Geoscience Reference
In-Depth Information
1.4
1.2
1
0.8
1
0.6
0.4
2
0.2
0
0
1
2
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x
Fig. 6.3 The perpendicular magnetic field components in the vicinity of field line resonance
position versus normalized variable x= n . The components LJ LJ ıB y LJ LJ
2
2 are shown with solid
and
j
ıB x j
line 1 and dashed line 2 , respectively
magnetosphere. We recall that in the model the coordinate x plays a role of the radial
distance in the actual magnetosphere. In this picture the resonance components,
ıB y and E x , are analog of the azimuthal magnetic field variations and the radial
electric field variations, respectively. A schematic plot of the amplitude variations
as a function of L-shell is shown Fig. 6.4 .
As one example, consider the MHD wave excited due to, say, plasma instabilities
at the magnetopause. A scheme of penetration of MHD wave from the magneto-
spheric boundary into its inner region can be summarized as follows. At first the
initial perturbations propagate as an FMS-wave from the magnetospheric boundary
to the turning point where wave reflection occurs. The electromagnetic field in this
region may be oscillatory in character. Once the turning point has been passed, the
amplitude of the FMS-wave falls off exponentially with distance up to the region
where the FLR conditions will occur. This implies that in this region the wave
frequency becomes close to the Alfvén resonance frequency of the magnetic shell.
In the vicinity of the resonance shell the energy of the FMS-wave is transferred in
part into the energy of the Alfvén oscillations by virtue of the mode coupling to
the shear Alfvén and FMS modes. The shear Alfvén wave can get trapped in this
region thereby exciting the FLR. At the resonance point a phase shift of between
the toroidal field components (ıB y and E x in the box model) on both sides of the
resonance is apparent. Some complication arises in this scenario as there are several
turning points or resonance shells.
 
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