Geoscience Reference
In-Depth Information
circuit, we ignore this interesting phenomenon by setting
J
z
(
is
then the field-aligned current entering the ionosphere from above and is related
to the divergence of the perpendicular current density. Now, since
E
z
0
)
=
0.
J
z
(
0
)
is inde-
pendent of
z
, we may move it and the divergence operator through the integral
to yield
⊥
J
z
=∇·
(
·
⊥
)
E
(2.50)
where
is the perpendicular height-integrated conductivity tensor
P
−
H
=
H
P
and we have dropped the argument of
J
z
and assume that we measure
J
z
at a
sufficiently high altitude that all perpendicular ionospheric currents are below
it. Since conductivity has units of mhos per meter,
has units of mhos. The
E-region values vary from a few tenths of a mho in the nighttime midlati-
tude region to several tens of mhos during a strong auroral precipitation event.
F-region values maximize at the magnetic equator where the field lines are very
long and rapidly decrease at midlatitudes and higher.
Some insight can be achieved by letting
be uniform in the horizontal
directions. Then the perpendicular divergence operator does not operate on it
and
)
−
H
∂
x
+
H
∂
y
+
P
∂
y
J
z
=
P
(∂
E
x
/∂
x
E
y
/∂
E
x
/∂
E
y
/∂
which can be written
⊥
)
+
H
∂
x
J
z
=
P
(
∇
⊥
·
E
E
x
/∂
y
−
∂
E
y
/∂
The last term is the
z
component of
∇×
E
, which vanishes for steady magnetic
fields, and we have
J
z
=
P
(
∇
⊥
·
E
⊥
)
(2.51)
10
−
5
m, which
P
≈
⊥
∼
/
∇
⊥
∼
∼
In the auroral zone
10mho,
E
50mV
m, and
1/
L
m
2
. Small-scale currents can be more
than an order of magnitude higher. Field-aligned currents at mid- and low lati-
tudes aremuch smaller but still play a very important role in the physics. Equation
(2.51) plus Poisson's equation (2.25b) show that current flows downward in the
Northern Hemisphere where the net charge density in the ionosphere is positive.
μ
/
yields a typical large-scale
J
z
of order 5
A
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