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.

中文翻译：

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研究等离子体中X射线脉冲自聚焦过程的正反问题

摘要

提出并描述了解决正反问题的方法，以研究等离子体中平面X射线脉冲的自聚焦过程。数学模型在准流体力学近似中考虑了电子等离子体成分的动力学。该模型是一个非线性系统，包含四个二阶偏微分方程，并且要遵循相应的初始值和边界值条件。为了解决直接问题，构造了二阶保守差分方案，并开发了使用该方案进行计算的无迭代算法。为了解决在给定X射线脉冲自聚焦后的测量（或所需）特性后确定初始等离子体和脉冲参数的反问题，提出使用等价集方法来解决伪度量标准空间中的多目标问题。描述了一种应用该方法解决感兴趣的问题的算法。