Beam-beam interaction effects on particle dynamics

The effects of the beam-beam interaction on particle dynamics in a synchrotron collider are investigated. The main highlight of this work is the investigation of collective effects of the beam-beam interaction in a self-consistent approach that naturally incorporates the correct single-particle dynamics. The most important target of this simulation is to understand and predict the long-time (108-109 rotations) behavior of the beam luminosity and lifetime. For this task a series of computer codes in one spatial dimension has been developed in increasing order of sophistication. They are: the single-particle dynamics tracking code, the strong-strong particle-in-cell (PIC) code, and the particle code based on the δf algorithm. The latter two include the single-particle dynamics of the first. The third approach is used to understand beam lifetime by trying to improve the numerical noise problem in the second. Scans in tune ν0 and tune shift Δν0 show regions of stability and instability that correspond to the regions predicted by a lineax theory. Strong resonance beam blowup is observed just above ν0 = 1/2 and ν0 = 1/4, where the rate of beam blowup drops with the order of the resonance. In both the strong-strong code and δf code using the reference parameters of the Superconducting Super Collider, oscillations in the tune shift, Δν, are observed. The odd moments of the beam are increasing in oscillation amplitude with rotation number, while the amplitudes of the even moments either decrease or remain constant. The ''flip-flop'' effect is observed in the strong-strong code simulations and is found to be sensitive to the initial conditions