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v
V
i
Plasma density
increase
s
v
Up
V
i
Plasma density
decreases
Plasma density
increases
North
v
East
I
V
i
B
v
V
i
B
B
B
Plasma flow
Neutral wind
Magnetic field lines
Figure 6.8
Meridional and neutral wind (horizontal vector) and ion flow vectors (large
arrows) due to a gravity wave with a large wavelength in the
y
direction and a smaller
wavelength in the
z
direction.
sign, the plasma either converges to or diverges from the altitude where the shear
occurs. A layer of ionization will arise in the convergence zone. This wind shear
theory for layer formation was first suggested by Dungey (1959), was extended
by Whitehead (1961), and seems to explain many of the observations quite well
for intermediate layers. The situation illustrated in Fig. 6.8 is most effective in
the lower F region. At higher altitudes, diffusion parallel to
B
keeps sharp layers
from forming. This can be seen by comparing the time constant at which plasma
converges, which is of the order of
)
−
1
, with the time constant at
(
k
z
v
cos
I
k
z
D
A
)
−
1
. For
which it diffuses, which is of the order of
(
k
z
diffusion is too strong for layers to form. For
D
A
≥
v
cos
I
/
10m/s,
we can estimate the critical value for
D
A
to be roughly 10
4
m
2
/s at 200 km. For
molecular ions at 500
◦
K,
D
A
=
λ
z
≤
2
π
H
and
v
cos
I
/ν
n
m
2
/s and thus we find that gravity
waves are not very efficient in producing layers above about 200 km because
diffusion is too fast.
At heights below 130 km, the high collision frequency with neutrals merely
pushes the ions horizontally, and no layers are formed due to meridional winds.
However, shears in the zonal wind component can take over the production of
layers below about 130 km. The mechanism stems from the Lorentz force felt by
the ions when subject to a wind field. For example, referring to (2.22b), which
gives a general relation for the ion velocity, we are interested in the equilibrium
case where
d
V
i
/
10
4
64
×
n
, and
g
and
consider collisions between ions and neutrals only. Then, expressing (2.22b) for
ions in the earth-fixed frame, we have
κ
i
V
i
×
B
=
dt
=
0. In addition, we ignore the effects of
E
,
∇
V
i
−
U
(6.12)
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