Effects of wigglers and undulators on beam dynamics

Synchrotron light facilities are making ever increasing use of wigglers and undulators, to the extent that these devices are becoming a significant part of the beam optical system of the storage ring itself. This paper presents a theoretical formulation for investigating the effect of wigglers and undulators on beam dynamics in the approximation that the wiggler parameter, K, divided by ..gamma.. is a small number and that the number of wiggler periods in one device is large. In addition to the linear forces which must be taken into account when tuning and matching the ring, nonlinear stop bends are created, with even orders more serious than odd orders. Some numerical examples are given for devices similar to those proposed for the 1-2 GeV Synchrotron Radiation Source at Lawrence Berkeley Laboratory