The Earth’s Magnetic Field - Ultra and Extremely Low Frequency Electromagnetic Fields - page 35

The magnetic substorms and storms trigger ULF MHD waves and the cos-
mic particle precipitation, which in turn influences the ionosphere conductivity
and radiowave reflectivity allowing for disruption of radio communications. The
enhancement of trapped particles may greatly affect the satellites even making the
electronic equipment and solar batteries inoperative. The magnetic storm may have
an impact on the power lines on the Earth, the atmosphere and biosphere and etc.
In relation to the next sections, it is pertinent to note that the interaction of
solar wind with the Earth's magnetosphere is similar in part to the global seismo-
tectonic phenomena such as earthquakes. The energy of solar wind plasma first
tends to pile up at the magnetotail followed by sudden energy release that in turn
gives rise to power fluxes of energetic particles and global redistribution of the
magnetospheric currents. At this point the magnetic storm and substorms play a role
of “magnetospherequake” while the major mechanism of these dramatic phenomena
has been something of a mystery.

1.4 MHD Waves

1.4.1 Basic Equations for MHD Waves in a Homogeneous

Conducting Medium

Variations in the solar wind dynamic pressure result in changes of plasma and field
properties throughout the excitation of MHD waves propagating in the solar wind
and the Earth's magnetosphere. A variety of MHD waves can be split into several
classes including the field line resonances, cavity modes, waveguide modes, and
so on.
Alfvén ( 1950 ) was the first who studied the MHD waves, which can propagate in
a conducting medium immersed in the external magnetic field. The MHD approach
can be applied to the waves propagating in both the plasma of solar wind and
magnetospheric plasma. To study these waves in a little more detail we consider
a homogeneous single fluid/plasma. The quiet state of the fluid is described by
the constant mass density 0 , the pressure P 0 , zero mass velocity, and the uniform
magnetic field B 0 . So, we use the subscript zero to describe the unperturbed values
of the medium parameters. Let ı be the small perturbation of the mass density, so
that ı 0 . The continuity equation ( 1.10 ) can thus be linearized, and we obtain

@ t ı C 0 r V D 0; (1.48)

where V is the mass velocity of the conducting medium.