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1
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Observation of Strong Inward Heat Transport In Tore Supra
with Off-Axis ECRH
S.D. Song, X.L. ZOU, G. Giruzzi
CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France
2
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Electron thermal transport: one of the key issues in plasma controlled fusionEmpirically divided into two parts:
- Diffusion: proportional to the temperature gradient.
- Convection: proportional to the temperature.
Heat pinch in tokamaks : a controversy. Actual pinch or ‘pseudo’ pinch?
How to separate the convection and the diffusion ?
Previous heat pinch experiments with ECRH:
DIII-D [T.C. Luce, 1992], RTP [P. Mantica 2000],
ASDEX-U [P. Mantica 2006], FTU [A. Jacchia 2002]
with different conclusions.
On Tore Supra?
Motivation
3
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Methodology (1/2)
Power balance method (no separation between diffusion and convection)
Temperature perturbation method (possible separation between diffusion and convection)
Modulation of the heat source
Transport coefficients are directly determined from the amplitude and phase of the harmonics of the Fourier transform of the temperature perturbation.
In slab geometry, we have:
ECRH modulation
Localized and pure electron heating.
4
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Previous ECRH modulation experiments Frequency ranging from 30Hz to 300Hz
Tore Supra ECRH modulation experiments Low frequency : 1Hz
Advantages of Low frequency > High amplitude (S/N);
> Many harmonics (1st to 11th);
> Less affected by sawteeth and other perturbations;
> More sensitive to the pinch.
Disadvatages> Transport coefficient varying along with the heat pulse
> Additional parameter: Damping time (losses)
Methodology (2/2)
5
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Experimental Layout
PlasmaD plasma; R=2.43m; a=0.7m; Ip=0.7MA; Bt=3.7T.
ECRH - Gyrotron frequency: 118GHz
- Injection angleGyrotron A1(high): Φtor=0° Φpol=-7.5°
Gyrotron A2(middle): Φtor=0° Φpol=0°
- Deposition: off-axis heating with ρdep~0.5, width~3cm
- Output Power: A1~300KW; A2~270KW
DiagnosticsECE (32 channels)Reflectometry
A1
A2
Ip
t
6
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Experimental Results
4 6 8 10 12 140
0.5
1
t (s)
PE
CR
H (M
W) 0
0.5
1
1.5
2
2.5
TS#40504
Te (
ke
V)
0
1
2
3
4
5
6
Te (
ke
V)
TS#43234
4 6 8 10 12 14 16 180
0.5
1
PE
CR
H (M
W)
t (s)
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
r/a
Te (
ke
V) TS#43234
OhmECRHn
e
0 0.2 0.4 0.6 0.8 10
1
2
3
4
r/a
Te (
ke
V)
TS#40504
OhmECRHn
e
1) High density: 2) Low density :
7
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
0 0.2 0.4 0.6 0.8 10
1
2
3
4
5
6
r/a
a/L
Te
TS40503
OhmicECRH
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
r/a
T
e (
ke
V)
shot 40503
t = 11 st = t
0 +28.6 ms
t = t0 +47.9 ms
t = t0 +69.1 ms
t = t0 +89.4 ms
t = t0 +157 ms
Experimental Results
1) High density 2) Low density
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
r/a
T
e (
ke
V)
shot 43234
t = 10 st = t
0 +16.6 ms
t = t0 +32.5 ms
t = t0 +49.1 ms
t = t0 +67.7 ms
t = t0 +140 ms
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
r/a
a/L
Te
TS43234
Ohmic (t=10s)
ECRH (t=10.15s)
8
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
r/a
R (
m)
TS 43234 Te Perturbation
9 9.05 9.1 9.15 9.2 9.25
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3-0.2
0
0.2
0.4
0.6
0.8
2D Image of Te
t (s)
R (
m)
TS40503 Te Perturbation
10 10.05 10.1 10.15 10.2 10.25 10.3
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3 -0.05
0
0.05
0.1
0.15
0.2
0.25
ECRH Deposition
1) High density 2) Low density
Strong inward heat transport
Magnetic AxisSawteeth Magnetic AxisSawteeth
ECRH Deposition
9
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Fourier Analysis
1) High density (40504)
0
0.05
0.1
0.15
0.2
A (
ke
v)
TS#40504
1.01Hz2.98Hz5.01Hz6.97Hz 9Hz 11Hz
0 0.2 0.4 0.6 0.8 10
0.5
1
1.5
2
r/a
(
rad
)
0
0.1
0.2
0.3
0.4
0.5
A (
ke
V)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
r/a
(
rad
)
2) Low density (43234)
10
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Density Effect
0.1
0.2
0.3
0.4
0.5TS#43234 Fundemantal Harmonic
A (
ke
V)
0 0.2 0.4 0.6-0.2
0
0.2
0.4
0.6
r (m)
(
rad
)
raw
processed
0 0.2 0.4 0.60
0.05
0.1
0.15
0.2TS#43234 Third Harmonic
A (
ke
V)
0 0.2 0.4 0.60
0.5
1
1.5
r (m)
(ra
d)
raw
processed
8 9 10 11 12 131.8
2
2.2
2.4
2.6
2.8
3
3.2
t (s)
Te
(ke
V)
Fourier Analysis Interval
= 0.38
8.5 9 9.5 10 10.5 11 11.5 12 12.50
0.5
1
1.5
2
TS#43234
t (s)
ne (
x10
19m
-3)
0.140.250.360.470.590.710.830.96
Fundamental harmonic is strongly affected, while higher ones are not affected.
