DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

field, the force due to the magnetic field (the
Lorentz force) per unit volume is:
fB = 1
µ (∇×B) × B
where µ is the magnetic permeability.
In a medium characterized by a scalar electrical
conductivity σ , the electric current density
J in cgs units is given by Ohm’s law
J = σ (E + V×B/c) ,
where E is the electric field, B the magnetic field,
and c the (vacuum) speed of light. Many fluids
of importance for space physics and astrophysics
have essentially infinite electrical conductivity.
For these systems to have finite current
density,
E + V×B/c = 0 .
Thus, the electric field can be eliminated from
the magnetohydrodynamic equations via Faraday’s
law. Also, the current density has disappeared
from Ohm’s law, and has to be calculated
from Ampère’s law (the displacement
current is negligible in nonrelativistic magnetohydrodynamics).
Thus, for a nonrelativistic inviscid
fluid that is a perfect electrical conductor,
the Euler equations for magnetohydrodynamics
are the equation of continuity
∂ρ
∂t
+∇·(ρV) = 0 ,
where ρ is the mass density, the momentum
equation
∂
ρ + V·∇ V =−∇P + fB
∂t
where P is the pressure, and F is the body force
per unit volume (due, for example, to gravity),
plus some additional condition (such as an energy
equation, incompressibility condition, or
adiabatic pressure-density relation) required for
closure of the fluid-mechanical equations. Faraday’s
law completes the magnetohydrodynamic
equations.
Magnetohydrodynamics has been applied
broadly to magnetized systems of space physics
and astrophysics. However, many of these systems
are of such low density that the mean-free
© 2001 by CRC Press LLC
magnetometer
paths and/or times for Coulomb collisions are
longer than typical macroscopic length and/or
time scales for the system as a whole. In
such cases, at least in principle, a kinetic-theory
rather than fluid-mechanical description ought
to be used. But plasma kinetic theories introduce
immense complexity, and have not proved
tractable for most situations. Fortunately, experience
in investigations of the solar wind and its
interaction with planetary and cometary obstacles
has shown that MHD models can give remarkably
good (though not perfect) agreement
with observations. This may be so partly because,
absent collisions, charged particles tend
to be tied to magnetic field lines, resulting in a
fluid-like behavior at least for motion transverse
to the magnetic field.
Moreover, moments of the kinetic equation
give continuity equation and momentum equation
identical to their fluid counterparts except
for the fact that the scalar pressure is replaced
by a stress tensor. Turbulent fluctuations can
also influence transport properties and enforce
fluid-like behavior. On the other hand, predictions
from kinetic theory can and do depart from
the MHD description in important ways, particularly
for transport phenomena, instability, and
dissipation.
magnetometer An instrument measuring
magnetic fields. Until the middle of the 20th
century, most such instruments depended on
pivoted magnetized needles or needles suspended
from torsion heads. Compass needles
measured the direction of the horizontal component
(the magnetic declination, the angle between
it and true north), dip needles measured
the magnetic inclination or dip angle between
the vector and the horizontal component, and the
frequency of oscillation of a compass needle allowed
the field strength to be determined. Alternatively,
induction coils, rotated rapidly around
a horizontal or vertical axis, produced an induced
e.m.f. which also gave field components.
Induction coils have also been used aboard
spinning Earth satellites, but most spaceborne
instruments nowadays use fluxgate magnetometers,
also widely used for geophysical prospecting
from airplanes and for scientific observations
on the ground. These are not absolute but
require calibration, and for precision work there-
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