The Ionosphere and Atmosphere - Ultra and Extremely Low Frequency Electromagnetic Fields - page 52

Fig. 2.5 Typical profiles of
the parallel k , Pedersen P ,
and Hall H conductivities
for the mid-latitude
ionosphere. Adapted from
Kelley ( 1989 )

s P

10 −6 s ×

s H

S /m

10 −8 10 −7 10 −6 10 −5 10 −4 10 −3

The Hall conductivity, H , amounts to the value of about .3-8/ 10 4 S=matthe
altitude range 100-110 km. In the nighttime the maximum value of H becomes as
much as .0:8-1:5/ 10 5 S=m. This conductivity is significant only in a narrow
altitude range of the E layer since H falls off more rapidly with altitude than
does P . The Hall conductivity is important due to its role in a mode coupling
mechanism, which relates the shear Alfvén and compressional waves in the E layer.

2.2.2 Shear Alfvén and Compressional Waves

in a Homogeneous Magnetized Plasma

It is customary to introduce the tensor of dielectric permittivity of the plasma via

" D O 1 i O =." 0 !/: (2.16)

Here O 1 denotes a unit matrix, " 0 is the electric constant (dielectric permittivity of
free space), and tensor is given by Eq. ( 2.5 ). The conduction and displacement

currents entering the Maxwell's equation ( 1.1 ) can be expressed through the tensor
of dielectric permittivity to yield

O

i!
c 2 "

r B D E : (2.17)

At high altitudes above 200-300 km the collisionless approach is more appro-
priate to study the electrodynamics of plasma. In the extreme limit when the
collision frequencies e and i are negligible compared with ! the parallel and
Pedersen conductivities in Eqs. ( 2.7 )-( 2.9 ) are reduced to pu re i maginary quantities
k D ie 2 n=.m e !/ and P D i! 0 =B 0 , where 0 D nm i is the plasma mass
density. The Hall conductivity becomes insignificant at higher altitudes and thus can
be dropped. This means that in the reference frame with z axis parallel to the
magnetic field the plasma dielectric permittivity tensor becomes diagonal