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dc.contributor.advisorDodin, Ilya Y
dc.contributor.authorLopez, Nicolas Alexander
dc.contributor.otherAstrophysical Sciences—Plasma Physics Program Department
dc.date.accessioned2022-10-10T19:51:22Z-
dc.date.available2022-10-10T19:51:22Z-
dc.date.created2022-01-01
dc.date.issued2022
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/dsp01bc386n43w-
dc.description.abstractRay optics is an intuitive and computationally efficient model for wave propagation through nonuniform media. It is therefore the standard choice for multiphysics simulations that involve wave physics in some capacity, such as designing and analyzing nuclear fusion experiments. However, the underlying geometrical-optics (GO) approximation of ray optics breaks down at caustics such as cutoffs and focal points, erroneously predicting the wave intensity to be infinite and thereby limiting the predictive capabilities of these codes. Full-wave modeling can be used instead, but the added computational cost brings its own set of tradeoffs. Developing cheaper, more efficient caustic remedies has therefore been an active area of research for the past few decades. In this thesis, I present a new ray-based approach called 'metaplectic geometrical optics' (MGO) that can be applied to any linear wave equation. Instead of evolving waves in the usual x (coordinate) or k (spectral) representation, MGO uses a mixed X = Ax + Bk representation. By continuously adjusting the matrix coefficients A and B along the rays via sequenced metaplectic transforms (MTs) of the wavefield, corresponding to symplectic transformations of the ray phase space, one can ensure that GO remains valid in the X coordinates without caustic singularities. The caustic-free result is then mapped back onto the original x space using metaplectic transforms, as demonstrated and verified on a number of examples. Besides outlining the basic theory of MGO, this thesis also presents specialized fast algorithms for MGO. These algorithms focus on the MT, which is a unitary integral mapping used in MGO that can be considered a generalization of the Fourier transform. First, a discrete representation of the MT is developed that can be computed in linear time [O(Np) for Np sample points] when evaluated in the near-identity limit; finite MTs can then be implemented as successive applications of K >> 1 near-identity MTs. Second, an algorithm based on Gauss-Freud quadrature is developed for efficiently computing finite MTs along their steepest-descent curves, which may be useful in catastrophe-optics applications beyond MGO. These algorithms lay the foundations for the development of an MGO-based ray-tracing code.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherPrinceton, NJ : Princeton University
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=http://catalog.princeton.edu>catalog.princeton.edu</a>
dc.subjectCaustics
dc.subjectFast algorithms
dc.subjectGeometrical Optics
dc.subjectTheoretical Physics
dc.subject.classificationPlasma physics
dc.subject.classificationOptics
dc.titleMetaplectic Geometrical Optics
dc.typeAcademic dissertations (Ph.D.)
pu.date.classyear2022
pu.departmentAstrophysical Sciences—Plasma Physics Program
Appears in Collections:Plasma Physics

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