Direct and Inverse Problems of Investigating the Process of Self-Focusing of X-Ray Pulses in Plasma

• Published in: Computational mathematics and mathematical physics Vol. 60; no. 2; pp. 327 - 340
• Main Author: Khachaturov, R. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.02.2020; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Electron plasma; Inverse problems; Iterative methods; Mathematical models; Mathematics; Mathematics and Statistics; Metric space; Multiple objective analysis; Nonlinear systems; Partial differential equations; Plasma; mathematical modeling; self-focusing; equivalence set method; inverse problems
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542520020086

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.