36th EPS Conference on Plasma Phys. Sofia, June 29 - July 3, 2009 ECA Vol.33E, P-2.155 (2009)

Deconvolution of JET CORE LIDAR Data and Pedestal Detection in Retrieved Electron Temperature and Density Profiles D.Stoyanova,c, T.Dreischuha,c, L.Gurdeva,c, M.Beurskensb,d, O.Fordb,d, J.Flanaganb,d, M.Kempenaarsb,d, I.Balboab,d, M.Walshb,d and JET EFDA Contributors* a

Institute of Electronics, Bulg.Acad.Sci.72 Tzarigradsko Shosse, 1784 Sofia, Bulgaria b

JET -EFDA Culham Science Centre OX14 3DB, Abingdon, UK

c

EURATOM-INRNE Fusion Association, 72 Tzarigradsko Shosse, 1784 Sofia, Bulgaria d

EURATOM-UKAEA Fusion Association, Culham Science centre, Abingdon, UK *

See appendix of F. Romanelli, IAEA, Geneva, Switzerland, 2008

The high-confinement mode (H-mode) is considered as one of the most promising regimes of operation of the thermonuclear reactors. The H-mode is characterized by the formation of an edge pedestal region in which steep gradients in the density and temperature are observed as a result of formation of a particle and energy transport barrier near the plasma edge. The Lidar Thomson scattering diagnostic [1] (Fig.1) has been successfully used for reliable and robust measurement of the electron temperature Te and density ne profiles on JET. The resolution of 12-15 cm is however practically insufficient for resolving the narrow pedestal area.

Deconvolution techniques [2, 3] can be used to improve the achievable spatial resolution with the existing core Lidar system. As an inverse problem the deconvolution is noise sensitive and requires

careful

analysis

of

each

processing step [4]. Here we present the first results on deconvolution of JET core

Lidar data and their comparison with untreated data. The deconvolution is applied to the raw JET Lidar profiles

Lout p (r ) , p = 1..6 is the spectral channel number, and r is a LOS coordinate. The Fig.1

output lidar profiles are given by:

36th EPS 2009; D.Stoyanov et al. : Deconvolution of JET CORE LIDAR data and Pedestal Detection in Retriev...

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~ p inp p Lout RTSp (r ) = R ADC (r ) ⊗ Rdetp (r ) ⊗ Rlas (r ) p (r ) = RTS (r ) ⊗ L p (r ) + W p (r ) ,

(1)

where "⊗" denotes convolution; RTSp (r ) is the total instrument function for the p-th channel, p expressed in (1) by a convolution of the partial instrument functions of the ADCs R ADC (r ) , p the photon detectors Rdet (r ) and the laser pulse shape Rlas (r ) ; Linpp (r ) are the input lidar

~ profiles at δ − type total instrument function; W p (r ) are noises. The main differences in

retrieved convolved & deconvolved electron temperature and density profiles can be expected in the pedestal area as it follows from (1). The deconvolved profiles inside the torus will tend to the convolved profiles in the area of their low spatial variations. Thus, the deconvolution of JET data can be estimated as a good approach to analyze the plasma parameters in the pedestal area or in other areas with steep gradients inside the torus. The total instrument function RTSp (r ) is extracted by a computer model, based on the p expressions in (1) and some well known models for the partial functions R ADC (r ) , Rdetp (r ) and

Rlas (r ) . Then, tuning precisely the parameters of partial instrument functions during the deconvolution process and controlling the quality of deconvolved profiles, one could find the ~ best estimate of RTSp (r ) providing the tolerable quality of deconvolved profiles (Fig.2a). The success of such approach can be explained by the low number of samples per FWHM as well as by the smoothness of the Fourier spectrum within the entire spectral range without any zero ~ spectral components (Fig.2b). The FWHM of RTSp (r ) providing the tolerable performance is ~ 13.6 cm. This value corresponds to the estimates of the JET core Lidar resolution. 1,0

amplitude

0,8

detector response

0,6

ADC response

0,4

total ref.function

0,2

0,0 75

Fig.2a

80

85

90

time in steps 250ps

95

spectral amplitude

1

laser shape

Power spectrum of ref. function

0,1 0,01

FNyq=2GHz

1E-3 1E-4 1E-5 0

50

Fig.2b

100

150

200

250

300

frequency

Examples of 6-channels untreated and deconvolved lidar profiles for the JET pulse #73337, laser shot #77, are shown in Figs.3a and 3b, respectively. As seen, the deconvolved profiles are slightly noisier than the untreated ones as can be expected. They are steeper in the pedestal area (marked on both the figures) as a result of deconvolution.

36th EPS 2009; D.Stoyanov et al. : Deconvolution of JET CORE LIDAR data and Pedestal Detection in Retriev...

