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.
Highlights
The Integrable Optics Test Accelerator (IOTA) [1], whose design is based on an integrable Hamiltonian system with two invariants of motion [2,3], paves the way for a new class of highly nonlinear storage rings
The storage rings used as dedicated synchrotron light sources are designed in a different way: a linear achromat lattice with a desired beam emittance is designed first, and the nonlinear dynamics is optimized with sextupoles and/or octupoles
III and IV, on-momentum lattices were constructed with two quasi-invariants, and the off-momentum acceptances were checked with tracking simulations
Summary
The Integrable Optics Test Accelerator (IOTA) [1], whose design is based on an integrable Hamiltonian system with two invariants of motion [2,3], paves the way for a new class of highly nonlinear storage rings. The lattice is tuned to provide one or more analytically known invariants of motion, resulting in a dynamic aperture (DA) that is large and robust to the presence of resonances. The motivation for constructing such lattices is that, they are not completely integrable, the DA is large and robust to the presence of resonances. The remainder of this paper is outlined as follows: Sec. II explains the concept of Poisson-commuting invariants in integrable Hamiltonian systems, and describes a numerical approach for optimizing the nonlinear lattice to produce approximate invariants using symplectic tracking. A technique to modify the action-like invariants to reshape the invariant tori (and the resulting DA) is described in the Appendix
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