The Propagation of Electromagnetic Waves Through, Along and Over a Three-Dimensional Conducting Half Space: Em Waves Over a Conducting Earth David S. Gilliam

ISBN: 9783820489057

Published: December 31st 1986

Paperback

209 pages


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The Propagation of Electromagnetic Waves Through, Along and Over a Three-Dimensional Conducting Half Space: Em Waves Over a Conducting Earth  by  David S. Gilliam

The Propagation of Electromagnetic Waves Through, Along and Over a Three-Dimensional Conducting Half Space: Em Waves Over a Conducting Earth by David S. Gilliam
December 31st 1986 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, RTF | 209 pages | ISBN: 9783820489057 | 7.61 Mb

A representation in terms of explicitly given generalized eigenfunctions is obtained for the semigroup S(t) = exp(-ixt) solving the Cauchy problem for the time-dependent Maxwell equations in the case of two distinct media filling the upper and lowerMoreA representation in terms of explicitly given generalized eigenfunctions is obtained for the semigroup S(t) = exp(-ixt) solving the Cauchy problem for the time-dependent Maxwell equations in the case of two distinct media filling the upper and lower half spaces of R3, whereby the upper medium is loss-free, while the lower has finite conductivity.

The solution u = S(t)f, fED(1), can be written in the form u = uo+uo+uso+us++us-+op+up. Here uo and uo are, respectively, static and quasistatic parts of the solution: us+ and us+ consists of a superposition of AH modes -- modes whose frequencies have no real part and thus do not propagate- uxx consist of superpositions of surface-wave modes, propagating in opposite directions according to + or -- uop and up are superpositions of plane-wave modes having the frequencies of the upper and lower media respectively.

The structure of the AH and surface-wave components is determined: the are essentially scalar waves, and it is shown how such waves can be constructed explicitly from solutions of a simple problem for the scalar wave equation.



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