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

Area of Science:

• Plasma Physics and Fusion Energy
• Electromagnetism and Wave Propagation

Background:

• Geometrical Optics (GO) is widely used for radiofrequency (RF) wave system design in fusion applications but fails at wave cutoffs and caustics.
• Accurate modeling in these challenging regions often requires computationally expensive full-wave simulations.
• Metaplectic Geometrical Optics (MGO) offers a generalized framework to overcome GO limitations near caustics.

Purpose of the Study:

• To develop and present a novel algorithm for numerically evaluating the MGO integral representation of the wavefield.
• To validate the algorithm's accuracy by comparing its results against known analytical solutions.
• To demonstrate the MGO approach as a more efficient alternative to full-wave simulations for specific regions.

Main Methods:

• Implementation of an algorithm utilizing Gauss-Freud quadrature along steepest-descent contours for MGO integral evaluation.
• Benchmarking the algorithm using the standard Airy problem, which has a known analytical solution.
• Comparison of numerical MGO results with the exact analytical solution and previous MGO analytical approximations.

Main Results:

• The developed algorithm provides a numerical MGO solution that exhibits remarkable agreement with the exact analytical solution for the Airy problem.
• The numerical MGO results significantly outperform previously derived analytical approximations of the MGO integral.
• The study demonstrates the feasibility and accuracy of the proposed numerical method for MGO wavefield computation.

Conclusions:

• The new Gauss-Freud quadrature-based algorithm offers an accurate and efficient method for computing wavefields using the MGO framework.
• This approach effectively addresses the limitations of geometrical optics in critical regions like wave cutoffs and caustics.
• The MGO method, implemented with this algorithm, presents a viable and computationally advantageous alternative to full-wave simulations for certain fusion applications.