Symmetry Exploitation in Orbit Feedback Systems of Synchrotron Storage Rings

TL;DR

This paper demonstrates how exploiting structural symmetries in synchrotron storage rings can lead to more efficient control algorithms, potentially enhancing real-time optimization and improving research quality in light sources.

Contribution

It introduces a method to utilize the inherent symmetries of the orbit response matrix for computationally efficient control decompositions in synchrotrons.

Findings

Structural symmetries are inherited by the orbit response matrix.

Block-circulant and centrosymmetric properties enable efficient decompositions.

Addressing broken symmetry cases extends the method's applicability.

Abstract

Structural symmetries in the storage ring of synchrotrons are intentionally created during the design phase of the magnetic lattices, but they are not considered in the design of control algorithms that stabilize the beam of accelerated particles. The choice of control algorithm, however, is limited by the speed requirements of the synchrotron. 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. Based on the periodicity and the reflection properties of the betatron function, we show that these structural symmetries are inherited by the orbit response matrix. We 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 due to odd placements of magnets and monitors. Our efficient decomposition could enable the use of more advanced control techniques for synchrotrons, such as control algorithms that require real-time optimization. These advanced control techniques could in turn increase the quality of research in synchrotron light sources.