400

73337 shot 77

350 300 250 200 150 100

JET Convolved Ch-1 Ch-2 Ch-3 Ch-4 Ch-5 Ch-6

50 0 20

40

60

80

time in ADC sampling steps 250ps

Fig.3a

Amplitude (ADC discretes)

Amplitude (ADC discretes)

400

73337 shot 77

350

3 of 4

JET Deconvolved

Ch-1 Ch-2 Ch-3 Ch-4 Ch-5 Ch-6

300 250 200 150 100 50 0

100

20

Fig.3b

40

60

80

100

time in ADC steps 250ps

The Te and ne retrieval algorithms are based on the dependence of the mass center of the relativistic Doppler spectrum on the electron temperature and the calibration parameters of the JET Lidar. In the simulations, we found this approach as less affected by the uncertainties in the determination of the plasma light and the spectral channel sensitivities. The electron density is calculated using the electron temperature profile, measured lidar signals and the full relativistic Doppler spectrum. The plot in Fig.4a displays the mean electron temperature profiles extracted from convolved & deconvolved profiles averaged over 25 laser shots within a stationary state period of the H-mode of the pulse #73337. As is seen, the Te profile, retrieved from deconvolved profiles provides better determination of the pedestal area with respect to the untreated profiles. Inside the torus both profiles are overlapped. The pedestal width is of the order of one ADC discrete (3.75 cm) as can be expected. The retrieval of the pedestal area in electron density profiles is given in Fig.4b. The profiles of standard deviation in retrieving Te and ne profiles before and after deconvolution are shown in Fig.5a,b. Here we also displayed the Te and ne profiles, but averaged over 25 single temperature and density profiles, retrieved from each of the single laser shots. The standard deviation of Te profiles (Fig.5a) is below 250 eV inside the torus. It is increased up to 750 eV within the pedestal mainly due to noises, as SNR is lower just in this area. The fluctuations of averaged Te profiles are of the order of 50 eV for the both convolved and deconvolved profiles. The standard deviations for ne profiles (Fig.5b) have a similar behavior as in Fig.5a. Here the fluctuations (~0.12 of the maximum) are not increased within the pedestal area as for the profile of Te. The next Fig.6 displays the retrieved history of deconvolved ne profiles for the entire JET pulse, containing 117 laser shots. The creation of the H-mode is well seen. In conclusion, we demonstrated a successful deconvolution of JET core Lidar data and retrieving the electron temperature and density profiles of improved resolution. We evaluated the standard deviations of retrieved electron temperature and density profiles. As a result of

36th EPS 2009; D.Stoyanov et al. : Deconvolution of JET CORE LIDAR data and Pedestal Detection in Retriev...

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20

4,0

1,0x10

73337 mean 70-95

3,5

73337 mean 70-95 19

8,0x10

Ne [m ]

2,5

-3

Te [KeV]

3,0

r/a~0.5

2,0

deconvolved

19

6,0x10

r/a~0.5 19

4,0x10

1,5

Deconvolved

1,0

laser beam

0,5

JET convolved

0,0 0

10

20

30

40

JET convolved

19

2,0x10

laser beam

0,0 50

0

60

Fig.4a

10

20

30

40

distance in steps 3.75cm

distance in steps 3.75cm r/a~1.0

50

60

r/a~1.0

Fig.4b

deconvolution the pedestal area can be detected and the pedestal parameters can be estimated. The resultant improvement of resolution is about 3 times. As mentioned above, the JET core Lidar system is very successful and a workhorse for the JET operations. However, the technology employed is quite old. This extends particularly to the detectors and the data acquisitions systems. A recent upgrade to the Edge Lidar system [5] has shown that this technology can be deployed very successfully. The basic spatial resolution has been enhanced by more than a factor of 2 and the sampling rate has been increased up to 20GS/s from 4GS/s. With a hardware upgrade of detectors, digitizers and improved optics, and combined with a deconvolution, the spatial resolution of JET core Lidar can be brought down to 1 cm; similar to the best performing JET diagnostics. 20

1,0x10

3,0

73337 shots 70-95

deconvolved 19

8,0x10

deconvolved

73337 shots 70-95

2,0 -3

Ne [m ]

Te[KeV]

2,5

1,5 1,0

convolved

StDev (deconvolved)

laser beam

StDev (convolved)

0,5

convolved

19

6,0x10

StDev (deconvolved)

19

4,0x10

StDev (convolved)

laser beam

19

2,0x10

0,0

0,0

0

2

r/a=0.8

4

6

8

10

12

14

16

0

2

4

6

8

10

12

14

16

r/a=0.8 distance in steps 3.75cm r/a=1.0

distance in steps 3.75cm r/a=1.0

Fig.5b b

Fig.5a

H-mode Fig.6

range

Shot number

References: [1] H.Salzmann, et al., Rev. Sci. Instrum. 59, 1451 (1988); [2] L.Gurdev, et al., D.Stoyanov, JOSA A 10, No.11, pp.2296-2306 (1993); [3] L.Gurdev, et al., Proc. of SPIE 7027, 702711 (2008); [4] O.Ford et al., 36th EPS Conference on Plasma Physics, Sofia, Bulgaria, 29th June 2009; [5] M.Kempenaars et al., Rev. Sci. Instrum. 79, 10E728 (2008)