Study of Periodic Tune Modulation with the Beam-Beam Effect

Simulations of weak-strong pp collisions with a periodic tune modulation show the possiblity of beam blowup at sufficiently strong modulation amplitudes. This beam blowup is associated with the appearance of nonrepeatable "chaotic" trajectories and occurs when low order resonances are crossed by the modulation. In this paper we also report results of an investigation of the dependence of this blowup upon the modulation frequency, with the modulation amplitude fixed. It is determined that a threshold freqency exists, modulations at frequencies greater than the threshold do not lead to beam blowup.