Geoscience Reference
In-Depth Information
1
1
ξy
0.1
t = 0
t = 0
ξ
x
0
0
0.08
1
1
1
1
0.06
t =
τ
t =
τ
E
T
0
0
0.04
1
1
E
p
0.5
1
t = 3τ
t = 3τ
0.02
0
0
0.5
1
0
0
0.5
1
0
0.5
1
0
1000
2000
x
x
t
Fig. 5.8.
(Left frames) Consecutive couples of figures demonstrate temporal evo-
lution of
x
-distributions of
ξ
x
(radial) and
ξ
y
(azimuthal) displacements. The top
panel shows the initial displacement (
t
= 0 ), the middle is at
t
=
τ
and the bottom
is at
t
=3
τ
. The time scale
τ
corresponds to the time when the energies of toroidal
and poloidal components are equal. (Right frame) The time evolution of the poloidal
E
p
and toroidal
E
T
energy densities. After Mann and Wright [13]
Behind the turning point FMS-waves damp exponentially up to the magnetic
shell with the coordinate
x
n
where the frequency of the initial FMS-wave be-
comes equal to the FLR-frequency of the Alfven oscillations. In the vicinity of
x
=
x
n
the amplitude of the wave is growing, and the amplitude distribution
tends to the Lorentzian function. This picture can be more complicated be-
cause of the existence of several turning points or several FLR points. Due to
the tunnel effect, waves propagate through the region of exponential damping
up to the next turning point and again gets to the transmission region.
The distribution of FLR-periods shown in Figure 5.9 approximately cor-
responds to the dependence of the resonance period of the fundamental
harmonic on the magnetospheric parameter
L
. For the disturbances of the
period
T
shown with the horizontal dot-line, there are three FLR-points (ver-
tical solid lines). Thin horizontal line segments shows the region of the wave
damping.
The resonant increase of the amplitude of oscillations is also possible at fre-
quencies close to the frequencies of global resonances. Within the box' model,
the
Q
-factor of the cavity spectral line is high, and in the real magnetosphere
it may be significantly lower because of losses in the outer magnetosphere and
energy transport through the magnetic tail and the magnetopause into the
interplanetary space.
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