Two General Orbit Theorems for Efficient Measurements of Beam Optics

Closed-orbit perturbations and oscillating beam solutions in storage rings are closely related. While techniques exist to fit accelerator models to closed-orbit perturbations or to oscillation data, the exploitation of their relation has been limited. In this work, two orbit theorems that allow an efficient computation of optical parameters in storage rings with older hardware are derived for coupled linear beam motion. The monitor theorem is based on an uncoupled case study described by the author in an earlier work and has been generalized as well as simplified in mathematical abstraction to provide a reliable and computationally stable framework for beam optics measurements. It is based on a closed-orbit measurement utilizing 4 dipole correctors (2 for each plane). The corrector theorem allows to obtain parameters of these dipole correctors using two turn-by-turn monitors at almost arbitrary positions in the ring (which do not need to be located in a drift space), so that it is possible to uniquely resolve closed orbits into optical parameters without sophisticated lattice models.