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The Voyager mission discovered a system of rings and ring arcs around Neptune. It was later found that the arcs appear to be azimuthally and radially confined by resonant interactions with the nearby satellite, Galatea, yielding a maximum spread in ring particle semimajor axes of 0.6 km and a spread in forced eccentricities large enough to explain the arc's 15 km radial widths (Porco, 1991, Science 253 , 995).
We have modified an N-body simulation method (e.g. H\"anninen and Salo, 1992, Icarus 97 , 228) to include Neptune's second and fourth gravitational harmonics in order to be able to study the effects of collisions and self-gravity on the stability of the ring arcs. We have tested the simulation method and verified the shepherding mechanism in the collisionless and non-self-gravitational case. Preliminary simulation results with collisions over $\frac{1}{2}$ a libration period indicate that collisions among putative 10-m sized source bodies within the arcs are indeed capable of arc disruption. However, whether or not collisions occur over this time scale depends, among other factors, on the number density of such bodies. We will explore the effects on arc stability of varying simulation parameters, such as the sizes and number density of the source bodies and the coefficient of restitution. Also, we will examine the effect of Galatea's previously neglected nearby vertical resonance on arc particle orbits.
