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Article information
2020 , Volume 25, ą 1, p.5-38
Bazhenov A.N., Zatylkin P.A.
Small angle reconstruction of plasma luminosity for spherical tokamak
The problems of reconstruction of plasma luminosity are important for physics and technology of power plants-tokamaks. The Globus-M research tokamak obtained a large amount of data using a matrix detector in pinhole camera geometry. From the mathematical point of view, finding the luminosity for different regions of the plasma volume according to the matrix detector is an inverse problem related to the field of integral geometry. An essential feature of the particular task is the use of a single fixed camera with a small viewing angle. In this regard, application of methods of harmonic analysis of data is not enough. The paper investigates the geometric aspects of the problem. In the general view, a threedimensional object is projected onto a two-dimensional plane through a diaphragm. Under the assumption of azimuthal symmetry, there is a central projection of the luminosity of the body of rotation onto a flat matrix detector. The initial information for the calculation is the plasma boundary obtained from magnetic sensors. There is no reliable information about the internal structure of the plasma, so its division into regions of the equal luminosity is not unambiguous. The paper presents an algorithm for finding the projections of the luminosity of plasma volumes on the plane of the matrix detector. A set of model direct problems for the construction of algorithms for their recognition according to the detector data was investigated. Images of supposed macroscopic structures and microscopic inclusions were obtained. The methodological basis of the work is the use of interval analysis methods for solving geometric and algebraic problems. This approach allows obtaining qualitative and quantitative results that takes into account the uncertainty of the input data with the minimum amount of computational costs. Algebraic solvability is investigated in the interval formulation using response functionality. Solutions for a set of test problems are obtained, which demonstrate the availability of successful reconstruction for real data. An important result of the study is an information about the presence of uncertainties in geometric data and related calculations by obtaining results about the luminosity of the plasma by solving linear programming problems.
[full text]
Keywords: interval system of linear algebraic equations, tolerance set, measure of variability, recognizing functional, linear programming
doi: 10.25743/ICT.2020.25.1.002
Author(s):
Bazhenov Alexander Nikolaevich
PhD. , Associate Professor
Position: Senior Research Scientist
Office: Federal state budgetary institution of science A.F. Ioffe Physical-Technical Institute, SPBPU Peter the Great
Address: 194021, Russia, St-Petersburg, Polytechnic str., 29
E-mail: a_bazhenov@inbox.ru
Zatylkin Pavel Alexandrovich
Position: assistant
Office: SPBPU Peter the Great
Address: 194021, Russia, St-Petersburg, Polytechnic str., 29
E-mail: a_bazhenov@inbox.ru
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Bibliography link:
Bazhenov A.N., Zatylkin P.A. Small angle reconstruction of plasma luminosity for spherical tokamak // Computational technologies. 2020. V. 25. ą 1. P. 5-38
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