Spectrum of classical two-dimensional Coulomb clusters

The frequency spectrum of a system of classical charged particles interacting through a Coulomb repulsive potential and which are confined in a two-dimensional parabolic trap is studied. It is shown that, apart from the well-known center-of-mass and breathing modes, which are independent of the number of particles in the cluster, there are more "universal" modes whose frequencies depend only slightly on the number of particles. To understand these modes the spectrum of excitations as a function of the number of particles is compared with the spectrum obtained in the hydrodynamic approach. The modes are classified according to their averaged vorticity and it is shown that these "universal" modes have the smallest vorticity and follow the hydrodynamic behavior.