DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

magnetoacoustic wave
or a remnant field. The moon and Mars currently
do not have active magnetic fields, but
rocks from both bodies indicate that magnetic
fields were present in the past. The large Jovian
moons also appear to have weak magnetic fields.
The Earth’s magnetic field has undergone polarity
reversals throughout history, the discovery
of which helped advance the hypothesis of sea
floor spreading, which eventually led to the theory
of plate tectonics. The area of space where
a planetary body’s magnetic field interacts with
the solar wind is called the magnetosphere.
magnetoacoustic wave Any compressive
hydromagnetic wave; frequently called magnetosonic
wave. Magnetoacoustic waves are characterized
by fluctuations of density and magnetic
field strength, and by linear polarization of
fluctuations in the velocity and magnetic field
vectors. Their phase and group velocities are
anisotropic in the sense that they depend on
the direction of propagation with respect to the
mean magnetic field.
The theory of magnetoacoustic waves can be
developed in the framework of either magnetohydrodynamics
or kinetic theory. The magnetohydrodynamic
approach gives two different
kinds of magnetoacoustic wave, conventionally
called the fast and slow magnetoacoustic
modes. For propagation parallel to the mean
magnetic field, the fast (slow) mode propagates
at the greater (lesser) of the sound speedCS and
Alfvén speed CA; for propagation transverse to
the mean magnetic field, the fast mode propagates
at the speed
C⊥ =
C 2 A +C2 1
2
S ,
and the slow mode has zero propagation speed.
The other qualitative difference between the two
modes is that the fluctuations in density and
magnetic field strength are correlated positively
for the fast mode, negatively for the slow mode.
In the limit of strong magnetic field, the slow
mode disappears, and the fast mode propagates
at CA for all directions; in the limit of weak
magnetic field, the slow mode disappears once
again, and the fast mode is simply a sound wave.
The phase speed of a magnetoacoustic wave, unlike
the Alfvén wave, depends on amplitude, so
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that magnetoacoustic waves can steepen to form
shock waves.
The kinetic-theory approach yields analogs
of the fast and slow modes, but additionally
gives other, very strongly damped modes.
Moreover, in a hot plasma like the solar wind,
even the fast and slow modes are subject to
strong Landau damping. Indeed, although solar
wind fluctuations have often been identified
with Alfvén waves, they can rarely be associated
with magnetoacoustic waves. Landau damping
of magnetoacoustic waves may be an important
mechanism of plasma heating in some circumstances.
In particular, it may severely restrict
the formation of shock waves from magnetoacoustic
disturbances. See Alfvén wave, hydromagnetic
wave.
magneto-fluid mechanics See magnetohydrodynamics.
magnetogram Graphic representation of solar
magnetic field strength and polarity. Magnetograms
show a hierarchy of spatial scales in
the photospheric magnetic field from sunspots
to the general magnetic network.
magnetohydrodynamics (MHD) The study
of the dynamics of a conducting fluid in the presence
of a magnetic field, under the assumption
of perfect, or partial (resistive MHD) locking of
the plasma to the field lines. Important in many
branches of physics, but in geophysics it is primarily
important in the study of planetary magnetospheres,
ionospheres, and cores. In these
non-relativistic cases, Maxwell’s equations for
electrodynamics and the Lorentz field transformation
yield the induction equation (Faraday’s
law):
∂B
∂t
=∇×(V × B) −∇×(η∇ ×B)
where B is the magnetic field, V is the velocity of
the conducting fluid, and η is the magnetic diffusivity
of the fluid. The first term on the righthand
side represents the effects of fluid flow on
the magnetic field, and the second term on the
right-hand side represents diffusion of the magnetic
field, and in a region where η is constant
may be written +η∇ 2 B. In the case of a simple
conducting fluid in the presence of a magnetic