ABSTRACT
Unlike single pass systems, the dynamics of the beam in a repetitive system such as a storage ring is not necessarily dominated by the largest aberrations in the one turn transfer map. Due to the fact that particles go around many times, the impact of those terms that are nearly in phase with the linear motion are amplified and the dynamics is, to a large extent, shaped by them. The motion generated by one of those terms is called a resonance. In this chapter, the authors study the dynamics in a ring when one or more dipole magnets have errors in the field. They consider the case that one magnet has a dipole error in the field. Linear coupling between transversal planes arises from solenoids, roll of quadrupoles, vertical misalignment and orbit offset at sextupole locations. The authors study the effect of skew quadrupoles, which can be present intentionally or due to the roll of normal quadrupoles.
