Symmetry Exploitation in Orbit Feedback Systems of Synchrotrons for Computational Efficiency

Structural symmetries in the storage ring of synchrotrons are intentionally created during the design phase of the magnetic lattices, but they are rarely considered in the design of control algorithms that stabilize the beam of accelerated particles. The choice of control algorithm, however, is limited by the high actuation frequency and the large number of inputs and outputs. Standard control algorithms for synchrotrons are based on a singular value decomposition (SVD) of the orbit response matrix. SVD controllers neither exploit the structural symmetries nor exhibit any speed advantages. By considering the periodicity and the reflection properties of the betatron function, we show that these structural symmetries are inherited by the orbit response matrix. We then show that the resulting block-circulant and centrosymmetric properties of the matrix can be used for different computationally efficient decompositions of the controller. We also address the case of broken symmetry caused by odd placements of individual magnets and monitors. Our efficient decomposition enables the use of more advanced control techniques for synchrotrons, such as control algorithms that require real-time optimization. These advanced control techniques can in turn increase the stability of photon beams in synchrotron light sources.