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Highly accurate approximate solutions of the Stokes equation for high electron density and long laser wavelength

机译：高电子密度和长激光波长的斯托克斯方程的高精度近似解

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摘要

We have transformed the Stokes equation to equations written in the polarization ellipse parameters. Since the transformed Stokes equations directly describe change in each polarization ellipse parameter, they enable us to easily and comprehensively understand change in the polarization ellipse in a plasma. We have obtained highly accurate approximate solutions of the transformed Stokes equation in order to connect the measured polarization state to the plasma parameters (the electron density and the magnetic field) in a short CPU time. We have compared our solutions and the other approximate solutions proposed by previous studies. Only our solutions have shown good agreement between the polarization parameters and the line-integrated plasma parameters. The errors of our solutions are less than 2% of the domain of each polarization parameter up to the high electron density (～7 × 10 ~(20) m ~(-3)) and the long laser wavelength (～170 μm). The CPU time of our solutions is 10 times shorter than that of the Stokes equation.
机译：我们已将斯托克斯方程转换为以极化椭圆参数写入的方程。由于变换后的斯托克斯方程式直接描述了每个极化椭圆参数的变化，因此它们使我们能够轻松，全面地了解等离子体中极化椭圆的变化。我们已经获得了转换后的斯托克斯方程的高精度近似解，以便在短CPU时间内将测量的极化状态与等离子体参数（电子密度和磁场）联系起来。我们已经比较了我们的解决方案和先前研究提出的其他近似解决方案。只有我们的解决方案在极化参数和线积分等离子体参数之间显示出良好的一致性。我们的解决方案的误差小于每个极化参数的域的2％，直到高电子密度（〜7×10〜（20）m〜（-3））和长激光波长（〜170μm）。我们解决方案的CPU时间比Stokes公式短10倍。

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