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Approximate solutions and error bounds for the wave equation in a stratified ionosphere with turning points
Author(s) -
Nalesso G. F.,
Jacobson A. R.
Publication year - 1991
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/91rs00934
Subject(s) - mathematical analysis , series (stratigraphy) , plane (geometry) , term (time) , mathematics , gaussian , plane wave , ionosphere , complex plane , simple (philosophy) , function (biology) , physics , geometry , optics , quantum mechanics , paleontology , astronomy , biology , philosophy , epistemology , evolutionary biology
In this paper we present a solution of the problem of a plane electromagnetic wave traveling parallel to a constant magnetic field ( k ‖ B 0 ‖ z /| z |) in a horizontally stratified ionosphere. We assume, in particular, that the permittivity of the medium can be decomposed as the sum of an unperturbed and a perturbed part and that the unperturbed term is a smooth function of the height z that can be analytically continued in the complex plane and has furthermore a single simple zero (turning point) in a simply connected region D which includes the interval (α, ∞) of the real axis. The method gives approximate solutions valid in the region D and therefore also through the turning point. These solutions are obtained by truncating certain formal (generally divergent) series solutions of the wave equation. Furthermore, a realistic error bound for the remainder term associated with the truncated series is also derived and discussed. This method is successively applied to the case of a linearly varying permittivity of a lossless ionosphere with a superimposed Gaussian perturbing term. The possibility of applying the method when an odd number of turning points are present is also discussed.