Geoscience Reference
In-Depth Information
The existence of metallic ions helps the generation of the two-stream waves in
several ways: (1) they reduce the acoustic speed and thus the threshold drift; (2)
their meteoric origin most likely leads to the patchy horizontal structures that
polarize; and (3) they yield a higher
σ
H
/σ
P
ratio than molecular ions (Haldoupis
et al., 1997). Operating against all these positive features is the load the polar-
ization electric field must maintain. Typically,
F
P
E
P
and the source must
drive two F regions and the conjugate E region. This reduces
E
x
and most likely
explains why the midlatitude two-stream instability is relatively rare. On the
other hand,
>
H
=
E
B
, where
h
is the layer thickness, may be the appropriate
internal conductance. For
h
neh
/
10
5
cm
−
2
,
E
=
5 km,
n
max
=
H
=
2 mho, which is
sizeable.
Before leaving this subject, we explore the general case including neutral winds
and the possibility of polarization fields in
both
directions. In the plane perpen-
dicular to
B
, the two-dimensional current vector in the coordinate system used
by Haldoupis et al. (1997) is given by:
σ
P
E
x
+
E
x
+
u
s
B
cos
I
−
σ
H
J
=
(6.29)
E
y
+
E
y
−
+
σ
H
σ
P
u
e
B
where
u
s
is the southward wind,
u
e
is the eastward wind, and
I
is the dip angle.
We have included the polarization electric fields in both directions. Solving for
J
x
and
J
y
,weget
J
x
=
σ
P
E
x
+
u
s
B
cos
I
−
σ
H
E
y
+
u
e
B
E
x
+
E
y
−
J
y
=
σ
P
E
y
+
u
e
B
+
σ
H
E
x
+
u
s
B
cos
I
E
y
−
E
x
+
For the ideal case in which the local F region and conjugate E and F regions
are ignored, we set
J
x
=
0 and
J
y
=
0 and solve for the polarization fields
E
y
+
u
e
B
E
x
=+
σ
H
E
y
−
E
x
−
−
u
s
B
cos
I
(6.30a)
σ
P
E
x
+
u
s
B
cos
I
=−
σ
H
σ
P
E
y
E
x
+
E
y
+
−
u
e
B
(6.30b)
Simplifying the two equations, we get
E
x
=−
E
x
−
E
y
E
y
+
;
=−
u
s
B
cos
I
u
e
B
(6.30c)
and, finally,
E
x
=−
;
E
y
=
u
s
B
cos
I
u
e
B
(6.30d)
In this case, (6.30c) shows that large polarization fields do not build up. Further-
more, (6.30d) shows that since the electrons
E
×
B
drift in the total electric field
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