COLLECTIVE PROCESSES IN PLANETARY RINGS

The aim of this paper is to study numerically the equilibrium properti es of planetary rings in a small local quadratic patch with periodic b oundary conditions. Contrary to previous approaches, we use a special TREE-code to compute the long-range gravitational interaction between the equal sized particles in our molecular dynamics model. The main re sult of the simulations is the presence of coherent trailing particle chains at all levels of the optical depth. We find that the height-cor rected stability number Q of Toomre in relaxed equilibrium disks canno t fall below a critical value, which lies about Q(c) similar to 2.5 fo r a Keplerian shear flow. Especially in cases of high optical depths t he self-excited coherent trailing ''wakes'' are precursors for small m oonlets in the disk. Therefore we believe that the most promising expl anation for the fine scale ringlet structure of the B-ring of Saturn i s the assumption that a great number of moonlets is orbiting inside th e dense particle disk.