Abstract
Electron lenses for the head-on beam-beam compensation are under construction at the Relativistic Heavy Ion Collider. The bunch length is of the same order as the {beta}-function at the interaction point, and a proton passing through another proton bunch experiences a substantial phase shift which modifies the beam-beam interaction. We review the effect of the bunch length in the single pass beam-beam interaction, apply the same analysis to a proton passing through a long electron lens, and study the single pass beam-beam compensation with long bunches. We also discuss the beam-beam compensation of the electron beam in an electron-ion collider ring.
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