Degeneration of electromagnetic creeping waves in a vicinity of critical values of anisotropic impedance

I. V. Andronov, D. P. Bouche

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1 Citation (Scopus)

Abstract

Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(τ - q2) where τ is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(τ - q2) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size κ-2/9 (where κ is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter κ-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.

Original languageEnglish
Pages (from-to)1984-1992
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume56
Issue number7
DOIs
Publication statusPublished - 1 Jul 2008

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Electromagnetic waves
Boundary conditions
Decomposition

Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

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title = "Degeneration of electromagnetic creeping waves in a vicinity of critical values of anisotropic impedance",
abstract = "Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(τ - q2) where τ is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(τ - q2) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size κ-2/9 (where κ is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter κ-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.",
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T1 - Degeneration of electromagnetic creeping waves in a vicinity of critical values of anisotropic impedance

AU - Andronov, I. V.

AU - Bouche, D. P.

PY - 2008/7/1

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N2 - Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(τ - q2) where τ is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(τ - q2) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size κ-2/9 (where κ is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter κ-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.

AB - Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(τ - q2) where τ is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(τ - q2) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size κ-2/9 (where κ is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter κ-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.

KW - Boundary layer

KW - Creeping waves

KW - Degeneration

KW - Electromagnetic propagation

KW - High frequency asymptotics

KW - Impedance

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JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 7

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