Statistical analysis of the limitation of half integer resonances on the available momentum acceptance of a diffraction-limited storage ring

In a diffraction-limited storage ring (DLSR), the momentum acceptance (MA) might be limited by the half integer resonances (HIRs) excited by focusing errors, associated with the large detuning terms from the strong focusing and strong sextupoles required for an ultralow emittance. Taking the High Energy Photon Source (HEPS) as an example and through statistical analysis, we found that the horizontal HIRs have stronger impact on dynamics than the vertical ones; and the probability of MA reduction caused by a HIR is closely correlated with the level of the beta beats at the same plane, but independent of the error sources. For the HEPS design, to reach a small MA-reduction probability of about 1%, the rms amplitude of the beta beats at the nominal tunes should be kept below 1.5% horizontally and 2.5% vertically. The presented analysis can provide useful reference for other DLSR designs.