Optimizing SLS-2 Nonlinearities Using a Multi-Objective Genetic Optimizer

An upgrade to the SLS is currently under development. This upgrade will likely utilize the same hall and same machine circumference, 288 m, of the SLS. Achieving a sufficiently low emittance with such a small circumference requires tight focusing and low dispersion. These conditions make chromaticity correction difficult and minimization of 1st and 2nd order non-linear driving terms does not yield sufficient dynamic aperture and Touschek lifetime. In this proceeding, we discuss the multi-objective genetic optimization method implemented at SLS to aid the design of a chromaticity correction scheme for SLS-2. INTRODUCTION An upgrade to the SLS, which we will refer to as SLS-2 in this paper, is under development [1]. The upgrade is envisioned as a complete replacement of the SLS storage ring while keeping the same hall, shielding, and booster. The beamline locations will be kept, but the beamlines themselves may be upgraded. The SLS-2 will utilize small vacuum chambers, as pioneered by MAX-IV, to obtain higher field strengths, and also longitudinal gradient bends and anti-bends [2] to reduce the horizontal emittance from 5.6 nm to approximately 130 pm. The new ring will maintain the 12 cell topology of the existing SLS. 3-fold periodic lattices, like the existing SLS, and also 12-fold periodic lattices have been considered. The new lattice uses strong quadrupole fields which induce a large chromaticity. This, in combination with small dispersion, necessitates a scheme of strong chromatic sextupoles to correct the chromaticity. These strong sextupoles generate strong nonlinearities which must in turn be compensated using harmonic sextupoles and octupoles. Layout constraints prevent zeroing resonant driving terms (RDTs) beyond 1st order (in sextupole strength). Therefore, the optimal map has some combination driving terms and tune shift terms of 2nd order and higher. In fact, the optimal map may even have non-zero 1st order terms. Weighting 1st, 2nd, and higher order RDTs to obtain the best map, and locating the global minimum, is not straightforward. This is especially so given that RDTs are only a heuristic for the actual objectives, which are acceptance and lifetime. An application of perturbation theory to 1st and 2nd order terms as described in [3] yields only marginally acceptable dynamic aperture (DA) and beam lifetime. We find that the direct genetic optimizer described in this proceeding consistently does better. For example, the direct optimizer finds ∗ michael.ehrlichman@psi.ch high order corrections to the tune footprint far away from the closed orbit. Elements of the traditional approach are maintained in our genetic optimization scheme. Chromatic and harmonic sextupoles and octupole locations are set by hand taking into consideration β-functions and phase advances. The working point is positioned considering the locations of low order resonances such that the tune footprint does not cross any dangerous resonances. Features of the optimization scheme described here are: 1) It does not use RDTs. 2) It requires only moderate computing resources, typically about 12 hours on 64 PC cores. 3) A robust constraint system. 4) It seems to reliably converge to the global minimum. 5) Does not require seeding. SYSTEM The accelerator physics simulation is developed using the Bmad [4] subroutine library. The multi-objective genetic optimization scheme is the aPISA extension [5] to the PISA framework [6]. The sorting algorithm is aspea2, a version of the spea2 [7] sorting algorithm modified to support dominance constraints. The parallelization is implemented using Fortran COARRAYs, which are implemented as a high level layer on top of MPI. The computing resource is a Linux cluster running SGE consisting of distributed Intel Xeon compute nodes. The scheme is naturally loadbalancing and works fine in heterogeneous environments. The results from the optimizer are portable to other codes, in particular OPA [8], for further analysis. Effort in this project includes understanding the usage and modeling differences of different calculation codes so as to keep the development process consistent and flexible. OPTIMIZATION PROBLEM The goal of the optimization problem is to maximize injection acceptance and maximize the Touschek lifetime. Injection acceptance is maximized by maximizing the onenergy DA. The Touschek lifetime is maximized by maximizing the momentum aperture. However, the elementby-element momentum aperture is expensive to calculate. Therefore, instead of calculating the momentum aperture we calculate the off-momentum DA and constrain the chromatic tune footprint. As will be shown later, we find this is an effective and efficient proxy for maximizing the Touschek lifetime. Objectives Three objectives are used by the optimizer. The objective function, depicted for Nangle = 7 in Fig. 1, is calculated as MOPJE074 Proceedings of IPAC2015, Richmond, VA, USA ISBN 978-3-95450-168-7 486 Co py rig ht © 20 15 CC -B Y3. 0 an d by th er es pe ct iv ea ut ho rs 5: Beam Dynamics and EM Fields D02 Nonlinear Dynamics Resonances, Tracking, Higher Order the DA relative to the linear aperture along a ray, min f (x) = 1 Nang ∑ Nang ⎪⎨ ⎪ ⎩ ( LLA−LDA LLA )2 , if LDA < LLA 0, otherwise (1) The objectives consist of Eq. 1 evaluated on-energy, at ΔE = −3%, and at ΔE = +3%.