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 adopted to optimize the integrals of the undulator field along the electron beam axis by optimizing the sizes of the end bulks.

配备 1 m 长短周期体高温超导体波荡器 (BHTSU)的新型硬X射线束线 I-TOMCAT的开发已计划用于升级保罗谢勒研究所的瑞士光源。非常难的x与其他最先进的波荡器技术相比，BHTSU 产生的 β 射线源将光束线的亮度提高一个数量级以上，并允许以超过 60 keV 的光子能量进行实验。设计 1 m 长（100 个周期）BHTSU 的主要挑战之一是对 200 个交错阵列体超导体内的磁化电流进行大规模模拟。一种简化电磁模型的可行方法是在 1 m 长 BHTSU 的两端保留五个周期，将自由度数减少到百万级。在本文中，最近提出的 2D A -V 理论 基于公式的反向计算方法扩展到计算 3D 中十周期交错阵列 BHTSU 中的临界状态磁化​​电流。将磁化电流和沿电子束轴的相关波场的仿真结果与众所周知的 3D H公式和高效的 3D H - ϕ公式进行比较，所有方法都显示出良好的一致性以及与实验结果。混合H - ϕ公式避免了计算空气子域中的涡流，并且比完全H公式方法快得多，但与A -V相比速度较慢 基于公式的反向计算。最后，采用在 ANSYS 2020R1 Academic 中实施的最快和最有效的A- V公式，通过优化末端块的尺寸来优化沿电子束轴的波荡器场的积分。