DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

focal mechanisms
rays arriving parallel from infinity appear to diverge
(negative focal length).
focal mechanisms Earthquakes send out
compressional P-waves that are either compressional
or tensional. The azimuthal variation in
the first arrivals defines the focal mechanism.
This variation provides information on whether
the fault displacement was thrust, normal, or
strike-slip and information on the orientation of
the fault.
focus In optics, the point where light rays
converge and/or from which light rays (appear
to) diverge.
In geometry, in a circle, the center of the circle.
In an ellipse, each of the two points on the
major axis located at aɛ from the center, where
a is the semimajor axis, andɛ is the eccentricity.
In a hyperbola, the point located inside the hyperbola,
on the axis a distance ofa(ɛ− 1) from
the point the orbit crosses the axis, such that the
transverse distance to the orbit at that point is
a(ɛ 2 − 1). Here a is called the semiaxis of the
hyperbola, and ɛ is 1/(cosα) with α the slope
of the asymptote to the hyperbola.
In a parabola, the point inside the parabola
on the axis of the parabola a distance p/2 from
the point the orbit crosses the axis, such that the
transverse distance to the orbit at that point is
2p.
In Newtonian physics, gravitational motion
is an orbit that is a conic section (circle, ellipse,
parabola, hyperbola) with the sun at one focus.
focused transport equation Model suggested
by Roelof (1969) to describe the interplanetary
transport of charged energetic particles
in terms of field-parallel propagation, focusing
on the diverging interplanetary magnetic
field, and pitch-angle scattering:
∂f
∂t
1 −µ2
+µv v
2ζ
∂f ∂
−
∂µ ∂µ
=Q(so,µ,t).
κ(µ) ∂f
∂µ
Here f is the phase space density, v the particle
speed,µ the particle’s pitch-angle,κ(µ) the
pitch-angle diffusion coefficient (see diffusion,
in pitch-angle space, slab model), s the spatial
coordinate along the Archimedian spiral, and
© 2001 by CRC Press LLC
178
ζ =−B(s)/(∂B/∂s) the focusing length (see
focusing). The term Q on the right-hand side
describes a particle source.
focusing In plasma physics, reduction of a
particle’s pitch angle as it propagates outward
in a slowly diverging magnetic field such as the
interplanetary magnetic field. Focusing can be
characterized by a focusing length ζ
ζ=− B(s)
∂B/∂s
withs being the spatial scale along the magnetic
field B. In interplanetary space, the divergence
of the magnetic field would reduce a particle’s
pitch-angle from nearly 90 ◦ on the sun to about
0.7 ◦ at the orbit of Earth.
Focusing is a direct consequence of the constancy
of the magnetic moment (first adiabatic
invariant). Its reverse effect is the increase of
the particle’s pitch angle in a convergent magnetic
field, eventually leading to mirroring. See
adiabatic invariant, interplanetary propagation,
magnetic mirror.
foehn Hot winds on the down-slope side of a
mountain on which background winds impinge.
There are two basic types of foehns of thermodynamic
and dynamic causes, respectively.
Thermodynamic foehns occur when the lower
atmosphere is humid and the uplift by the mountain
forces water vapor to condense on the upstream
side, causing temperature increases on
the down-slope side. Dynamic foehns occur
when the atmosphere is strongly stratified on the
up-slope side and the air near the surface cannot
flow over the mountain and is blocked. As the
upper air is forced to descend downslope, adiabatic
compression raises its temperature. The
second-type of foehn occurs when the Froude
number U/Nh is below a certain critical value,
where U is the background wind speed, N the
Brunt–Väisälä frequency, and h the height of the
mountain.
fog A situation in which clouds form at
ground level which reduces visibility below
1 km; consisting of water droplets too small to
fall out of suspension.