This chapter reviews multichannel broadband measurement of the soft-X-ray radiation and total radiation in magnetically confined fusion plasma experiments Common detector types used (including bolometers), details of their application, and interpretation of their measurements are described An introduction is given to the application of computed tomography methods in the mathematical reconstruction of emission profiles from multiple (approximately) line-integral measurements, taking into account the specific circumstances common in magnetically confined fusion plasma experiments Although the emphasis is on two-dimensional tomography of poloidal cross sections, the applications of Abel inversion, three-dimensional tomography, vector tomography, and other specific methods are briefly discussed Several examples of the application and the plasma parameters that can be derived are given

Chapter 7: Tomography Diagnostics: Bolometry and Soft-X-Ray Detection

SXR cross-sectional distributions measured in the European reversed field pinch (RFP) experiment RFX by means of a tomographic diagnostic are described. Various reconstruction techniques have been compared. A correction technique to minimize the systematic effect due to the non-identical thicknesses of the material filters has been developed. A number of experimental situations have been explored, and a study of the correlation between the MHD and SXR properties of the plasma has been made. The analysis concentrates both on standard discharges and on the recently discovered quasi-single-helicity states, whose signature is the growth of a sizeable m = 1 structure in the emissivity distributions. Detailed imaging of the plasma in these conditions is presented.

https://iopscience.iop.org/article/10.1088/0029-5515/41/6/304/pdf

Soft X ray tomographic imaging in the RFX reversed field pinch

Natural basis functions (NBF), also known as natural pixels in the literature, have been applied in tomographic reconstructions of soft x-ray (SXR) measurements in the JET (Joint European Torus) tokamak. The results are compared with those obtained with local basis functions (LBF), and those obtained with a conventional constrained-optimization tomography method. Truncated singular value decomposition is used as the inversion method. Reconstructions without a priori information, such as the NBF reconstructions, are, as can be expected, less good than reconstructions in which a priori information is used, as in the conventional method, but the reconstructions are shown to be reliable by means of phantom simulations. Reconstructions with the same number of LBFs as NBFs without a priori information are comparable to NBF reconstructions, although the latter seem to be somewhat better. No significant changes in results, apart from smaller reconstruction errors, are obtained if the measuring system has more regular or complete coverage than the JET SXR system. The various tomography methods are used to assess whether a newly observed in-out asymmetry in the SXR emission during the injection of nickel into an RF-heated plasma, with the peak on the inboard side, is real. A possible explanation for the asymmetry in emissivity is an increased nickel density on the inboard side as a result of an RF-induced increase of the hydrogen-minority density on the outboard side.

https://iopscience.iop.org/article/10.1088/0741-3335/42/2/308/pdf

Comparison of basis functions in soft x-ray tomography and observation of poloidal asymmetries in impurity density

The JET neutron profile monitor coverage of the neutron/gamma emissive region enables tomographic reconstruction. However, due to the availability of only two projection angles and to the coarse sampling, tomography is a highly limited data set problem. A comparative study concerning the applicability to JET tomography of four methods—maximum likelihood, maximum entropy, Tikhonov regularization and a Monte Carlo back-projection algorithm—is reported. The methods have been tested on numerically simulated phantoms with shapes characteristic for this kind of tomography. The retrieval of sophisticated structures in the emissive distribution has been addressed in order to have a complete image of the quality and reliability of the methods. A both qualitative and quantitative evaluation is reported.

A comparison of four reconstruction methods for JET neutron and gamma tomography

The soft X-ray (SXR) emission provides valuable insight into processes happening inside of high-temperature plasmas. A standard method for deriving the local emissivity profiles of the plasma from the line-of-sight integrals measured by pinhole cameras is the tomographic inversion. Such an inversion is challenging due to its ill-conditioned nature and because the reconstructed profiles depend not only on the quality of the measurements but also on the inversion algorithm used. This paper provides a detailed description of several tomography algorithms, which solve the inversion problem of Tikhonov regularization with linear computational complexity in the number of basis functions. The feasibility of combining these methods with the minimum Fisher information regularization is demonstrated, and various statistical methods for the optimal choice of the regularization parameter are investigated with emphasis on their reliability and robustness. Finally, the accuracy and the capability of the methods are demonstrated by reconstructions of experimental SXR profiles, featuring poloidal asymmetric impurity distributions as measured at the ASDEX Upgrade tokamak.

/pdf/optimized-tomography-methods-for-plasma-emissivity-34apzka2in.pdf

Optimized tomography methods for plasma emissivity reconstruction at the ASDEX Upgrade tokamak.

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.

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

A plasma-induced bi-polar arc and its plasma response were studied in a tokamak configuration, and a drastic change in the plasma potential near the arcing metal rod was found. Cylindrically concentric equi-potential surfaces are formed around the cathode spot, and a small change in the plasma potential observed at the plasma-wall interface breaks an ambipolarity there, forming a current channel across the toroidal plasma between the cathode spot and the vacuum chamber.

Plasma-Induced Arc and Its Plasma Response in a Toroidal Device

The effect of radio frequency electric field on the initiation of plasma induced bi-polar arc was studied with a titanium rod inserted inside a toroidal plasma. The superposition of relatively low frequency field on the voltage impulse made the arc initiation voltage lower than that without RF. On the contrary the superposition of relatively high frequency field made it higher than that. The physical mechanisms for explaining these apparently opposite results were proposed. The relation between the arcing and the impurity release in high power wave heating experiments was discussed.

Yun Shen

Papers

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

Plasma-Induced Arc and Its Plasma Response in a Toroidal Device

The effect of high-frequency electric field on a plasma induced arc.