Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods

The development of a new hard x-ray beamline I-TOMCAT equipped with a 1 m long short-period bulk high-temperature superconductor undulator (BHTSU) has been scheduled for the upgrade of the Swiss Light Source at the Paul Scherrer Institute. The very hard x-ray source generated by the BHTSU will increase the brilliance at the beamline by over one order of magnitude in comparison to other state-of-the-art undulator technologies and allow experiments to be carried out with photon energies in excess of 60 keV. One of the key challenges for designing a 1 m long (100 periods) BHTSU is the large-scale simulation of the magnetization currents inside 200 staggered-array bulk superconductors. A feasible approach to simplify the electromagnetic model is to retain five periods from both ends of the 1 m long BHTSU, reducing the number of degrees of freedom to the scale of millions. In this paper, the theory of the recently-proposed 2D A -V formulation-based backward computation method is extended to calculate the critical state magnetization currents in the ten-period staggered-array BHTSU in 3D. The simulation results of the magnetization currents and the associated undulator field along the electron beam axis are compared with the well-known 3D H -formulation and the highly efficient 3D H -phi formulation method, all methods showing excellent agreement with each other as well as with experimental results. The mixed H -phi formulation avoids computing the eddy currents in the air subdomain and is significantly faster than the full H -formulation method, but is slower in comparison to the A -V formulation-based backward computation. Finally, the fastest and the most efficient A -V formulation, implemented in ANSYS 2020R1 Academic, is adopted to optimize the integrals of the undulator field along the electron beam axis by optimizing the sizes of the end bulks.

Automated summary

The development of a new hard X-ray beamline I-TOMCAT equipped with a 1 m long short-period bulk high-temperature superconductor undulator (BHTSU) is planned for the Swiss Light Source at the Paul Scherrer Institute. The key challenge lies in designing a 1 m long BHTSU, particularly in simulating the magnetization currents inside 200 staggered-array bulk superconductors. Simplifying the electromagnetic model by retaining five periods from both ends has been proposed to reduce the number of degrees of freedom to millions.