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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
�������
���
• 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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���
-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+
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
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.
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���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.
20 3Saturated ohmic 0.93 10en m-= ´
r/a0.5 0.6 0.7
1.0
0.5
0.0
1.5
2.0
2.5n_n~
(%)ee
Flux-tubeSimulation
�������
���
Experimental PCI Synthetic PCI
Assuming vE×B~ 2 km/sec for the Doppler shift, the synthetic and experimental spectra are similar.
20 3Saturated ohmic 0.93 10en m-= ´
• 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
�������
���
20 3Saturated ohmic 0.93 10en m-= ´
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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���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
_
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���
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:
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���
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
• ε is the reduction factor of a/LTi :
�������
��� 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
• ε is the reduction factor of a/LTi :
• 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.
�������
���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
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���
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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���
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%.
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