Geoscience Reference
In-Depth Information
Poole
et al
. [14] expressed
V
∗
as the sum of four addends
V
∗
=
V
1
+
V
2
+
V
3
+
V
4
,
(12.10)
where
∂µ
∂
B
L
dz,
z
0
∂
B
L
∂t
∂µ
d
B
T
∂
B
T
∂t
V
1
=
+
(12.11)
0
z
0
∂µ
∂N
e
(
v
e
·
∇
V
2
=
−
)
N
e
dz,
(12.12)
0
z
0
∂µ
∂N
e
N
e
∇
·
V
3
=
−
v
e
dz,
(12.13)
0
z
0
∂µ
∂N
e
(
Q
V
4
=
−
L
)
dz.
(12.14)
0
V
1
Mechanism
For a vertically propagating radio signal
∂
∂t
B
L
=
∂t
(
B
0
z
+
b
z
)=
∂b
z
∂
∂t
.
The time derivative of the transverse component
B
T
can easily be found in
the linear approximation with respect to
|
b
|
/
B
0
:
B
T
=
(
B
0
T
+
b
x
)
2
+
b
y
+
b
x
B
0
T
2
+
b
y
B
0
T
2
1+2
b
x
B
0
T
=
B
0
T
≈
B
0
T
+
b
x
.
Therefore
∂B
T
∂t
=
∂b
x
∂t
.
Substitution this relation into (12.11) for harmonic perturbations
∝
exp(
−
iωt
)
leads to
dµ
dB
L
b
z
+
b
x
dz.
z
0
dµ
dB
T
V
1
=
−
iω
(12.15)
0
Equation (12.15) describes the contribution to the Doppler velocity
V
∗
associ-
ated with the dependence of the refractive index on magnetic field variations.
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