Geoscience Reference
In-Depth Information
where
R
AA
is the reflection coecient of the Alfven wave into itself (see
(11.27)). From (14.33) we find
2+
X
c
/
√
ε
m
u
3
ρ, t
2
R
AA
2
h
c
A
q
(
ρ, t
)
2+
X
c
/
√
ε
m
,
u
1
(
ρ, t
)=
−
−
2+
X
c
/
√
ε
m
R
AA
u
3
ρ, t
X
c
/
√
ε
m
+
2
h
c
A
q
(
ρ, t
)
2+
X
c
/
√
ε
m
.
u
3
(
ρ, t
)=
−
(14.34)
This allows us to study the Alfven wave emission from the cloud. Until
t<
2
h/c
A
, the downward propagating Alfven wave does not yet 'know' that below
it, at distance
h
, there is a conductive layer. At
t
=2
h/c
A
the wave has reached
the ionosphere and has returned. Between 2
h/c
A
<t<
4
h/c
A
, the emission is
a superposition of the direct wave and the wave reflected from the ionosphere;
between 4
h/c
A
<t<
6
h/c
A
,
the waves twice reflected from the ionosphere
and once from the cloud are added, etc.
Let us suggest that the MHD-pulse is induced by a plasma release with
parameters like 'Trigger' (see Table 14.1). At
1 s after the emission 500 m
from it, the dynamo-field
E
d
(14.22) amplitude reaches 50-100 mV/m. The
height variations of the estimated electric field between 150 and 300 km did
not exceed
≈
20 mV/m. Thus the numerical simulations demonstrate that
E
d
is weakly dependant on the release altitude. For example, peak values of the
electric field are
≈
≈
25 mV/m at an altitude of 150 km, and
≈
40 mV/m at
300 km.
From (14.32) and (14.34) one can find the electric and magnetic fields in
the Alfven wave radiated from the cloud. The field is reduced from
∼
100 nT
at
t
1 s, this confirms the validity of the qualitative
dynamics pattern of the expanding cloud which was discussed above.
The longitudinal currents can be estimated from (14.31). It follows from
the calculations that the current in the radiated pulse 1 s after release is 10
∼
0.1sto10nTat
t
∼
−
−
20
µ
A
/
m
2
. Currents of such magnitude, obviously lead to the development
of various plasma instabilities, to the appearance of anomalous resistance
along the field-lines, to the excitation of appreciable longitudinal electric fields
and to the acceleration and precipitation of particles.
Up to now, we have not considered the finite longitudinal resistance.
By substituting collision frequencies and electron concentrations typical for
≈
150 km into (1.127), we find that a finite longitudinal resistivity must be
included in the consideration if the transversal scale is less than
1km. In-
cluding the longitudinal resistivity reduces by several orders of magnitude the
electric and magnetic fields and the longitudinal current. To summarize, at
the initial stage, up until
≈
∼
10 ms, the equations we have used break down.
And at
1 s it is possible to have an order of magnitude estimation. The
amplitude values given in the estimation above are 2-3 times larger than the
expected values. Neglecting the longitudinal resistivity is only possible after
∼
∼
10 s. And it is only after such a time, that the theoretical concepts developed
in the preceding chapters may be correctly applied.
Search WWH ::
Custom Search