arXiv subjects

Jan-Magnus Christmann

Publications and source records attributed to Jan-Magnus Christmann.

3 recordsLinked to original sources

arXiv2026

Experimental Validation of HomHBFEM Simulations of Fast Corrector Magnets for PETRA IV

This paper presents experimental validation of the homogenized harmonic balance finite element method (HomHBFEM), which we have developed as a dedicated simulation technique for magnets with fast excitation cycles, in particular the fast corrector (FC) magnets for PETRA IV at DESY. The HomHBFEM allows efficient three-dimensional nonlinear eddy-current simulations of laminated magnets at elevated frequencies with a relatively coarse finite element (FE) mesh and without computationally expensive time-stepping. This is achieved by combining a frequency-domain-based homogenization technique with the harmonic balance FE method. The simulation results for the magnetic flux density along the axis of the FC magnets as a function of frequency and the resulting integrated transfer function (ITF) are compared to Hall probe and search coil measurements of the first prototype FC magnet for PETRA IV. A good agreement between simulated and measured ITFs is achieved for excitation frequencies from 10 Hz to 10 kHz.

physics.acc-ph↗

arXiv2025

DC-Biased Homogenized Harmonic Balance Finite Element Method

The homogenized harmonic balance finite element (FE) method enables efficient nonlinear eddy-current simulations of 3-D devices with lamination stacks by combining the harmonic balance method with a frequency-domain-based homogenization technique. This approach avoids expensive time stepping of the eddy-current field problem and allows the use of a relatively coarse FE mesh that does not resolve the individual laminates. In this paper, we extend the method to handle excitation signals with a dc bias. To achieve this, we adapt the original homogenization technique to better account for ferromagnetic saturation. The resulting formula for the homogenized reluctivity is evaluated using a look-up table computed from a 1-D FE simulation of a lamination and containing the average magnetic flux density in the lamination and the corresponding skin depth. We compare the results of the proposed method to those from a fine-mesh transient reference simulation. The tests cover different levels of ferromagnetic saturation and frequencies between 50 Hz and 10 kHz. For moderate ferromagnetic saturation, the method gives a good approximation of the eddy-current losses and the magnetic energy, with relative errors below 10%, while reducing the required number of degrees of freedom at 10 kHz by 1.5 orders of magnitude. This results in a reduction in simulation time from 2 days on a contemporary server to 90 minutes on a standard workstation.

cs.CE↗

arXiv2025

Homogenized harmonic balance finite element method for nonlinear eddy current simulations of fast corrector magnets

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, to conduct 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 a 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 65 kHz. 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 two to three orders of magnitude larger mesh and prohibitive computational effort, with simulation times of a few weeks on a contemporary computer server.

physics.acc-ph↗