The theory of radio windows in the ionosphere and magnetosphere.

Radio waves in a stratified plasma can sometimes penetrate through a region where, according to a simple ray theory, they would be evanescent. They emerge on the far side in a different magnetoionic mode. This occurs when the incident wave normal is within a small cone of angles, called a radio window. The best known example is the Ellis window, used to explain the Z-trace in ionosonde records. Other phenomena where windows may be important have recently been studied. Simple approximate formulae are given for the transmission coefficient of a window and for its angular widths. These show the dependence on frequency, electron concentration gradient and direction of the ambient magnetic field. Comparison with more accurate calculations shows that these formulae are likely to be reliable in practical applications. The tracing of rays near a window is discussed, and the properties of a second kind of window are described.