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Farley showed that (1) larger-scale features map more efficiently to the F region
from the E region than small-scale features; (2) the height of the source field is
very important, with upper E-region structures very much favored as F-region
sources compared to lower E-region sources; and (3) roughly speaking, perpen-
dicular structures with scale sizes greater than a few kilometers map unattenu-
ated to F-region heights. The implication here is that if very large-scale electric
fields are generated in the E region, the potential differences thereby created map
up into the F-region ionosphere and beyond along the magnetic field lines deep
into space. As we shall see, these low-altitude electric fields dominate motions
of the plasma throughout the dense plasma region around the earth, termed the
plasmasphere.
Considering sources at F region and even higher altitudes, in the magneto-
sphere and solar wind, for example, the previous analysis can be used to show
that the mapping efficiency to the E region is even greater. In fact, within the mag-
netospheric and solar wind plasmas, the parallel conductivity is often taken to be
infinite, and thus the parallel electric field vanishes even when finite field-aligned
currents flow. As we shall see later, this assumption that
E
0 is a powerful
analytical device, allowing great conceptual simplifications in the understand-
ing of magnetospheric electric field and flow patterns. On the other hand, it
is exactly in the regions where the assumption of infinite conductivity breaks
down that very interesting phenomena occur. The generation of the aurora is an
example.
Since large-scale electric fields map along the magnetic field lines, we may
consider them to be independent of
z
in the magnetic coordinate system just used
(
B
in the
z
direction). This has some interesting consequences for ionospheric
electrodynamics. Consider the current divergence equation separated into its
perpendicular and parallel parts:
||
=
∇
⊥
·
J
⊥
=−
∂
J
z
/∂
z
⊥
=
σ
⊥
·
(
)
where
J
2 perpendicular conductivity
matrix. Ignoring the neutral wind for the moment,
E
⊥
+
U
×
B
and
σ
⊥
is the 2
×
∇
⊥
·
(
σ
⊥
·
E
⊥
)
=−
∂
J
z
/∂
z
Remembering that the
z
-axis is parallel to the magnetic field and integrating
from the top of the Northern Hemisphere ionosphere (
z
=
0) to a value
z
0
below
which no significant perpendicular currents flow yields
z
0
J
z
(
0
)
−
J
z
(
z
0
)
=
[
∇·
(
σ
⊥
·
E
⊥
)
]
dz
0
Although small currents do exit the base of the ionosphere and link up with
atmospheric electrical currents to complete the global atmospheric electrical
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