Finite-length field error and its compensation in superconducting miniundulators

Superconducting miniundulators (supraminis) are being developed for their potential to produce either higher photon energy beams at given electron energy facilities or to save accelerator cost by using lower electron energy for given photon energy beams as compared to permanent-magnet undulators. Based on a wire model, analytical formulae are derived to describe the spatial distribution of the magnetic field as determined by the parameters of the undulator. It is shown that the location of the field zeros is shifted compared with the position of the wires. This finite-length field error is systematic and alters the radiation spectrum significantly. After introducing a simple compensation coil, the field quality, locations of zeros, field integrals, and radiation spectrum become satisfactory. The analytical results are shown to be in good agreement with numerical simulations.