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Transverse proton diffusion

A semi-analytical approach is described for evaluating diffusion rates due to different processes, such as Arnold diffusion, resonance streaming, modulational diffusion, and ‘sweeping diffusion’, in a proton storage ring. This approach makes use of parameters for high-order resonances in the transverse phase space, which may be obtained, for example, by normal-form algorithms using differential-algebra software, and is applied to the HERA proton ring at DESY. While neither Arnold diffusion nor resonance streaming nor sweeping diffusion can explain the dynamic aperture observed in HERA, the effect of modulational diffusion is consistent with the measurements.