Study of crab cavity option for LHC

It is prefered to make a larger crossing angle to avoid parasitic collisions between beams in LHC. The transverselongitudinal aspect ratio of the LHC beam is 17 μm/7.5 cm=0.23 × 10−3. Crossing angle larger than the aspect ratio causes geometrical degradation of luminosity. Crab cavity can realizes head-on collision without crossing angle effectively, with the result that it recovers these luminosity degradation. However crab cavity can also be a source of diffusion: that is, Jitter of RF phase of crab cavity and main acceleration cavity induce a random transverse offset at the collision point, which causes diffusion due to beam-beam ineteraction. We discuss feasibility of the crab cavity for hadron colliders from the viewpoint of dynamics of the beam-beam interaction.