Many particle accelerators are proposing the use of crab cavities to correct for accelerator crossing angles or for the production of short bunches in light sources. These cavities produce a rotation to the bunch in a well-defined polarization plane. If the plane of the rotation does not align with the horizontal axis of the accelerator, the bunch will receive a small amount of spurious vertical bunch rotation. For accelerators with small vertical beam sizes and large beam-beam effects, this can cause significant unwanted effects. In this paper we propose the use of a 2nd smaller crab cavity in the vertical plane in order to cancel this effect and investigate its use in numerical simulations
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