Some aspects of the long range beam-beam interaction in storage rings

In this paper we develop a linear model of the long range beam-beam tune shift for cases when the electron and positron orbits are separated at all crossing points. Theoretical considerations show that the tunes of coherent beam-beam modes depend crucially on the betatron phase advance between crossing points. Under certain conditions the tune split may be reduced, or even made equal to zero in spite of a strong beam-beam interaction. Measurements of coherent beam-beam modes were made at CESR. In most cases, the experimental results are in good agreement with the linear model. The behavior of coherent beam-beam modes was examined theoretically, taking into account the coherent tune shift caused by impedance effects