Hadron beam-beam diffusion in 2.5-D

The standard analysis of modulational diffusion for general nonlinearities is qualitatively summarized, and compared to the particular case of a beam-beam simulation with two kicks per turn, plus tune modulation. A simulation with realistic Tevatron parameters shows amplitude growth over long timescales of order 10{sup 4} synchrotron periods. The simulated amplitude growth is qualitatively similar to the predictions of modulational diffusion, showing large discrete steps in the evolution speed as the tune distance from the nearest 2-D weak coupling resonance is varied. However, the simulation shows a fundamental difference in that the observed amplitude growth is approximately exponential in time, and not approximately root time as predicted in the standard analysis. Possible reasons for this and other discrepancies are briefly discussed