Coherent modes for multiple non-rigid bunches in a storage ring

A method is presented for determining the stability of a system consisting of several highly relativistic bunches of charged particles circulating in a storage ring. The particles interact with magnets designed to guide the beam as well as with electromagnetic fields induced by the particles themselves. Previous work has considered modes where all bunches in the ring are executing the same type of internal oscillation. This dissertation considers the results of allowing those modes to couple to one another. The formalism begins with a self-consistent distribution, and analyzes small perturbations to that distribution to determine if they grow exponentially. The formalism allows one to do this computation for an arbitrary magnetic lattice, as well as an arbitrary distribution of wakefield sources around the ring. The method also allows for the inclusion of a feedback system which is designed to damp multibunch oscillations. The PEP-II B-factory with a linear lattice is used as an example to demonstrate and explain the phenomenology that results from this coupling of multibunch modes. The effect of adding feedback is also explored