Frequency Scaling Study of Crab Cavity for Future Colliders with Crab Crossing

Crab crossing is an essential concept in the newly proposed colliders or the upgrades. It enables crossing angles to achieve lower β∗ without a loss of luminosity. The frequency of the crab cavity shall be chosenwith various considerations, including the luminosity degradation, emittance growth due to synchro-beta resonances and RF noises. Here, as the first step, we use the figure of merits to establish the frequency scaling relations with important design parameters, which guide the choice of crab cavity frequency for new designs.