Calculation of the Virtual Height and Absorption of Radio Waves in the Ionosphere

Calculations for the ordinary ray under different conditions show that the effect of collisions can considerably reduce the virtual heights given by ray theory. This reduction is, however, caused entirely by the errors inherent in ray theory. Phase mtegral calculations show that the simplest ray theory result, ignoring collisions, is accurate to within 0.1 percent except under those conditions which require a full wave treatment. Calculations of absorption by integrating the absorption coefficient k up to the level X = 1 also give incorrect results, because of ray theory limitations. These errors are exactly counterbalanced by the errors in a commonly used approximation for k. The use of this approximation therefore gives results which are more accurate, by several orders of magnitude, than the use of the exact expression.