A unified theory on radiation of a vertical electric dipole above a dissipative earth
Abstract
Analytical expressions are derived for the electromagnetic field associated with a vertical electric dipole (VED) above a dissipative earth. The scattered field is shown to consist of a direct contribution from a perfect image source, and a correction due to the finite conductivity of earth which is expressible in terms of an incomplete Hankel function. The resultant expression readily reduces to the wellknown asymptotic solutions in both the spacewave and groundwave regions. Validity of the spacewave expression in the far zone is found to be dependent upon the observation angle as well as the refractive index of earth. In the near field, alternative approximate formulas in closed form are derived from the incomplete Hankel function expression for different elevation angles. These formulas are shown to yield accurate results whenever the distance from the image source is greater than about 0.2λ_{c} where λ_{c} is the effective wavelength (or skin depth) of earth. For distance smaller than 0.2λ_{c}, however, an analytical expression based upon a quasistatic approximation is generally applicable and has been discussed elsewhere.
 Publication:

Radio Science
 Pub Date:
 December 1974
 DOI:
 10.1029/RS009i012p01129
 Bibcode:
 1974RaSc....9.1129C
 Keywords:

 Earth Surface;
 Electric Dipoles;
 Electromagnetic Scattering;
 Radiation Sources;
 Refracted Waves;
 Aerial Explosions;
 Dipole Antennas;
 Ground Wave Propagation;
 Hankel Functions;
 High Altitude Nuclear Detection;
 Lightning;
 Mathematical Models;
 Nuclear Explosions;
 Remote Sensors