Design of Nb$_{3}$Sn Wiggler Magnets for the Compact Linear Collider and Manufacturing of a Five-Coil Prototype

To achieve the luminosity requirements of the Compact Linear Collider (CLIC) at the collision point, damping rings (DRs) equipped with superconducting wiggler magnets should be used to produce ultralow emittance with high bunch charge. Although Nb-Ti wigglers meet the specifications for CLIC DRs, the more challenging Nb$_{3}$Sn technology could be used to increase the magnetic flux density amplitude in the gap and reduce the total length of wigglers in the DRs. To test the Nb$_{3}$Sn technology, a small wiggler prototype is under design and will be built and tested at CERN. Magnetic calculations concerning the selection of the main wiggler's parameters are presented in this paper, which include the optimization of the main coil dimensions and the period length, in order to fulfill the normalized emittance and intrabeam scattering effect constraints, while decreasing the amount of wigglers in the DRs. Another advantage of using Nb$_{3}$Sn, instead of Nb-Ti, as superconducting material is the possibility of increasing the working margin. Several scenarios well suited for CLIC damping wigglers, in which the working point is less than 80% of the magnet's current limit, are addressed in this work. In addition, the description of the manufacturing process and the current status of the Nb$_{3}$Sn prototype fabrication are presented.