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.
Key words:inverse problems, equivalence set method, mathematical modeling, self-focusing.
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