Abstract
A formalism presented in a previous paper for the analysis of cumulative beam breakup (BBU) with arbitrary time dependence of the beam current and with misalignment of the cavities and focusing elements [J. R. Delayen, Phys. Rev. ST Accel. Beams 6, 084402 (2003)] is extended to include time dependence of the focusing and coupling between the beam and the dipole modes. Such time dependence, which could result from an energy chirp imposed on the beam or from rf focusing, is known to be effective in reducing BBU-induced instabilities and emittance growth. The analytical results are presented and applied to practical accelerator configurations and compared to numerical simulations.
Highlights
The cumulative beam breakup instability (BBU) in linear accelerators results when a beam is injected into an accelerator with a lateral offset or an angular divergence and couples to the dipole modes of the accelerating structures [1]
Cumulative BBU has been studied in the past mostly in the context of high energy electron accelerators where the beam current profiles were comprised of periodic trains of pointlike bunches [2 –8] or for high-current quasi-dc beams [9,10,11,12,13]
We present here an analysis that provides an exact solution for arbitrary beam current profile, wake function, offset parameters, misalignment of cavities and focusing elements, and time dependence of focusing and BBU coupling strengths
Summary
The cumulative beam breakup instability (BBU) in linear accelerators results when a beam is injected into an accelerator with a lateral offset or an angular divergence and couples to the dipole modes of the accelerating structures [1]. In the case of bunches of finite length, a particle will experience the wakefield generated by all the particles ahead of it within the same bunch In this process the transverse displacement can be amplified and lead to a degradation of beam quality and possibly beam loss. More recently a general analysis of BBU with arbitrary time dependence of the beam current and injection offsets, as well as random displacement of cavities and focusing elements, was developed [17,18]. This analysis is extended here to include time dependence of the focusing and of the coupling between the beam and the dipole mode in order to. The analytical results are compared to numerical simulations and are found to be in complete agreement
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