B.J. Peterson

H. Hosoda

K. Abe

K. Mukai

M. Kobayashi

M. Teranishi

N. Iwama

R. Sano

National Institute for Fusion Science (NIFS-Repository)

  It is important to measure electron temperature turbulence in plasma for controlling turbulence induced transport. We have been developing and improving a correlation ECE radiometer (cECE), however, we have not had any evidences of successful measurement of turbulence. The measurement of the turbulence by the ECE is difficult, because, in principle, amplitude of the ECE contains noise which amplitude is proportional to the electron temperature. The small amplitude turbulence is easily masked by the larger noise component. So, cross-correlation analysis is applied between multi-channel data which measurement points are separated radially in plasma. To detect a turbulence signal with smaller amplitude, longer analysis time window and/or wider detectable IF frequency band are necessary. However, applicably of longer analysis window and wider IF band depend on temporal and spatial scale of target turbulence. Fig. 1 shows a block diagram of the cECE radiometer that we have developed. This radiometer utilizes first IF (2-26GHz) of the existent radiometer signal (RADH-L). The developed radiometer divides the IF signal into 4ch signals, and detects the amplitude of the signal with bandwidth of 50MHz at the selected frequency.   5$'+/VW,)*+]FK0+]%:5DGLRPHWHU$'&RQYHUWHU([LVWHQW5DGLRPHWHU*+]    Fig. 1 A block diagram of 4ch cECE radiometer and a picture of the installed cECE radiometer system.  We have applied this cECE system to LHD plasma during 17th cycle experiment. Up to the present experiment, only noise has been measured by means of the cECE signals. However, signals taken by the LADH-L sometimes contain detectable amplitude of the electron temperature fluctuation, which is analyzed by the auto-correlation method, not by the cross-correlation. The LADH-L system has higher signal amplitude and better S/N ratio than the cECE system, because, IF bandwidth is 20 times wider than that of cECE. Utilization of the 4-way power-divider and the frequency-converter in the cECE system also degrades S/N ratio. Nevertheless the cECE system cannot detect this fluctuation by the cross-correlation method, we consider that the cECE signal also contains a fluctuation originated signal detected by the RADH-L. Figure 2 shows a cross-correlation result between the cECE and the RADH-L signals. We can find fluctuations around 4s and 5kHz. So, we have estimated the S/N ratio numerically as the following experiment. We add a monotonically sinusoidal signal to the raw data taken by the RADH-L. Here, amplitude of the added signal is adjusted to become equal to amplitude of the fluctuation , which is analyzed by the auto-correlation analysis. The S/N ratio of the RADH-L is estimated to be 2/5 by comparing amplitude of the added signal and the raw signal. Then, we analyze the cECE and the RADH-L signals by the cross-correlation analysis. Here, artificial sinusoidal signal is added to both signals. Amplitude of added signal to the RADH-L data is same to the fluctuation level. While, amplitude of the added signal to the cECE raw data is adjusted so both the cross-spectral density of the added signal and the fluctuation as to become same spectral density. We have estimated the S/N ratio of the cECE to be 1/70 by comparing amplitude of the added signal to the cECE signal and the raw data. This estimation seems to be consistent with estimation of the S/N ratio by means of components specifications utilized in the cECE system and RADH-L S/N ratio of 2/5. 7LPH>V@)UHTXHQF\>N+]@ Fig. 2 Cross-spectral density between cECE and RADH-L data.   Further improvements need for our cECE system to detect turbulence, which amplitude is considered to be at least one tenth as low as the detected fluctuation level. We consider the cECE system needs dedicated receiver system with a large aperture antenna.          The arrangement of software for image reconstruction is in progress in order to realize the 3D tomography of radiation from LHD.  Using the observation ports 6.5-U, 6.5-L, 6-T and 10-O, the system of four imaging bolometers was carefully improved in sightline positioning design [1] and installed on LHD for the 17th cycle of experiments.  Assuming the toroidal periodicity and symmetry of the plasma, one half period of toroidal angle 18° was taken as the region of interest.      Numerical simulations were carried out on the improved layout of the four-camera system.  With the geometry of the layout and on the basis of the physics of radiation detection, the projection matrix H that relates the unknown 3D plasma image f to its projection g in camera system was theoretically calculated with the aid of the CAD software.  The 3D radiation distributions obtained with the EMC3-EIRENE code of impurity behavior were used as phantoms.  By omitting the non-radiation voxels from image reconstruction, the size of the matrix H was decreased to 2,528x13,161 so that the singular value decomposition could be accomplished with a personal computer. Figs. 1 and 2 show the result of applying the Tikhonov (unit matrix) regularization to the under-determined linear equation Hf=g.  Changing the value of the regularization parameter γ lead to the changes of the reconstructed image fˆ and its projection Hfˆ as in Fig. 1.  Uniform random numbers, whose upper limit of interval was 10% of the mean of the true projection values, were added to produce the data vector g, and the Lagrange function to be minimized was defined as Λ(f) = γ ||f||2+||Hf−g||2/M with M=2,528.  While the mean of the squared residuals ε2 monotonically decreased with γ, the generalized cross validation GCV was minimized and well reflected the minimum of the reconstruction error δ2.  The value of ε =2.17x10−6 at the minimum of GCV was much smaller than the root mean square 5.08x10−5 of the added random numbers.  If we had taken the Morozov condition, we would have got a smoothed reconstruction similar to (C) in Fig. 1.  This result shows the validity of computation and reconfirms the usefulness of GCV [2, 3] for the tomography in which the angular loss of projection data is very large.  The condition number of the matrix H was evaluated as 7.71x1034 using the software IDL. For a better regularization according to the non-negativity constraint, additional study has been made to build fast iterative algorithms. Finally, we obtained the first result of image reconstruction from experimental data of LHD.                    Fig. 1. Result of a numerical simulation: (left) a 3D phantom fo and its projection Hfo, which are displayed in one poloidal section and in the 6.5-L port camera, respectively; (right) reconstructed images fˆ and their projections  Hfˆ displayed in the same section and camera for γ    values of  (A) 4.0x10−16, (B) 1.9x10−13  (min. GCV), and (C) 2.7x10−9.                Fig. 2. Changes of GCV, ε2 and δ2 with the regularization parameter γ  ; while ε2 changed monotonically with γ , both GCV and δ2 were minimized for the same discrete value of γ  =1.9x10−13 in this case.  The research was supported by the budget NIFS13KLEH032.  1) Sano, R. et al.: Plasma Fusion Res. 8 (2013) 2402138. 2) Iwama, N. , Hosoda, Y. et al.: Bulletin of the Daido   Inst. of Tech. 41 (2005) 105. 3) Iwama, N. et al.: J. Plasma Fusion Res. SERIES 8 (2009) 691. 191§17. Numerical Simulation of 3D Image Reconstruction of LHD Plasma with IR Imaging Video BolometersIwama, N. (Center of Novel Science Initiatives, NINS),  Teranishi, M. (Hiroshima Inst. of Tech.),  Hosoda, H. (Univ. Fukui),  Abe, K. (Gifu Shotoku Gakuen Univ.),  Sano, R., Peterson, B.J., Kobayashi, M., Mukai, K.

Numerical Simulation of 3D Image Reconstruction of LHD Plasma with IR Imaging Video Bolometers

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Numerical Simulation of 3D Image Reconstruction of LHD Plasma with IR Imaging Video Bolometers

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