Short note on undulator alignments and beam tolerances for the APS FEL at 220 MeV

The APS FEL consists of a series of undulators that must be carefully aligned for optimum gain and high spectral output. In order to get a better understanding of acceptable tolerance levels for undulator alignments and for the electron beam, the authors have performed computer calculations to simulate misalignments of one undulator (undulator number 2) with respect to adjacent undulators and to check the sensitivity to unmatched beam parameters (α and β) at the entrance and to a noncentered incident beam xo, xoprime, yo, yoprime. They have not simulated horizontal misalignments because the undulators focus only in the vertical direction and horizontal alignments are therefore much more relaxed than vertical alignments. The exact placement and strength of the quadrupoles in the breaks need also to be addressed in follow up studies and are not presented here. Further, inherent undulator magnetic field errors have not been investigated here and will also be the subject for another study. Note, the tolerances listed in this note may be used for guidance only and will need to be updated when they have updated beam parameters