25aE14P
直線プラズマにおけるトモグラフィと Fourier-Bessel 展開を用いた構造解析
Structure analysis using tomography and Fourier-Bessel expansion in the linear plasma濵本直紀1, 藤澤彰英2,3, 永島芳彦2,3, 柴田遼介1, 福永史樹1, 江藤健太1, 稲垣滋2,3 , 糟谷直宏2,3, 山田琢磨3,4
小菅佑輔5, 佐々木真2,3, 伊藤早苗2,3, 伊藤公孝3,61
Naoki Hamamoto , Akihide Fujisawa2,3, Yoshihiko Nagashima2,3, Ryosuke Shibata1, Fumiki Fukunaga1, et al.
九大総理工1, 九大応力研2, 九大極限プラズマ研究連携セ3, 九大基幹教育院4, 九大高等研究院5, 核融合研6
IGSES Kyushu Univ.1, RIAM Kyushu Univ.2, RCPT Kyushu Univ.3, FAS Kyushu Univ.4,
IAS Kyushu Univ.5, NIFS6
Plasma turbulence is a system of micro-scale fluctuations
and meso- and macro-scale structures generated by themicro-scale fluctuations. Tomography is a method that canobserve the fluctuations and structures in every scale. We
have made a tomography system on a linear cylindricaldevice, named Plasma Assembly for Nonlinear Turbulence
Analysis (PANTA)[1], and have obtained local emission
profiles using a tomography algorithm, Maximum
Likelihood-Expectation Maximization (ML-EM). The
spatial structure of the ML-EM image can be analyzed using
Fourier-Bessel series. Here we present the obtained resultsof ML-EM image and the decomposition with
Fourier-Bessel series.
The experiments were performed in a cylindrical linear
magnetized plasma device, PANTA in Kyushu University.
The plasma has the diameter of 100 mm and axial length of
4000 mm. The magnetic field is 900 G and filling Ar
pressure is 1 mTorr. In this study, we observed ArI emission
with the wavelength around 810 nm. The device has four
detector arrays that are installed on the position of different
azimuthal angles with 45 degree interval. Each detector
array contains 33 fiber channels, thus, totally 132 channels
are prepared to obtain line-integrated emission of plasma.
The channels in an array are aligned with 5 mm interval toface the plasma radially. The range of observation is from L= -80 to 80 mm, where L means distance from the center
position of the detector array.
The ML-EM method is tomography algorithm to invert theline-integral data to local emission. The local emission
distribution is obtained as the values on 121(=11x11) grids
in the observation square (16 cm x16 cm) with the grid
width of ~1.45 cm. The reconstructed images are calculatedwith parallel computing using 120 cores in every 1 µs. The
image of ML-EM, ε(r,θ), is expanded with theFourier-Bessel series to decompose mode structure as

determined using Akaike Information Criterion (AIC),
which is defined as(2)
where M and N are the number of data and that of functions,
respectively, and χ is the residual error between theML-EM and vectorized image of the Fourier-Bessel fitting.
Figure 1 shows examples of images obtained with ML-EM
and Fourier-Bessel expansion. Based on the images, theinner products in descending order of the content arecalculated as shown in Figs.2 (a) and (b), together with thecorresponding AIC value and residual error χ2, respectively.
The AIC value takes a minimum at the optimized number N= 18 for this case.
Finally, we present the application result of theFourier-Bessel series expansion to an MLEM image with amethod to optimize the number and selection of the basefunctions. As a future work, the method should be applied
on temporal sequential data of ML-EM images to obtaintemporal behavior of spatial modes, e.g., excitation,annihilation, and competition between them.

Fig.1(a) Reconstructed image of ML-EM, (b)vectorized
image of Fourier-Bessel expansion. (c) Image is fitted
Fourier-Bessel function when the AIC has a minimum
value.

(a)ε (r, θ ) = ∑∑[amn cos mθ + bmn sin mθ ]J m (kn , r) (1)nselected for kn L to be the n-th zero point of the m-th order
Bessel function. In the real situation, the number of fitting
functions is limited, therefore, the number or thecombination of the fitting functions should be optimized.
For the purpose, we utilize orthonormal property ofFourier-Bessel function system. The content of a
Fourier-Bessel function can be evaluated by the innerproduction between an ML-EM image vector and avectorized Fourier-Bessel function. After the inner products
are calculated, the least square fitting is carried out withvarying the number of the fitting functions in descendingorder. The optimized number of the fitting function isAIC(b)２χ6003002001005000400

10203040２J m (kn , r) is the Bessel function. kn is700

χ [a.u.]square fitting, andAIC [a.u.]mwhere the coefficients amn and bmn are found by least050

NFig.2(a) Inner products between image of ML-EMand Fourier-Bessel series (b) AIC and residual error ε2[1] S.Oldenbürger, et al., Plasma Phys. Control. Fusion 54055002 (2012)[2] Y. Nagayama, J. Appl. Phys. 62, 2702 (1987)