Horanyi, M., J.A. Burns and D.P. Hamilton 1992. The dynamics of
Saturn's E-ring particles. Icarus 97, 248-259.
Saturn's tenuous E ring, located between 3 and 8 Saturnian radii
(R$_S$), peaks sharply near Enceladus' orbit (3.95R$_S$) and has
recently been found to be composed predominantly of grains 1 micron in
radius. We study analytically and numerically the motion of such
grains launched from Enceladus as they evolve under the action of
Saturn's oblate gravity field, solar radiation pressure, and
electromagnetic forces. The latter arise because grains are charged
(usually to negative values) and also orbit through a dipolar magnetic
field. The orbital precession rates caused by the planetary oblateness
and the Lorentz force on grains of 1 $\mu$m radius are shown to be
approximately equal in magnitude but opposite in sign at Enceladus'
distance. In the absence of planetary shadowing, solar radiation
pressure cannot change an orbit's semimajor axis, but it can produce
periodic changes in orbital eccentricity that vary at the orbital
precession rate. The near-equality of these precessions for
micron-sized grains introduced at Enceladus allows very large orbital
eccentricities and correspondingly large radial excursions to develop
in just a few years. Although particles on eccentric orbits are
preferentially found at apocenter, the area covered by an annulus of
width $\Delta r$ is smallest at pericenter; these two effects combine
such that the normal optical depth distribution is radially symmetric
about the source. Owing to the long time spent at small
eccentricities, however, particles injected at Enceladus are most
commonly located near its orbit.
In addition, solar radiation has a time-dependent component out of the
ring plane arising from Saturn's obliquity and motion about the Sun.
This force will cause orbital inclinations to develop and is most
effective when particles are on highly eccentric orbits. Furthermore,
because the pericenter precession rates nearly cancel, the
out-of-plane component of radiation pressure is strong enough to lock
the orbital nodes at radial distances similar to that of the source,
hence the greatest ring thickness occurs furthest from the planet
while the ring is thinnest near the source. By plotting the position
of a single particle over time, we show the distribution of 1 $\mu$m
grains that are injected at Enceladus and move swiftly under the above
forces; this distribution has many of the characteristics of the
observed E ring. Finally we note that particles with slightly
different sizes attain much smaller eccentricities since the
gravitational and electromagnetic contributions to the pericenter
precession rate do not cancel nearly as well.
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