  A model of the ionospheric global conductor is designed. The ionospheric
conductor is considered in the framework of a two-dimensional approximation
based on high conductivity in the direction of the magnetic field. Under this
assumption the magnetic field lines are equipotential, and the charge transfer
between them is determined only by integral Pedersen and Hall conductivities.
The model is constructed as the first approximation in the small parameter
expansion of the solution of the three-dimensional problems of electrical
conductivity. The small parameter is the ratio of Pedersen and field-aligned
conductivities. The space distributions of the Pedersen and Hall conductivities
are calculated using the empirical models IRI, MSISE, IGRF and applied to
construct the maps of the integral conductivities. The parts of the
magnetosphere with high conductivity across the magnetic field lines, namely,
the cusps and the plasma layer are analyzed. It is shown that the connection of
these magnetospheric conductors to the ionosphere in parallel makes the auroral
zones equipotential regions. As a consequence, for the ionospheric electric
fields, which generators are located in the ionosphere or in the atmosphere,
the global problem of electrical conductivity is separated into three
independent boundary value problems in three regions: two polar caps and the
main part of the ionosphere which includes the mid- and low-latitude parts of
the ionosphere. The model can be used for the analysis of the ionospheric part
of the Global Electric Circuit, for calculation of the ionospheric dynamo
electric field and as a fragment in more complex ionospheric and magnetospheric
models.
