ith the maximum electron density. the magnetic field is nearly horizontal. This means, that on North- South paths, there may be as much as 6dB coupling loss. The effect cos a > (6.91) is at its greatest on East-West paths near the equator, where the polarisation coupling loss can be very large. This results in no skywave energy being returned to Earth closer 6.5.6 The refractive index of the ionosphere to the transmitter than a range referred to as the 'skip distance', as shown in Figure 6.26. The refractive index of an ionised medium without a magnetic field For any given distance, at a particular time, there is a maximum and negligible loss of energy is given by Equation 6.88 where N is frequency that can be used, such that the signal will arrive at the the number of electrons per cubic centimetre, and f is the frequency receiver via the ionosphere. This frequency is called the 'maximum in kilohertz. usable frequency' or MUF. This frequency is also liable to be the one giving the strongest sky wave signal. The MUF is an important (6.88) parameter in the propagation of short waves i.e. frequencies from 1.6MHz to 30MHz. It is given by Equation 6.92. MUF = (6.92) If the Earth's magnetic field and electron collisions are included, the complex refractive index u is given by the Appleton-Hartree formula, as in Equation 6.89 where Y is the gyrofrequency divided The maximum skip distance is about 1700km for the E layer and by wave frequency, 0 is the angle between magnetic field and ray, 3300km for the F layer. Transmission can also take place by two or and 2 IT Z is the collision divided by wave frequencies. more hops, to be received at much greater distances. 6.5.10 Sporadic E propagation Sometimes, waves are returned to Earth by the E layer at frequen- cies greater than the nominal MUF. This phenomenon is called (6.89) sporadic E. It is assumed that this is caused by strongly ionised 'clouds' in the lower part of the E-region. By this means, it is possible for propagation to occur over long distances at frequencies 