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PIER PIER B PIER C PIER M PIER Letters
2010-04-29
Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium
By
Oleksandr M. Dumin,

    Dr. Oleksandr M. Dumin

    Department of Applied Electrodynamics

    V. N. Karazin Kharkiv National University

    Ukraine

    Homepage

O. O. Dumina,

    Dr. O. O. Dumina

    Department of Higher Mathematics

    Ukrainian State Academy of Railway Transport

    Ukraine

    Homepage

Victor A. Katrich

    Dr. Victor A. Katrich

    Department of Radiophysics

    V. N. Karazin Kharkov National University

    Ukraine

    Homepage

Progress In Electromagnetics Research, Vol. 103, 403-418, 2010
doi:10.2528/PIER10011909
Abstract
To solve radiation problems in time domain directly the modal representation of transient electromagnetic fields is considered. Using evolutionary approach the initial nonstationary three-dimensional electrodynamic problem is transformed into the problem for one-dimensional evolutionary equations by the construction of the modal basis for electromagnetic fields with arbitrary time dependence in spherical coordinate system. Elimination of the radial components of electrical and magnetic field from Maxwell equation system permits to form the four-dimensional differential operators. It is proved that the operators are self- adjoint ones. The eigen-functions of the operators form the basis. The completeness of the basis is proved by means of Weyl Theorem about orthogonal detachments of Hilbert space. The expansion coefficients of arbitrary electromagnetic field are found from the set of evolutionary equations. The transient electromagnetic field can be found directly without Fourier transform application by means of one-dimensional FDTD method for the medium with dependence on longitudinal coordinate and time or using Laplace transform and wave splitting for the case of homogeneous stationary medium. The above mentioned methods are compared with the three-dimensional FDTD method for the case of the problem of small loop excitation by transient current.
Citation
Oleksandr M. Dumin, O. O. Dumina, and Victor A. Katrich, "Evolution of Transient Electromagnetic Fields in Radially Inhomogeneous Nonstationary Medium," Progress In Electromagnetics Research, Vol. 103, 403-418, 2010.
doi:10.2528/PIER10011909
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