Abstract
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)] 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.
Highlights
Cumulative beam breakup (BBU) in linear accelerators results when a beam traverses the accelerating structures off axis and couples to the dipole modes of the structure. This can occur when the beam enters the accelerator with a lateral offset or angular divergence
The coupling between beam and dipole modes can occur when the structures themselves or the focusing elements are displaced from the nominal accelerator beam line
Such displacements occur in a random fashion and the displacement of the beam along the accelerator will exhibit a random behavior
Summary
Cumulative beam breakup (BBU) in linear accelerators results when a beam traverses the accelerating structures off axis and couples to the dipole modes of the structure. This can occur when the beam enters the accelerator with a lateral offset or angular divergence. The coupling between beam and dipole modes can occur when the structures themselves or the focusing elements are displaced from the nominal accelerator beam line. The formalism presented in [1] can be applied to the situation of random displacements of the cavities and focusing elements and a general solution was presented in that paper. This general solution is investigated here, its statistical properties are determined and applied here to specific examples
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