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by field-aligned currents and, as noted previously, evidence does exist for their
generation. This wave mode arises when
V
th
i
V
th
e
≤
J
||
/
ne
≤
which corresponds to parallel current due to a differential drift between ions and
electrons which falls between the ion and electron thermal speeds. In the lower
ionosphere collisions must be taken into account, while higher up collisionless
theory is adequate. The threshold parallel current density for O
+
and NO
+
cyclotron waves is plotted in Fig. 10.22 for
a
reference ionospheric profile and for
a wavelength corresponding to
√
2. The calculation includes collisions.
The required current densities are higher than the average observed field-aligned
currents but not higher than some of the largest reported examples of
J
(
kr
gi
)
=
(e.g.,
Burke et al., 1980). Thus, oxygen cyclotron waves should occur in the ionosphere
but are rare and may be restricted to the edges of auroral arcs and/or regions of
strong velocity turbulence.
||
600
550
500
450
400
350
O
1
300
NO
1
250
200
150
100
10
20
30
40
50 60
J
5
n
e
eV
d
(
amp/m
2
)
70
80
90
100
110
120
Figure 10.22
Threshold currents required to excite O
+
and NO
+
EIC waves in O
+
and NO
+
plasmas, respectively. The parameters used are
k
1
/
2
and
k
||
/
ρ
i
=
(
2
)
k
⊥
=
0
06. [After Satyanarayana and Chaturvedi (1985). Reproduced with permission of the
American Geophysical Union.]
.
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