Analysis of the first magnetic results of the PSI APPLE X undulators in elliptical polarisation

The new APPLE X undulators are novel elliptically-polarised undulators, which have a highly symmetric geometry. Theoretically, all the elliptical polarisation states are expected to have the same deflection parameter if the magnetic and geometrical errors are negligible. Nonetheless, the magnetic measurements of the first ten APPLE X undulators performed at Paul Scherrer Institut (PSI) contradicted this simple statement and numerical simulations were required to understand and validate the results. After the valuation of the magnetic-force induced mechanical deformations of the undulator frame, the central role played by the magnetic susceptibility χ was investigated. The simulation results indicate that the impact of different magnet types in the Halbach array, the anisotropic properties, and the choice of shaped field radial magnets are critical for the achieved magnetic field. The numerical results are compared with the measurement data.