Dynamic aperture and transverse proton diffusion in HERA

The dynamic aperture caused by persistent‐current nonlinear field errors is an important concern in the design of superconducting hadron storage rings. The HERA proton ring is the second superconducting accelerator in operation. In this lecture note, its measured dynamic aperture is compared with that inferred from comprehensive tracking studies. To understand the difference between prediction and measurement, a semi‐analytical method is developed for evaluating transverse diffusion rates due to various processes, such as modulational diffusion or sweeping diffusion. This analysis makes use of parameters for high‐order resonances in the transverse phase space, which are obtained by normal‐form algorithms using differential‐algebra software. The semi‐analytical results are consistent with the measurements, and suggest that the actual dynamic aperture is caused by an interplay of tune modulation and nonlinear magnetic fields.