Propagation of long radio waves in an inhomogeneous ionosphere

Abstract

An outline is given of work which has been done on VLF and ELF radio waves. In most theoretical work on ionospheric propagation at these frequencies, the ionosphere has been regarded as a sharply bounded homogeneous medium. A more realistic model would be one in which the ionosphere is continuously stratified, and it is the purpose of this thesis to investigate some models of this type. In the past, extension of the theory to account for continuously stratified ionospheric models has been hampered by lack of exact wave functions for fields of electric type. The propagation of electromagnetic waves in an ionized medium is considered. Approximate expressions, applicable at VLF and ELF, are obtained for the permittivity and conductivity of such a medium. Equations governing propagation in inhomogeneous media are derived. Planar stratified media are considered using a general cylindrical coordinate system, which is then specialized to a type in which the wave equations are separable. Spherically stratified media are also considered. Some new exact wave functions are derived for fields of both electric and magnetic types in planar and spherically stratified media. The wave functions for the plane case are used to investigate the reflection of waves from semi-infinite stratified regions. The Stokes phenomenon is outlined and the theory for Whittaker and Bessel functions is applied to the study of the reflection of waves in media having linear and hyperbolic profiles of the refractive index. Some of the results obtained earlier in the thesis are applied to the waveguide mode theory of ELF propagation. The model taken consists of a continuously stratified, isotropic ionosphere above a flat, perfectly conducting earth. Linear and exponential profiles of the ionospheric refractive index are considered. A novel formula is derived which implies the existence of a minimum in the ELF attenuation rate as a function of frequency, in agreement with observations. This formula is found to give a quantitative agreement with some experimental results on the attenuation rate at ELF. Finally, some possible extensions to the work are mentioned.