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of light just off the magnetic equator, a remarkable visual representation of the
equatorial anomaly region. In recent years, this emission line has been detected
by instruments on the IMAGE and TIMED satellites.
5.1.7 The Corotation Electric Field and Formation of the Plasmasphere
An important dynamical effect involves the nontrivial fact that the plasma on
low-latitude flux tubes to first order corotates with the earth. That this must
occur can be proved as follows. If the ionospheric plasma did not corotate,
in the nonrotating plasma frame there would be a very large neutral wind
U
R
and a current
J
depends on altitude, this current is
not divergence-free, and an electric field will build up in the E region of the
nonrotating frame until
J
=
σ
·
(
U
R
×
B
)
. Since
σ
=
σ
·
(
E
R
+
U
R
×
B
)
=
0. The current vanishes when the
plasma
E
B
drifts at exactly the same velocity as the earth rotates. Transforming
back to the rotating frame, we find
E
×
0. Now it is a remarkable fact that the
electric field in the nonrotating frame is transmitted along the magnetic field and
causes the entire inner magnetosphere to corotate with the earth, even though
there is virtually no neutral gas at high altitudes on those flux tubes.
Turning this argument around, it is exactly on those flux tubes that corotate
with the earth that cold ionospheric plasma can build up to the extent that is
observed in the dense plasma-filled region termed the plasmasphere. A crude
estimate of the latitude below which corotation dominates can be formed by
equating the corotation electric field to the electric field of magnetospheric and
solar wind origin. The comparison is properly done in the nonrotating frame.
At latitudes where the former dominates, flux tubes and the plasma attached to
them make a complete circuit of the earth in one day, allowing the trapping and
buildup of a cold hydrogen plasma of ionospheric origin (taking into account
the charge exchange process that converts O
+
into H
+
, of course). At higher
latitudes the flux tubes follow trajectories in which they are at times connected
to the solar wind or extend to very great distances down the magnetic tail. In
either case, the flux tube volume is so large that plasma almost continuously flows
outward, never building up a high density such as occurs in the plasmasphere.
Quantitatively, we can proceed as follows. The corotational electric field
at ionospheric heights is in the meridional direction and is given by Mozer
(1973) as
=
1
1
/
2
mV
3 sin
2
E
c
=
14 cos
θ
+
θ
/
m
(5.18)
where
is the latitude and a centered dipole field has been assumed. The coef-
ficient 14 in this expression is determined by the rotation speed of the earth, its
radius, and the magnitude of the magnetic dipole moment. For a planet such
as Jupiter, these parameters are all larger and the latitude region of corotation
dominance is quite a bit higher than for the earth. Notice that for
θ
θ
=
0 and
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