Abstract

An inverse problem with distributed parameters for the process of the self-focusing of cylindrical X-ray pulses in a plasma is considered, and a mathematical model of the studied process in a cylindrical coordinate system is described, taking into account the symmetry of the pulse relative to the direction of its propagation. A similar process in the case of plane pulses is compared, a computational method for solving the direct problem of interaction between the plasma and pulse for the given parameter values is presented, the second order of approximation and the asymptotic stability of the constructed difference scheme are proved. It is proposed to use the equivalence set method to solve the inverse problem of determining the initial parameters of the plasma and pulse from the shape of a cylindrical X-ray pulse passing through it and the dynamics of its maximum intensity. Using this problem as an example, an algorithm for using the equivalence set method to solve inverse problems is described.

中文翻译：

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脉冲技术分布式系统的反演问题

摘要

考虑了等离子体中圆柱X射线脉冲自聚焦过程的分布参数反问题，并描述了圆柱坐标系中所研究过程的数学模型，同时考虑了脉冲的对称性相对于其传播方向。比较了平面脉冲情况下的类似过程，提出了在给定参数值下求解等离子体与脉冲之间相互作用的直接问题的计算方法，所构造的差分格式的二阶近似和渐近稳定性为证实。提出使用等价集方法来解决从穿过等离子体和脉冲的圆柱形X射线脉冲的形状及其最大强度的动态确定等离子体和脉冲的初始参数的反问题。以此问题为例，描述了利用等价集法求解反问题的算法。