Part I. Scattering of Electromagnetic Missiles. Part II. Vertical Electric Dipole Radiation Over Spherical Earth.

Part I: Scattering of electromagnetic missiles. An Electromagnetic Missile is a pulse of finite total radiated energy for which the attenuation of its energy with distance, in the direction of maximum radiation, is slower than predicted by radiation-zone analysis. Backscattering of an electromagnetic missile from a perfectly conducting curved obstacle is the subject of this investigation. The obstacle is assumed to have zero curvature just at the point of reflection of the incident pulse. The objective is to determine the asymptotic dependance of the backscattered energy, as the distance separating the obstacle from the source of the incident pulse tends to infinity. The problem is first formulated in two dimensions. Asymptotic methods are employed in order to simplify the expression for the backscattered energy. The asymptotic behavior of the backscattered energy with distance is found to depend on the rate at which the frequency spectrum of the pulse energy decays with increasing frequency, as well as on the degree of flatness of the obstacle at the point of incidence. Analogous results are obtained in the three-dimensional case. Part II: Vertical electric dipole radiation over spherical earth. In this part, the radiation of a vertical electric dipole over a spherical and electrically homogeneous earth is examined. The dielectric constant of the earth is assumed to be large compared to one. Both the dipole and the point of observation are assumed to lie on the spherical surface of the earth. The exact solution for the electromagnetic field is first obtained in terms of series. Subsequently, an equivalent representation of the solution is derived in terms of a series of integrals. Asymptotic methods are then applied to these integrals in order to analyze the behavior of the fields as the wavelength in the air becomes small compared to the radius of the sphere. A general framework for the study of the various contributions to the value of the fields is developed and a number of special cases are considered. Contributions to the value of the fields come, on the one hand, from the waves that propagate along the surface with the velocity in the air, and, on the other hand, from the waves that propagate through the earth. In many ways, the latter waves can be described in terms of ray optics. The behavior of the fields near the source and the relevance of the solution for a planar earth are studied in detail. A new approach towards finding correction formulae is introduced. Analytical formulae are tested by numerical calculations.