Introduction

We now have to consider how results such as those of ch. 12 for an isotropic plasma must be modified when the earth's magnetic field is allowed for. The dispersion relation (4.47) or (4.51) is now much more complicated so that, even for simple electron height distribution functions N(z), it is not possible to derive algebraic expressions for such quantities as the equivalent height of reflection h′(f) or the horizontal range D(θ). These and other quantities must now be evaluated numerically. The ray direction is not now in general the same as the wave normal. Breit and Tuve's theorem and Martyn's theorems do not hold. These properties therefore cannot be used in ray tracing. Some general results for ray tracing in a stratified anisotropic plasma have already been given in ch. 10.

The first part of this chapter §§ 13.2–13.6 is concerned with vertically incident pulses of radio waves on a stratified ionosphere, since this is the basis of the ionosonde technique, § 1.7, which is widely used for ionospheric sounding. The transmitted pulses have a radio frequency f which is here called the ‘probing frequency’. It is also sometimes called the ‘carrier frequency’. The study of this subject involves numerical methods that are important because of their use for analysing ionospheric data and for the prediction of maximum usable frequencies. It has already been explained, § 10.2, that the incident pulse splits into two separate pulses, ordinary and extraordinary, that travel independently.