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

Abstract

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-φ formulation method, all methods showing excellent agreement with each other as well as with experimental results. The mixed H-φ 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

Review and prospects of world-wide superconducting undulator development for synchrotrons and FELs

“…In 2019, Calvi et al experimentally demonstrated that a 5-period BHTSU10 model shown in figure 13(c) could obtain an on-axis field B 0 of 0.85 T at 6 mm magnetic gap after FC magnetization with ∆B s = 7 T at 10 K and that further increase of ∆B s would result in a premature quench [107]. Numerical simulations were later carried out by Hellmann et al with COMSOL H-formulation for understanding the complex correlation between B 0 and design parameters and by Zhang et al with ANSYS A-V formulation based backward computation method for optimizing the on-axis field integrals in a 10-period staggered-array 3D BHTSU model [110][111][112]. In 2021, it was experimentally demonstrated that a 10-period BHTSU10 model could obtain an on-axis field B 0 of ∼1.54 T @ 10 K at 4 mm magnetic gap and that a subcooling from 10 K to 8 K could help to freeze the trapped magnetic flux in GdBCO bulks, resulting in a long decay time constant of 3.2 years [3].…”

“…In 2005, Alexeev et al first adopted the FEM software ANSYS for calculating the magnetic field in a helical SCU designed for a MIR-FEL experiment [11]. Further studies based on ANSYS were reported for the magnetic and mechanical design study of Nb 3 Sn planar SCU [77,151] and staggered-array bulk HTSU [111,112,152]. In 2010, Majoros et al first adopted the FEM software FLUX 3D for simulating the magnetic fields in a 3D Nb 3 Sn helical SCU model [22].…”

“…In the staggeredarray BHTSU model with certain λ and g, the DVs include the geometry sizes-coil width w, coil height h and the magnetization field change ∆B s ; no SVs are required to constrain the analyses. The magnetization of staggered-array BHTSU is simulated by using a fast and efficient backward computation method implemented in ANSYS [111,112]. In the Halbach type and two hybrid-holmium CPMUs with certain λ and g, the DVs include the geometry sizes-magnet width w, magnet height h, total length l 2 and the holmium length l 1 ; no SVs are required to constrain the analyses.…”

Transient research on distribution networks incorporating superconducting cables utilizing field–circuit coupling method

“…With the progress in co-simulation methodology, the circuit model of a 10 kV cable system was modeled in Matlab/Simulink, while its field model modeled in ANSYS did not take into account the superconducting properties [20]. To cope with the HTS simulation in ANSYS, the resistivity adaptation algorithm was first explored in 2005 [21][22][23], while the E-J relation was not introduced until 2021 using an iteration approach [24][25][26][27]. Combining the field-circuit coupling methods [28][29][30], more work is needed to develop new models for an accurate system characterization, which is also applicable to other multi-physics software.…”

Electromagnetic force behavior of superconducting bulks passing electromagnetic turnout

“…Based on COMSOL Multiphysics, the indirect coupling approach in the partial differential equation (PDE) module [36] and the moving grid approach in the AC/DC module [37,38] are extensively utilized. Based on ANSYS, the A-V formulation is implemented to optimize the superconducting electromagnetic device [39].…”