Comparison of Achievable Magnetic Fields with Superconducting and Cryogenic Permanent Magnet Undulators – A Comprehensive Study of Computed and Measured Values
Magnetic modeling was performed to estimate achievable magnetic field strengths of superconducting undulators (SCUs) and to compare them with those of cryogenically cooled permanent magnet undulators (CPMUs). Starting with vacuum (beam stay-clear) gaps of 4.0 and 6.0 mm, realistic allowances for beam chambers (in the SCU case) and beam liners (in the CPMU case) were added. (A 6.0-mm vacuum gap is planned for the upgraded APS). The CPMU magnetic models consider both CPMUs that use NdFeB magnets at ~150 K and PrFeB magnets at 77 K. Parameters of the magnetic models are presented along with fitted coefficients of a Halbach-type expression for the field dependence on the gap-to-period ratio. Field strengths for SCUs are estimated using a scaling law for planar SCUs; an equation for that is given. The SCUs provide higher magnetic fields than the highest-field CPMUs – those using PrFeB at 77 K – for period lengths longer than ~14 mm for NbTi-based SCUs and ~10 mm for Nb3Sn-based SCUs. To show that the model calculations and scaling law results are realistic, they are compared to CPMUs that have been built and NbTi-based SCUs that have been built. Brightness tuning curves of CPMUs (PrFeB) and SCUs (NbTi) for the upgraded APS lattice are also provided for realistic period lengths.