Mode Coupling Theory in Collisions With a Large Crossing Angle

We discuss a novel coherent beam-beam instability in collisions with a large crossing angle. The instability appears in the correlated head-tail motion of the two colliding beams. Cross wake force is introduced to represent the head-tail correlation between colliding beams. The cross wake force is localized at the collision point. Mode coupling theory based on the cross wake force is developed. Collision scheme with a large crossing angle is being very popular in design of electron positron collider. In SuperKEKB project, a collision with a large crossing angle is performed to boost the luminosity ~ 10³⁶ cm⁻²s^{−1}. Future circular collider, FCC is also designed with a large crossing angle. Strong-strong simulations have shown a strong coherent head-tail instability, which can limit the performance of proposed future colliders. The mode coupling theory using the cross wake force explains the instability. The instability may affect all colliders designs based on the crab waist scheme.