Stability of a Large Synchrotron with Closed Orbit Distortions

In a large synchrotron or a storage ring, the random closed orbit distortions are generally large. When combined with the sextupole magnets for chromaticity correction, they produce linear stopbands because effective gradient errors appear. Further, the vertical closed orbit distortion produces a vertical dispersion because there appears a vertical bend in the quadrupole and sextupole magnets. These effects are studied by an analytical method.