Inhomogeneous Ionosphere - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 278

b − ( k )= 4 π
c

ik 0

I y ( k ) ,

k 2

k A Z ( m ) − − ik 0

a

E − ( k )= Z ( m )
a

b − .

(9.22)

The next step is to make the transition from (9.22) to expressions for ground
fields and to the inverse-Fourier transform of the obtained field.

9.2 Numerical Modeling

Let the ionosphere have a complicated spatial distribution of its tensor con-
ductivity including inclination of B 0 . This leads to the growth of ionospheric
conductivity tensor components on the geomagnetic equator. The distribu-
tion also includes a significant conductivity difference between the dayside
and nightside ionospheres.
The main idea of the numerical simulation is to use quasi-static field-
aligned currents (Alfven wave) and electric fields (FMS-wave) as the sources
of ground magnetic variations.
In the examples considered above, the Alfven wave was incident on the
ionosphere. This allowed us to uniquely determine the longitudinal currents
flowing into and out of the ionosphere. We could also determine the field-
aligned currents generated by horizontal inhomogeneities of the ionospheric
co nd uctivity. The longitudinal currents arising thereby are proportional to
√ ε m and connected with the transverse polarizing current by

ε m
4 π

∂ E
∂t .

To find the currents spread out over the ionosphere requires us to solve the
problem of MHD-wave propagation in the magnetosphere-ionosphere system.
The spread-out currents on one of the ionospheres are determined not only by
the properties of this ionosphere, but also by the conductivity of the conjugate
ionosphere. A solution of this problem is only possible for very simplified
models. An example of such a model is the box model with constant Alfven
velocity inside the box and with variable integral conductivity on its walls.
However, consideration of horizontal changes of integral conductivity in this
model obviously exceeds its 'accuracy' and can hardly help us to understand
the situation in the real magnetosphere.
The situation is simplified for quasi-static fields, the potential along a
field line is constant and determined by (9.10). In this case the problem with
two conjugate ionospheres can be reduced to one ionosphere conductivity of
which is the sum of their integral conductivities. This approach is only true
for frequencies

ω 1 ,
where ω 1 is the frequency of the fundamental FLR-harmonic.

ω