Research on the impact of structural resonances in hybrid multi-bend achromat lattice

Background Compared to the third-generation synchrotron radiation light sources, which typically employ double- or triple-bend achromat lattices, the fourth-generation synchrotron radiation light sources based on hybrid multi-bend achromat (H-MBA) lattices exhibit stronger transverse focusing. This leads to the use of stronger sextupoles for chromaticity correction, and octupoles in some designs, introducing more pronounced nonlinear effects. Moreover, H-MBA lattices adopt distinct nonlinear cancellation strategy, resulting in beam dynamics that differ significantly from those of third-generation light sources. Thus, findings from earlier structural resonance studies are not directly applicable to H-MBA lattices.

Purpose This study systematically investigates the impact of structural resonances on momentum acceptance (MA) and dynamic aperture (DA) in H-MBA lattices, widely adopted in the fourth-generation synchrotron light sources.

Methods A combined optimization approach of particle swarm optimization and genetic algorithms was employed to simultaneously optimize the linear and nonlinear beam dynamics of H-7BA lattice, generating a diverse set of statistical data across a broad tune space. The impact of various structural resonances was analyzed empirically through numerical statistics and image analysis.

Results The results indicate that for the MA and the highly concerned horizontal DA, structural resonances up to the third order exert significant impacts within the H-7BA lattice. Specifically, v_x, v_y, 2v_x strongly influence MA but weakly affect DA; v_x+2v_y has a weak impact on both MA and DA; 3v_x shows a weak effect on MA and negligible impact on DA; and v_x-2v_y has a weak impact on DA and negligible impact on MA; Among fourth- and higher-order structural resonances, only 2v_x+2v_y shows a weak effect on DA in specific scan regions, with no noticeable impact on MA. A validation study based on the H-9BA lattice confirmed similar resonance effects on MA and DA.

Conclusions These results indicate that, unlike the situation with the third-generation synchrotron light sources, in H-MBA lattices, the effects of the fourth-order and higher-order structural resonances on DA are generally very small. Therefore, when selecting tunes for H-MBA lattices, priority should be given to avoiding 1st- to 3rd-order structural resonances (v_x, v_y, 2v_x, 3v_x, v_x+2v_y, v_x-2v_y), while the restrictions on higher-order resonances can be appropriately relaxed.