Geoscience Reference
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Then (12.26) becomes
c
B
0
E
y
sin
I
j
z
N
e
e
cot
I,
v
xe
=
−
c
B
0
sin
I
E
x
,
v
ye
=
−
c
B
0
E
y
cos
I
j
z
N
e
e
,
v
ze
=
−
(12.27)
or in the vector form
j
N
e
e
v
e
=
c
E
×
B
0
B
0
−
B
0
B
0
.
(12.28)
The expression for
V
2
in view of only electron drift can be written
z
0
∂µ
∂N
e
∂N
e
∂z
cos
I
B
0
V
2
=
−
c
E
y
dz.
(12.29)
0
Equation (12.29) describes the so-called 'motor' part of dynamo action [16],
in which
V
∗
equals to the vertical component of electron velocity under the
action of the east-west component of the electric field. This mechanism can
be identified by a reflection level motion. Indeed,
∂µ
∂z
∂µ
∂N
e
∂N
e
∂z
∂µ
∂B
L
∂B
L
∂z
∂µ
∂B
T
∂B
T
∂z
.
=
+
+
(12.30)
B
L
and
B
T
change slowly with altitude
z
. Simple numerical estimations show
that the terms containing
∂B
L
/∂z
and
∂B
T
/∂z
in (12.30) can be neglected.
Therefore,
∂µ
∂z
≈
∂µ
∂N
e
∂N
e
∂z
.
(12.31)
E
y
changes slowly with altitude, therefore it follows from (12.29) that
z
0
c
cos
I
B
0
dµ
=
c
cos
I
B
0
V
2
=
−
E
y
E
y
.
(12.32)
0
Thus
V
2
is indeed equal to the vertical component of electron velocity and by
virtue of being independent of altitude, coincides with the velocity of reflection
level motion.
V
3
Mechanism
Transform now the expression for
V
3
. We neglect changes in
B
0
. Then
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