Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2022. №8

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DOI: https://doi.org/10.30898/1684-1719.2023.5.2

an APPROXIMATE ASYMPTOTIC SOLUTION FOR THE ELECTROMAGNETIC FIELD OF SOURCES

NEAR A SMOOTH CONVEX CONDUCTING SURFACE OF ROTATION

M.V. Indenbom

All-Russian Scientific Research Institute of Radio Engineering

105082, Moscow, B. Pochtovay str., 22.

The paper was received November 25, 2022

Abstract.Approximate asymptotic solution is developed for the electromagnetic field due of a surface magnetic and electric currents located near an arbitrary smooth convex conducting surface of rotation of large size. The expressions of field are valid in a near-surface layer with a thickness of the order of the wavelength and have the form of a sum of a series of azimuthal harmonics and an integral over a continuous spectrum of eigenfunctions of the field. The coefficients of the series are expressed by integrals from the product of a given distribution of sources with eigenfunctions. For eigenfunctions, both general integral representations and closed expressions in terms of Airy functions are obtained, which are uniformly valid along surface of a rotation for the case of one pole by the parabolic equation method. The field expressions take into account the inseparability of the field by the sum in term of E- and H-type fields, are uniformly valid in the near-surface layer, excluding the vicinity of the poles of the rotation surface, and have no discontinuities on the caustics of surface rays. The expressions obtained were used to calculate the mutual admittancesbetween two annular slots on a semi-infinite and smoothly truncated conical surface. Numerical results obtained by the proposed and rigorous methods for a semi-infinite cone were compared. It is shown that in the case of in-phase annular slots in a semi-infinite cone, the obtained asymptotic expression for mutual admittance coincides with the main term of the asymptotic of a strict solution based on the method of eigenfunctions.

Key words:electromagnetic field, surface of rotation, uniform asymptotic, parabolic equation, electric current, magnetic current, eigenfunctions, Airy functions, mutual admittance.

Corresponding author:Mikhail V. Indenbom, mindenbom@mail.ru

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Forcitation:Indenbom M.V.

An approximate asymptotic solution for the electromagnetic field of sources near a smooth convex conducting surface of rotation.Jhurnal radioelektroniki[Journal of Radio Electronics] [online]. 2023. №5. https://doi.org/10.30898/1684-1719.2023.5.2 (In Russian)