An Investigation of Topological Structures in Radiation Profiles and on

Impurity Confinement by Laser Ablation

B. Zurro, A. Baciero, K. J. McCarthy, M. A. Ochando, F. Medina, T. Estrada, A. López-Fraguas, A. López-Sánchez, J.

Vega and TJ-II Team

Laboratorio Nacional de Fusión, CIEMAT, Asociación EURATOM/CIEMAT, 28040 Madrid, Spain

Motivation

The scope of our research on transport using spectroscopic techniques covers:

- Impurity injection experiments to search for non-exponential decays that are characterized by stretched exponentials, A0 exp (-(t/)).

- Investigation of topological structures in radiation profiles and their correlation with confinement .

- Study of non-thermal velocities via Doppler spectroscopy of heavy ions injected by laser ablation.

Non-Exponential Relaxation and Transport

<x2(t)> ~ 2 D t

second moment of the Gaussian [hallmark of Brownian motion, =1] distribution that governs the probability of being at site x at time t

subdiffusion superdiffusion

(0 1 2

normal diffusion ballistic diffusion

Typical Raw Data

Plot of the most relevant traces for the impurity injection experiment.

Temporal evolution of two Fe XVI lines as recorded by a CCD mounted on a normal incidence VUV spectrometer.

0

1

2

3

4

5

1050 1100 1150 1200 1250 1300

shot_008363

t(ms)

n

e

bol

phos

RX

C V

T

ECE

laser

0

250

500

750

1000

0 10 20 30 40

Fe XVI 36.06 nm

Fe XVI 33.53 nm

I(a.u.)

t(ms)

Effect of Strong Injection

0

1

2

3

4

5

6

1050 1100 1150 1200 1250

shot_007168.qda

signals(a.u.)

t(ms)

T

ECE

(0)

phos

n

e

C V

rx 0

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1

r_07168_1141_1143

r_07168_1155_1157

r_07168_1157_1159

r_07168_1161_1163

r_07168_1165_1167

r_07168_1167_1169

r_07168_1173_1175

r_07168_1179_1181

r_07168_1189_1191

n

e

(10

19

m

-3

)

ρ

Effect of strong Fe injection in TJ-II plasma monitors (lhs).

Temporal evolution of the density profile during Fe injection as observed by a reflectometer (rhs).

Impurity Confinement Time vs ne

Plot of the decay parameter versus line-averaged electron density for a series of TJ-II discharges having different magnetic configurations (lhs).

Plot of the beta parameter versus density for 32_102_65 (rhs)

0

20

40

60

0.3 0.4 0.5 0.6 0.7 0.8 0.9

100_28_59

32_102_65

( )ms

n

e

(10

19

m

-3

)

0.5

1

1.5

2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

ne(10 19 m-3 )

Ne Scan at [(bar(0) = 1.375, bar(a) = 1.458)]

Plot of and parameters versus ne for a single magnetic configuration (lhs).

Comparison of from relaxation in ne and rad (top right) and (bottom right) .

0

5

10

15

20

25

0.5

1

1.5

0.35 0.4 0.45 0.5 0.55 0.6

( ρ =0) (ρ =0)

( )ms

n

e

(10

19

m

-3

)

0

10

20

30

40

0.35 0.4 0.45 0.5 0.55 0.6

(100_28_59)

Δne

(bolo ρ=0)

( )ms

ne(10

19m

-3)

0

0.5

1

1.5

2

0.35 0.4 0.45 0.5 0.55 0.6

(100_28_59)

Δne

( .)Rad bol ρ=0

ne(10 19 m-3 )

Density scan (100_44_63)

Plots of parameters versus ne from:

1 from radiation -avg / local- (lhs)2 from central signals after

tomographic reconstruction (rhs)0

2

4

6

8

10

12

14

0

0.5

1

1.5

2

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

bol-8363

( )ms

ρ

0

0.5

1

1.5

2

2.5

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

betarad-avg-betabolo(0)-local-betabolo(0)-local-

ne(10 19 m-3 )

100_44_63100_28_59

0

10

20

30

40

0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

100_44_63

rad-chord-avgbolo(0) -local-

( )ms

ne(10 19 m-3 )

VUV / X-RAY Linear Camera

Torioidal mirror

Plasma

Quartz window

Phosphor screen

Quartz window

Optic system

Photodiode array

Filterwheel

0

200

400

600

800

1000

0 200 400 600 800 1000

counts

pixel

5 m m Be

10m m Be

0

0.2

0.4

0.6

0.8

1

100 1000 104

5 mm10mm25mm

( )Photon energy eV

1 m

CAMERA

Baciero, Zurro, McCarthy et al. Rev. Sci. I. 73, 287(2002)

Position of flattenings/humps

0

100

200

300

400

0 10 20 30 40

t1,t

2,t

3

t2

feature order

This plot was calculated from the data from 4 discharges belonging to the same TJ-II configuration.

Open red circles correspond to features from profiles at 3 different times while blue ones correspond to time t2.

Good symmetry is observed in the location of features.

