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E
F
1
PF
1
PF
R
F
R
F
k
2
2
k
2
2
∫
B
1
∫
B
1
R
0
R
0
R
0
R
0
0
0
E
E
1
PE
R
E
s
I
uE
PE
V
uE
( a )
( c )
E
F
1
PF
1
PF
R
F
R
F
V
uF
k
2
2
∫
B
1
k
2
2
∫
B
1
R
0
R
0
R
0
R
0
0
0
1
PE
R
E
s
V
uE
1
PE
R
E
s
I
uE
E
E
( b )
( d )
Figure 6.41
Circuit models for E-F coupling. (a) Mapping of an electric field from an
E
s
layer to the F layer. (b) Wind driven
E
s
layer source. (c) Thévenin equivalent for (b).
(d) Wind-driven sources in both
E
s
and F layers.
conductivity of the F region (
PF
), and the FLI Pedersen conductivity of the
E
s
layer (
PE
) as shown. It is assumed that the source has a sinusoidal form with
wavenumber
k
. Figure 6.41a shows how the electric field in the F layer due to
an electric field applied in the
E
s
layer is given by a voltage divider between
the field-aligned resistor
R
0
and the F-layer resistor
R
F
. Figure 6.41b shows
the voltage divider applicable to determining the F- and
E
s
-layer electric fields
due to a wind-driven Hall current, such as in the wind-driven Haldoupis et al.
(1996) polarization mechanism. Figure 6.41c shows the Thevenin equivalent of
Fig. 6.41b, and Fig. 6.41d shows the generalization to sources in both the
E
s
and
F layers.
Using Fig. 6.41d, Cosgrove and Tsunoda (2004b) derive the following approx-
imate expression for the coupled system growth rate in term of the isolated
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