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@ARTICLE{Christmann:639234,
      author       = {Christmann, Jan-Magnus and D'Angelo, Laura Anna Maria and
                      De Gersem, Herbert and Pfeiffer, Sven and Mirza, Sajjad
                      Hussain and Thede, Matthias and Aloev, Alexander and
                      Schlarb, Holger},
      title        = {{H}omogenized harmonic balance finite element method for
                      nonlinear eddy current simulations of fast corrector
                      magnets},
      reportid     = {PUBDB-2025-04354, arXiv:2503.19657},
      year         = {2025},
      note         = {18 pages, 27 figures, to be published in Physical Review
                      Accelerators and Beams},
      abstract     = {This paper develops a homogenized harmonic balance finite
                      element method (HomHBFEM) to predict the dynamic behavior of
                      magnets with fast excitation cycles, including eddy current
                      and skin effects. A homogenization technique for laminated
                      yokes avoids resolving the individual laminates and the skin
                      depth in the finite element (FE) mesh. Instead, the yoke is
                      represented by a bulk surrogate material with
                      frequency-dependent parameters. The ferromagnetic saturation
                      of the yoke at higher excitation currents is tackled by a
                      harmonic balance method, which accounts for a coupled set of
                      frequency components. Thereby, a computationally expensive
                      time stepping of the eddy-current field problem and a
                      convolution of the homogenized yoke model are avoided. The
                      HomHBFEM enables, for the first time, nonlinear simulations
                      of fast corrector magnets, which are embedded in a fast
                      orbit feedback system to counteract orbit disturbances over
                      a broad frequency spectrum, and thus guarantee stable
                      light-source operation. The results show the impact of the
                      nonlinearity on the phase lag and the field attenuation, as
                      well as the eddy current losses at frequencies up to several
                      tens of kilohertz. The numerical validation for a C-dipole
                      magnet example shows that the HomHBFEM achieves a sufficient
                      accuracy at an affordable computational effort, with
                      simulation times of a few hours. In comparison, standard 3D
                      transient FE simulations need to resolve the lamination
                      thickness and the skin depth in space and the largest
                      relevant frequency in time, which leads to a 2 to 3 orders
                      of magnitude larger mesh and prohibitive computational
                      effort, with simulation times of a few weeks on a
                      contemporary computer server.},
      cin          = {MSK / MEA1},
      ddc          = {530},
      cid          = {I:(DE-H253)MSK-20120731 / I:(DE-H253)MEA1-20210408},
      pnm          = {621 - Accelerator Research and Development (POF4-621) / GRK
                      2128 - GRK 2128: AccelencE: Beschleunigerphysik und
                      –technologie für Teilchenbeschleuniger mit
                      Energierückgewinnung (264883531)},
      pid          = {G:(DE-HGF)POF4-621 / G:(GEPRIS)264883531},
      experiment   = {EXP:(DE-H253)PETRAIV-20220101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2503.19657},
      howpublished = {arXiv:2503.19657},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2503.19657;\%\%$},
      url          = {https://bib-pubdb1.desy.de/record/639234},
}