The transient transmission of an electromagnetic wave through cold, unmagnetized and collisionless plasmas is described both analytically and numerically for its normal incidence from vacuum upon a plasma half-space. Exact formulas for the electromagnetic field are written in integral forms, which are convenient for approximate analysis and comparison with the results of direct numerical simulations. The time when the plasma particle oscillations become self-consistent with the electromagnetic field can be calculated from the simplified formulas for an arbitrary distance from the plasma–vacuum interface. Special attention is paid to the formation of the electrostatic oscillation in the case when the frequency of the incident wave is equal to the plasma frequency. The amplitudes of the vanishing magnetic field and the forming electrostatic oscillation are calculated as functions of time and the distance from the plasma–vacuum interface. The formation of the electrostatic oscillation is a slow process because the electromagnetic power penetrating into the plasma tends to zero with time. The transmitted plasma electromagnetic field is also simulated by the a finite-difference time-domain (FDTD) code. The difficulties of the numerical simulation of the quasi-electrostatic field are discussed. The analytical results can be used for the validation of the FDTD codes for plasma waves.

中文翻译：

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电磁波通过冷等离子体的瞬态传输的有限差分时域法精确解析计算和数值模拟

电磁波通过冷的、未磁化的和无碰撞的等离子体的瞬态传输被描述为从真空垂直入射到等离子体半空间的分析和数值。电磁场的精确公式以积分形式写成，便于近似分析和与直接数值模拟的结果进行比较。等离子体粒子振荡与电磁场自洽的时间可以从与等离子体-真空界面任意距离的简化公式中计算出来。在入射波的频率等于等离子体频率的情况下，要特别注意静电振荡的形成。消失的磁场和形成的静电振荡的幅度被计算为时间的函数和到等离子体-真空界面的距离。静电振荡的形成是一个缓慢的过程，因为渗透到等离子体中的电磁功率随时间趋于为零。传输的等离子体电磁场也由有限差分时域 (FDTD) 代码模拟。讨论了准静电场数值模拟的难点。分析结果可用于验证等离子体波的 FDTD 代码。静电振荡的形成是一个缓慢的过程，因为渗透到等离子体中的电磁功率随时间趋于为零。传输的等离子体电磁场也由有限差分时域 (FDTD) 代码模拟。讨论了准静电场数值模拟的难点。分析结果可用于验证等离子体波的 FDTD 代码。静电振荡的形成是一个缓慢的过程，因为渗透到等离子体中的电磁功率随时间趋于为零。传输的等离子体电磁场也由有限差分时域 (FDTD) 代码模拟。讨论了准静电场数值模拟的难点。分析结果可用于验证等离子体波的 FDTD 代码。