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A numerical method to design nonlinear double- and multi-bend achromat (DBAand MBA) lattices with approximate invariants of motion is investigated. Thesearch for such nonlinear lattices is motivated by Fermilab's Integrable OpticsTest Accelerator (IOTA), whose design is based on an integrable Hamiltoniansystem with two invariants of motion. While it may not be possible to design anachromatic lattice for a dedicated synchrotron light source storage ring withone or more exact invariants of motion, it is possible to tune the sextupolesand octupoles in existing DBA and MBA lattices to produce approximateinvariants. In our procedure, the lattice is tuned while minimizing theturn-by-turn fluctuations of the Courant-Snyder actions $J_x$ and $J_y$ atseveral distinct amplitudes, while simultaneously minimizing diffusion of theon-energy betatron tunes. The resulting lattices share some important featureswith integrable ones, such as a large dynamic aperture, trajectories confinedto invariant tori, robustness to resonances and errors, and a largeamplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, thesingle- and multi-bunch instability thresholds are increased and thebunch-by-bunch feedback gain can be reduced.

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants