Effective Conductivity of a Cloudy Ionosphere - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 310

contributions to the effective Pedersen conductivity are not equal because of
different magnetization of electrons ( β e >> 1) and ions ( β i << 1).
Let us illustrate the relative contribution of inhomogeneities to the effec-
tive conductivity of the ionospheric E -layer. This layer provides the main
contribution to the integrated conductivities. In this case we have strong
magnetizations of electrons and a weak magnetizations for ions. Formally
expressions (10. A.3), (10. A.5) are appropriate for calculations of both elec-
tron and ion components of the effective conductivity. However, a correction
for ion conductivity due to concentration fluctuations is very small when ions
are not magnetized β i << 1.
One can estimate the relative values of electron and ion contributions to
the E

layer σ P . The effective collision frequency of ions is ν in =10 − 10 N m √ T/
300 where N m and T are the concentration and temperature of neutrals, re-
spectively. For N m =10 13 cm − 3 and T = 300 ◦ Kwehave ν in ∼

−

10 3 s − 1 . Here

10 2 s − 1 . Hence β i = ω ci /ν in ∼

ω ci =2 . 5 × 0 . 2. For electrons β e = ω ce /ν en ∼

10 2 . In homogeneous E -layer σ P ∼ Ne 2 ν en / ( m e ω ce ) , σ i P ∼ Ne 2 / ( m i ν in ).

10 − 2 .
The Pedersen conductivity of a homogeneous ionosphere is defined by the
ion component. But in an ionosphere with stochastic inhomogeneities, the
electron component can match the component produced by ions. From (10.29)
it follows that ξ 3 = 1 when ( β e ε 2 ) 2 / 3 =20 , or ε =0 . 9. The effective current
will be quadratic with respect to ε . Therefore, the perturbation due to the ion
current will be approximately 0.8 and the perturbation due to the electron
current will be 1. The total value of the effective current will be 2.8 instead of
1.8 as was expected from perturbation theory. The contribution of stochastic
inhomogeneities to the effective Pedersen conductivity becomes comparable
with the background Pedersen conductivity of lower ionosphere for relative
concentration perturbations of ε =0 . 9.
Estimates for 2D media in a strong magnetic field ( δσ e P

σ P σ i P So, / =5 ×

σ P

)have
shown [19] that the transverse conductivity perturbation may be found from
the relationship

L L z 1 / 2

ε
β e

δσ e P ∼ σ 0 ,

where L z ,L ⊥ are the characteristic scale-size of the ionospheric E -layer and
the transverse scale-size of the inhomogeneities, respectively. Taking into ac-
count σ P ∼ σ 0 /β e , then for example for L ⊥ ∼

L z , we find

ξ 2 = δσ e P

δσ e P δσ e P

σ P ∼ σ i P ∼ ∼

β e · ε/ 20 .

σ P

· 20

One can see, that ξ 2 =1for ε =0 . 2. A comparison of the 3D and 2D cases
shows that ε comes into prominence in the 2D case for smaller values of ε .In
this case, we expect an enhancement of the effective Pedersen conductivity by
a factor 2.