Simulation of feature position

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

abs(xmax)

pixel

feature order

1.52

1.54

1.56

1.58

1.6

0.2

0.4

0.6

0.8

1

1.2

0.0 0.2 0.4 0.6 0.8 1.0

/2 π

relative strength

/2π

relative strength

reff

Simulation of chord-averaged effects on the feature algorithm, including the influence of islands on local radiation profiles at positions defined by the iota profile (rhs) and with its estimated theoretical widths.

Comparison simulation-experiment

0

100

200

300

400

0 10 20 30 40

t1, t

2, t

3

t2

pixel

feature order

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

abs(xmax)

pixel

feature order

A comparison of feature positions obtained from simulation (lhs) and experimental (rhs) profiles when using the same algorithm to recover such features (Baciero, Zurro, McCarthy et al. EPS 2002).

Correlation topological structures-confinement

The relevance of these topological structures, as characterised by two parameters (up and sum), is plotted versus density together with the energy content of the plasmas, as quantified by the robust product ne Te.

Density scan in ECRH plasmas

0

10

20

30

40

0

0.2

0.4

0.6

0.8

0.2 0.4 0.6 0.8 1

x10-2 upx10-3 sum

neT

e

ne

ConclusionsCONFINEMENT BY IMPURITY INJECTION

•Impurity confinement time () rises dramatically above a certain density.

•Non-exponential relaxation is observed in impurity injection experiments with the beta parameter of the stretched exponential ranging from ~ 0.5 to 2.

•Electron and ion confinement seems to exhibit some difference as a function of density (a more detailed analysis is needed).

TOPOLOGICAL STRUCTURES

•We have shown that low level signals in radiation profiles can be associated with structures in plasmas: symmetry and coincidence with rational surfaces position.

•When we quantify features in profiles, we have note some relationship with plasma energy.

APPARENT TEMPERATURE OF HEAVY IONS

•Mass dependence of the apparent impurity temperature validate the role played by non-thermal velocities (astrophysical model).

•Its dependence with density will allow its correlation with confinement to be studied.

References

IMPURITY INJECTION

1Seguin, F.H. and Petrasso R., Phys. Rev. Lett. 51, 455 (1983)2Fussmann G., Report IPP III/105 (1985)3Leung, W. K. et al., Plasma Phys. Control. Fusion 28, 1753 (1986)4Horton L. D. et al., Nucl. Fusion 32, 481 (1992)5Zurro B. et al., Proc. 1998 ICPP & 25th CCFPP, Praha 1670-1673 (1998).6Zurro B.et al., Plasma Phys. Control. Fusion 30, 1767 (1988)7Navarro A.P., M A Ochando and Weller A.W., IEEE Transactions on Plasma Science, 19, 569 (1991)8 Ochando M. A. et al., 12th IAEA Stellarator Workshop, Madison (1999)

TOPOLOGICAL STRUCTURES9Baciero A., Zurro B., McCarthy K.J. et al., Rev. Sci. Instrum. 73, 283 (2002).10Arsenault H.H. and P. Marmet, Rev. Sci. Instrum. 48, 512 (1977)11Baciero A., Zurro B., McCarthy K.J. et al. Plasma Phys. Control. Fusion (2001)12Zurro B., McCarthy K.J. et al., Europhys. Lett. 40, 269 (1997)

NON-THERMAL VELOCITIES13McCarthy et al. EPS (2002)14Zurro et al. Phys. Rev. Lett. 69, 2919 (1992)

TJ-II Stellarator

CURRENT TJ-II PARAMETERS

R = 1.5 m

<a> ≤ 0.22 m

Bo = 1.2 T

Pecrh ≤ 2 300 kW

tpulse ≤ 300 ms

ne(0)ech ≤ 1.7 19 m-3

Te(0)ech ≤ 2 keV

Neutral Beam Injectors

Ion mass

Injected energy

Energy mix ratio

Pulse length

Ho

40 keV

80:10:10

≤300 msec.

INJECTION PARAMETERS

BEAM 1(Counter)BEAM 4

(Co)

TF-1

HC

Beam Exit

TJ-II Experimental Set-up

ECH(QTL2)

2mmInterferometer

Normal-incidencevacuum

Spectrometer

NORTH

LaserBlow-Off

Multi-channelNeutral Particle Analysers

ThomsnonScattering

Non-thermal Velocities. Motivation

- Doppler spectroscopy of emission lines is one of the most powerful ways to measure ion temperatures. It is assumed that ions at the same location and time have the same kinetic temperature. So by measuring it for one, the correct ion temperature is found. However superimposed micro- and macro-turbulence could affect this and result in line-widths that do not fit the general interpretation framework.

- An obvious test is to measure the Doppler temperatures of several ions of different masses that are well localised in a hot plasma and that have sufficient residence time so as to be well thermalised. In this way, thermal and non-thermal contributions can be separated and the linear mass dependence claimed by the model can be checked.

Non-thermal velocities. Background

- In astrophys., the theory of non-thermal velocities is used to account for excess broadening of spectral emission lines. The spectral line shape is taken as a convolution of a thermal Gaussian distribution and a turbulent one.

