The Earth’s Magnetic Field - Ultra and Extremely Low Frequency Electromagnetic Fields - page 40

As long as the magnetic field B 0 is weak or the fluid is practically incompressible
.c s !1 /, the Alfvén velocity V A can be neglected compared to the sound velocity
c s . In this extreme case the dispersion relation for the FMS wave is reduced to
!=k D c s . The FMS wave propagation brings the changes in distances between
the field lines that in turn is accompanied by plasma compressions and rarefaction,
that is, by plasma density variations. The implication here is that the FMS wave
can transform into the conventional sound wave, which propagates isotropically.
The FMS wave is often called a compressional mode in analogy to the acoustic
longitudinal wave. In the same limit the dispersion relation of the SMS wave
coincides with Eq. ( 1.59 ) for the Alfvén wave.
Conversely, if V A c s , that is B 0 0 0 c s , then the dispersion relation for
the FMS wave is reduced to !=k D V A , while the SMS mode is described by the
relation !=k D c s cos . This extreme case is of special interest in magnetospheric
plasma dynamics because the magnetic pressure of the plasma is much greater than
the thermal pressure in most regions of the Earth's magnetosphere. However, in
regions of the ring current the thermal pressure might not be negligible. In practice,
the phase velocity of the slow wave is rather small and therefore this wave is subject
to Landau attenuation. The SMS wave is usually not observed in space plasmas so
that this mode is of minor importance. There are therefore two most important MHD
modes in the homogeneous magnetized plasma. The first mode is the shear Alfvén
wave, which is guided by magnetic field lines according to Eqs. ( 1.59 )-( 1.61 ). The
next one is the FMS/compressional mode, which propagates isotropically at the
Alfvén velocity [Eq. ( 1.60 )].
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