Particle diffusion in overlapping resonances

Longitudinal bunch dilution was studied in the IUCF Cooler Ring with phase modulation of a higher-order harmonic rf. Diffusion in the presence of overlapping parametric resonances has been identified as the dilution mechanism. We found that fast growth is associated with the rapid particle motion along separatrices of dominant parametric resonances, slow growth is related to particle diffusion in the chaotic sea, and saturation occurs when particles are bounded by an invariant torus