7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Estimation of parameter profiles and their derivatives from arbitrary linear
observations by using Gaussian processes
T. Nishizawa1, S. Tokuda2, T. Kobayashi3, K. Tanaka3, H. Funaba3, I. Yamada3, Y. Takamura3, T.
Tokuzawa3, R. Yasuhara3, U. Uehara3, K. Ida3, H. Takahashi3, Y. Kawachi3, S. Inagaki4, S. Kado4, M.
Sasaki5, and A. Fujisawa1
1
Research Institute for Applied Mechanics, Kyushu University, 2 Research Institute for Information
Technology, 3 National Institute for Fusion Science, National Institutes of Natural Science,4
Institute of Advanced Energy, Kyoto University, 3 College of Industrial Technology, Nihon
Universitye-mail (speaker): t.nishizawa@riam.kyushu-u.ac.jp
Gaussian process regression (GPR) has been used atmajor magnetic confinement fusion experiments
including LHD[1], ASDEX-Upgrade[2], JET[3], andAlcator C-mod[4] to determine the spatial gradients ofplasma parameters, which play crucial roles in thetransport processes. Although largely successful inpractical use, finite spatial resolution of diagnostics isneglected in the standard GPR. In this contribution, weintroduce an alternative GPR, in which any linear
observation can be analyzed. This approach not only
considers the sampling volumes of local measurements
such as TS and CXS but also allows for the inversion ofinterferometer data within an identical framework.
We applied the alternative GPR to the electron density
profile measurements at LHD. Figure 1 shows theelectron density profiles and their derivates estimatedfrom TS and FIR data. The shaded regions represent thestandard deviations calculated from the diagonal
elements of the covariance matrices. Reasonableagreements between the two diagnostics are seen forboth the original electron density profile and its
derivative. While Fig. 1 looks encouraging, these results
are based on a single realization. If the analysis isrepeated for another set of data with different random
errors, the similarity between the probability
distributions is expected to differ. Therefore, we next
investigate the robustness of the profile measurements
based on FIR by using synthetic data sets. As an input
profile, we employ 𝜇!!" shown in Fig. 2(a). Then, wegenerate synthetic FIR data by adding random noise withthe relative amplitude of 3% to the noise free observation
given. We repeat this procedure and calculate theelectron density profiles and their derivatives 10,000
times for different realizations. The 16th, 50th, and 85th
percentiles of the profile distributions and the input
profiles are shown in Fig. 2. Over all spatial positions,the input profiles fall within the 16th and 84th
percentiles.
Since GPR estimates profiles through linear operations,computation can be sufficiently fast for real-time
applications. The findings in this work indicate that realtime monitoring of the density profile and its derivativeby using an interferometer may be possible. Since theconventional TS system will probably not be available in
a commercial fusion reactor due to the harsh radiation

environment, an interferometer-based density monitoring
may become a powerful tool to stably sustain a burning
plasma by feedback controls. In addition, the proposed
GPR is expected to find use in other scientific disciplines
where the derivatives of spatial or temporal profiles carry
important information.

Figure 1. (a) shows the TS data points and the probability
distributions of the electron density profile estimated fromTS and FIR. In (b), the probability distributions of thederivative of the electron density profiles are shown forboth diagnostics.

Figure 2. Percentiles of the density profile (a) and its
derivative (b) estimated from 10,000 sets of FIR synthetic
data. The red dashed lines represent the input profiles.
References[1] K. Fujii et al, Rev. Sci. Instrum. 88, 013508 (2017)[2] R. Fischer et al, Fusion Sci. Technol. 76(8), 879-893[3] A. Ho et al, Nucl. Fusion. 59, 056007 (2019)[4] M.A. Chilenski et al, Nucl. Fusion. 55, 023012(2015)