Abstract
Closed orbit feedback (COFB) systems used for the global orbit correction rely on the pseudo-inversion of the orbit response matrix (ORM). A mismatch between the model ORM used in the controller and the actual machine ORM can affect the performance of the feedback system. In this paper, the typical sources of such model mismatch such as acceleration ramp ORM variation, intensity-dependent tune shift and beta beating are considered in simulation studies. Their effect on the performance and the stability margins are investigated for both the slow and fast regimes of a COFB system operation. The spectral radius stability condition is utilized instead of the small gain theorem to arrive at the theoretical limits of COFB stability and comparisons with simulations for SIS18 of GSI and experiments at the Cooler synchrotron (COSY) in the Forschungzentrum J\"ulich (FZJ) are also presented.
Highlights
Closed orbit feedback (COFB) systems are implemented in modern synchrotrons and storage rings to ensure the transverse beam stability against external perturbations as well as local dipolar magnet field errors [1,2,3,4,5,6,7,8,9]
The spectral radius condition of stability is defined for the correction matrix M which yields a higher and practical stability margin in comparison to the previously used small gain theorem, against the spatial model mismatch
It is shown that the stability margins yielded by the two conditions can be related through the condition number of the nominal orbit response matrix (ORM), with exact equality for the circulant symmetry
Summary
Closed orbit feedback (COFB) systems are implemented in modern synchrotrons and storage rings to ensure the transverse beam stability against external perturbations as well as local dipolar magnet field errors [1,2,3,4,5,6,7,8,9]. For the symmetric and the near-symmetric arrangements of BPMs and corrector magnets, a discrete Fourier transform-based diagonalization and inversion method is recently discussed in the context of closed orbit correction [16] as an alternate to SVD and harmonic orbit correction method [17] resulting in a sparse representation for changing lattices These special matrices will be utilized in this report for deriving exact relations due to their favorable properties. It is important to note that, if the time scale of the ORM variation due to aforementioned effects is longer (an order of magnitude) than the delays and time constants of the temporal response of BPMs and corrector magnets, the ORM can still be considered as a separate part R in the total system model GðsÞ. Spectral radius is put forward as a general figure of merit for the optimal operation of the COFB systems in the presence of a model mismatch
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
