  The development of a new hard x-ray beamline I-TOMCAT equipped with a
1-meter-long short-period bulk high-temperature superconductor undulator
(BHTSU) has been scheduled for the upgrade of the Swiss Light Source (SLS 2.0)
at the Paul Scherrer Institute (PSI). 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-meter-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-meter-long BHTSU, reducing the number of degrees of freedom (DOFs) 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 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.
