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Hill - Siscoe PCP (stat AMIE
60 lot)
Weimer PCP
Figure 8.1c
Weimer Convection Model PCP (thin line), along with the Hill-Siscoe polar
cap potential prediction (thick curve). [After Kelley et al. (2009). Reproduced with per-
mission of Elsevier Science Ltd.]
distance
s
where the ionospheric currents flow (200 to 80 km). Assuming that
no current flows out of the bottom of this region, we obtain an expression for
the field-aligned current (which is approximately vertical in the polar cap) at the
top of the region:
∇
⊥
·
ds
J
||
=
J
(8.12)
⊥
s
Since the electric field is independent of the variable
s
, we can substitute (8.7)
in (8.12) and remove the electric field and divergence operator from the integral
to yield the expression
||
=
∇
⊥
·
(
⊥
·
E
I
)
J
(8.13)
where
is the height-integrated horizontal conductivity tensor. Breaking this
expression into Hall and Pedersen components, we finally have
⊥
J
||
=
p
(
∇
⊥
·
E
I
)
+
E
I
·
∇
⊥
p
+
H
[
∇
⊥
·
(
E
I
×
s
)
]
+
(
E
I
×
s
)
·
∇
⊥
H
(8.14)
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