Phase memory in W.K.B. and phase integral solutions of ionospheric propagation problems
Abstract
In a slowly varying medium, the propagation of waves remote from turning points or coupling points can be expressed in terms of W.K.B. solutions. For an isotropic medium, a W.K.B. solution includes a factor that is an exponential of a phase integral or eikonal function and has been called the 'phase memory'. For an anisotropic medium such as the ionosphere, however, each W.K.B. solution may contain another factor which is also the exponential of an integral and which has a memory content because it cannot be absorbed into the local factor. The properties of this new memory term, including its physical explanation, are examined for radio waves obliquely incident in a horizontally stratified ionosphere. The omission of this extra term from phaseintegral solutions can sometimes lead to serious errors. This is demonstrated by adopting several typical models of the ionosphere and comparing fullwave solutions for radio reflection coefficients with solutions calculated by the phaseintegral method with and without the extra memory term. A method is also described in which fullwave solutions and the phaseintegral method are combined.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 October 1975
 DOI:
 10.1098/rspa.1975.0166
 Bibcode:
 1975RSPSA.346...59S
 Keywords:

 Ionospheric Propagation;
 Magnetoionics;
 Phase Shift;
 Radio Wave Refraction;
 WentzelKramerBrillouin Method;
 Anisotropic Media;
 Differential Equations;
 Incident Radiation;
 Radio Transmission;
 Spatial Dependencies;
 Wave Reflection;
 Communications and Radar