arXiv subjects

Arjan Verweij

Publications and source records attributed to Arjan Verweij.

At least 19 recordsLinked to original sources

arXiv2026

Surface Contact Approximation for Magneto-Thermal Finite Element Analysis of No-Insulation HTS Coils

High-temperature superconducting (HTS) coated conductors (CCs) can be wound into no-insulation (NI) coils, in which electrical current can partially bypass local normal zones via turn-to-turn contact layers (T2TCLs). Accurate magneto-thermal simulation of such coils, therefore, requires an efficient representation of the electrical and thermal behavior of the T2TCLs. This paper introduces a magneto-thermal surface contact approximation (SCA) for finite element analysis of NI HTS coils. The formulation is derived as a special case of the more general thin shell approximation (TSA) by introducing suitable approximations such as negligible tangential surface currents and eddy-current effects inside the T2TCL. The resulting SCA formulation replaces the thin volumetric contact layer with a dedicated surface weak formulation based on the electric contact resistance and thermal contact conductance. In contrast, the TSA formulation requires the definition of electric resistivities and thermal conductivities as well as the thickness of the T2TCL. The SCA is implemented in the Pancake3D module of the free and open-source Finite Element Quench Simulator. It is verified through transient magneto-thermal simulations of a model NI pancake coil. Numerical results are compared against the established TSA formulation. The results show that the SCA accurately reproduces the relevant electromagnetic and thermal behavior. For the TSA, there is a trade-off between choosing large (potentially unphysical) thicknesses with low resistivities leading to inaccurate results, or small thicknesses with large resistivities making the linear system harder to solve, increasing the computational effort. In contrast, the SCA, thanks to using contact resistances and conductances directly without the necessity to define a thickness, is easy to use and robust.

physics.comp-ph↗

arXiv2026

Modelling Conduction Cooling of Superconducting Accelerator Magnets using a Thermal Thin Shell Approximation

Understanding the thermal behaviour of superconducting accelerator magnets is essential to ensure their stable and reliable operation. This work presents an extension of the Finite Element Quench Simulator (FiQuS) Multipole module to include collar and pole regions of accelerator magnets, which influences the overall thermal response. A thermal thin shell approximation (TSA), which is shown to be effective from previous works, is employed to model thermal insulation layers efficiently, replacing an insulation surface mesh. The main novelty of this work lies in the development of a method to model the thermal connection between the magnet winding and the collar and pole regions via the TSA. To assess the accuracy and computational efficiency of this method, temperature and field variations are computed for a current ramp-up scenario. The thermal solution is coupled to a fully resolved magnetodynamic solution to capture the interaction between thermal and electromagnetic behaviour. The results obtained with the TSA are then compared to classical finite element (FE) solutions with explicitly meshed insulation domains. The TSA predicts the maximum temperature within 2-4 % of the reference solution while substantially reducing mesh complexity and achieving up to a 5 times speed-up in computation time. While the TSA has traditionally been employed for short-duration quench simulations with high heat fluxes between magnet turns, these results demonstrate its reliability and efficiency for current ramp scenarios with low heat fluxes, significantly expanding its application range beyond what has been previously reported in the literature. To illustrate potential applications of this new functionality, conduction cooling through the collar region is studied, comparing different cooling configurations and collar materials.

physics.acc-ph↗

arXiv2025

Distributed Inter-Strand Coupling Current Model for Finite Element Simulations of Rutherford Cables

In this paper, we present the Distributed Inter-Strand Coupling Current (DISCC) model. It is a finite element (FE) model based on a homogenization approach enabling efficient and accurate simulation of the transient magnetic response of superconducting Rutherford cables without explicitly representing individual strands. The DISCC model reproduces the inter-strand coupling current dynamics via a novel mixed FE formulation, and can be combined with the Reduced Order Hysteretic Magnetization (ROHM) and Flux (ROHF) models in order to reproduce the effects of internal strand dynamics: hysteresis, eddy, and inter-filament coupling currents, as well as ohmic effects. The DISCC model offers a massive reduction of the computational time compared to fully detailed FE models and still accounts for all types of loss and magnetization contributions. As a result, Rutherford cables homogenized with the DISCC model can be directly included in FE models of magnet cross-sections for efficient electro-magneto-thermal simulations of their transient response. We present two possible FE formulations for the implementation of the DISCC model, a first one based on the h-phi-formulation, and a second one based on the h-phi-a-formulation, which is well suited for an efficient treatment of the ferromagnetic regions in magnet cross-sections.

physics.acc-ph↗

arXiv2025

Reduced Order Hysteretic Flux Model for Transport Current Homogenization in Composite Superconductors

