Electrodynamic Properties of Space - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 36

This is a great step forward. In most of the problems we will present, we
simply replace the tensor of the specific ionospheric conductivity σ ij ( r ,z )bya
tensor of the integral conductivity Σ ij ( r ) that depends only on the horizontal
coordinates r . The ionosphere is presented as a thin conductive layer

or an interface between the magnetosphere and atmosphere with conductiv-
ity Σ ij (model of the 'thin' ionosphere). Magnetic fields above and below
the ionosphere are according to the Biot-Savart law a result of integration
throughout the volume occupied by electrical currents. In the approach based
on the integral conductivities the volume currents are replaced by the surface
currents J

{ x, y }

.
Note that great care must be exercised in moving from σ ij to Σ ij .First,
doing this, real polarized electric fields arising due to local inhomogeneities
can be much greater than the fields calculated on the basis of the integral
conductivities. We discuss this problem in Chapter 10 devoted to the effective
conductivity of a cloudy ionosphere. The second is the location of the surface
currents. Height dependencies of the Pedersen and Hall components of σ ij are
distinct from each other. As a consequence of that, the corresponding surface
currents should be placed at different heights. For example (see Fig. 2.4), a
small additional maximum of the Pedersen conductivity appears at the night
F -layer heights. Despite its smallness, its contribution to the Σ P of the entire
thickness of the ionosphere turns out to be roughly the same as that of the
E -region. And the last point that should be mentioned is the substitution of
σ by Σ to the loss of the inter ionosphere waveguide that can trap a certain
type of MHD-oscillations.
The ionospheric conductivity increases sharply in the auroral zones and
near the equator. The high-latitude maximum is caused by precipitations
of auroral particles. The integral Pedersen and Hall conductivities are
larger here by an order of magnitude than those of the middle-latitude
ionosphere.

{ J x ,J y }

Geomagnetic Equator

Contrary to the high latitude ionosphere where the conductivity is defined
mainly by precipitations of high energy particles, the equatorial conductivity is
determined by the geometry of the geomagnetic field. A peculiar phenomenon
appears in the vicinity of the geomagnetic equator in the form of a sharp
conductivity increase, first described by Cowling ([17], [18]). Its mechanism is
associated with the polarized charges arising on the upper and low ionospheric
boundaries.
Suppose that an electric field, excited in the equatorial ionosphere, is di-
rected along the equator across the geomagnetic field-lines. The nature of
the field is of no significance. It may presumably originate from high-latitude
sources producing global fields and currents, or from local near-equatorial per-
turbations, or from MHD-waves that penetrated into the region of the middle-
and low-latitude ionosphere. Let us choose, as before, the y -axis as pointing