Linear effects of dispersion on the beam-beam interaction

The linear effects due to the presence of a dispersion at the interaction point in the beam-beam collision are studied. A linear analysis shows a synchro-betatron coupling, which leads a synchrotron tune shift and a synchro-betatron resonance in addition to the well-known betatron tune shift. The beam sizes and the emittances are computed. The effects might be serious for the collision with dispersion.