# 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.