Coherent dispersion effects in 2D and 3D high-intensity beams

Both space charge and dispersion have an effect on high-intensity beams in circular accelerators or transport sections with bending magnets and may lead to emittance growth and beam loss. In this paper, we present an investigation of the combined effect of dispersion and space charge on two-dimensional beams deepening the understanding of the 120 (degrees) dispersion-induced instability. We also investigate the 90 (degrees) envelope instability, which in the absence of the dispersion, mixes the confluent and parametric resonances. We show here that the presence of dispersion and high intensity breaks the overlapping and separates the two resonances. Furthermore, we study the beam dynamics of three-dimensional bunched beams and find the surprising result that the synchrotron motion can split the dispersion mode into two equally separated "sideband" modes according to the beam intensity and synchrotron frequency.