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where
and ignore the
magnetic declination. Then we can solve (6.12) for the three components of the
ion velocity
κ
i
=
eB
/
Mv
in
. Let the wind be strictly zonal
(
U
=
u
a
x
)
ˆ
u
u
κ
i
cos
I
κ
i
+
V
iz
=
=
(6.13a)
)
−
1
κ
i
(
tan
I
sin
I
+
cos
I
)
+
(κ
i
cos
I
1
V
iz
κ
i
cos
I
V
ix
=
(6.13b)
V
iy
=
V
iz
tan
I
(6.13c)
For small
I
and at a height where
κ
i
=
1, which occurs at about 130 km, (6.13a)
and (6.13b) yield:
V
ix
=
V
iz
=
u
/
2
,
V
iy
=
0
The ions therefore have a component parallel to
U
but are also deflected in
the direction of the Lorentz force
q
, giving a net motion at a 45
◦
angle
to the neutral wind
U
, the deflection being upward for an eastward wind. The
net velocity is illustrated in Fig. 6.9a. For larger
(
U
×
B
)
κ
i
the deflection angle is larger
and for smaller
κ
i
the ion motion is nearly parallel to
U
. The mechanism that
creates the plasma layers is illustrated in Fig. 6.9b for the case of a vertical shear
in the zonal wind. As shown by (6.13a), ions above the shear point drift down-
ward, while those below drift upward. Plasma accumulates where the zonal wind
is zero.
Note that in the last sentence we shifted from a discussion of
ion motion
to
a statement about
plasma accumulation
. In the geometry of Figs. 6.9a, with
the magnetic field perfectly horizontal, the highly magnetized (high
κ
e
) electrons
could not move perpendicular to
B
to join the converging ions. Furthermore,
the field lines bend into a very low plasma region, and there is no source of
electrons to move along the magnetic field lines and neutralize the ions. A huge
space charge electric field would build up, and the whole process would grind to
a halt.
However, if there is even a slight dip angle, electrons can move along the mag-
netic field from a region of ion divergence to one of ion convergence in response
V
i
V
iz
â
z
â
x
V
ix
B
U
Figure 6.9a
Ion velocity vector (
V
i
) and its components subject to an eastward neutral
wind when
κ
i
=
1.
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