Effect of the crab waist and of the micro-beta on the beam–beam instability

We calculate the luminosity and the strengths of the beam–beam resonances for colliders with large horizontal crossing angles. Achievable luminosities of such colliders can reach high values provided that the number of particles in colliding beams can be increased while the vertical ββ-function can be decreased till the mini-beta range. The crab waist option of the optics in the interaction region decreases (or, even vanishes) the strengths of two-dimensional betatron weak–strong beam–beam resonances and of their synchro-betatron satellites provided that ββ-functions at the interaction point can be decreased till the micro-beta range. This can help to increase the achievable value of the collider luminosity.