Coherent Beam-Beam Instability in Collisions with a Large Crossing Angle.

In recent years the "crab-waist collision" scheme [P. Raimondi, Proceedings of 2nd SuperB Workshop, Frascati, 2006.; M. Zobov et al., Phys. Rev. Lett. 104, 174801 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.174801] has become popular for circular e^{+} e^{-} colliders. The designs of several future colliders are based on this scheme. So far the beam-beam effects for collisions under a large crossing angle with or without crab waist were mostly studied using weak-strong simulations. We present here strong-strong simulations showing a novel strong coherent head-tail instability, which can limit the performance of proposed future colliders. We explain the underlying instability mechanism starting from the "cross-wake force" induced by the beam-beam interaction. Using this beam-beam wake, the beam-beam head tail modes are studied by an eigenmode analysis. The instability may affect all collider designs based on the crab-waist scheme. We suggest an experimental verification at SuperKEKB during its commissioning phase II.