Crab Cavity Voltage and Luminosity Calculation

The luminosity is a very important parameter for an accelerator, because it describes the interaction rate per unit cross section. One of the goals of the designer is to improve as much as possible the luminosity, but there are factors which can affect and reduce it. The crossing angle is a scheme which mitigates the effect of the long-range beam-beam interaction on the accelerator, but also reduces the luminosity. One possible solution to keep low the long-range beam-beam effects, but improve the luminosity is the Crab Cavity (CC). The CC is a superconducting RF cavity operated in a transverse dipole mode, which provides a transverse kick on the beam particles that varies with the longitudinal position along the bunch. The kick produces a rotation of the bunch at the collision point so as to achieve an effective head-on collision and, therefore, restores the luminosity otherwise lost by the crossing angle.