observation of strong inward heat transport in tore supra with off-axis ecrh

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


TORE SUPRA


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

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TORE SUPRA


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.

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TORE SUPRA


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)

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TORE SUPRA


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

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TORE SUPRA


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 :

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TORE SUPRA


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)

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TORE SUPRA


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

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TORE SUPRA


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)

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TORE SUPRA


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.

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TORE SUPRA


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

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TORE SUPRA


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

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TORE SUPRA


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

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TORE SUPRA


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


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

)


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


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

)


Good agreement for all harmonics using pinch model.

15


TORE SUPRA


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)

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TORE SUPRA


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


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


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


TORE SUPRA


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


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.

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TORE SUPRA


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


TORE SUPRA


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,

20


TORE SUPRA


21


TORE SUPRA


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:

observation of strong inward heat transport in tore supra with off-axis ecrh

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