- ΔFWHM) = 1.665(/c)(2kTi/mi + NT2)1/2

where NT2 = 2kT(Tz - Ti)/mi and Tz = Ti + (mi / mp) TT

- NT2

is the dispersion of the isotropic micro-turbulence velocity distribution, Ti and TT are the ion temperature and the temperature associated with the micro-turbulence, mi and mp are the ion and proton mass.

Impurity Lines

0

500

1000

1500

2000

2500

3000

3500

4000

33 34 35 36 37 38

Intensity (arb. units)

Wavelength (nm)

Fe XVI

Fe XVI

Fe XIII

Si XI

Si X

Si X

B IVSi IX

Fe XIV

Before Injection

After Injection

400

800

1200

1600

2000

162 163 164 165 166 167 168 169

Intensity (arb. units)

Wavelength (nm)

O VII

O VII & He II

C IAr III

Ar IIIAr III

B II

- Spectrum about 36 nm before and after iron injection (lhs).

- Spectrum about 165 nm of O VII lines (rhs).

- All spectral lines used are emitted by ions in plasma centre.

Line Profile Fitting

0 100

4 103

8 103

1.2 104

1.6 104

2 104

2.4 104

2.8 104

33.5 33.52 33.54 33.56 33.58 33.6

Intensity (arb. units)

Wavelength (nm)

FWHMZ = 0.01309 ± 0.00012 nm

FWHMinstrm

= 0.01146 ± 0.00011 nm

mi = 55.85

=33.54nmT

z=333.8±71eV

Fe XVI

200

400

600

800

1000

1200

163.6 163.7 163.8 163.9 164 164.1 164.2

Intensity (arb. units)

Wavelength (nm)

O VII

He II & O VII

FWHMZ = 0.0762 +/- .0017 nm

FWHMinstm

= 0.0653 +/- .0015 nm

mi = 16

=163.83nmT

Z=154.5+/-32eV

- Fe XVI line at 33.54 nm (lhs) & O VII line at 163.8 nm (rhs).

- Lines are isolated and can be well fitted by Gaussian profile.

- After deconvolution of line width with instrument function excess broadening is observed.

Apparent Ion Temp. vs. Ion Mass

0

100

200

300

400

0 10 20 30 40 50 60 70

Tz

, Apparent Ion Temp. (eV)

Ion Mass (a.m.u.)

-Fe XVI-Fe XIII-Fe XVI

- Si XI

- O VII

Tz = 79.82 + 5.023 m

i

- Proton

0

100

200

300

400

500

600

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tz, Apparent Ion Temp. (eV)

Central Electron Density, (1019

m-3

)

Emiting Ion Fe XVI

-The proton temperature profile is flat, Ti ~65 ± 10 eV.

-The mass dependence of the apparent impurity temp. validates the role played by non-thermal velocities (astrophys. model).

-Its dependence with density will allow its correlation with confinement to be studied.

TJ-II Experimental Set-up

ECH(QTL2)

2mmInterferometer

Normal-incidencevacuum

Spectrometer

NORTH

LaserBlow-Off

Multi-channelNeutral Particle Analysers

ThomsnonScattering

Iron Injection

0

500

1000

1500

2000

2500

3000

3500

4000

33 34 35 36 37 38

Intensity (arb. units)

Wavelength (nm)

Fe XVI

Fe XVI

Fe XIII

Si XI

Si X

Si X

B IVSi IX

Fe XIV

Before Injection

After Injection

Oxygen VII Lines

400

800

1200

1600

2000

162 163 164 165 166 167 168 169

Intensity (arb. units)

Wavelength (nm)

O VII

O VII & He II

C IAr III

Ar IIIAr III

B II

Fe XVI Line Profile Fitting

0 100

4 103

8 103

1.2 104

1.6 104

2 104

2.4 104

2.8 104

33.5 33.52 33.54 33.56 33.58 33.6

Intensity (arb. units)

Wavelength (nm)

FWHMZ = 0.01309 ± 0.00012 nm

FWHMinstrm

= 0.01146 ± 0.00011 nm

mi = 55.85

=33.54nmT

z=333.8±71eV

Fe XVI

OVII Line Profile Fitting

200

400

600

800

1000

1200

163.6 163.7 163.8 163.9 164 164.1 164.2

Intensity (arb. units)

Wavelength (nm)

O VII

He II & O VII

FWHMZ = 0.0762 +/- .0017 nm

FWHMinstm

= 0.0653 +/- .0015 nm

mi = 16

=163.83nmT

Z=154.5+/-32eV

Proton Temperature Profile

0

20

40

60

80

100

-1 -0.5 0 0.5 1

Proton Temperature (eV)

Effective radius, ρ

Apparent Ion Temp. vs. Ion Mass

0

100

200

300

400

0 10 20 30 40 50 60 70

Tz

, Apparent Ion Temp. (eV)

Ion Mass (a.m.u.)

-Fe XVI-Fe XIII-Fe XVI

- Si XI

- O VII

Tz = 79.82 + 5.023 m

i

- Proton

Density Scan

0

100

200

300

400

500

600

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tz, Apparent Ion Temp. (eV)

Central Electron Density, (1019

m-3

)

Emiting Ion Fe XVI