等离子体波焦散线的最速下降算法及后向几何光学
Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics
摘要：
用于核聚变的射频波系统的设计和优化通常使用依赖于几何光学（GO）近似的射线跟踪代码来执行。然而，GO在波截止和焦散处失败。为了准确地模拟这些区域中的波浪行为，通常使用更先进且计算昂贵的“全波”模拟，但这不是严格必要的。提出了一种新的广义公式，称为元几何光学（MGO），恢复焦散线附近的GO。MGO框架产生波场的积分表示，通常必须进行数值计算。我们提出了一种算法，用于计算这些积分使用高斯-弗洛伊德正交沿最陡下降轮廓。基准进行标准艾里问题，其精确的解决方案是已知的分析。新算法提供的数值MGO解与精确解非常吻合，并显着改善了以前推导的MGO积分的解析近似。
英文摘要：
The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive "full-wave" simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. The numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves upon previously derived analytical approximations of the MGO integral.
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