 4

a/L T

e

0

1

2

3

4

5

Gro

wth

Rat

e: [1

03 sec-1

]

0

500

250

(b)

a/LTi

0 1 2 3 4a/

L Te

0

1

2

3

4

5

Stable Stable

Frequency Growth Rate

,

•The other plasma parameters are taken from r/a=0.63 at the lowest density plasma with . 20 30.34 10 men

Linear stability analysis in the a/LTi-a/LTe plane shows that ITG remains the most unstable mode even after varying a/LTi and a/LTe by 50%.

��

��

•Nonlinear flux-tube simulation shows , which is significantly below the experimental level .

•The other plasma parameters are taken from r/a=0.63 at the lowest density plasma with .

Gro

wth

Rat

e: [1

03 sec-1

]

0

500

250

(b)

ν ei/(

c s/a

)a/LTi

0 1 2 3 40.00

0.02

0.04

0.06

0.08

0.10

ITG ITG

TEMTEM

Freq

: [kH

z]

ν ei/(

c s/a

)

a/LTi

ExpExp

0 1 2 3 40.00

0.02

0.04

0.06

0.08

0.10

-120

120

0

(a)Frequency Growth Rate

20 30.34 10 men

x

sim 20.08 m / sece exp 21.5 0.5 m / sece

Linear stability analysis in the a/LTi-νei plane shows that ITG remains the most unstable mode even after varying a/LTi and νei by 50%.

comparison of experimental measurements and gyrokinetic turbulent … · 2011-04-20 · pci b i+...

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