369 research outputs found
Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms
The optimization of radiofrequency-wave (RF) systems for fusion experiments
is often performed using ray-tracing codes, which rely on the
geometrical-optics (GO) approximation. However, GO fails at caustics such as
cutoffs and focal points, erroneously predicting the wave intensity to be
infinite. This is a critical shortcoming of GO, since the caustic wave
intensity is often the quantity of interest, e.g. RF heating. Full-wave
modeling can be used instead, but the computational cost limits the speed at
which such optimizations can be performed. We have developed a less expensive
alternative called metaplectic geometrical optics (MGO). Instead of evolving
waves in the usual (coordinate) or (spectral)
representation, MGO uses a mixed representation. By continuously adjusting the matrix
coefficients and along the rays, one can ensure that
GO remains valid in the coordinates without caustic singularities.
The caustic-free result is then mapped back onto the original
space using metaplectic transforms. Here, we overview the MGO theory and review
algorithms that will aid the development of an MGO-based ray-tracing code. We
show how using orthosymplectic transformations leads to considerable
simplifications compared to previously published MGO formulas. We also prove
explicitly that MGO exactly reproduces standard GO when evaluated far from
caustics (an important property which until now has only been inferred from
numerical simulations), and we relate MGO to other semiclassical
caustic-removal schemes published in the literature. This discussion is then
augmented by an explicit comparison of the computed spectrum for a wave bounded
between two cutoffs.Comment: Invited paper for APS DPP 2021. 21 pages, 6 figures, 5 appendice
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