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summer polar cap has much smaller electric fields in this scale size regime than
does the winter polar cap (Vickrey et al., 1985). For such a current source,
B
would be fixed by the source and, from (8.17b), the electric field would then
be determined by the ionospheric conductivity. The electric field would then be
inversely proportional to
δ
p
and thus, larger in the winter polar cap, where the
lack of solar illumination makes
p
small. Figure 8.1b shows that this idea may
be true, even at large scales.
Further insight comes from considering the Poynting flux. In the geometry
of Fig. 8.4,
δ
×
δ
E
H
is downward between the current sheets and the energy
m
2
. This energy must be dissipated as Joule heat in the
ionosphere at the rate of
W
(δ
δ
/μ
0
)
/
input is
E
x
B
y
W
E
x
. Integrating over the vertical extent
of the ionosphere yields a dissipation rate of
=
J
·
E
=
σ
p
δ
m
2
. Since the Poynting
flux yields the power flow into the region per unit area, we may equate the two
expressions, and once again we have the result (8.17c):
E
x
)
(
p
δ
W
/
δ
B
y
/δ
E
x
=
μ
0
P
The two approaches are therefore self-consistent.
To summarize, mechanical energy is converted into electromagnetic energy
in the solar wind generator. It flows down the magnetic field lines to the iono-
sphere as Poynting flux, where it is converted into heat by Joule dissipation.
For the typical parameters of
δ
E
x
=
50mV
/
m and
δ
B
y
=
500 nT, we can esti-
m
2
cm
2
mate the Poynting flux to be
s. This
is a substantial amount of energy, roughly 10
11
W over the whole region. It is
important to notice also that an energy flux of 20 ergs
δ
E
x
δ
B
y
/μ
0
=
0
.
02W
/
=
20 ergs
/
·
cm
2
/
·
s is very large com-
pared to typically observed energy fluxes in auroral particle precipitation except
for extremely intense localized auroral arcs. In fact, the Joule heat input is the
primary reason that the thermosphere has a local temperature maximum in the
high-latitude region, which competes with the solar photon-driven temperature
maximum that occurs near the subsolar point.
8.1.4 Additional Complexities
Before leaving this introductory discussion, we emphasize several important con-
siderations to keep in mind when examining the observations of high-latitude
ionospheric plasma motion in the next section. First, the qualitative discussion
presented previously is centered around a direct connection between the earth's
magnetic field and the IMF. The subsequent communication of the interplane-
tary electric field to the ionosphere and the magnetosphere gives rise to a two-
cell convection pattern as shown in Fig. 8.3a. This process, which produces
antisunward flow on open field lines if the IMF has a component in the south-
ward direction, was first described by Dungey (1961). Axford and Hines (1961)
showed that a similar motion of the plasma at high latitudes would result if
solar wind momentum was transferred across the magnetopause without any
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