Effective Conductivity of a Cloudy Ionosphere - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 294

where β i 1, the electric conductivity is therefore determined only by

electrons, i.e. both Pedersen σ P ( x, y, z ) and Hall σ H ( x, y, z ) conductivities
are electron conductivities, respectively, σ Pe ( x, y, z )and σ He ( x, y, z ), with
σ He ( x, y, z ) σ Pe ( x, y, z ). Hence, an electric field applied to such plasma

produces a large Hall current j H and a very small Pedersen current j P .
Since our concern is the integral magnetic field on the ground, caused
by a large-scale MHD-wave that can simultaneously 'cover' a vast number
of small random inhomogeneities, the magnetic effect caused by these ir-
regular currents is equivalent to the magnetic effect of an average current
flowing over the ionosphere with an effective conductivity σ eff . Therefore the
problem reduces to the following question: how can we define σ eff if we have
detailed information either about every inhomogeneity or about the corre-
lation properties of the random inhomogeneous distribution of the specific
conductivities?
At first glance it would seem that σ eff is the sum of the mean conductivity
and its variability. But, this is not necessarily so. The reason for this is that
the specific conductivity is a tensor. And therefore the current is a product of
the electric field vector and this tensor. The resulting current is rotated with
respect to the applied electric field. In the degenerate case, in which σ P is
much smaller than the σ H and the plasma is homogeneous, only Hall current
is generated by the applied electric field. A small inhomogeneity creates a
polarized electric field and a Pedersen current collinear with the applied elec-
tric field. These are, of course, extensively simplifying assumptions. In reality,
it turns out that for magnetized electron plasma the total j P is defined by
δN e ·

β e. [17].
This effect occurs because the two tensor elements of the electron con-
ductivity depend differently on strong magnetic field ( β e 1). In the case

of a medium containing only one sort of charge carriers, let us say elec-
trons, σ 0 /B 0 and

σ 0 /B 0 . The polarization fields produce
additional Pedersen and Hall currents. Their contributions to the effective
Pedersen conductivity are not equal, since δσ P ∝

σ Pe ∝ σ He ∝

ε/B 0

while δσ H ∝

ε/B 0

where

( N e ( r )

) 2 1 / 2

δN e ( r ) 2 1 / 2

=

1 / 2

− N e ( r )

δσ 2

ε = ≡ (10.1)

N e ( r ) N e ( r ) σ

2

is a value which characterizes inhomogeneities.
At height h 100 (see Fig. 2.5). This means that a 10%

perturbation of the electron density N e can produce a Pedersen conductiv-
ity anomaly

≈ 100 km β e ≈

β e = 10 times greater than the unperturbed conductivity.
Obviously, the connection between the initial j H and the induced j P and
with it the effect of the anomalous σ eff , disappears if instead of a finitely
thick ionosphere we use the 'thin sheet' approximation, and instead of σ
we use Σ .

∝ ε ·