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

TL;DR

This paper introduces a steepest-descent algorithm for efficiently computing wavefields in plasma physics using metaplectic geometrical optics, improving accuracy near caustics without resorting to full-wave simulations.

Contribution

It presents a novel steepest-descent algorithm for evaluating MGO integrals, enhancing wavefield modeling accuracy at caustics in plasma simulations.

Findings

Numerical MGO solutions match exact Airy solutions remarkably well.

The algorithm significantly improves upon previous analytical approximations.

Efficient computation of wavefields near caustics is achieved without full-wave methods.

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.