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| Titel |
Full wave description of VLF wave penetration through the ionosphere |
| VerfasserIn |
Ilya Kuzichev, David Shklyar |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250033013
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| Zusammenfassung |
| Of the many problems in whistler study, wave propagation through the ionosphere is among
the most important, and the most difficult at the same time. Both satellite and ground-based
investigations of VLF waves include considerations of this problem, and it has been in the
focus of research since the beginning of whistler study (Budden [1985]; Helliwell [1965]).
The difficulty in considering VLF wave passage through the ionosphere is, after all,
due to fast variation of the lower ionosphere parameters as compared to typical
VLF wave number. This makes irrelevant the consideration in the framework of
geometrical optics, which, along with a smooth variations of parameters, is always
based on a particular dispersion relation. Although the full wave analysis in the
framework of cold plasma approximation does not require slow variations of plasma
parameters, and does not assume any particular wave mode, the fact that the wave of a
given frequency belongs to different modes in various regions makes numerical
solution of the field equations not simple. More specifically, as is well known (e.g.
Ginzburg and Rukhadze [1972]), in a cold magnetized plasma, there are, in general, two
wave modes related to a given frequency. Both modes, however, do not necessarily
correspond to propagating waves. In particular, in the frequency range related to
whistler waves, the other mode is evanescent, i.e. it has a negative value of N2 (the
refractive index squared). It means that one of solutions of the relevant differential
equations is exponentially growing, which makes a straightforward numerical approach
to these equations despairing. This well known difficulty in the problem under
discussion is usually identified as numerical swamping (Budden [1985]). Resolving the
problem of numerical swamping becomes, in fact, a key point in numerical study of
wave passage through the ionosphere. As it is typical of work based on numerical
simulations, its essential part remains virtually hidden. Then, every researcher, in order to
get quantitative characteristics of the process, such as transmission and reflection
coefficients, needs to go through the whole problem. That is why the number of
publications dealing with VLF wave transmission through the ionosphere does not run
short.
In this work, we develop a new approach to the problem, such that its intrinsic difficulty is
resolved analytically, while numerical calculations are reduced to stable equations
solvable with the help of a routine program. Using this approach, the field of VLF
wave incident on the ionosphere from above is calculated as a function of height,
and reflection coefficients for different frequencies and angles of incidence are
obtained. In particular, for small angles of incidence, for which incident waves
reach the ground, the reflection coefficient appears to be an oscillating function of
frequency.
Another goal of the work is to present all equations and related formulae in an
undisguised form, in order that the problem may be solved in a straightforward way, once the
ionospheric plasma parameters are given.
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References
Budden, K.G. (1985), The Propagation of Radio Waves, Cambridge Univ. Press, Cambridge,
U.K.
Ginzburg, V.L., and Rukhadze, A.A. (1972), Waves in Magnetoactive Plasma. In Handbuch der Physik (ed.
S. Flügge). Vol. 49, Part IV, p. 395, Springer Verlag, Berlin.
Helliwell, R. A. (1965), Whistlers and Related Ionospheric Phenomena, Stanford University Press,
Stanford, California. |
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