Time Domain of Sommerfelds Problem of Lossy Half-Space

Adel A. S. Abo Seliem, Fathia Alseroury

Department of Mathematics, Faculty of Science, University of Kafr el-Sheikh, Kafr el-Sheikh, Egypt;.
Department of Physics, Fac- ulty of Science for Girls, King Abdulaziz University, Jeddah, KSA..

DOI: 10.4236/jemaa.2013.53021                

Abstract

This paper solved the problem of the scattering of radiation from a material half-space by the transient spectral domain method. The transient spectral domain method is a general theoretical approach for the exact solution to the time-dependent source radiation in the presence of media. It is located in the air region in the vicinity of lossy half-space. The apply of the integral transform to the wave equation in the horizontal coordinates in space by a two-dimensional Fourier transform is theoretical formulation of the problem. A source used is an electrically short vertical magnetic dipole with Impulse current distribution in the domain. Leads, under consideration of initial boundary and transition condition, the form expressions is achieved in terms of spectral domain variable and time. The integral representation determines the electromagnetic field anywhere the closed-form expressions is an achieved in terms of spectral domain variable and time.

Keywords

Vertical Dipole; Electromagnetic Field; Wave Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. R. Wait, “Electromagnetic Waves in Stratified Media,” Pergamon Press, Oxford, 1970.
[2]	A. Sommerfeld, “Uber die Ausbreitnng der Wellen in der Drahtlosen Telegraohie,” Annalen der Physik, Vol. 333, No. 4, 1909, pp. 665-736. doi:10.1002/andp.19093330402
[3]	H. Weyl, “Ausbrieiting Electromagnetischer Wellon uiber Einium Ebenen Letier,” Annalen der Physik (Leipzig), Vol. 13, 1919, pp. 481-500.
[4]	A. Banons, “Dipole Radiation in the Presence of a Conduting Half-Space,” Pergamon Press, New York, 1966.
[5]	I. V. Lindell and E. Alanen, “Exact Image Theory for the Sommerfeled Half-Space Problem, Part II. Vertical Electric Dipole,” IEEE Transactions on Antennas and Propagation, 1984, pp. 2758-2761.
[6]	S. I. Dvorak and M. M. Mechaik, “Application of the Contour Transformation Method of a Vertical Electric Dipole over Earth,” Radio Science Journal, Vol. 28, No. 3, 1993, pp. 309-307.
[7]	L. Cagniard, “Reflexion et Refraction des Ondes Seismiques Progressive Cambridge,” Gauther-Villard, Cambridge, 1939.
[8]	A. A. Abo-Seliem, “The Transient Response above an Evaporation Duct,” Journal of Physics D: Applied Physics, Vol. 31, 1998, pp. 3046-3050. doi:10.1088/0022-3727/31/21/010
[9]	A. A. Abo-Seliem, “Transient Electromagnetic Field of a Dielectric Layer,” Applied Mathematics and Computation, Vol. 157, No. 3, 2004, pp. 759-764. doi:10.1016/j.amc.2003.08.118
[10]	J. A. Stratton, “Electromagnetic Theory,” McGraww-Hill 1941.