The path of a radio wave is affected by any free charges in the medium through which it is travelling. The refractive index is governed by the electron concentration and the magnetic field of the medium and the frequency and polarisation of the transmitted wave. These lead to some important properties for waves propagating in the ionosphere;
The ionisation in the atmosphere is in the form of several horizontal layers, and so the electron concentration and therefore the refractive index of the ionosphere vary with height. By broadcasting a range of frequencies, and measuring the time it takes for each frequency to be reflected, it is possible to estimate the concentration and height of each layer of ionisation.
An ionosonde broadcasts a sweep of frequencies, usually in the range of 0.1 to 30 MHz. As the frequency increases, each wave is refracted less by the ionisation in the layer, and so each penetrates further before it is reflected. As a wave approaches the reflection point, its group velocity approaches zero and this increases the time-of-flight of the signal. Eventually, a frequency is reached that enables the wave to penetrate the layer without being reflected. For ordinary mode waves, this occurs when the transmitted frequency just exceeds the peak plasma frequency of the layer. In the case of the extraordinary wave, the magnetic field has an additional effect, and reflection occurs at a frequency that is higher than the ordinary wave by half the electron gyrofrequency.
The frequency at which a wave just penetrates a layer of ionisation is known
as the critical frequency of that layer. The critical frequency is related to
the electron density by the simple relation;
F_c = 8.98*sqrt(Ne) for the ordinary mode.
and
F_c = 8.98*sqrt(Ne) + 0.5*Be/m for the extraordinary mode.
Here F_c is the critical frequency in Hz, Ne is the electron
concentration per metre cubed, B is the magnetic field strength,
e is the charge on an electron and m is the mass of an electron.
All transmitted frequencies above this critical frequency will penetrate the layer without being reflected. Their group velocity will however, will be slowed by any ionisation, and this will add to the time-of-flight. If such a wave encounters another layer, whose plasma frequency is higher than the frequency of the wave, it will be reflected, and the return signal will be further delayed as it travels back through the underlying ionisation. The apparent, or virtual height indicated by this time delay will therefore be greater than the true height. The difference between true-height and virtual height is governed by the amount of ionisation that the wave has passed through. Recreating the true-height profile of electron concentration from ionogram data is an important use of ionosonde data. Such a procedure is known as true height analysis.