DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

of C. The conservation equation ∂C/∂t =
−div(JC)+λC is often referred to as the second
Fickian law.
field A mathematical construct that represents
physical interactions as spread through
space and time. Any quantity that can be defined
at every point of (a region of) space (or
spacetime) can be defined to be a field. Classical
examples include the electromagnetic and
the gravitational field.
field capacity (θfc) The maximum amount
of water in the unsaturated zone of the soil that
can be held against the pull of gravity.
field line motion A theoretical formalism
that helps visualize the effects of electric fields
and varying magnetic fields on the plasma they
permeate. In a magnetic field B, it ascribes to
each point a velocity v that satisfies ∂B/∂t −
∇×(v × B) = 0.
If the field is embedded in a highly conducting
fluid (e.g., the molten metal in the Earth’s
core) or in a collision-free plasma (such as is
found in space around Earth), the bulk flow
velocity v of the fluid or plasma in general
comes close to satisfying the MHD condition
E =−v × B, where E is the ambient electric
field. By Maxwell’s equations, the curl of this
is the equation defining field line motion; hence,
the fluid or plasma moves with the field lines.
In a collisionless plasma the MHD condition
is related to the electric drift of the plasma. In all
such cases, two particles of the fluid or plasma
which initially share the same field line continue
doing so as time advances. It should, however,
be noted that this is only the motion perpendicular
to field lines: in addition, the fluid or plasma
may also slide along field lines.
Field line motion helps intuitive understanding
of plasma motions. In limiting cases where
the motion dominates the magnetic field — e.g.,
the solar wind which is known to move (more
or less) radially — field line motion provides
a shortcut to calculating the magnetic field B,
given the sources of B on the sun. On the other
hand, if B completely dominates the plasma
(e.g., where it is very rarefied), if we know the
way B changes (i.e., ∂B/∂t), the observed field
© 2001 by CRC Press LLC
field ordering
line structure can help derive the bulk flow velocity
v.
field of view The angular size of the full image
formed in an optical instrument; the angular
separation of two points that lie at the edges of
the optical field.
field ordering In condensed matter physics,
when the temperature of a ferromagnet goes below
the critical point, Tc, a non-zero magnetization
M develops. The rotational symmetry previously
possessed by the system is then broken
due to the presence of a preferred direction, the
one fixed by M. The value of M, zero for the
high-temperature phase and non-zero for temperatures
below Tc, plays the role of the order
parameter of the phase transition.
In cosmological transitions, the role of the
order parameter is played by the vacuum expectation
value of the Higgs field (here denoted
φ). Standard topological defects (like
monopoles, walls, strings) involve regions in
space where this order parameter remains in the
high-temperature symmetric phase (vanishing
φ). In this case the field potential energy (the
false vacuum trapped inside the defect) is the
main source of the energy associated with the
defects.
There are, however, other types of defects
where the bulk of energy is concentrated not as
potential energy but in spatial gradients. Cosmic
textures are one example of this. They have the
property that the broken-symmetry phase vacuum
manifold M of the order parameter φ has
the same dimension as space (equal to three, for
cosmological applications), and this allows φ to
always stay on M, regardless of the location
considered. Hence, possessing no potential energy,
all the relevant dynamics comes from the
ordering of this field φ, that is from the tendency
to minimize its gradients.
Texture knots will shrink (instability to collapse)
as explained by the Derrick theorem. This
will result in the ordering field becoming increasingly
tightly wound in the vacuum manifold.
Then the spatial gradients (kinetic energy
terms) in the configuration will eventually
become so high as to be able to exceed the energy
of the symmetric state and unwind the knot.
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