MHD-Waves in Layered Media - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 184

Two wave ionospheric transformations are:

• a direct transformation of the Alfven/FMS waves into Alfven/FMS waves,

and

• a cross transformation Alfven waves are transformed into FMS waves and

vice-versa.
In order to explore these wave transformations, consider the ULF wave
propagation in the whole system; the ground-atmosphere-ionosphere-
magnetosphere modeled with a layered medium (see Chapter 2 and Fig.
2.10).

• In so doing, the ground is presented as a conductor with the conductivity

depending only on depth.

• The atmosphere can be conceived as a perfect insulator in the most of the

wave phenomena in the ULF range with rare exception such as penetra-
tion of vertical currents from the ionospheric heights to the ground and
vice versa and influence of the vertical electric field produced by light-
ning discharges, surface and sub-surface high-energy sources (e.g. volcano
eruptions, earthquakes, tsunami, etc.) on the ionosphere.

• We consider the ionosphere as an anisotropic conductor with the perfect

longitudinal conductivity.
The equipotentiality of the ionospheric field-lines allows us to change from
the real ionosphere to the model of a thin ionosphere with integral anisotropic
conductivity. Thus the ionospheric currents produced by the MHD-waves can
be replaced by the total current spreading over the whole ionospheric thick-
ness. In spite of the fact that this is an idealization, it enables us to reveal
the basic physical effects which are conserved in the more complicated models
that can be studied numerically.
Contrary to the previous chapters, where the MHD-wave features have
been studied in rather complicated magnetospheric models, consider here
the magnetosphere as a homogeneous half-space filled with collisionless mag-
netized cold plasma. The magnetosphere in this case can be approximated
as an anisotropic dielectric with infinite longitudinal dielectric permeability,
whereas the transversal component of the permeability is the ratio c 2 /c 2 A (see
Chapter 2).
In addition to the ionospheric penetration of the MHD-wave, a valid
demonstration of the applied ionospheric boundary conditions for the magne-
tospheric resonances will also be presented.

7.2 Model and Basic Equations

Plain Stratified Model

As a model of the ionosphere-magnetosphere, we consider a plasma in a ho-
mogeneous straight magnetic field B 0 . The inclination or dip of B 0 is I (see