In many studies on the laser impinging on a plasma surface, an assumption is made that the reflection of a laser pulse propagating to a plasma surface takes place only at the turning point, at which the plasma density exceeds the critical one. A general reflection amplitude of light R from an arbitrary inhomogeneous medium can be obtained by solving a Riccati-type integral equation, which can be solved analytically in low-reflection conditions, i.e., |R|² ≪ 1. In this work, we derive an intuitive analytic solution for the reflection amplitude of light R from a plasma surface by integrating all possible reflection paths given by the Fresnel equation. In the low-reflection condition, reflection paths having only one reflection event can be used. By considering the higher-order reflection paths, our analytic expression can describe reflection in the high-reflection condition. We show the results of a one-dimensional particle-in-cell simulation to support our discussions. Since our model derived for static plasmas is well corroborated by the simulation results, it can be a useful tool for analyzing light reflection from dynamically varying plasmas.

中文翻译：

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静态无碰撞等离子体中光传播的路径积分公式及其在动态等离子体中的应用

在许多关于激光撞击等离子表面的研究中，假设传播到等离子表面的激光脉冲仅在等离子密度超过临界点的转折点处发生反射。可以通过求解Riccati型积分方程来获得来自任意非均匀介质的光R的一般反射幅度，该方程可以在低反射条件下解析地求解，即| r。R | ² «1.在这项工作中，我们推导出光的反射振幅的直观解析解ř通过积分由菲涅耳方程式给出的所有可能的反射路径来从等离子体表面反射。在低反射条件下，可以使用仅具有一个反射事件的反射路径。通过考虑高阶反射路径，我们的解析表达式可以描述高反射条件下的反射。我们显示一维单元内粒子模拟的结果以支持我们的讨论。由于我们的静态等离子体模型得到了模拟结果的充分证实，因此它可以用作分析动态变化等离子体的光反射的有用工具。