The techniques of normal form analysis, well known in the literature, can be used to provide a straightforward characterization of linear betatron dynamics in a coupled lattice. Here, we consider both the beam distribution and the betatron oscillations in a storage ring. We find that the beta functions for uncoupled motion generalize in a simple way to the coupled case. Defined in the way that we propose, the beta functions remain well behaved (positive and finite) under all circumstances, and have essentially the same physical significance for the beam size and betatron oscillation amplitude as in the uncoupled case. Application of this analysis to the online modeling of the PEP-II rings is also discussed.

LOCO is a computer code for analysis of the linear optics in a storage ring based on the closed orbit response to steering magnets. The analysis provides information on focusing errors, BPM gain and rotation errors, and local coupling. Here, we discuss the details of the LOCO implementation at the KEK-ATF Damping Ring, and report the initial results. Some of the information obtained, for example on the BPM gain and coupling errors, has not previously been determined. We discuss the possibility of using the data provided by the LOCO analysis to reduce the vertical emittance of the ATF beam.

LOCO is a code for analysis of the linear optics in a storage ring based on the closed orbit response to steering magnets. The analysis provides information on focusing errors, BPM gain and rotation errors,and local coupling. Here, we report the results of an application of LOCO to the KEK-ATF. Although the analysis appears to have provided useful information on the optics of the machine, it appears that one of the main aims of the study to reduce the vertical emittance by correcting the local coupling was not successful, and we discuss some possible reasons for this.

The damping rings of a future linear collider will have demanding alignment and stability requirements in order to achieve the low vertical emittance necessary for high luminosity. The Accelerator Test Facility (ATF) at KEK has successfully demonstrated the vertical emittance below 5 pm that is specified for the GLC/NLC Main Damping Rings. One contribution to this accomplishment has been the use of Beam Based Alignment (BBA) techniques. The mode of operation of the ATF presents particular challenges for BBA, and we describe here how we have deduced the offsets of the BPMs with respect to the quadrupoles. We also discuss a technique that allows for direct measurements of the beam-to-quad offsets.