Effective Conductivity of a Cloudy Ionosphere - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 306

6.0

σ 01 =1.0
σ 02 =0.9

σ 01 =1.0
σ 02 =0.8

4.0

x 1 =0.5

2.0

x 1 =0.75

x 1 =0.1

0.0

0 20 40 60 80 100

Magnetization, β

Fig. 10.3. The ratio of effective Pedersen conductivity σ e P to spatial average
Pedersen conductivity σ P as a function of magnetization parameter β = β e =
ω ce /ν e . σ 1 and σ 2 refer to the local conductivities of inhomogeneities of the 1-st and
2-nd kind respectively. The curve with x 1 =0 . 5 relates to the case when areas of
two phases are equal. The curve with x 1 =0 . 1 shows σ e P ( β e ) /σ P ( β e ) in which
10% of the whole area is occupied by highly conductive component of σ P 1 , whereas
the rest of the mixture is σ P 2 =0 . 9 σ P 1

becomes

σ P 1 ) x 1 −

1
2

σ e P =( σ P 2 −

( σ P 1 + σ P 2 ) 2

+ 1
2

σ P 2 ) 2 .

− 4 x 1 x 2 ( σ P 1 − (10.38)

Hence, for example, for a mixtur e with equal portions of two components
x 1 = x 2 =0 . 5 , we have σ e P = √ σ P 1 σ P 2 .If σ P 2 =0 . 9 σ P 1 , as in Fig. 10.3,

then

=2 √ σ P 1 σ P 2
σ P 1 + σ P 2

σ e P

=0 . 6

σ P

independently of the intensity of the applied magnetic field as distinguished
from an open system in which σ e P / σ P ∼ 2 − 5for β e ∼ 30 − 100 .

Experimental Laboratory Simulation

The type of behavior predicted in the preceding theoretical considerations has
been confirmed in experiments with semiconductor films in strong magnetic