R&D Status of KSTAR Soft X-ray Tomographic Array Diagnostic System

Transcription

1 R&D Status of KSTAR Soft X-ray Tomographic Array Diagnostic System Seung Hun Lee, Junghee Kim, and W. Choe Department of Physics KAIST (Korea Advanced Institute of Science and Technology) JA-KO Joint Workshop on RF Heating and Current Drive in Fusion Plasmas NFRI, Daejeon, Korea 1

2 Outline Various tomography algorithm for tokamak plasmas Soft X-ray array system for KSTAR plasma tomography and its application Fabrication of X-ray detector array system for KSTAR and calibration of each detector element. 2

3 Introduction to the tomography Tomography : A non-invasive imaging tool for observing the inner structure of the plasmas Acquiring soft x-ray x signal (f(l) f(l)) from many lines of sight Solving inverse problem (ill-posed problem) : f ( L) = g( x, y) dl L Coordinate system for defining tomography system Reconstruction of 2-D 2 D local emissivity (g(x,( y)) y 3

4 Overview of suitable tomography methods Tomography problem : a matrix equation with the geometrical weight matrix and the measured values Ill-posed noisy problem inversion requires regularization Various regularization approaches : e.g. whether to use statistical or physical information - Truncated Singular Value Decomposition (TSVD) may be adequate in cases that do not require a priori information. - Alternatively, objective functionals describe a desirable property for the expected emission profile. minimum norm : Phillips-Tikhonov Maximum entropy multi-order smoothness 4

5 Fast maximum entropy method Unbiased reconstruction and higher accuracy of the tomographic calculation than conventional ME Maximum entropy method (ME) : Adjacent pixel values are not correlated. Modified fast ME method : Simple vector calculations and the correlation between adjacent pixels are provided. Pre-tomography process (SVD) provides the correlation to the image pixels Flat model Directly inverted model -1 f = K g g = K f dimension of system matrix K = ( total detector # total pixel # ) K = U S V (SVD) decomposed into invertible matrices T ur ur pg ( f, σ, I) = 1 Λ MaxEnt = αs χ, χ = 2 ur ur ur pp( gip ) l( f g, σ, I) ur p( f I) e N S = g m g i= 1 i i i N M f 2 2 k W i 1 k, ig = i g ln m i i k = 1 σ Maximizing posterior probability density function k 2 5

6 Phillips-Tikhonov method Laplacian of g We set J 2 2 γ L g + f W g M and minimize J by J g i = 0 regularization parameter error number of detectors Solution is ˆ( ) T T 1 T g γ = (W W+ L L) W f M γ To find out optimized Goodness γ M 1 M M 2 P( γ) = ρ jukjz j ρ jukj M k= 1 j= 1 j= 1 should be minimized by P( γ ) γ = 0 6

7 Minimum Fisher Information method M = U -1 T f i = signal from the i th detector g jτ = local emissivity of the j th pixel at the τ th time slice T = geometrical weight matrix B = gradient matrix λ = regularization parameter S = total number of time slices L = number of detectors M = transfer matrix U = functional matrix P = number of pixels w k = inverse of the k th image pixel σ i = standard deviation of the i th measurement Minimizing the functional matrix U Minimum Fisher Information method chi-square Fisher Information The regularization parameter is iterated until. 7

8 8 Coverage mapping 6 arrays 5 arrays 3 arrays 4 arrays VU1 VU2 HU VU2 HU VU2 HU 1 VU2 HU VD2 VD1 HD VD2 HM HD VD2 1 HD HD 6-array system : the best choice Spatial resolution = 1.5 ~ 2.5 cm Calculated coverage value (occupied area by the detectors / total area) 6-array : 0.57, 5-array : array : 0.42, 3-array : 0.3

9 Tomography test using KSTAR phantom Phantom P-T Modified MEM 70Х50 pixels, 192 detectors (6 arrays) Modified fast maximum entropy method fast and accurate, intershot analysis Phillips-Tikhonov method more accurate, post-shot analysis Method Conventional MEM Modified fast MEM Phillips-Tikhonov method Profile Mean Error 0% (%) Mean Error 2% (%) Single Hollow Single Hollow Single Hollow Reconstructi on Time (sec) 15 2 (0.3) 8 9

10 High-resolution tomography test Source Phantom Fast MEM Low Resolution High Resolution High-resolution (3500 pixels) tomography shows more reliable reconstruction result despite the increased ill-posedness. The calculation time of the three methods shows that all can be reliably utilized for tokamak plasmas. PTM is most accurate in both low and high resolution. Fast MEM was performed by parallel-computation. Methods MFI (TCV code) Fast MEM PTM Relative error / calculation time σ (%) Time (s) σ (%) Time (s) σ (%) Time (s) Low Resolution (0.09) High Resolution (0.19)

11 3-D D Tomography R z ( α) R y ( β ) Voxel Sight Cone R R z y cosα sinα 0 ( α) = sinα cosα cos β 0 sin β ( β ) = sin β 0 cos β o Euler angle : α = 38, β =± 9 o Z ϕ R f ( u, v) = g( x, y, z) dl L Vacuum vessel uv f = i th measurement on the detector (u-v) plane g = local emissivity in the (x, y, z) coordinates W = toroidal weight matrix based on (u-v) coordinates W uv Camera #1 Camera #2 g 11

