A mapping, called synchro-beam mapping, is proposed which describes the effects of the beam-beam interaction in presence of synchrotron motion. The mapping is symplectic in six dimensional phase space. In addition to the usual transverse kick, this mapping cludes the bunch-length effect on the collision point and the energy variation caused by the electric field of the opposite bunch. The case of weak-strong interaction is investigated
by simulation, showing that the beam-beam energy exchange has an influence on the distribution tail.
A symplectic beam-beam interaction with energy change
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Beam-beam_Hirata-1992
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