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

Abstract

A numerical method to design nonlinear double- and multibend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator, whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing double- and multibend achromat lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J_{x} and J_{y} at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune spread. Compared to the nominal National Synchrotron Light Source-II lattice, the single- and multibunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.