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.
Simulation ProcedureIn pToton-antiproton (pp) collisions in the "Tevatron" particle trajectories will be affected by the higly nonlinear force of the "beam-beam"interaction the electromagnetic force field of the opposite beam in the collisions. The trajectories between collisions will be subject to tune modulation from turn to turn through sources such as power supply ripple or synchrotron oscillations with uncorrected chromaticity. Previous investigations of the beam-beam interaction by the present authors have considered a constant "beam-beam" interaction form and particle transport.In this paper we add the complication of tune modulation and investigate its effects.Without this modulation a remarkable beam stability has been found.2We approximate particle circulation around the accelerator ring as the product of two transformations: a linear transport around the storage ring followed by a nonlinear beam-beam "kick" at the interaction area.Transport around the ring can be re presented by a 2x2 matrix for both transverse (x and y) dimensions. In this linear transport x and y motion are decoupled.
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