Resorting the NIST undulator using simulated annealing for field error reduction

We have used a simulated annealing algorithm to sort the samarium cobalt blocks and vanadium permendur poles in the hybrid NIST undulator to optimize the spectrum of the emitted light. While simulated annealing has proven highly effective in sorting of the SmCo blocks in pure REC undulators, the reliance on magnetically 'soft' poles operating near saturation to concentrate the flux in hybrid undulators introduces a pair of additional variables - the permeability and saturation induction of the poles - which limit the utility of the assumption of superposition on which most simulated annealing codes rely. Detailed magnetic measurements clearly demonstrated the failure of the superposition principle due to random variations in the permeability in the 'unsorted' NIST undulator. To deal with the issue, we measured both the magnetization of the REC blocks and the permeability of the NIST's integrated vanadium permendur poles, and implemented a sorting criteria which minimized the pole-to-pole variations in permeability to satisfy the criteria for realization of superposition on a nearest-neighbor basis. Though still imperfect, the computed spectrum of the radiation from the re-sorted and annealed NIST undulator is significantly superior to that of the original, unsorted device