Geoscience Reference
In-Depth Information
In the F region
σ P σ H and the conductivity tensor is diagonal, although it
still holds that
σ P σ 0 . To a very good approximation,
ne 2
ν in
σ P =
2
i
in the F region. Assume first that the horizontal magnetic field lines extend for-
ever or, equivalently, that they terminate at both ends in an insulating layer. In
fact, the field lines bend and enter the E region, which has a finite conductivity
that varies with local time, season, and solar activity. (We return to this point
later.) The vertical component of the large-scale neutral wind field in the atmo-
sphere is always small, so we consider a simple model in which the thermospheric
wind is eastward and has a magnitude u that is uniform with height. In the text
we use the meteorological notation in which U
M
= (
,
,
)
, where u , v , and w
correspond to the zonal (positive eastward), meridional (positive northward),
and upward components, respectively. From (2.41), an electric current will flow
with magnitude and direction given by
u
v
w
J
σ · (
u a x ×
B
)
The wind-driven current is therefore vertically upward with magnitude J z
=
m 2 .
σ P uB . The current J z is quite small with a peak value of the order of 0.01
μ
A
/
However,
σ P varies considerably with altitude due to its dependence on the prod-
uct n
ν in . The zonal wind component, u , may also vary with height, but we assume
for now that viscosity keeps this variation small. At any rate, d
0,
and an electric field must build up in the z direction to produce a divergence-free
current. However, the “insulating plates” we have assumed at the ends of the
magnetic field lines do not allow a magnetic field-aligned current to flow at all
(i.e., J y =
P uB
)/
dz
=
, so in this first approximation a stronger condition on J holds than
the expression
0
)
0.
A plasma density profile for the postsunset equatorial F layer is shown in
Fig. 3.8a. As we noted in Section 2.2, gravitational forces do not cause the plasma
(with large
∇·
J
=
0, namely, J
=
to fall at the magnetic equator, since the velocity due to gravity
is perpendicular to the gravitational force. Recombination “eats away” at the
molecular ions on the bottomside, forming a steep upward-density gradient.
The result is a dense O + plasma with a well-defined lower boundary. To study
the electrodynamics of this region in a little more detail, we approximate the
actual situation shown in Fig. 3.8a with the configuration illustrated in Fig. 3.8b,
which shows a slab geometry with
κ i ,
κ e )
σ P constant inside the slab and zero elsewhere
and with zonal wind u constant everywhere. Since the current is upward inside
the layer and zero outside, charges pile up at the two boundaries as shown in
the figure. The magnitude of the electric field that builds up as a result of these
charges is such that
J z = σ P E z + σ P uB
=
0
 
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