Modified Phillips–Tikhonov regularization for plasma tomography (original) (raw)

Phillips-Tikhonov regularization with a priori information for neutron emission tomographic reconstruction on Joint European Torus

Review of Scientific Instruments, 2015

A method of tomographic reconstruction of the neutron emissivity in the poloidal cross section of the Joint European Torus (JET, Culham, UK) tokamak was developed. Due to very limited data set (two projection angles, 19 lines of sight only) provided by the neutron emission profile monitor (KN3 neutron camera), the reconstruction is an ill-posed inverse problem. The aim of this work consists in making a contribution to the development of reliable plasma tomography reconstruction methods that could be routinely used at JET tokamak. The proposed method is based on Phillips-Tikhonov regularization and incorporates a priori knowledge of the shape of normalized neutron emissivity profile. For the purpose of the optimal selection of the regularization parameters, the shape of normalized neutron emissivity profile is approximated by the shape of normalized electron density profile measured by LIDAR or high resolution Thomson scattering JET diagnostics. In contrast with some previously developed methods of ill-posed plasma tomography reconstruction problem, the developed algorithms do not include any post-processing of the obtained solution and the physical constrains on the solution are imposed during the regularization process. The accuracy of the method is at first evaluated by several tests with synthetic data based on various plasma neutron emissivity models (phantoms). Then, the method is applied to the neutron emissivity reconstruction for JET D plasma discharge #85100. It is demonstrated that this method shows good performance and reliability and it can be routinely used for plasma neutron emissivity reconstruction on JET. [

Into the Fast Tomographic Postprocessing in Tokamaks

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2017

The collaboration of authors led to implementing advanced and fast systems for diagnostics of plasma content in tokamaks. During the development of systems it is planned to add new functionalities, in particular, the algorithms of tomographic reconstruction to obtain information on three dimensional distribution of plasma impurities. In the article the idea of tomographic reconstruction is introduced and issues of performance and adequate hardware selection are presented.

Tomographic Measurements of Plasma Temperature Fields

Beiträge aus der Plasmaphysik, 1984

The paper presents a mathematical description of tomographic algorithms for experimental data reduction. In a numerical experiment, problems of selection of optimum parameters of a measuring system to attain a prescribed accuracy of the emission coefficient reconstruction were investigated.

Singular Value Decomposition Combined With Analytical Method for Tokamak Plasma Tomography

2010

Several arrays of soft X-ray detectors are used with the Fourier expansion for angular direction and Zernicke polynomial on radial direction during an analytical method tomography. A truncation of two expansions is necessary. We used singular value decomposition in order to solve the set of equations. This technique reconstructs better images of tomography.

Current Research into Applications of Tomography for Fusion Diagnostics

Journal of Fusion Energy, 2018

Retrieving spatial distribution of plasma emissivity from line integrated measurements on tokamaks presents a challenging task due to ill-posedness of the tomography problem and limited number of the lines of sight. Modern methods of plasma tomography therefore implement a-priori information as well as constraints, in particular some form of penalisation of complexity. In this contribution, the current tomography methods under development (Tikhonov regularisation, Bayesian methods and neural networks) are briefly explained taking into account their potential for integration into the fusion reactor diagnostics. In particular, current development of the Minimum Fisher Regularisation method is exemplified with respect to real-time reconstruction capability, combination with spectral unfolding and other prospective tasks.

Diffuse reflection model and noise stabilization for tangential image tomographic reconstruction (TITR) code

Nuclear Fusion, 2009

A tomographic reconstruction code had been reported by us for inferring the poloidal emissivity of tokamak plasma from tangentially acquired images. Here we present modifications to the code that account for any diffuse reflections from the surfaces of walls enclosing the plasma. It is generally recognized that such reconstruction codes are highly susceptible to noise in the data. In this work we have analyzed the sensitivity to noise for varying degrees of over-determinism in the set of equations; Over-determinism is defined as the ratio of the number of detector signals available to the grid resolution of reconstruction. A tractable scheme for dividing the poloidal cross section into finite number of unknown sub-tori and voids, while still keeping the over-determinism high, is incorporated. Finally it is shown that noise level >20 percent can be handled with over-determinism achievable from present day detector array/cameras. The Singular Value Decomposition (SVD) of the matrix, as used here, can be expected to converge even if any ill conditioned matrix is encountered due to computational round off errors in the estimation of chord lengths through sub-tori and voids.

Modern regularisation techniques in data analysis for space plasma observations

Advances in Space Research, 2006

This paper is aimed to summarize the main philosophy of the Regularisation technique for inverse problems in space plasma observations. This unified approach is based around a general criterion for the Regularisation parameter selection. This approach was tested on various space plasma observation problems. It is demonstrated that for these problems a deviation is necessary from the traditional Least Squares Method in favour of the Regularisation technique. Particular problems were considered in more details in other publications by the authors. However, this paper is a first attempt to emphasize mathematical peculiarities of the Regularisation approach in space plasma observations in a general manner in order to provide a useful and versatile schema for the wide range of space plasma problems.

Design of multi-range tomographic system for transport studies in tokamak plasmas

Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment, 2010

The integrated spectroscopic system for visible plasma radiation, soft X-ray, and bolometric measurements has been designed for the COMPASS tokamak. This diagnostic allows tomographic reconstruction at a few microseconds time base and features an improved spatial resolution about 1 cm in the pedestal region, where the highest gradient of plasma pressure drives turbulent structures and their propagation towards the wall. In combination with other developed diagnostics on COMPASS, it represents an ideal tool for a measurement and characterization of these radiating plasma structures, which are responsible for an extremely high particle/energy transport across magnetic field. The design of the new integrated multi-channel spectroscopic diagnostics is reviewed and corresponding technical challenges are described. Additionally, the methods, which will be used for data processing, are briefly mentioned and target physics is discussed.