Design of ${\rm Nb}_{3}{\rm Sn}$ -Based Short Period Model Superconducting Helical Undulator

Superconducting undulators are being constructed to satisfy an increasing need within the synchrotron radiation community for higher and higher energy photon beams. The paper focuses attention on the design of a helical undulator for the ILC photon (hence positron) source. Finite element method (FEM) modeling was performed to extend the design of our existing 14 mm period undulator design to shorter periods with a view towards the final design, construction and testing of a 10 mm undulator. To launch this task we modeled the properties of 10 mm period undulators formed around bore tubes of the 6 mm and 8 mm OD with winding-pack cross-sections of 3 mm × 6 mm and 3 mm × 11 mm. These windings do allow a pole width of 2 mm and can take advantage of the corresponding about 0.2 T field increment due to it. In order to reach the target bore field of 1.1 T it is necessary to either reduce the bore size and tighten the associated tolerances, or to use a higher performing strand. In the present work we have chosen to optimize the undulator design basing it on the properties of an advanced tube-type strand keeping the bore tube diameter at 6-8 mm in order to see the needed performance to meet this undulator specification.