Steepest-descent algorithm for simulating plasma-wave caustics via metaplectic geometrical optics

Abstract

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.

Quasioptical propagation and absorption of electron cyclotron waves: simulations and experiment

“…Note that this framework is inapplicable to wave transformations near cutoffs and other caustics, where the ordering (2) fails. Although extensions are possible using the recently developed metaplectic geometrical optics [40][41][42][43][44], they are yet to be implemented. Because we are not concerned with the excitation of electrostatic waves in this paper, we also assume the cold-plasma ε H .…”