Inverse modeling of circular lattices via orbit response measurements in the presence of degeneracy

Vilsmeier, D.; Singh, Rahul; Bai, Mei

doi:10.1103/physrevaccelbeams.26.032803

Inverse modeling of circular lattices via orbit response measurements in the presence of degeneracy

Journal Article · Mon Mar 27 04:00:00 EDT 2023 · Physical Review Accelerators and Beams

DOI:https://doi.org/10.1103/physrevaccelbeams.26.032803· OSTI ID:2002895

Vilsmeier, D. ^[1]; ^[2]; ^[3]

Goethe Univ., Frankfurt (Germany); SLAC
GSI-Helmholtz Centre for Heavy Ion Research, Darmstadt (Germany)
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

The number and location of beam position monitors (BPMs) and steerers with respect to the quadrupoles in a circular lattice can lead to degeneracy in the context of fitting linear optics and extracting lattice information from measured closed orbits. Furthermore, the measurement uncertainties due to the imperfection of BPMs and steerers can be propagated by the fitting process in ways that prohibit the successful extraction of discrepancies between lattice elements in the real machine and their description in the corresponding model. We systematically studied the influence of the placement of BPMs and steerers on the reconstruction of linear optics and corresponding lattice information. The derivative of orbit response coefficients with respect to the quadrupole strengths, the Jacobian, is derived as an analytical formula. This analytical version of the Jacobian is used to further derive the theoretical limitations of fitting linear optics from closed orbits in terms of the placement of BPMs and steerers. It is further demonstrated that when evaluating the Jacobian during the fitting procedure, the analytical version can be used in place of the conventional finite-difference computation. This allows for greatly improved efficiency when computing the Jacobian during each iteration of the fitting procedure. The approach is tested with large-scale simulations and the findings are verified by measurement data taken on SIS18 synchrotron at GSI Helmholtz Centre for Heavy Ion Research. The presented methods are of general nature and can be applied to other accelerator lattices as well. The fitting procedure by using the analytical Jacobian is tested in conjunction with various methods for mitigating quasidegeneracy and the results agree with those obtained by using the conventional Jacobian via finite-difference approximation.

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 2002895

Journal Information:: Physical Review Accelerators and Beams, Journal Name: Physical Review Accelerators and Beams Journal Issue: 3 Vol. 26; ISSN 2469-9888

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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