Geoscience Reference
In-Depth Information
Induced Magnetospheric MHD-Wave
Let us suppose that the perturbation of the neutral gas propagates in the
meridional plane in the middle latitude E-layer. Denote the neutral velocity
transversal to
B
0
as
v
n⊥
. Then the dynamo-field
E
dy
=
B
0
v
n⊥
/c
produces
the Pedersen
j
Pd
=
j
yd
y
and Hall
j
Hd
=
j
xd
x
currents (see (2.8) for
σ
→∞
)
σ
H
sin
I
v
n
c
yd
=
σ
P
v
n
c
j
xd
=
B
0
,
B
0
.
j
Pd
= 0 and the current does
not generate the longitudinal currents and does not excite an Alfven wave.
However, for the Hall current
Since
v
n⊥
is independent on
y
, then
∇
·
= 0. From the continuity
equation for the total current it follows that the Hall current, induced by the
neutral motion, is closed by the longitudinal current.
The MHD-equation for the field-aligned current
j
∇
·
j
Hd
=
∂
x
j
xd
(
x, z
)
of an Alfven wave in
the magnetosphere can be obtained from (7.136)
∂
2
j
∂t
2
∂
∂s
c
2
A
∂
∂s
j
−
=0
,
(15.28)
where
s
is the coordinate along the field-line.
For approximate estimates we take the geomagnetic field-lines to be
equipotential in the
E
-layer. This assumption holds for disturbances with
large enough horizontal scales. A typical spatial scale,
l
of the electric po-
tential along the field line is related to the horizontal scale,
l
⊥
,
across the
magnetic field as
σ
σ
⊥
1
/
2
l
≈
l
⊥
.
(15.29)
In the E-layer,
σ
/σ
⊥
≈
10
4
then the perturbations with scales of
l
⊥
≈
1km
are equipotential in the ionosphere of thickness of
l
≈
100 km. Since
σ
/σ
⊥
grows rapidly with height, condition (15.29) does not impose any significant
constraints on
l
⊥
at
E
-layer heights, or higher.
Let us now estimate
j
the emitted Alfven pulse. We replace the conductive
layer with a thin film of integral conductivity
Σ
P,H
, and external surface
current
I
xd
=
B
0
Σ
H
sin
I
v
n
c
.
(15.30)
The acoustic pulse, while propagating in the ionosphere, can generate sur-
face current (15.30). This surface current is not zero as long as the vertical
scale of the change in Hall conductivity is less than, or comparable with, the
vertical scale of the acoustic pulse. Then the current (15.30) will be generated
by the compression and rarefaction part of the acoustic pulse. At shorter
scales, the magnetic fields are produced by the thin currents , interfere with
each other and the resulting field vanishes and (15.30) is inapplicable.
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