Transient behaviour of magnetic and electric fields at any height above an atmospheric duct

Abstract

We model the atmosphere by a surface duct underlying a half-space. A derivation is given for the electromagnetic field created by a vertical magnetic dipole, in the half-space above the duct, with an arbitrary time-varying moment. The method used for the solution is essentially based on the application of two functional transforms. Starting from the wave equation for the magnetic field and applying a Laplace transform in time, we obtain a two-dimensional Fourier transform in the horizontal spatial coordinates leading to an integral representation of the solution of the wave equation in the transform space. The transient behavior of the magnetic-field strength at any distance above the duct is determined.PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy