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Transverse instabilities for multiple nonrigid bunches in a storage ring.

We describe a method 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 calculations considered multibunch modes with one type of internal motion; our method includes coupling between these modes. We also include effects of feedback systems designed to correct these dipole motions. We include an example from a real storage ring design.