Scalar wave diffraction by an open-ended sphere-conical cavity: the Abel integral transform in the Dirichlet and Neumann problems
Dozyslav Kuryliak, Victor Lysechko
TL;DR
This paper studies wave diffraction in a cavity shaped like a truncated cone with a spherical cap, using mathematical techniques to analyze resonance and scattering.
Contribution
The paper introduces a novel regularization method for solving wave diffraction problems using Abel integral transforms and mode matching.
Findings
Analytical solutions for cavity resonance frequency perturbations are derived for small aperture sizes.
New approximate formulas are developed for determining resonance behavior based on cavity geometry.
Scattering characteristics of various structures are analyzed for different surface properties.
Abstract
Two scalar wave diffraction problems for an open-ended sphere-conical cavity formed by a semi-infinite truncated cone with an internal termination in the form of the spherical cap in one of the conical regions are considered in the case of an axial excitation by a plane wave. The problems are formulated in terms of mixed boundary value ones with respect to the scalar potentials for the Helmholtz equation with Dirichlet or Neumann boundary conditions. Our technique is based on the mode matching, which is applied to reduce the problems to the infinite system of linear algebraic equations (ISLAEs) of the second kind by the method of analytical regularization. This includes the Abel integral transformation of the Legendre series equation to the Dirichlet one to justify the unique transition to ISLAE, separating the singular operators from them and deriving their inverse ones. To extend the…
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Taxonomy
TopicsElectromagnetic Scattering and Analysis · Algebraic and Geometric Analysis · Quantum Mechanics and Non-Hermitian Physics