In this paper, we present the Reduced Order Hysteretic Flux (ROHF) model to describe the relationship between time-varying transport current and internal magnetic flux for composite superconductors. The ROHF model is parametrized using reference simulations of the conductor response, after which it enables the computation of macroscopic quantities such as voltage and power loss without requiring detailed electromagnetic field solutions. It is therefore suitable for the homogenization of transport current effects in large-scale superconducting magnets, avoiding a fine discretization of the composite strand small scale structures, allowing to drastically reduce the computational effort. The approximation can be implemented either (i) as a rate-independent model, neglecting eddy current effects in the normal conducting matrix, or (ii) as a rate-dependent model, including those eddy current effects. In this paper, the complete modeling workflow, including parameter identification, coupling with the other fields (temperature and magnetic field), and post-processing of the results, is described and verified using a twisted multifilamentary strand as an example.

physics.acc-ph↗

arXiv2025

Transient Finite Element Simulation of Accelerator Magnets Using Thermal Thin Shell Approximation

Thermal transient responses of superconducting magnets can be simulated using the finite element (FE) method. Some accelerator magnets use cables whose electric insulation is significantly thinner than the bare electric conductor. The FE discretisation of such geometries with high-quality meshes leads to many degrees of freedom. This increases the computational time, particularly since non-linear material properties are involved. In this work, we propose to use a thermal thin-shell approximation (TSA) to improve the computational efficiency when solving the heat diffusion equation in two dimensions. We apply the method to compute the thermal transient response of superconducting accelerator magnets used for CERN's Large Hadron Collider (LHC) and High-Luminosity LHC. The TSA collapses thin electrical insulation layers into lines while accurately representing the thermal gradient across the insulation's thickness. The TSA is implemented in the multipole module of the open-source Finite Element Quench Simulator (FiQuS), which can generate the multipole magnet models programmatically from input text files. First, the TSA approach is verified by comparison to classical FE simulations with meshed surface insulation regions for a simple block of four cables and a detailed model of the MBH dipole. The results show that the TSA approach reduces the computational time significantly while preserving the accuracy of the solution. Second, the quench heater (QH) delay computed with the TSA method is compared to measurements for the MBH magnet. To this end, the thermal transient simulation is coupled to a magnetostatic solution to account for magneto-resistive effects. Third, the TSA's full capabilities are showcased in non-linear magneto-thermal simulations of several LHC and HL-LHC superconducting magnet models. The full source code, including all input files, is publicly available.

physics.acc-ph↗

arXiv2024

Influence of Critical Current Distribution on Operation, Quench Detection and Protection of HTS Pancake Coils

High-temperature superconductor (HTS) coated conductors (CC) are often wound into pancake coils with electrical insulation in-between the turns. The copper terminals are used for current injection and conduction cooling. An inherent variation of the critical current along the CC length results from its manufacturing process. This variation causes non-uniform heat generation, particularly when the coil is operated at a high fraction of the nominal critical current or when large critical current defects are present. The temperature distribution resulting from the balance between cooling and heating, in combination with the magnetic field and critical current distributions, determines whether a thermal runaway occurs. Accurately predicting the level of critical current defects that can be tolerated during conduction-cooled operation is difficult and requires a 3D coupled electromagnetic and thermal simulation. This paper presents the results of simulations that are performed with the open-source Finite Element Quench Simulator (FiQuS) tool developed at CERN as part of the STEAM framework. The 3D coupled magnetodynamic-thermal simulations are based on the H-phi formulation and use thin shell approximations, a CC homogenization and conduction-cooling. The critical current (Ic) is varied along the CC length. The effect of a single defect specified as a reduction of Ic along the CC length is investigated in terms of the coil's ability to reach and maintain the operating conditions. The Ic and length of the defect that results in a thermal runaway are analyzed in terms of defect location. In addition, a classical 1D scenario with a quench heater is studied. Both the local defect and the heater cases are compared in terms of the voltage signal available for quench detection. These cases result in very different requirements for quench detection, and their implications are discussed.

physics.acc-ph↗

arXiv2024

Simulation of Rutherford Cable AC Loss and Magnetization with the Coupled Axial and Transverse Currents Method

The coupled axial and transverse currents (CATI) method was recently introduced to model the AC loss and magnetization in twisted composite superconducting strands with low computational cost and high accuracy. This method involves two-dimensional finite element (FE) models coupled with circuit equations representing the periodicity of the strand. In this paper, we propose to adapt the CATI method to Rutherford cables, which are periodic structures made of transposed superconducting strands. We focus on reproducing the interstrand coupling currents flowing across contact resistances between the strands and we analyze the associated AC loss. We show that results of a reference three-dimensional FE model are accurately reproduced with a strongly reduced computational cost.

