Geoscience Reference
In-Depth Information
Estimations of
N
T
Modulation
An MHD-wave coming from the magnetosphere to the ground produces TEC-
variations
N
T
the time derivative of which is
R
∂N
T
∂t
∂N
e
∂t
=
dz,
(12.47)
S
where
∂N
e
/∂t
is found from the continuity equation (12.9). For the times
considered fluctuations in the rates of ion production
Q
and loss
L
prove to
be insignificant, (12.9) becomes
∂N
e
∂t
=
−
N
e
∇
·
v
e
−
(
v
e
·
∇
)
N
e
.
(12.48)
The second term in (12.48) does not contribute to the time variations
N
T
if
N
e
= 0 in the boundary points [13]. It is easy to confirm by integrating (12.48)
over
z
for
N
e
= 0 at the end points of the integration. The main effect comes
from the first term in the right-hand part of (12.48) describing the plasma
compression in the wave field (for details, see [13]).
In the
F
-layer, which gives the dominant contribution into
N
T
,wecan
assume the velocity to be given by the
E
×
B
drift, so the electron velocity
c
B
0
v
e
=
E
×
B
0
.
In order to simplify consideration, let us assume that
B
0
is homogeneous and
directed vertically upward. Then
c
B
0
(
∇
·
v
e
=
∇
×
E
)
z
.
(12.49)
The right hand of the last equation can be rewritten using Faraday's law.
Then, (12.48) becomes
∂b
∂t
,
1
N
e
∂N
e
∂t
1
B
0
=
(12.50)
where
b
=(
b
B
0
)
/B
0
.
To simplify calculations, we make the inessential assumption that the mag-
netospheric radio beacon is located in the zenith above the receiver
R
. Then
·
b
B
0
dz
N
e
dz .
=
N
e
δN
T
N
T
(12.51)
Integrating in (12.51) is performed in fact from the
E
-layer (
z
=0)upto
2
10
3
km. Let us make use of the results of Chapter 7.
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