Investigations of cumulative beam breakup in radio-frequency linacs

An analytic model of cumulative beam breakup has been developed which is applicable to both low-velocity ion and high-energy electron linear accelerators. The model includes arbitrary velocity, acceleration, focusing, initial conditions, beam-cavity resonances, and variable cavity geometry and spacing along the accelerator. Both the steady-state and transient displacements of the beam bunches are calculated. As examples, the solution is applied to hypothetical high-current ion accelerators comprised of superconducting coaxial half-wave resonators. In this paper the steady-state transverse motion of particles comprising a longitudinal halo between bunches is also calculated, and effects of nonzero bunch length and arbitrary bunch shape are investigated. The role of focusing in controlling beam breakup is quantified for these cases