Statistical analysis of the limitation of half integer resonances on the available momentum acceptance of the High Energy Photon Source

In a diffraction-limited storage ring, half integer resonances can have strong effects on the beam dynamics, associated with the large detuning terms from the strong focusing and strong sextupoles as required for an ultralow emittance. In this study, the limitation of half integer resonances on the available momentum acceptance (MA) was statistically analyzed based on one design of the High Energy Photon Source (HEPS). It was found that the probability of MA reduction due to crossing of half integer resonances is closely correlated with the level of beta beats at the nominal tunes, but independent of the error sources. The analysis indicated that for the presented HEPS lattice design, the rms amplitude of beta beats should be kept below 1.5% horizontally and 2.5% vertically to reach a small MA reduction probability of about 1%.