Beam-beam modulational diffusion in 2 1/2 dimensions

T. Satogata, S. Peggs
Proceedings of International Conference on Particle Accelerators  
Qualitative theoretical predictions for single particle modulational diffusion in 2 l/2 dimensions are compared with simulation results. Typical Fermilab Tevatron parameters are used for two beam-beam interactions under the influence of tune modulation created by synchrotron oscillations. When sideband overlap occurs on a purr onedimensional resonance, diffusive growth is predicted and observed in the other transverse dimension. However exponential amplitude growth is observed in simulation
more » ... d in simulation instead of cl;issically predicted root-time diffusive growth. Exponential growth rates are measured in particle tracking and possible impact on Tevatron luminosity upgrades is mentioned. Timescales of modulational diffusion are tens to tens of thousands of modulation periods; in a collider such as the Tevatron these timescales can range up to minutes. This mechanism is therefore a source of emittance growth and luminosity degradation that would significantly impact operations yet be difficult to diagnose. Since modulational diffusion requires sideband overlap, it is present only in a region of the tune modulation parameter space where such overlap creates a thick layer of stochasticity. We assume tune m"dulation of the form Q -Q + q sinWQ,wt) ,
doi:10.1109/pac.1993.308946 fatcat:3toytk65kfaeho5w7qlw4hkuba