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

TL;DR

This paper presents a numerical method to design nonlinear DBA and MBA lattices with approximate invariants of motion, aiming for large dynamic aperture and improved stability in storage rings.

Contribution

It introduces a tuning procedure that minimizes action fluctuations and tune diffusion to create lattices with properties similar to integrable systems.

Findings

Lattices exhibit large dynamic aperture and invariant tori.

Enhanced stability with increased instability thresholds.

Reduced feedback gain requirements.

Abstract

A numerical method to design nonlinear double- and multi-bend 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 (IOTA), 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 DBA and MBA 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 NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.