Betatron-Function Measurement in Lattices with 90-Degrees Sections

Lattice functions derived from betatron phase-advance measurements have been used successfully at many e{sup +}-e{sup -} facilities in the world, including at the PEP-II High Energy Ring. For the Low energy Ring of PEP-II, however, extraction of meaningful beta functions is hampered by the 90{sup o} phase advance/cell in the arcs, which causes a singularity in the expressions for beta. An algorithm has been developed calculating beta functions based on {beta} and {alpha} at the beginning of an arc and tracking the Twiss parameters through the arc while matching the observed phase advance/cell. Stability of the algorithm is improved by doing the same calculation 'backward' as well as forward and averaging the result. The algorithm allows estimating beta functions at bad BPMs in many cases. The paper presents the algorithm used as well as examples of use in PEP