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We investigate multipass beam breakup (BBU) in a recirculating linear accelerator in the framework of a single cavity model. We present expressions for the beam breakup threshold current for various situations derived from a perturbative solution of BBU equations. These formulae should serve as a guide to understand the BBU phenomenon for a particular system and also as a tool to estimate the BBU threshold current quickly. Many of the results presented are more general than previous considerations because they include the effects of coupling between the two transverse polarizations in each dipole higher order mode

Expressions for the threshold current of multipass beam breakup in recirculating linacs from single cavity models