GSI, Darmstadt, Germany
TEMF, TU Darmstadt, Darmstadt, Germany
A closed orbit feedback system is under development at the GSI SIS18 synchrotron for usage during the whole acceleration cycle including the acceleration ramp. Singular value decomposition (SVD) is the most widely used technique in global closed orbit correction for eigenmode decomposition, mode selection and pseudo-inversion of Orbit Response Matrix (ORM) for robust calculation of corrector magnet strengths. A new faster inversion technique based upon Discrete Fourier Transform (DFT) has been proposed for SIS18 ORM exploiting the Circulant symmetry, a class of matrices which can be diagonalized by the DFT using only one row or column of the matrix. The existence of a clear relationship between SVD modes and singular values to DFT modes and coefficients for such matrices has been described. The DFT based decomposition of Circulant ORM gives hints on physical interpretation of SVD and DFT modes of perturbed closed orbit in a synchrotron. As a first practical application, DFT modes were used to provide robustness against sensor failures such as one or two malfunctioning BPMs.
