The coalescence of coupling points in the theory of radio waves in the ionosphere
Abstract
The present work considers the propagation of a radio wave obliquely or vertically incident on a horizontally stratified ionosphere in the case where two coupling points in the complex height plane are close together or coalesce, in which case the Airy integral function approximation fails and must be modified. In particular, the case where the same two waves are coupled at the adjacent coupling points is investigated. Two different kinds of coalescence are distinguished for this type of coupling. In coalescence of the first kind (C1), the coupling between the two waves remains strong when the coupling points move close together and when they coalesce. In coalescence of the second kind (C2), the coupling becomes weaker when the coupling points move close together and disappears completely when they coalesce. The conditions for coalescence are set forth, and it is shown how the equations for conditions near C1 can be reduced to Weber's equation. A different form of Weber's equation must be used for C2, and the Stokes constants are shown to be different in this case. The application to 'crossover' in the theory of ion cyclotron whistlers is discussed.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 October 1974
 DOI:
 10.1098/rspa.1974.0169
 Bibcode:
 1974RSPSA.341....1B
 Keywords:

 Coupling Coefficients;
 Ionospheric Propagation;
 PlasmaElectromagnetic Interaction;
 Radio Wave Refraction;
 Wave Equations;
 Airy Function;
 Ion Cyclotron Radiation;
 Points (Mathematics);
 Reflected Waves;
 Stokes Law Of Radiation;
 WentzelKramerBrillouin Method;
 Whistlers;
 Communications and Radar