Ray-theory interpretation of reflection of radio waves by a linearly graded plasma

When a beam of microwaves is incident at an angle ¿i on a linearly graded plasma, it emerges at a distance D from the point of incidence, given by ray theory as D = 2 xe sin 2 ¿i. A more accurate result can be obtained by applying the principle of stationary phase to the reflected angular spectrum of waves, making use of the reflection coefficient, which can be expressed simply in terms of Airy functions when the electric vector is perpendicular to the plane of incidence. This more accurate result can be represented, to a very close approximation, by taking into account a reflection arising from the discontinuity of gradient at the boundary of the plasma, and combining this with the geometrical-optics result which leads to the equation quoted above. The ray-theory interpretation is shown to have practical implications with the oblique-incidence diagnostic technique introduced by Kharadly.