Emittance optimization under magnet strength limitation for a multi-bend achromat lattice

Abstract

Diffraction-limited storage rings (DLSRs) based on multi-bend achromat (MBA) lattices are being developed towards much lower emittances. For instance, for the future development, MAX IV designed a 19BA lattice to replace the present 7BA lattice, achieving an emittance of 16 pm·rad. While this 19BA lattice, with a significantly increased number of unit cells, requires extremely strong quadrupoles and sextupoles, which will result in very small vacuum chambers and can thus significantly increase beam coupling impedance and potentially enhance beam instabilities. This issue raises a question of how we can reduce magnet strengths while achieving the emittance goal. In this paper, based on a simplified model where an MBA lattice is considered to consist of a number of identical unit cells, emittance optimization is numerically studied under magnet strength limitation. The studied results show that for a given arc length and emittance goal, choosing an appropriate number of unit cells with relatively large horizontal cell tunes can significantly reduce magnet strengths. As a practical example, an 11BA lattice with relatively large unit cell tunes is designed and compared with a 17BA lattice with smaller unit cell tunes. The two lattices have roughly the same emittance with the same energy, ring circumference and number of periods, while the magnets of the 11BA lattice are significantly weaker.