physics.acc-ph↗

arXiv2024

Reduced Order Hysteretic Magnetization Model for Composite Superconductors

In this paper, we propose the Reduced Order Hysteretic Magnetization (ROHM) model to describe the magnetization and instantaneous power loss of composite superconductors subject to time-varying magnetic fields. Once the parameters of the ROHM model are fixed based on reference simulations, it allows to directly compute the macroscopic response of composite superconductors without the need to solve the detailed current density distribution. It can then be used as part of a homogenization method in large-scale superconducting models to significantly reduce the computational effort compared to detailed simulations. In this contribution, we focus on the case of a strand with twisted superconducting filaments subject to a time-varying transverse magnetic field. We propose two variations of the ROHM model: (i) a rate-independent model that reproduces hysteresis in the filaments, and (ii) a rate-dependent model that generalizes the first level by also reproducing dynamic effects due to coupling and eddy currents. We then describe the implementation and inclusion of the ROHM model in a finite element framework, discuss how to deduce the model parameters, and finally demonstrate the capabilities of the approach in terms of accuracy and efficiency over a wide range of excitation frequencies and amplitudes.

physics.acc-ph↗

arXiv2024

Energy Shift with Coupling (ESC): a new quench protection method

Quench protection of full-size high-field accelerator magnets poses significant challenges. Maintaining the hot-spot temperature and peak voltage-to-ground within acceptable limits requires a protection system that quickly transitions most of the coil turns to the normal state. Existing magnet protection technologies, such as quench protection heaters or the Coupling Loss Induced Quench system (CLIQ), have been successfully applied. However, they both present shortcomings since they require either thin insulation between the heaters and the magnet conductor or direct electrical connections to the magnet coil. A novel quench protection method, Energy Shift with Coupling (ESC), is presented which can achieve excellent quench protection performance without the above-mentioned drawbacks. ESC relies on normal-conducting auxiliary coils strongly magnetically coupled with the magnet coils to protect. Upon quench detection capacitive units connected across such coils introduce a high current change in the auxiliary coils causing a rapid shift of magnet stored energy from the magnet coils to the auxiliary coils. This has three beneficial effects: sudden reduction of ohmic loss in the normal zone of the magnet conductor, introduction of high transient losses in the magnet conductor, thus causing a quick transition to the normal state, and extraction of a part of the magnet stored energy to the auxiliary coils. The applicability of the ESC concept on an existing magnet design is analyzed with electromagnetic and thermal transient simulations performed with the STEAM-LEDET program. The advantages and disadvantages of ESC are discussed and compared to other conventional quench protection methods. Simulation results show that ESC can be applied to protect full-scale magnets with reasonable requirements in terms of size and location of the auxiliary coils and of capacitive unit parameters.

physics.app-ph↗

arXiv2024

Coupled Axial and Transverse Currents Method for Finite Element Modelling of Periodic Superconductors

In this paper, we propose the Coupled Axial and Transverse currents (I) (CATI) method, as an efficient and accurate finite element approach for modelling the electric and magnetic behavior of periodic composite superconducting conductors. The method consists of a pair of two-dimensional models coupled via circuit equations to account for the conductor geometrical periodicity. This allows to capture three-dimensional effects with two-dimensional models and leads to a significant reduction in computational time compared to conventional three-dimensional models. After presenting the method in detail, we verify it by comparison with reference finite element models, focussing on its application to twisted multifilamentary superconducting strands. In particular, we show that the CATI method captures the transition from uncoupled to coupled filaments, with accurate calculation of the interfilament coupling time constant. We then illustrate the capabilities of the method by generating a detailed loss map and magnetization curves of given strand types for a range of external transverse magnetic field excitations, with and without transport current.

physics.acc-ph↗

arXiv2024

Parallel-in-Time Integration of Transient Phenomena in No-Insulation Superconducting Coils Using Parareal

High-temperature superconductors (HTS) have the potential to enable magnetic fields beyond the current limits of low-temperature superconductors in applications like accelerator magnets. However, the design of HTS-based magnets requires computationally demanding transient multi-physics simulations with highly non-linear material properties. To reduce the solution time, we propose using Parareal (PR) for parallel-in-time magneto-thermal simulation of magnets based on HTS, particularly, no-insulation coils without turn-to-turn insulation. We propose extending the classical PR method to automatically find a time partitioning using a first coarse adaptive propagator. The proposed PR method is shown to reduce the computing time when fine engineering tolerances are required despite the highly nonlinear character of the problem. The full software stack used is open-source.

