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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
2
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
3
• 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
4
• 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
5
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
6
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
7
• 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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
-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
16
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 !
17
• 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
18
• 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
19
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
20
• 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
21
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
22
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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