DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Generic shape of a string segment at the location of a
cusp.
the sunward boundary. In simple idealized models,
the cusps contain neutral points, located on
the magnetopause. The models predict that at
those points field lines intersect, and the field
intensity drops to zero. In the actual magnetosphere,
the cusps are observed as regions of
weak varying field.
The term polar cusp is also applied to the
funnel-shaped regions extending from the above
weak-field regions near the magnetopause to
their footprints on the ionosphere (those regions
are also sometimes referred to as the cusps). The
polar cleft is the name applied to the same region
by researchers who propose its shape to be
slit-like rather than funnel-like.
cutoff energy Of cosmic ray protons at a
given point P on Earth, the energy below which
such protons can no longer reach P. For heavier
particles, the cutoff energy can be derived from
that of protons.
Proton orbits arriving at P can be trapped in
the Earth’s magnetic field (as those of radiation
belt protons are), or they can extend beyond the
Earth’s magnetic field. All low energy proton
orbits at P are trapped, while at sufficiently high
energy, none are. The cutoff energy at P may be
viewed as the energy below which all orbits at
P are trapped.
Actually at any point P, the transition between
trapped and non-trapped orbits is somewhat
irregular and depends on direction. At
high energy E, protons can arrive from any direction.
At lower energies, some orbits arriving
from the east are trapped and, therefore,
empty of cosmic ray protons. As E decreases,
the trapped/free boundary (its structure is com-
© 2001 by CRC Press LLC
cyclone
plex) expands across zenith until it reaches the
western horizon, at the value of E below which
all access is cut off.
cut-off rigidity Cosmic rays below the cutoff
rigidity cannot penetrate down to the Earth’s
surface but are reflected back towards space (see
Störmerorbits). Sincethisshieldingisduetothe
geomagnetic field, the cut-off rigidity depends
on the geomagnetic latitude and the altitude of
the observer: for normally incident protons the
cut-off rigidity at the geomagnetic equator is
about 15 GeV, that is all particles below 15 GeV
are unable to reach the Earth, while the cut-off
rigidity is only about 1.4 GeV at 58 ◦ geomagnetic
latitude at sea level. In general, the cut-off
rigidityPcutoff is related to the geomagnetic latitude
c by
P cutoff = 14.9 GeV cos 4 c . (1)
Thus, the magnetosphere acts as a giant mass
spectrometer.
Historically, the term cut-off rigidity refers
to the rigidity at which the lower part of the
spectrum of galactic cosmic rays is cut off. The
cut-off rigidity is also used to characterize the
energy threshold of a neutron monitor.
cyclic coordinate In classical mechanics, a
coordinate that does not explicitly appear in the
Lagrangian (or in the Hamiltonian) for a system,
though its velocity may be present. Via
Lagrangeequations, ifpa =∂L/∂˙q a (wherethe
coordinate q a does not appear in the Lagrangian
though ˙q a does), then
d
dt pa = ∂L
= 0 .
∂qa Hence, momenta conjugate to cyclic coordinates
are constants and provide first integrals
for the system. See first integral.
cyclone In meteorology, a 3-dimensional depression
vortex system with closed cells and low
central pressure. Its horizontal scale is from
200 to 3000 km. A cyclone has a characteristic
pattern of wind circulation (counterclockwise
in the northern hemisphere, clockwise in
the southern). Mid-latitude cyclones are associated
with the convergence of polar and tropical