cs.CE↗

arXiv2023

An Open-Source 3D FE Quench Simulation Tool for No-Insulation HTS Pancake Coils

A new module, Pancake3D, of the open-source Finite Element Quench Simulator (FiQuS) has been developed in order to perform transient simulations of no-insulation (NI) high-temperature superconducting (HTS) pancake coils in 3-dimensions. FiQuS/Pancake3D can perform magnetodynamic or coupled magneto-thermal simulations. Thanks to the use of thin shell approximations, an $\vec{H}-ϕ$ formulation, and anisotropic homogenization techniques, each turn can be resolved on the mesh level in an efficient and robust manner. FiQuS/Pancake3D relies on pre-formulated finite-element (FE) formulations and numerical approaches that are programmatically adjusted based on a text input file. In this paper, the functionalities and capabilities of FiQuS/Pancake3D are presented. The challenges of FE simulation of NI coils and how FiQuS/Pancake3D addresses them are explained. To highlight the functionalities, the results of a magneto-thermal analysis of a double pancake coil with 40 turns per pancake with local degradation of the critical current density are conducted and discussed. Furthermore, a parameter sweep of the size of this local degradation is presented. All the FiQuS input files for reproducing the simulations are provided.

cond-mat.supr-con↗

arXiv2023

Magneto-Thermal Thin Shell Approximation for 3D Finite Element Analysis of No-Insulation Coils

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.

physics.acc-ph↗

arXiv2021

Numerical Analysis of the Screening Current-Induced Magnetic Field in the HTS Insert Dipole Magnet Feather-M2.1-2

Screening currents are field-induced dynamic phenomena which occur in superconducting materials, leading to persistent magnetization. Such currents are of importance in ReBCO tapes, where the large size of the superconducting filaments gives rise to strong magnetization phenomena. In consequence, superconducting accelerator magnets based on ReBCO tapes might experience a relevant degradation of the magnetic field quality in the magnet aperture, eventually leading to particle beam instabilities. Thus, persistent magnetization phenomena need to be accurately evaluated. In this paper, the 2D finite element model of the Feather-M2.1-2 magnet is presented. The model is used to analyze the influence of the screening current-induced magnetic field on the field quality in the magnet aperture. The model relies on a coupled field formulation for eddy current problems in time-domain. The formulation is introduced and verified against theoretical references. Then, the numerical model of the Feather-M2.1-2 magnet is detailed, highlighting the key assumptions and simplifications. The numerical results are discussed and validated with available magnetic measurements. A satisfactory agreement is found, showing the capability of the numerical tool in providing accurate analysis of the dynamic behavior of the Feather-M2.1-2 magnet.

physics.acc-ph↗

arXiv2020

A Coupled A-H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets

The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled $\textbf{A}$-$\textbf{H}$ field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength $\textbf{H}$ accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential $\textbf{A}$ represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a slab approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet.

physics.acc-ph↗

arXiv2018

STEAM: A Hierarchical Co-Simulation Framework for Superconducting Accelerator Magnet Circuits

Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection systems. Nevertheless, the numerical analysis is traditionally done separately for each element in the circuit, leading to possible non-consistent results. We present STEAM, a hierarchical co-simulation framework featuring the waveform relaxation method. The framework simulates a complex system as a composition of simpler, independent models that exchange information. The convergence of the coupling algorithm ensures the consistency of the solution. The modularity of the framework allows integrating models developed with both proprietary and in-house tools. The framework implements a user-customizable hierarchical algorithm to schedule how models participate to the co-simulation, for the purpose of using computational resources efficiently. As a case study, a quench scenario is co-simulated for the inner triplet circuit for the High Luminosity upgrade of the LHC at CERN.

physics.acc-ph↗

arXiv2017

Coupling of Magneto-Thermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based Interpolation

In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the optimization of the magnetic field quality under nominal conditions. The magneto-thermal models allow for the analysis of transient phenomena occurring during quench initiation, propagation, and protection. Mechanical analysis of quenching magnets is of high importance considering the design of new protection systems and the study of new superconductor types. We use field/circuit coupling to determine temperature and electromagnetic force evolution during the magnet discharge. These quantities are provided as a load to existing mechanical models. The models are discretized with different meshes and, therefore, we employ a mesh-based interpolation method to exchange coupled quantities. The coupling algorithm is illustrated with a simulation of a mechanical response of a standalone high-field dipole magnet protected with CLIQ (Coupling-Loss Induced Quench) technology.

physics.acc-ph↗

arXiv2017

A 2-D Finite-Element Model for Electro-Thermal Transients in Accelerator Magnets

Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring within the magnet, and can, therefore, help to prevent disruptive consequences. We present a 2-D FEM model for the simulation of electro-thermal transients occurring in superconducting accelerator magnets. The magnetoquasistatic problem is solved with a modified magnetic vector potential formulation, where the cable eddy currents are resolved in terms of their equivalent magnetization. The heat balance equation is then investigated, and the relevant heat sources are discussed. The model implements a two-port component interface and is resolved, as part of an electrical circuit, in a cooperative simulation scheme with a lumped-parameter network.

physics.comp-ph↗