### 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 - q^{2}) 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 - q^{2}) 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 language | English |
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Pages (from-to) | 1984-1992 |

Number of pages | 9 |

Journal | IEEE Transactions on Antennas and Propagation |

Volume | 56 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2008 |

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### Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

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*IEEE Transactions on Antennas and Propagation*, vol. 56, no. 7, pp. 1984-1992. https://doi.org/10.1109/TAP.2008.924719

**Degeneration of electromagnetic creeping waves in a vicinity of critical values of anisotropic impedance.** / Andronov, I. V.; Bouche, D. P.

Research output

TY - JOUR

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

Y1 - 2008/7/1

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

UR - http://www.scopus.com/inward/record.url?scp=47249146949&partnerID=8YFLogxK

U2 - 10.1109/TAP.2008.924719

DO - 10.1109/TAP.2008.924719

M3 - Article

AN - SCOPUS:47249146949

VL - 56

SP - 1984

EP - 1992

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 7

ER -