Harmonic Balance Finite Element Method Combined With a Homogenization of Laminated Yokes

The magnetoquasistatic simulation of laminated ferromagnetic structures at elevated frequencies is a challenging task, which quickly becomes impossible for three-dimensional models, especially if a nonlinear magnetization curve must be considered. In this contribution, we show how existing homogenization techniques for the linear case can be combined with the harmonic balance finite element method, to also account for the nonlinearity of the magnetization curve. This leads to a method which does not necessitate resolving the individual laminations with the finite element mesh and avoids time-stepping, thus allowing us to conduct nonlinear eddy current simulations of large three-dimensional models at frequencies in the kilohertz range efficiently. In particular, we demonstrate the usefulness of this new approach for simulating fast orbit corrector magnets in particle accelerators.