Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls

M A Lyalinov, N Y Zhu, Valery P Smyshlyaev

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We study electromagnetic plane wave diffraction by a hollow circular cone with thin walls modelled by the so-called impedance-sheet boundary conditions. By means of Kontorovich-Lebedev integral representations for the Debye potentials and a 'partial' separation of variables, the problem is reduced to coupled functional difference (FD) equations for the relevant spectral functions. For a circular cone, the FD equations are then further reduced to integral equations, which are subsequently shown to be Fredholm-type equations via a semi-inversion by use of Dixon's resolvent. We then solve the integral equations numerically using an appropriate quadrature method. Certain useful further integral representations for the solution of 'Watson-Bessel' and Sommerfeld types are developed, which gives a theoretical basis for subsequent calculation of the far-field (high-frequency) asymptotics for the diffracted field. Based on this asymptotics, the radar cross section in the domain, which is free from both the reflected and the surface waves, has been computed numerically.
Original languageEnglish
Pages (from-to)676-719
Number of pages44
JournalIMA Journal of Applied Mathematics
Volume75
Issue number5
DOIs
Publication statusPublished - Oct 2010

Fingerprint

Circular cone
Functional Difference Equation
Difference equations
Electromagnetic Wave
Integral Representation
Plane Wave
Electromagnetic waves
Integral equations
Cones
Integral Equations
Scattering
Radar Cross Section
Wave Diffraction
Quadrature Method
Radar cross section
Spectral Function
Separation of Variables
Friedrich Wilhelm Bessel
Surface Waves
Far Field

Keywords

  • numerical evaluation of the vertex diffracted wave
  • the far-field asymptotics
  • semi-transparent cone
  • functional difference equations
  • diffraction

Cite this

Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls. / Lyalinov, M A; Zhu, N Y; Smyshlyaev, Valery P.

In: IMA Journal of Applied Mathematics, Vol. 75, No. 5, 10.2010, p. 676-719.

Research output: Contribution to journalArticle

Lyalinov, M A ; Zhu, N Y ; Smyshlyaev, Valery P. / Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls. In: IMA Journal of Applied Mathematics. 2010 ; Vol. 75, No. 5. pp. 676-719.
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