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For finite element (FE) analysis of no-insulation (NI) high-temperature superconducting (HTS) pancake coils, the high aspect ratio of the turn-to-turn contact layer (T2TCL) leads to meshing difficulties which result in either poor quality mesh elements resulting in a decrease of the solution accuracy or a high number of degrees of freedom. We proposed to mitigate this issue by collapsing the T2TCL volume into a surface and using a so-called thin shell approximation (TSA). Previously, two TSA have been introduced, one to solve the heat equation and the other for an $\vec{H}-\phi$ magnetodynamic formulation. In this work, we propose to combine the magnetodynamic and thermal TSA to create a coupled magneto-thermal TSA for three-dimensional FE analysis. Particular attention is paid to the detailed derivation of the coupling terms. In the context of NI HTS pancake coils, the TSA represents the electric and thermal contact resistance of the T2TCL. For the HTS coated conductor (CC) itself, an anisotropic homogenization is used which represents its multi-layered structure. In axial and azimuthal direction, it resolves the current sharing between the HTS and other layers of the CC. The coupled TSA formulation is verified against a reference model with volumetric T2TCL. The coupled TSA is shown to significantly reduce the solution time as well as the manual effort required for high-quality meshes of the T2TCL. The implementation is open-source and a reference implementation is made publicly available.

In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a reduced basis (RB) approximation to bring down the computational costs. It is based on the greedy strategy from Horger et al. 2017 which considers multiple eigenvalues for elliptic eigenvalue problems. We extend this algorithm to deal with parameter-dependent domains and the Maxwell eigenvalue problem. In this setting, the RB may contain spurious eigenmodes, which require special treatment. We demonstrate our algorithm in an eigenvalue tracking application for an eigenmode classification.

Accelerator magnets made from blocks of permanent magnets (PMs) in a zero-clearance configuration are known as Halbach arrays. The objective of this article is the fusion of knowledge from the magnetic field and material measurements and domain knowledge (magnetostatics) to obtain an updated magnet model of a Halbach array. From Helmholtz coil measurements of the magnetized blocks, a prior distribution of the magnetization is estimated. Measurements of the magnetic flux density are used to derive a posterior distribution by means of Bayesian inference. The method is validated on simulated data and applied to measurements of a dipole of the FASER detector. The updated magnet model of the FASER dipole describes the magnetic flux density one order of magnitude better than the prior magnet model.

When simulating resistive–capacitive (RC) circuits or electroquasistatic (EQS) problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition number of the system matrix. Here, we propose several stable formulations by scaling the equation systems. This enables a reliable calculation of solutions for very low frequencies (even for the static case), or large time steps. Numerical experiments underline the findings.

When simulating no-insulation high-temperature superconducting pancake coils with the finite element (FE) method, the high aspect ratio of the thin turn-to-turn contact layer (T2TCL) leads to unfavorable meshes in these thin layers as manifested by a high number of degrees of freedom (DoF) or mesh elements of poor quality which decrease the accuracy of the simulation results. To mitigate this issue, we propose to collapse the T2TCL volume into a surface using a thin shell approximation (TSA) for three-dimensional FE analysis. A $\vec{H}-\phi$ formulation is used and solves for the magnetic field strength $\vec{H}$ in conducting domains and the magnetic scalar potential $\phi$ in insulating domains. This formulation avoids spurious currents and reduces the number of DoF in insulating domains. Automatically created thick cuts are used to deal with multiply connected domains. Particular attention is paid to the interpretation of these cuts and the corresponding basis functions in the context of pancake coil geometries. The efficiency of the formulation facilitates the resolution of each turn. In this way, local phenomena such as quench can be captured in a straightforward way. The TSA formulation is verified by comparison against a reference model with volumetrically meshed T2TCL and is shown to be accurate and efficient, significantly reducing the solution time while reducing the effort for creating high-quality meshes. The TSA is implemented in an open-source FE framework and the source code is shared alongside this paper.

In electrical engineering, for example, during the design of superconducting radio frequency cavities, eigenmodes must be identified based on their field patterns. This allows to understand the working principle, optimize the performance of a device, and distinguish desired from parasitic modes. For cavities with simple shapes, the eigenmodes are easily classified according to the number of nodes and antinodes in each direction as is obvious from analytical formulae. For cavities with complicated shapes, the eigenmodes are determined numerically. Thereby, the classification is cumbersome, if not impossible. In this article, we propose a new recognition method by morphing the cavity geometry to a pillbox and tracking its eigenmodes during the deformation.

This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, a hybrid Gauss-Process regression (GPR) model is employed. In contrast to classic Kriging or Bayesian optimization approaches, we train a GPR surrogate for the performance feature specifications, not for the objective function. A multi-objective optimization problem is formulated, maximizing simultaneously the reliability, i.e., the yield, and further performance objectives, e.g., the costs. A permanent magnet synchronous machine is modeled and simulated in commercial finite element simulation software. Four approaches for solving the multi-objective optimization problem are described and numerically compared, namely: $\varepsilon$-constraint scalarization, weighted sum scalarization, a multi-start weighted sum approach and a genetic algorithm. We show that the efficiency gain thanks to our hybrid GPR model enables even computationally heavy multi-objective optimization for real-world applications.

In the design phase of an electrical machine, finite element (FE) simulations are commonly used to numerically optimize the performance. The output of the FE simulation is used to characterize the electromagnetic behavior of the machine. The simulation workflow involves intermediate measures such as nonlinear iron losses, electromagnetic torque, and flux values at each operating point that are used to compute several key performance indicators (KPIs). We present a data-driven deep learning approach that replaces the computationally heavy FE calculations by a deep neural network (DNN). The DNN is trained by a large volume of stored FE data in a supervised manner. During the learning process, the network response (intermediate measures) is fed as input to a physics-based post-processing to estimate characteristic maps and KPIs. We show that this hybrid approach reduces the computational time while maintaining a high flexibility in the simulation workflow. Finally, the hybrid approach is compared to the existing direct prediction approach for KPIs.

Homogenization techniques are an appealing approach to reduce computational complexity in systems containing coils with large numbers of high temperature superconductor (HTS) tapes. Resolving all the coated conductor layers and turns in coils is often computationally prohibitive. In this paper, we extend the foil conductor model, well-known in normal conducting applications, to applications with insulated HTS coils. To enhance the numerical performance of the model, the conventional formulation based on $A-V$ is extended to $J-A-V$. The model is verified to be suitable for simulations of superconductors and to accelerate the calculations compared to resolving all the individual layers. The performance of both the $A-V$ and $J-A-V$ formulated models is examined, and the $J-A-V$ variant is concluded to be advantageous.