11
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
The electron energy transport equation for plasma electrons with temperature Te and density ne can be written in the form
Simplified heat transport equation
Simulation with Heat Pinch
Diffusion Convection Damping Source
Diffusivity : Damping time : Convective velocity:
3/2kdb /1
V
12
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Derivative of the phase : very sensitive to the diffusivity, less sensitive to the pinch and the damping time. Amplitude : sensitive to the diffusivity, very sensitive to the pinch for low harmonics, and not sensitive to the pinch for high harmonics.
Sensitivity with and V
13
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Sensitivity with b (1/Damp)
Minimum of the phase : very sensitive to the damping time, less sensitive to the diffusivity and the pinch.
0 1 2 3 4 5 6 7 8 9 10 11 12 130
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
f (Hz)
m
in (r
ad)
=0.5m2/s V=0m/s
TS#40494
Minimum of the phase at 1st, 3rd, 5th, 7th, 9th and 11th harmonics
=0.01s=0.02s=0.05s=0.1s=0.2s=0.5s
14
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Pinch Model Simulation
0 0.5 1-5
0
5
10
15
e (m2/s)
Ve (m/s)
1/ (s-1)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.02
0.04
0.06
0.08
0.1
0.12
0.14
A (
keV
)
f = 3
fexp = 2.9992
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
r/a
(r
ad)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
r (m)
A (
keV
)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
2.5
3
r (m)
(
rad
)
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.1
0.2
0.3
0.4
0.5
r (m)
A (
ke
V)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
2.5
3
r (m)
(
rad
)
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
Good agreement for all harmonics using pinch model.
15
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
CGM model
CGM (Critical Gradient Model) (F. Imbeaux PPCF 2001,X. Garbet PPCF 2004) semi-empirical pure diffusive threshold stiffness
Effective pinch (or ‘pseudo’ pinch) can be derived for Te perturbation transport:
The key point here is whether the pinch observed in the experiments is effective pinch, e.g. CGM derived effective pinch, or a real one. Simulation with CGM have been done to simulate the experimental results.
Figure from (F. Imbeaux PPCF 2001)
16
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
CGM Simulation (1)
κ=3; λ=2; β=1; α=1.5
0 0.5 10
0.2
0.4
0.6
0.8
1
e (
m2/s
)
0 0.5 10
2
4
6
8
10
b (
/s)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.5
1
1.5
2
2.5
3
r (m)
(
rad
)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
r (m)
A (
keV
)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.005
0.01
0.015
0.02
0.025
A (
ke
V)
TS#43234 Eleventh Harmonic
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
1
2
3
4
5
r (m)
(
rad
)
When simulating the higher harmonic, the lower harmonic disagree.
17
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
CGM Simulation (2)
κ=3; λ=1; β=1; α=1.5;
0 0.5 10
1
2
3
4
5
6
0 (m2/s)
1/ (s-1)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
r (m)
A (
keV
)
TS#43234
1Hz 3Hz 5Hz 7Hz 9Hz11Hz
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
r (m)
(
rad
)
1Hz 3Hz 5Hz 7Hz 9Hz11Hz0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
A (
ke
v)
TS#43234
0 0.2 0.4 0.6 0.8 1-0.2
-0.1
0
0.1
0.2
r/a
(
rad
)
1Hz
When simulating the lower harmonic, the higher harmonic disagree.
18
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
0
5
10
15
20
25
Am
plit
ud
e (
A.U
.)
ECRH modulation, TS#40500, density modulation
2.7 2.8 2.9 3 3.1 3.2 3.30
0.5
1
1.5
2
R (m)
Ph
ase
(ra
d)
Particle Transport Barrier
ECRH (rdep=2.82 m)
D2=0.3 m2/s
V2=-1.2m/s
D1=0.03 m2/s
V1=0
pITB (r=2.85 m)
Particle tansport barrier driven by ECRH ?
Particle Source
19
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Conclusions
Strong inward heat transport phenomenon has been observed in off-axis ECRH modulation experiments in Tore supra for low density.
Simulation using pinch model shows a good agreement for all harmonics.
Simulation using CGM cannot fully interpret the experimental results. If higher harmonic agrees, lower ones disagree; and the same for the other way round.
Observation of a particle transport barrier located close to the ECRH deposition,
21
AssociationEuratom-CEA
TORE SUPRA
EAST, China 7th Jan 2010 X.L. Zou
Pinch Model Comparison
0 0.2 0.4 0.6 0.8 10
0.5
1
A (
ke
v)
1Hz3Hz5Hz7Hz9Hz11Hz
0 0.2 0.4 0.6 0.8 10
1
2
3
r/a
(ra
d)
t (s)
r/a
Te Perturbation Evolution
0.95 1 1.05 1.1 1.15 1.2 1.25
0
0.2
0.4
0.6
0.8
1 0
0.2
0.4
0.6
0.8
1
1.2
t (s)
r/a
Te Perturbation Evolution
0.95 1 1.05 1.1 1.15 1.2 1.25
0
0.2
0.4
0.6
0.8
1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 10
5
10
15
20
25
e (m2/s)
Ve (m/s)
1/ (s-1)
Withpinch:
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
A (
ke
v)
1Hz3Hz5Hz7Hz9Hz11Hz
0 0.2 0.4 0.6 0.8 10
1
2
3
r/a
(
rad
)
0 0.5 10
5
10
15
20
25
'pinch'
e (m2/s)
Ve (m/s)
1/ (s-1)
Without pinch:
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