Abstract
This contribution compiles the benefits of lattice symmetry in the context of closed orbit correction. A symmetric arrangement of BPMs and correctors results in structured orbit response matrices of Circulant or block Circulant type. These forms of matrices provide favorable properties in terms of computational complexity, information compression and interpretation of mathematical vector spaces of BPMs and correctors. For broken symmetries, a nearest-Circulant approximation is introduced and the practical advantages of symmetry exploitation are demonstrated with the help of simulations and experiments in the context of FAIR synchrotrons.
Highlights
The closed orbit correction has been an integral part of the synchrotron and storage ring in light sources as well as in hadron machines for stable beam operations [1,2,3]
For SIS18, the dispersion function has the same value DðsÞ 1⁄4 D0 at all the beam position monitors (BPMs) locations, and the resultant dispersion-induced dc part of the closed orbit will couple to the pure dc mode of the BPM space corresponding to f 1⁄4 0 in the case of a circulant orbit response matrix (ORM) and can be ignored by removing the singular value corresponding to that mode
An efficient method relying on circulant symmetry properties in synchrotrons for the diagonalization and inversion of the ORM is introduced in this paper
Summary
The closed orbit correction has been an integral part of the synchrotron and storage ring in light sources as well as in hadron machines for stable beam operations [1,2,3]. SVD is a generalized technique based upon diagonalization and inversion of the matrices and, superseding all the above-mentioned methods, has become the de-facto algorithm for orbit correction. The technique is based upon the exploitation of circulant symmetry in the lattice and provides information compression into a diagonal matrix, since the left and right orthogonal matrices are standard Fourier matrices (defined later in the text). For larger ORMs, one can benefit from the reduced computational complexity of the technique This method serves as the transition between previously discussed harmonic analysis and SVD with an exact equivalence for symmetric lattices. The paper is arranged as follows: Section II A uses the example of the vertical plane of SIS18 in order to introduce the circulant symmetry in the ORMs, while the equivalence between SVD and DFT-based decomposition is worked out in Sec. II B.
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
