Barycentre motion of beams due to beam-beam interaction in asymmetric ring colliders

Abstract

The effects of the beam-beam interaction on the coherent motion of the barycentres of the colliding bunches are considered for asymmetric (two-ring) e +e − colliders, where circumference, energy, tune, etc. may be different between two rings. As well as integer and half-integer resonances, sum resonances occur. These resonances may be quite dense in the tune diagram, for the cases with different circumferences. This effectt poses a severe restriction on the choice of the circumference ratio. On these resonances, the beams separate spontaneously at the interaction point. In particular, on the sum resonance, the barycentres follow a limit cycle in four-dimensional phase space, rather than reaching a fixed point. This causes a severe drop in the luminosity. Results of analytical calculations and computer simulations for the motion of the barycentres and the excitation of the resonances are presented.