Modelling and Electromagnetic Design Optimization of Short Period Helical Undulator Wound With Low Temperature Superconducting Round Wires

A helical superconducting undulator (HSCU) wound with Nb-Ti/Cu or Nb3Sn/Cu round wires can produce large on-axis sinusoidal fields of B-x(z) and B-y(z) with short period and generate circularly polarized photons with short wavelength when high energy electron bunches travel through the undulator system. Although its suppression in the on-axis higher harmonic photons limits the HSCU's suitability for the synchrotron radiation light source, tis characteristic is advantageous for free electron laser facilities, which typically use radiation photons with the fundamental wavelength. In this paper, we introduce an accurate and efficient modelling approach for optimizing the electromagnetic design of helical undulators wound with low temperature superconducting round wires. The HSCU model is created as a pure conductor within the Opera 3D Postprocessor and segmented into multilayers, each carrying currents with progressively shifted directions. The peak magnetic field in the conductor and the undulator field along the beam axis are calculated using the integral method as the state variable and the objective function, respectively. To speed up the optimization process, we take advantage of an auto-optimized module which automatically updates all design variables, i.e., coil sizes and input current, after each iteration. It is observed that for a period of 12 mm and a magnetic gap of 6 mm, the Nb-Ti or Nb3Sn HSCU, with a packing factor of 0.85 and a safety margin of 20%, can achieve on-axis alternating magnetic fields of B-x(0) = B-y(0) = 0.90 T and B-x(0) = B-y(0) = 1.83 T, respectively.