Beam-beam Effects of 'Gear-changing' in Ring-Ring Colliders

In ring-ring colliders, the collision frequency determines the bunch structures, e.g. the time between the bunches in both rings should be identical. Because of relatively low relativistic speed of the hadron beam in sub-TeV hadron-hadron- and electron-ions-colliders, scanning the hadron beam's energy would require either a change in the circumference of one of the rings, or a switching of the bunch (harmonic) number in a ring. The later would cause so-called 'gear-changing', i.e. the change of the colliding bunches turn by turn. In this article, we study the difficulties in beam dynamics in this 'gear-changing' scheme.