Beam-Beam Issues for Colliding Schemes with Large Piwinski Angle and Crabbed Waist

Numerical simulations have shown that a recently proposed "crabbed waist" scheme of beam-beam collisions can substantially increase the luminosity of a collider. In this paper we give a qualitative explanation why this scheme works. For this purpose we use simple geometrical considerations and analyze peculiar properties of vertical motion modulations by synchrotron and horizontal betatron oscillations. It is shown that in the 'crabbed waist' scheme these modulations, which are the main sources of beam-beam resonances excitation, are significantly suppressed. Some numerical examples demonstrating the effect of the crabbed waist collisions are also given.