Theoretical and numerical investigation of dipole radiation over a flat earth

Details Theoretical and numerical investigation of dipole radiation over a flat earth Theoretical and numerical investigation of dipole radiation over a flat earth

Dec 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985phdt........27k&link_type=abstract

Ph.D. Thesis Case Western Reserve Univ., Cleveland, OH.

Statistics

Computation

Differential Equations, Earth (Planet), Electromagnetic Radiation, Magnetic Dipoles, Asymptotic Methods, Half Spaces, Series Expansion, Truncation Errors

Scientific paper

The electromagnetic problem of dipole radiation in the presence of a conducting half-space is old and has been treated extensively in the literature. Various writers, including such prominent names as H. Weyl and B. van der Pol, have given different but equivalent presentations of the solution. A short derivation, similar to that of van der Pol, is given in an appendix for the field along the surface of the earth. It is then shown how this representation can be used to derive a new form of an asymptotic expansion, whose first term is identical with the one to be found in the literature. A recurrence relation is derived for calculating the higher order terms of the expansion and a tight bound is derived which permits an easy estimate of the truncation error. A discussion is presented about the numerical computation of the complementary error function which figures prominently in the present problem. Two methods are presented, one in form of the solution of a simple system of ordinary differential equations of the first order and another in form of continued fractions.

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