Cumulative beam breakup in linear accelerators with arbitrary beam current profile

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