Geoscience Reference
In-Depth Information
V
2
Mechanism
Addends
V
2
and
V
3
are entirely determined by the electron velocity equal in
the first approximation to the drift velocity
v
e
=
c
E
×
B
0
B
0
.
(12.16)
In the general case, (12.16) must be supplemented by terms that take
into account, first, collisions in the ionosphere and, second, electron velocity
along the magnetic field, which is not equal to zero in the Alfven waves. The
directional electron velocity
v
e
is
N
e
e
j
e
+
j
⊥
,
1
v
e
=
−
(12.17)
σ
He
E
⊥
×
B
0
j
e
=
σ
e
E
,
j
⊥
=
σ
Pe
E
⊥
−
,
(12.18)
B
0
where
σ
e
,
σ
Pe
and
σ
He
are longitudinal, Pedersen and Hall electron conduc-
tivities, respectively.
E
and
E
⊥
are components of the wave electric field,
parallel and transverse to
B
0
. For the electron conductivities, we have from
(1.93), (1.94), and (1.98)
N
e
e
2
m
e
ν
e
,
σ
0
1+
β
e
2
,
σ
e
=
σ
0
=
Pe
=
He
=
β
e
σ
Pe
,
(12.19)
where
β
e
is the electron magnetization parameter,
ν
e
is the electron collision
frequency.
The mobility along field-lines exceeds transverse mobility by 5-6 orders.
Hence
E
= 0. This gives
E
z
=
−
E
x
cot
I.
(12.20)
Using transformation (7.1) and (12.20) from (12.18) we obtain
j
xe
=
σ
Pe
E
x
+
σ
He
E
y
sin
I
+
j
e
cos
I,
(12.21)
σ
He
sin
I
E
x
+
σ
Pe
E
y
,
j
ye
=
−
(12.22)
j
ze
=
−
σ
Pe
E
x
cot
I
−
σ
He
E
y
cos
I
+
j
e
sin
I,
(12.23)
The main contribution to the longitudinal current
j
comes from electrons.
Indeed, total
j
is a sum of electron
j
e
and ion
j
i
:
σ
i
σ
⊥e
j
e
,
j
=
j
e
+
j
i
and
j
i
=
where
σ
i
,j
i
are longitudinal ion conductivity and current. Hence
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