  Particles suspended in a viscous fluid circle in optical vortices generated
by holographic optical-tweezer techniques [Curtis J E and Grier D G 2003 Phys.
Rev. Lett. 90 133901]. We model this system and show that hydrodynamic
interactions between the circling particles determine their collective motion.
We perform a linear-stability analysis to investigate the stability of regular
particle clusters and illustrate the limit cycle to which the unstable modes
converge. We clarify that drafting of particle doublets is essential for the
understanding of the limit cycle.
