Diffraction of Cherenkov Radiation at the Open End of a Shallow Corrugated Waveguide

TL;DR

This paper investigates how a symmetrical TM mode diffracts at the open end of a shallow, corrugated cylindrical waveguide, using impedance boundary conditions and advanced mathematical techniques to analyze both vacuum and dielectric-filled cases.

Contribution

It introduces a novel application of the modified tailoring technique and Wiener-Hopf-Fock equation to solve diffraction problems in corrugated waveguides with simplified boundary conditions.

Findings

Derived reflection coefficients for the waveguide end

Validated the approach for both vacuum and dielectric cases

Provided a numerical method for solving the resulting equations

Abstract

A problem of diffraction of a symmetrical transverse magnetic mode $ \text{TM}_{0l} $ by an open-ended cylindrical waveguide corrugated inside is considered. A depth and a period of corrugations are supposed to be much less than the wavelength and the waveguide radius. Therefore a corrugated waveguide wall can be described in terms of equivalent boundary conditions, i.e. a corresponding impedance boundary condition can be applied. Both vacuum case and the case of uniform dielectric filling of the waveguide is considered. The diffraction problem is solved using the modified tayloring technique in Jones formulation. Solution of the Wiener-Hopf-Fock equation of the problem is used to obtain an infinite linear system for reflection coefficients, the latter can be solved numerically using the reduction technique.