Reflexion Levels and Coupling Regions in a Horizontally Stratified Ionosphere

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences 1959-10, Vol.252 (1004), p.53-68
• Main Author: Pitteway, M. L. V.
• Format: Article
• Language: English
• Subjects: Angle of incidence; Damping; Earth ionosphere; Equation roots; Ionospheres; Radio scattering; Resonance scattering; Wave equations; Wave packets; Zero
• ISSN: 1364-503X; 0080-4614; 1471-2962; 2054-0272
• DOI: 10.1098/rsta.1959.0014

The propagation of radio waves through a horizontally stratified and slowly varying ionosphere is governed, in the case of oblique incidence, by a quartic equation (Booker 1938). Ray theory breaks down when two roots of this quartic are equal, for then coupling occurs between the characteristic waves, and full wave theory must be used. This paper is concerned with determining the conditions under which the two roots are equal; it is not concerned with the full wave theory. Values of the plasma frequency, and electron collision frequency, which lead to equal roots, are determined, and are exhibited in a set of curves. A full solution of the ‘Booker’ quartic is also given for a case of special interest. It is pointed out that the electric wave-field is unlikely to become very large in a slowly varying ionosphere, so that, if the ionosphere were irregular, scattering cannot be unduly enhanced by a plasma resonance.