Radio Waves in the Lower Ionosphere

The study of the ionosphere has largely been performed by observation of the properties of radio wave propagation through this medium. In this work we will not attempt to present an exhaustive study of the interaction of electromagnetic waves and a weakly ionized plasma, nor 

The conditions of propagation of an electromagnetic wave in the ionospheric medium are determined by the Maxwell and Lorentz equations. These equations determine the properties of the electric (E) and magnetic (H) fields, as well as the displacement (D) and the induction (B) as a function of the electric charge and current densities (J) (see, for example, Budden, 1961 Davies, 1965)  

The most simple form of the Appleton equation is obtained by neglecting the effects of the magnetic field and collisions. This equation is adequate to describe the propagation of high frequency waves (above 30 MHz) in the ionosphere, and can be used to obtain an approximate understanding of the propagation characteristics of lower frequency waves. In this case, one obtains 

In the D-region, collisions cannot be neglected except for very high frequency propagation. Neglecting the effect of the magnetic field, the refractive index then becomes  

It follows that, to this order of approximation, a wave traveling through 

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