Statistics – Applications
Scientific paper
Dec 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996esasp.392..227b&link_type=abstract
Environment Modelling for Space-based Applications, Symposium Proceedings (ESA SP-392). ESTEC Noordwijk, 18-20 September 1996. E
Statistics
Applications
Scientific paper
Inhomogeneities of the electronic density inside the ionosphere develop in a number of cases along the terrestial magnetic field lines. Characteristic dimensions are of the order of 1 km. This can be set in evidence from satellite measurements. These inhomogeneities develop mostly during the night at equatorial latitudes and in polar regions. The high values of the electronic density reached during daytime in these regions create in nightime as a consequence of the deionization a number of inhomogeneities associated with the instability processes which develop inside the medium. The main difficulty to theoretically reproduce this phenomena is to obtain at the same time the mean value of the electronic density which is a first order phenomena and the fluctuations of this value which are second order phenomena, the required time and space steps for the analysis being rather different. The theoretical model which will be presented will describe a coupling between two models to try to reproduce the physics of the problem. Both models solve the plasma equations (continuity and momentum) inside the medium. The first model provides the mean value of the electronic density on a large area: typically the equatorial regions (+/- 20 deg) on a whole day (24 hours). Time and space steps will be relatively large such as to reproduce the average variation of the electronic density during the day and to take into account the "equatorial fountain" phenomena. The second model will put in evidence the development of instabilities. Hypotheses are slightly different in this case. In particular we will consider the local fluctuations of the electrostatic field. The first model solves the continuity equation for the ion O+. Other species of the medium, mainly N2 and O2, are however considered in the deionization process. The densities of these three major constituents of the high altitude ionosphere are obtained with the MSIS code. The momentum equation allows to obtain the velocity of the species. It is introduced in the right hand side of the continuity equation. As far as possible theoretical or experimental models are used in these equations to simplify the calculation. The continuity equation is finally set in the form of a parabolic equation which is solved using the classical Crank-Nicholson numerical scheme. The mean value of the electronic density acts as a source term in the second model. Continuity and momentum equations are transformed into a system of a time differential equation for the first one and of an elliptical equation with respect to the space for the second one. These two equations have to be solved simultaneously for each time step. Based of this analysis, theoretical models developed and examples of results will be presented.
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