Abstract
Methods for solving direct and inverse problems for investigating the process of self-focusing of plane X-ray pulses in plasma are proposed and described. The mathematical model takes into account the dynamics of the electron plasma component in quasi-hydrodynamic approximation; this model is a nonlinear system of four second-order partial differential equations subject to corresponding initial and boundary value conditions. To solve the direct problem, a second-order conservative difference scheme is constructed and an iteration-free algorithm for the computations using this scheme is developed. For solving the inverse problem of determining the initial plasma and pulse parameters given the measured (or desired) characteristics of the X-ray pulse after its self-focusing, it is proposed to use the method of equivalence set designed for solving multiobjective problems in a pseudo-metric space of criteria. An algorithm for applying this method for solving the problem of interest is described.
Similar content being viewed by others
REFERENCES
R. C. Elton, X-ray Lasers (Academic, New York, 1990).
S. A. Akhmanov, “Superstrong light fields in nonlinear optics, plasma physics, and technology of X-ray sources,” Itogi Nauki Tekh., Ser.: Sovr. Problemy Lazern. Optiki (VINITI, Moscow, 1991), Vol. 4, pp. 15–18.
Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
A. V. Andreev and R. V. Khachaturov, “Self-focusing of pulsе X-ray radiation in plasma,” Vestn. Mos. Gos. Univ., Ser. Fiz. Astron. 36 (3), 25–33 (1995).
R. V. Khachaturov, “A computational method for investigating the process of self-focusing of X-ray radiation in plasma,” Zh. Vychisl. Mat. Mat. Fiz. 36, 103–111 (1996).
R. V. Khachaturov, “Direct and inverse problems of determining the parameters of multilayer nanostructures from the angular spectrum of the intensity of reflected X-rays,” Comput. Math. Math. Phys. 49, 1781–1788 (2009).
R. V. Khachaturov, “Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering,” Comput. Math. Math. Phys. 54, 984–993 (2014).
R. V. Khachaturov, “Multiobjective optimization in a pseudometric objective space as applied to a general model of business activities,” Comput. Math. Math. Phys. 56, 1580–1590 (2016).
R. V. Khachaturov, “Single- and multiobjective optimization on the lattice of cubes,” J. Comput. Syst. Sci. Int. 57, 750–758 (2018).
A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979; Winston, Washington, 1977).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by A. Klimontovich
Rights and permissions
About this article
Cite this article
Khachaturov, R.V. Direct and Inverse Problems of Investigating the Process of Self-Focusing of X-Ray Pulses in Plasma. Comput. Math. and Math. Phys. 60, 327–340 (2020). https://doi.org/10.1134/S0965542520020086
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542520020086