Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-25T03:14:25.286Z Has data issue: false hasContentIssue false
  • English
  • Français

Coupled forms of the differential equations governing radio propagation in the ionosphere

Published online by Cambridge University Press:  24 October 2008

P. C. Clemmow  and
J. Heading
P. C. Clemmow
Affiliation:
Cavendish LaboratoryCambridge
J. Heading
Affiliation:
Cavendish LaboratoryCambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the equations governing oblique propagation in a horizontally stratified ionosphere with an oblique magnetic field can be cast into a form suitable for solution by successive approximations. In the general case this ‘coupled’ form consists of four first order differential equations, each being associated with one characteristic wave. In the special cases (a) horizontal magnetic field, (b) plane of incidence perpendicular to the magnetic meridian, two second order coupled equations of a particular type can be derived, each of which is associated with a pair of corresponding upgoing and downgoing characteristic waves. These latter equations are similar to, and include, those already given by Försterling(7) for vertical incidence.

The cases in which there is no coupling are briefly considered from the point of view of the first order equations.

The general formulation provides a basis for assessing the validity of the standard ‘ray’ approximation, alternative to that developed by Booker (2), and brings out the nature of its breakdown in coupling and reflexion regions.

Specific applications and extensions of the theory are left for later consideration.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 50 , Issue 2 , April 1954 , pp. 319 - 333
Copyright
Copyright © Cambridge Philosophical Society 1954

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Banerjea, B. K.Proc. roy. Soc. A, 190 (1947), 67.Google Scholar
(2)Booker, H. G.Proc. roy. Soc. A, 155 (1936), 235.Google Scholar
(3)Booker, H. G.Phil. Trans. A, 237 (1938), 411.Google Scholar
(4)Bremmer, H.Comm. pure appl. Math. 4 (1951), 105.CrossRefGoogle Scholar
(5)Budden, K. G.Proc. roy. Soc. A, 215 (1952), 215.Google Scholar
(6)Eckersley, T. L.Proc. phys. Soc. Lond., B, 63 (1950), 49.CrossRefGoogle Scholar
(7)Försterling, K.Z. hochf. Elekt. 59 (1942), 10.Google Scholar
(8)Gibbons, J. J. and Nertney, R. J.J. geophys. Res. 57 (1952), 323.CrossRefGoogle Scholar
(9)Hartree, D. R.Proc. Camb. phil. Soc. 25 (1929), 97.CrossRefGoogle Scholar
(10)Heading, J. and Whipple, R. T. P.Phil. Trans. A, 244 (1952), 469.Google Scholar
(11)Pfister, W.J. Geophys. Res. 58 (1953), 29.CrossRefGoogle Scholar
(12)Rydbeck, O. E. H.Comm. pure appl. Math. 4 (1951), 129.CrossRefGoogle Scholar
(13)Saha, M. N., Banerjea, B. K. and Guha, U. C.Proc. nat. Inst. Sci. India, 17 (1951), 205.Google Scholar
(14)Scheuktunoff, S. A.Comm. pure appl. Math. 4 (1951), 117.Google Scholar
(15)Wilkes, M. V.Proc. roy. Soc. A, 189 (1947), 130.Google Scholar