SVD Orbit Correction for ALPHA

This paper describes an orbit correction algorithm using singular value decomposition (SVD), and appli-cations of this correction algorithm to orbit correction in the ALPHA ring at Indiana University. 1 Theory Consider a beam traveling on a closed orbit in a synchrotron that contains nb beam position monitors (BPMs) and nc dipole correctors in a single plane. In the linear approximation, the closed orbit (or bunch centroid displacement) displacement ∆xm at BPM m from a dipole kick change ∆x k at corrector k is given by a response matrix element Amk: Amk ≡ ∆xm ∆x′