Effects of Geometrical Errors on the Field Quality in a Planar Superconducting Undulator

Short-period superconducting undulators are being developed at the Advanced Photon Source (APS). A 21period undulator prototype is being fabricated. Later, the short coil will be replaced with a longer one using the same cryostat. A high quality magnetic field with a phase error of 2 degrees rms was achieved in the prototype magnets due to accurate winding of the superconducting coils on the precisely machined formers. Manufacturing meterslong undulator magnetic structures is a challenging task. A detailed understanding of the impact of geometric tolerances on the spectral performance is essential and appropriate manufacturing techniques have to be applied. The magnetic fingerprints of positioning errors of the superconducting windings in a planar structure are derived. Using these data the field profile of a long nonideal undulator magnet is then built and analyzed with respect to phase errors. The spectral performance degradation due to random and systematic geometric errors is presented. * Work supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. INTRODUCTION Within the APS-upgrade project [1] several superconducting undulators (SCUs) are foreseen. Currently, a 42-pole NbTi-based undulatorprototype SCU0 is being built and magnetically characterized at the APS. The installation into the APS 7GeV-storage ring is planned for 2012. The magnetic design is not yet pushed to the limits (superconductor operates at about 70% of a short sample critical current). The purpose of the undulator prototype is rather a serious testing of the key components under realistic conditions, including the thermosyphon based cooling concept, the cryostat, the actively cooled 20K vacuum chamber and the magnetic measurement facility consisting of a Hall probe system and a rotating coil system [2]. Conventional shimming techniques using Fe-shims or permanent magnets cannot be applied to a SCU. Furthermore, the crosstalk between poles and, thus, the range of field errors can be rather large (several ten cm). It is intended to minimize field errors already during fabrication to avoid extensive shimming. As long as the Fe-yoke is not saturated, the field errors are determined by the mechanic tolerances of the yoke. At maximum excitation currents the impact of coil winding errors increases. Apart from these random errors systematic errors such as longitudinal gap taper or Fe-yoke bending degrade the spectral performance. Bobbs et al. demonstrated a strong correlation of the spectral performance and the phase errors whereas the correlation with the field errors is rather poor [3]. The correlation of the spectral performance and the phase error is described by [4]: