Abstract
An analytical formalism for the solution of cumulative beam breakup in linear accelerators with arbitrary time dependence of beam current is presented, and a closed-form expression for the time and position dependence of the transverse displacement is obtained. It is applied to the behavior of a single bunch and to the steady-state and transient behavior of dc beams and beams composed of pointlike and finite-length bunches. This formalism is also applied to the problem of cumulative beam breakup in the presence of random displacement of cavities and focusing elements, and a general solution is presented.
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 [2,3,4,5,6,7,8] or for high-current quasi-dc beams [9,10,11,12,13]
The formalism that was developed was found to be applicable to a wide range of problems and could be used to unify and expand previous work on cumulative BBU of continuous beams and beams comprised of pointlike bunches, both in the steady-state and transient regime
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]. During the course of this work, a formalism leading to a general expression for cumulative BBU with arbitrary time dependence of the beam current was found This formalism and the application of the results to various beam and accelerator configurations (single short bunch, steady-state and transient behavior of continuous beams and of beams composed of pointlike and finite-length bunches) are presented here. This formalism can lead to a general expression for the transient behavior in the presence of BBU and random displacement of cavities and focusing elements. The general results will be presented, but their development and application to more specific situations will be presented in another paper
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