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state, however,
J
0 and no net electric current can flow. In this state,
projection of the plasma and neutral flow perpendicular to
B
must be equal and,
when added to the parallel motion, the two fluids move horizontally together.
This is illustrated in Fig. 5.15a and can be seen mathematically as follows. Once
the neutrals begin to move with velocity
U
, they produce field-aligned motion
of the ions such that
V
i
||
=
×
B
=
. The final vector plasma velocity in geomagnetic
(primed) coordinates is given by
U
||
V
i
=−
(
E
e
/
)
ˆ
a
y
+
ν
ˆ
B
cos
I
a
z
(5.25)
where
a
z
is a unit vector parallel to
B
. In the final state the neutrals will be
driven geographically northward with the velocity
ˆ
)
−
1
. Finally,
substituting this result into (5.2) yields the plasma
geographic
velocity
V
y
ν
=
E
(
B
sin
I
=
)
−
1
, and
V
z
=
E
0. The plasma thus does not end upwith a vertical velocity
component at all, but moves horizontally at the same speed as the neutrals. The
time constant for horizontal (meridional) acceleration of the neutrals by a zonal
electric field can be estimated from the initial
J
(
B
sin
I
×
B
force via
=
J
B
·ˆ
∂ν/∂
t
×
a
y
/
n
n
M
=
(σ
P
EB
/
n
n
M
)
sin
I
ne
2
2
In the F-region,
σ
P
=
ν
in
/
M
i
, which is proportional to the neutral density
due to the
ν
in
term. Thus, the
n
n
terms cancel out, and the acceleration depends
only on the plasma density. The acceleration time is thus of the order of
2
10
15
δ
t
=
×
/ν
(δν
B
/
E
)
s
10
11
m
−
3
, a time of the order of 1 h is required to accel-
erate the neutral atmosphere to a velocity
and for a density of 3
×
B
. Thus, although
this mechanism does lead to a net horizontal motion for the plasma, a consider-
able time is required to establish the effect. In addition to the long time constant,
this explanation ignores the problem of the origin of the electric field, which pre-
sumably requires an external magnetospheric source or a field applied from the
other hemisphere that maps to the local ionosphere along
B
. This process is thus
not likely to explain the common observation of horizontal ion motion. Notice
that
J
ν
comparable to
E
/
0 initially, as required when electrical energy is converted to the
mechanical energy in the neutral atmospheric flow. This process can therefore
be termed a “motor.”
A dynamo explanation is more promising, since the process self-consistently
generates an electric field and operates on a much faster time scale, which is of
the order of
·
E
≥
(
i
)
−
1
. For example, if we start with zero electric field but a neutral
meridional wind,
a
y
, in the equatorward direction (see Fig. 5.15b), a zonally
eastward current given by
J
ν
ˆ
B
sin
I
.
If boundary conditions are applied that force the net zonal current to be zero, a
=
σ
P
U
×
B
will flow with magnitude
σ
P
|
ν
|
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