12 Feasibility test of 3-D 3 D tomography Emission boundary (n=0) Toroidal Emissivity Phantom Emission boundary (n=1) Emission boundary (n=2) Region #3 Region #2 Region #1 Reconstructed Results (core region) n=0 n=1 n=2 Red region (< 0.6 a) : reconstruction region Mean error relative to the source phantom Left figure : reconstruction result for n=0 Middle figure : reconstruction result for n=1 Right figure : reconstruction result for n=2 These figures show the local 3-D structures including toroidal modes. Fine structures are not seen in these reconstructions. mode # Region # n = 0 n = 1 n = % 11.0 % 11.1 % % 13.0 % 13.0 % % 15.5 % 15.6 % 12

13 Application (MHD Mode identification) Identification of poloidal modes using SVD m=1 m=2 Identification of m/n using poloidal array combined with tangential 2-D array Tomogaphic Plane Tangential 2D array Ray-tracing with a rectangular 3-D weight matrix Tangential Tomography Relative Intensity Toroidal direction Toroidal mode (n = 1) from the emissivity along the red line 0.04 Simulatedline-integratedSXR intensityat the red line Integrated relative intensity

14 AXUV Photodiode array and preamplifier AMP-16 remote panel AXUV-16ELG array AXUV-16ELTS socket AXUV-20ELG array cm cm AMP-16 main circuit AMP-16 : In-vacuum preamplifier developed for KSTAR SXR array Modified version for separable preamp Transimpedance gain : 10 4 ~ 10 6 Bandwidth : ~ 600 khz (be able to observe the fast MHD activities) AXUV-20ELG array (high spatial resolution)

15 Hemispherical Be Window Viewing chord Aperture 50 μm Be window Detector Thickness : 50 μm for KSTAR T e range : 1 ~ 10 kev ( 1 ~ 0.1 nm, AXUV array) Teflon socket with preamp Lower cut-off energy of photons penetrating the Be window along chords is same. Only relative calibration among detector elements is required.

16 16 Aperture Magnetic axis θ Y X φ r a View # 1 r y a x a Aperture dω = Solid angle ~ signal strength Entrance Pupil 5 mm Aperture 1.5 mm 8.0 mm y d x d 2.0 mm Poloidal direction < View# 1 > Detector Aperture Cap Optimized size of the aperture for KSTAR SXR array system : 2D aperture x a = 0.2 mm y a = 4.9 mm r = 17 cm D aperture View # 2 < schematic view of the 3-D aperture > 5 mm 7.5 mm Toroidal direction <View# 2>

17 Thermo-electric electric cooling system Active area Si bulk layer TE cooler Metal package for heat transport Detector TE cooler Conduction rod Flange Heat sink Conduction rod for heat transfer between the detector and the heat sink Multi-stage TE coolers (TE-cooling system only) External temperature controller

18 Prototype SXR array Linear motion feedthrough AXUV-16HYB1 preamp Compact SXR array <Outside> <Inside>

19 Data Acquisition and Control Acquired data is transferred to the analysis PC. Embedded PXI controller or Ethernet PC analyze the data. Final results are represented by the tomographic imaging or the mathematically treated data. Detector temperature is monitored and controlled by the PXI module. Compact SXR array Signals are fed into the PXI modules from the SXR arrays. PXI modules are operated by the LabView or EPICS under Linux platform. Precise position is controlled by the multi-function PXI module.

20 20 Data flow and parallel computation Link between the tomography code and the KSTAR MDSplus data tree MATHEMATICA or MATLAB based Tomography code load data save data MDS tree (soft x-ray raw data) MDS analysis tree (tomographic analysis results) For reduction of the calculation time, we employed the parallel-computing toolkit in our MATHEMATICA TM or MATLAB based tomography code (Fast MEM code). The pixelized image plane can be divided into the several arbitrary domains. Fast ME-based computations over all domains can be done simultaneously. Parallel computation Computation speed by parallel computation with three computers (two Windows, one Linux) is almost ten times faster than the case of only one computer Real time analysis can be possible. Communication among the computers : MathLink and TCP/IP protocol with ssh connections

21 21 Calibration (1) Chord # G (W/V) Chord # G (W/V) <Relative calibration of the AXUV-16ELG array>

22 22 Calibration (2) HhL e fficiency HmAL Photo C urren t HhL e fficiency AXUV-16ELG V = 6 μ m L p = 100 μm HhL Photon EnergyHeVL fficiency e HmAL AXUV-16ELG V = 6 μ m L p = 100 μ m Photon EnergyHeVL Photo C urren t HmAL red : 0 orange : 20 green : 40 blue : Photon EnergyHeVL Photo C urren t AXUV-20HE V = 6 μ m L p = 450 μ m Photon EnergyHeVL AXUV-20HE V = 6 μ m L p = 450 μ m Photon EnergyHeVL red : 0 orange : 20 green : 40 blue : Photon EnergyHeVL

23 Summary Three kinds of tomography methods for toroidal plasma diagnostics were presented. The developed Modified MEM and the Phillips-Tikhonov tomography algorithms show faster and better noise handling capabilities (suitable for inter-shot and post-shot analyses). Soft x-ray array system will be a key diagnostic system for observing MHD phenomena in KSTAR. Radiation hardened AXUV photodiode array (32 ~ 40 channels per an array) In-vacuum preamplifier (High gain (~ 10 6 ), High band width (~ 600 khz)) Curved beryllium window is used for obtaining constant lower cut-off energy of the incident x-ray photon. Thermo-electric cooler is adopted instead of using water-cooling. Prototype array system was fabricated and tested. Relative calibration with the intrinsic properties of the AXUV photodiode detector elevates the accuracy of the calibration. 23