Cumulative beam breakup in linear accelerators with random displacement of cavities and focusing elements

A formalism presented in a previous paper for the analysis of cumulative beam breakup with arbitrary time dependence of the beam current [J. R. Delayen, Phys. Rev. ST Accel. Beams 6, 084402 (2003)PRABFM1098-440210.1103/PhysRevSTAB.6.084402] is applied to the problem of beam breakup in the presence of random displacements of cavities and focusing elements. A closed-form solution is obtained and 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 bunches