Bahrdt, J.; Wüstefeld, G.: SYMPLECTIC TRACKING AND COMPENSATION OF DYNAMIC FIELD INTEGRALS IN COMPLEX UNDULATOR STRUCTURES. In: Proceedings of IPAC 2012, New Orleans, Louisiana, USA. , 2012, p. 4165-4169

This presentation covers analytical models that describe the interaction of a relativistic particle beam with the magnetic field of undulators. Analytic approximations to the Hamilton-Jacobi equation yield generating functions useful for particle tracking and, therefore, efficient simulation. Analytic expressions for kick maps of APPLE II undulators are presented as well. Passive and active shimming schemes including magic fingers and current sheets are also modelled. Applications at BESSY II are discussed which ensure efficient injection during top-up to satisfy machine protection and radiation safety requirements.