Introduction

This and the remaining chapters are mainly concerned with problems in which the approximations of ray theory cannot be made, so that a more detailed study of the solutions of the governing differential equations is needed. The solution of this type of problem is called a ‘full wave solution’. The subject has been studied almost entirely for plane stratified media. When the medium is not plane stratified, for example when the earth's curvature is allowed for, a possible method is to use an ‘earth flattening’ transformation that converts the equations into those for an equivalent plane stratified system; see §§ 10.4, 18.8. See Westcott (1968, 1969) and Sharaf (1969) for examples of solutions that do not use such a transformation.

This chapter is written entirely in terms of a horizontally stratified ionosphere and for frequencies greater than about 1 kHz, so that the effect of positive ions in the plasma may be neglected. The earth's curvature also is neglected.

The need for full wave solutions arises when the wavelength in the medium is large so that the electric permittivity changes appreciably within one wavelength and the medium cannot be treated as slowly varying (§§ 7.6, 7.10). Thus it arises particularly at very low frequencies, say 1 to 500 kHz. But even at higher frequencies the wavelength in the medium is large where the refractive index n is small, and some full wave solutions are therefore often needed for high frequencies too.