Regenerative multipass beam breakup in two dimensions

Abstract

In this paper, a formula, describing the threshold of regenerative multipass beam breakup (BBU) for a single dipole higher-order mode with arbitrary polarization in a two-pass accelerator with a general-form, 4×4 recirculation matrix, is derived. A new two-dimensional BBU code is also introduced. To illustrate specifics of the BBU in two dimensions, the formula is used to calculate the threshold in several cases including two-dimensional uncoupled optics, reflecting optics, and rotating optics. The analytical results are compared to results of simulations obtained with the new code. A mathematical relation between transfer matrices between cavities of the accelerating structure and recirculation matrices for each cavity, which must be satisfied in order to successfully suppress the BBU by reflection or rotation in several cavities, is presented.