Particle beam resonances driven by dispersion and space charge

We study parametric resonances in circular accelerators, incorporating the effect of space-charge self-fields. A general Hamiltonian formalism is constructed for this purpose. The particle-in-cell simulation technique is employed to systematically explore the role of space-charge forces on resonant instabilities in two-dimensional beams. It is shown that momentum dispersion peculiar to rings can be an additional source of resonances.