Symmetry Exploitation in Orbit Feedback Systems of Synchrotrons for Computational Efficiency

Structural symmetries in the storage ring of synchrotrons are intentionally created during design phase magnetic lattices, but they not considered control algorithms that stabilize beam accelerated particles. The choice algorithm, however, is limited by speed requirements synchrotron. Standard for based on a singular value decomposition (SVD) orbit response matrix. SVD controllers neither exploit structural nor exhibit any advantages. Based periodicity and reflection properties betatron function, we show these inherited We resulting block-circulant centrosymmetric matrix can be used different computationally efficient decompositions controller. also address case broken symmetry due to odd placements magnets monitors. Our could enable use more advanced techniques synchrotrons, such as require real-time optimization. These turn increase quality research synchrotron light sources.