UDC 532.59
INVERSE DIFFRACTION PROBLEM OF DETERMINING THE PROPERTIES
OF A PLASMA OBJECT
Abstract. We consider the ill-posed problem for a plasma inhomogeneity, which is diagnosed by the reflected diffraction field, i.e., backscattering from the irradiated object. In this case, there is no need for a more accurate restoration of the research object based on pseudo-inversion. An analytic solution of the inverse problem for a cylindrical plasma is constructed based on generalization of solutions for a spherical plasma. The possibilities of plasma diagnostics from measured values are shown.
Keywords: ill-posed problem, pseudoinversion, wave diffraction, backscattering, plasma diagnostics.
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REFERENCES
- Tikhonov A.N., Arsenin V.Ya. Methods for solving incorrect problems [in Russian]. Moscow: Nauka, 1974. 224 p.
- Sergienko I.V., Khimich A.N., Yakovlev M.F. Methods for obtaining reliable solutions to systems of linear algebraic equations. Cybernetics and Systems Analysis. 2011. Vol. 47, N 1. P. 62–73.
- Khimich A.N., Nikolaevskaya E.A. Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial data. Cybernetics and Systems Analysis. 2008. Vol. 44, N 6. P. 863–874.
- Kirichenko M.F., Krak Yu.V., Polishchuk A.A. Pseudoinverse and projective matrices in problems of synthesis of functional transformers. Cybernetics and Systems Analysis. 2004, Vol. 40, N 3. P. 407–419.
- Kryvonos Iu.G., Krak Iu.V., Barmak O.V., Shkilniuk D.V. Construction and identification of elements of sign communication. Cybernetics and Systems Analysis. 2013. Vol. 49, N 2. P. 163–172.
- Selezov I.T, Kryvonos Yu.G., Gandzha I.S. Some analytical and numerical methods in the theory of wave propagation and diffraction. In: Wave Propagation and Diffraction. Mathematical Methods and Applications. Springer, 2018. 237 p. https://doi.10.1007/978-981-10-4923-1.
- Gubarev V.F. Electromagnetic control of fast processes in toroidal plasma systems. Kibernetika i vychislitel'naya tekhnika. 1985. N 65. P. 140–151.
- Selezov I.T. To inverse problems of diagnosing plasma inhomogeneities. Distributed process control in continuous environments [in Russian]. Kiev: Institute of Cybernetics, Ukrainian Academy of Sciences, 1972. P. 22–48.
- Swiss Plasma Center — SPC. A cours suppoted by the European Fusion Educated Network, 2018.
- Kuznetsov E.I., Scheglov D.A. Diagnostic methods for high-temperature plasma [in Russian]. Moscow: Atomizdat, 1974. 161 p.
- Hutchinson I.H. Principles of plasma diagnostics. Cambridge University Press, 2005. 460 p.
- Rai V.N. Basic concept in plasma diagnostics. Bulletin of Laser and Spectroscopy Society of India. 2004. (13) 55. URL: https://arxiv.org/ftp/arxiv/papers/1407/1407.0461.pdf.
- Selezov I.T. Some models of coupled magneto elastic fields and their application to the investigation of propagation and diffraction of waves. J. Math. Sci. 2001. Vol. 104, N 5. P. 1490–1500.
- Ginzburg V.L. The propagation of electromagnetic waves in the plasma [in Russian]. Moscow: GIFML, 1960. 552 p.
- Selezov I.T. Simulation of wave and diffraction processes in continuous media [in Russian]. Kiev: Nauk. Dumka, 1989. 204 p.
- Jost R., Kohn W. Construction of a potential from a phase shift. Phys. Rev. 1952. Vol. 87, N 6. https://doi.10.1103/PhysRev 87.977.
- Prosser R.T. Formal solutions of inverse scattering problems. J. Math. Phys. 1969. Vol. 10, Iss. 10. https://doi.org/10.1063/1.1664766.
- Titchmarsh E. Introduction to the theory of Fourier integrals [Russian translation]. Moscow; Leningrad: HITTL, 1948. 416 p.