Electrodynamic Properties of Space - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 41

Anisotropic
dielectric

Magnetosphere

500 km

140 km

Anisotropic
conductor

90 km

60 km

Insulator

Co nd uc tor

Earth

σ g ~10 7 -10 10 s -1

Fig. 2.10. Sketch showing electrodynamic properties of the system Earth-
atmosphere-ionosphere-magnetosphere

field. The conductivity exhibits strong σ P and σ H . At that, σ P is determined
by ions and σ H by electrons. This layer can be represented by an anisotropi-
cally conductive layer.
In the F -layer motion of electrons and ions is governed by the geomagnetic
field. σ P steeply decreases, while σ H smoothly approaches zero.
In the outermost layer of the upper atmosphere, in the magnetosphere,
both electrons and ions are so strongly magnetized that there is no slip-
ping of electrons with respect to ions. As a result, the real part of the
transversal conductivity vanishes. The longitudinal conductivity tends to
infinity.
In the ionosphere, except the upper part of the F -layer, (1.102) for the ratio
of the polarized current to the Pedersen current, gives

| σ pol /σ P |≈ ω/ν i

1.
Thus, in the ULF-band we can restrict our consideration to the altitudes of
∼

−

1000 km only with the Pedersen and Hall conductivities. On the other
hand, in the magnetosphere, we can keep only the transversal polarized con-
ductivity. In this case, it is purely imaginary, and the dielectric permeability
ε m is real. Therefore, from here on we shall use ε m in the characterization of
the wave magnetospheric properties. Thus, the tensor of the dielectric perme-
ability ε m is diagonal. The transversal component of ε m is ε m = c 2 /c 2 A ,and
the longitudinal is

500

.
Such electrodynamic description of the magnetosphere-ionosphere plasma
applies only to large-scale perturbations. For the rather small transversal
scales L ⊥ we need to take into account the longitudinal resistivity. The L ⊥
can be estimated from the dispersion equation (1.119). For simplicity, let us
omit in (1.119) the Hall conductivity terms leaving only the terms with lon-
gitudinal conductivity. Then the left-hand side of (1.119) is a product of two
factors. Equating to zero each of them we obtain two equations. The first one
does not contain the longitudinal conductivity. And from the second equation

| ε |→∞