Longitudinal beam-beam effects for an ultra-high luminosity regime

High-luminosity projects imply collisions of intense short bunches with micro-beta at the IP, which entails high variations of the particle energy on the IP passage, due to the opposing bunch electric fields. This effect is shown to limit the attainability of the incoherent and coherent longitudinal motion which enhance the required RF voltage depending on the design beta minimum at the IP. The results of this analytical treatment and computer simulation of the off-axis particle synchrobetatron motion present the limitations, imposed on the space charge parameter by the longitudinal beam-beam effects, and the main parameters of the machine.< >