Naofumi Iwama

Phillips–Tikhonov regularization of plasma image reconstruction with the generalized cross validation

The use of the Phillips–Tikhonov regularization is proposed for numerically stabilizing the ill‐conditioned plasma image reconstructions. An objective function to be minimized leads to a linear estimator of the image intensity distribution and, with the aid of the singular value decomposition, makes it possible to use the generalized cross validation for optimizing a regularization parameter. An excellent behavior of the estimator with computational facility is obtained on the Hα emission computerized tomography of a toroidal plasma.

Estimation of wave‐number spectrum parameters from fixed probe‐pair data

Spectrum parameter estimation concerning a stationary and homogeneous random field is examined in terms of quantities obtainable from a pair of fixed probes. The estimators of the mean wave number and the wave‐number spectral width are derived by relating wave‐number spectral moments to spatial derivatives of the complex covariance of the field, the effect of finite probe size being taken into account. The estimate biases associated with the probe separation can be greatly reduced by employing an algorithm based on the polar‐form representation of the complex covariance, while the variances of the estimates have a tendency to be enhanced with the decrease of the probe separation. An optimum range of the probe separation is theoretically determined.

Least‐squares autoregressive (maximum entropy) spectral estimation for Fourier spectroscopy and its application to the electron cyclotron emission from plasma

A new procedure for the maximum entropy spectral estimation is studied for the purpose of data processing in Fourier transform spectroscopy. The fitting of the autoregressive model to the interferogram is examined under a least‐squares criterion based on the Yule‐Walker equations. A practical criterion is suggested for selecting the model order. The principal advantage of the new procedure lies in the enhanced frequency resolution, particularly for small values of the maximum optical path difference of the interferogram. The usefulness of the procedure is ascertained by some numerical simulations and further by experiments with respect to a highly coherent submillimeter wave and the electron cyclotron emission from a stellarator plasma.

A correlation method for estimating wave‐number spectrum moments of fluctuations

The covariance function of a stationary and homogeneous random field, represented by an analytic signal, is related to its wave‐number spectrum moments. By using a pair of fixed probes with an appropriately small separation, one can estimate the mean wave number and the wave‐number spectral spread. This method may be useful for the experimental study of fluctuation phenomena in plasmas, fluids, etc.

Maximum Entropy Estimation of Electron Cyclotron Emission Spectra from Incomplete Interferograms in ELMy H-mode Tokamak Experiment

To measure the electron temperature profile of tokamak plasma in a high confinement mode with edge localized mode (ELMy H-mode), a method of data analysis is presented on the fast-scanning Fourier transform spectrometer (FTS), and results in the JT-60U tokamak are described. In the ELMy H-mode, where the FTS interferogram of electron cyclotron emission (ECE) becomes incomplete due to nonthermal emission pulses of ELM, the spectrum of ECE is estimated by using the maximum entropy method (MEM) of nonparametric type. The optimization of the regularization parameter is studied in terms of adopting the generalized cross validation (GCV) from the linear regularization of Tikhonov–Phillips. A study is also performed on a method to remove the nonthermal emission pulses from interferogram data before the MEM analysis, and on an extension of minimum cross entropy in order to meet with the missing of interferogram values in the region of zero path difference. From the application to experimental data of many shots, it is found that the electron temperature profiles can be automatically measured using the FTS during the ELMy H-mode operation of the tokamak.

Three‐dimensional reconstruction of the ion velocity distribution function of plasma with a retarding‐grid analyzer

A study of computerized tomography is made for the purpose of reconstructing the ion velocity distribution function of plasma in the three‐dimensional velocity space. A conventional type of ion energy analyzer with retarding grids is rotated in a plasma in order to acquire the data to be processed. Experimental results are presented on an argon plasma with a low‐energy ion beam, which is generated in a double‐plasma machine.

Feasibility of Electron Density Measurement Using Relativistic Downshift Frequency Effect of Electron Cyclotron Emission in Tokamak Plasmas

The feasibility of electron density measurement using the relativistic downshift frequency effect of electron cyclotron emission in tokamak plasmas has been studied by numerical calculation. It is found that electron density measurement can be performed by observing the frequency shift from the nonrelativistic electron cyclotron frequency. The frequency shift is large when the observation is carried out from the high-field-side of torus. As this large frequency shift depends mainly on electron temperature and density, electron density can be determined while electron temperature is obtained from the observation of the low-field-side.

Singular Value Decomposition Analysis of Multichannel Electron Cyclotron Emission Signals of Tokamak Plasma

Singular value decomposition (SVD) was applied to multichannel signals obtained by an electron cyclotron emission diagnostic system in the JT-60U tokamak. As a result, on grating polychromator signals, the equilibrium and perturbative terms of electron temperature profile were successfully separated, and the structure of a magnetic island produced by the tearing mode was revealed. By neglecting the components of small singular values, the noise component of the signals was removed to improve the signal-to-noise ratio while conserving well the pulse-like waveforms. The usefulness of the SVD-based spectral analysis is shown by a typical set of signal waveforms.

Plasma image reconstruction by visible light computed tomography.

Visible light computed tomography is quite attractive as one of diagnostic techniques for edge plasma. In this paper, a special CT scanner designed for plasma experiments is developed. Using two types of algorithm, the spline function method (SFM) and the algebraic reconstruction technique (ART), experiments on plasma image reconstruction are performed for a visible emission distribution in a neon discharge tube and Hα emission distribution of tokamak plasma. An effective method to avoid light reflection at the vacuum wall is employed. Two reconstruction methods, ART and SFM, are compared with eath other on their characteristics, advantages and disadvantages, from the view points of simulation and experiment. The effects of data missing on image reconstruction, which is a common problem for all plasma CT algorithms, are also discussed.

Tomographic Approach Using an Electrostatic Analyzer for the Measurement of the Three-Dimensional Ion Velocity Distribution of Plasma

The measurement of the ion velocity distribution in full three-dimensional velocity space is studied with a planar retarding-grid rotating analyzer immersed in plasma. In spite of the plane geometry of the analyzer, the current-voltage measurement in different directions can provide useful information for the three-dimensional measurement with the aid of numerical techniques of computerized tomography. The practical usefulness of this method as a diagnostic tool is shown experimentally for a weakly ionized collisionless argon plasma into which a low-energy ion beam is injected uniformly. Discussions are made with emphasis on the optimization of measurement by compromising the contradiction between the spatial resolution and the statistical accuracy.