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Mariusz Wozniak

Publications and source records attributed to Mariusz Wozniak.

At least 19 recordsLinked to original sources
arXiv2026

Current patterns and loss contributions in CORT cables carrying AC current

Conductor-on-round-tube (CORT) cables are a potential solution for carrying AC power in a small cross-section. Due to the geometry of the cable and the helical arrangement of the coated conductors (CC), the current follows a non-trivial pattern inside each CC. For instance, for the case of a single-layer cable, the current flow is mostly axial along the outer face of the CCs and mostly azimuthal along their inner face. Such a current distribution, known as the Garber current pattern, affects the transport AC losses. In numerical models, commonly adopted simplifications are either based on straight conductors or infinitely thin CCs. Such approaches neglect the Garber current pattern and thus misrepresent both the detailed current flow within the CC and the resulting 3D distribution of the fields. In this work, the detailed 3D current distribution in the CCs is investigated in a one-layer CORT cable, as a function of the cable geometrical parameters such as the conductor thickness, the pitch angle, and the gap between adjacent CCs. In particular, the impact of the Garber current pattern is studied on the two largest contributions to the AC losses, namely the surface losses (associated with the penetration of the component of the magnetic field parallel to the wide faces of the superconducting layer) and the edge losses (associated with the penetration of the perpendicular component of the magnetic field occurring in the vicinity of the gaps between the CCs). The detailed distribution of the currents in the CCs is examined and its relationship with the different AC loss mechanisms is established. This study is carried out by means of an effective 2D model that uses a system of coordinates conforming with the helical structure of the cable.

cond-mat.supr-con↗
arXiv2026

Explicit Turn Resolution with Anisotropic Homogenisation for Efficient 3D Magneto-Thermal Finite-Element Simulation of Large-Scale No-Insulation HTS Magnets

No-insulation (NI) and metal-insulation (MI) high-temperature superconducting (HTS) magnets require three-dimensional (3D) models to describe the current distribution around critical current defects. In this work, we design and validate the EXTRA homogenisation method, standing for explicit turn resolution with anisotropic homogenisation method. It allows 3D magneto-thermal finite-element (FE) simulations of large-scale magnets to be performed with high accuracy at a reasonable computational cost. The method combines the anisotropic homogenisation of turn-to-turn contact layers (T2TCLs) and their neighbouring winding turns with the explicit resolution of specific T2TCLs. In particular, the inner- and outermost winding turns and adjacent contact layers are explicitly resolved to properly describe the current distribution near current leads. In addition, the method is able to simulate local $J_{\textrm{c}}$ defects for a broad range of turn-to-turn contact resistances, provided the winding turns and T2TCLs next to the defect are explicitly resolved. For efficiency, the resolved T2TCLs are modelled using the surface contact approximation. The consistency of the proposed method is first verified on a 50-turn single pancake benchmark. It is shown to reproduce AC losses and temperature distributions obtained with a turn-resolved FE reference model, for both nominal operation and during thermal runaway. The computational efficiency of the EXTRA method is demonstrated with the simulation of a stack of three 150-turn pancake coils, for which computation time is reduced by a factor of up to 13 with respect to a turn-resolved FE reference model. Finally, the results of a large-scale 3D FE simulation, currently out of reach of turn-resolved models, are provided for an insert HTS magnet with 10,000 turns. The EXTRA method is open-source and input files to reproduce all results are made available.

physics.acc-ph↗
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↗
arXiv2026

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

Acceleration of Multi-Scale LTS Magnet Simulations with Neural Network Surrogate Models

While the prediction of AC losses during transients is critical for designing large-scale low-temperature superconducting (LTS) magnets, brute-force finite-element (FE) simulation of their detailed geometry down to the length scale of the conductors is a computational challenge. Multi-scale methods, balancing between a coarse approximation of the fields at the scale of the magnet and a detailed description at the scale of the conductors, are promising approaches to reduce the computational load while keeping a sufficient accuracy. In this work, we introduce a neural network approach to accelerate multi-scale magneto-thermal simulations of LTS magnets by replacing costly single-turn FE models with neural network surrogates. The neural network architecture is presented and discussed, together with an automated procedure for generating simulation data for its training. The resulting accelerated multi-scale model is used to simulate current ramp-up procedures for the IBA S2C2 magnet. The surrogate-based multi-scale model is compared with a conventional multi-scale model based on a composite wire-in-channel FE model. The surrogate model is shown to reproduce single-turn filament hysteresis, inter-filament coupling, and eddy losses, while the computational time of the multi-scale method is reduced by a factor of 800.

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

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↗
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

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

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

Mortar Thin Shell Approximation for Analysis of Superconducting Accelerator Magnets

Thin layers can lead to unfavorable meshes in a finite element (FE) analysis. Thin shell approximations (TSAs) avoid this issue by removing the need for a mesh of the thin layer while approximating the physics across the layer by an interface condition. Typically, a TSA requires the mesh of both sides of the TSA interface to be conforming. To alleviate this requirement, we propose to combine mortar methods and TSAs for solving the heat equation. The mortar TSA method's formulation is derived and enables an independent discretization of the subdomains on the two sides of the TSA depending on their accuracy requirements. The method is verified by comparison with a reference FE solution of a thermal model problem of a simplified superconducting accelerator magnet.

cs.CE↗
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

A note on edge colorings distinguishing all triangles in a graph

We consider edge colorings of a graph in such a way that each two different triangles have distinct colorings. It is an extension of the well-known idea of distinguishing all maximal stars in a graph. It was introduced in literature in 1985 and studied by many authors in various variants, but always for stars. We estimate new invariants regarding triangles for proper and general colorings.

math.CO↗
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

Helicoidal Transformation Method for Finite Element Models of Twisted Superconductors

This paper deals with the modelling of superconducting and resistive wires with a helicoidal symmetry, subjected to an external field and a transport current. Helicoidal structures are three-dimensional, and therefore yield computationally intensive simulations in a Cartesian coordinate system. We show in this paper that by working instead with a helicoidal system of coordinates, the problem to solve can be made two-dimensional, drastically reducing the computational cost. We first introduce the state-of-the-art approach and apply it on the h-phi-formulation with helicoidally symmetric boundary conditions (e.g., axial external magnetic field, with or without transport current), with an emphasis on the function space discretization. Then, we extend the approach to general boundary conditions (e.g., transverse external magnetic field) and present numerical results with linear materials. In particular, we discuss the frequency-dependent losses in composite wires made of superconducting filaments embedded in a resistive matrix. Finally, we provide outlook to the application of the generalized model with nonlinear materials.

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

Efficient Reduced Magnetic Vector Potential Formulation for the Magnetic Field Simulation of Accelerator Magnets

The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included into the simulation model along Biot-Savart's law. Such an approach has already been successfully employed in ROXIE for the simulation of superconducting Large Hadron Collider magnets at CERN. This work presents an updated RMVP approach, which significantly outperforms the original method. The updated formulation is postulated, implemented, verified, compared to the original formulation, and applied for the simulation of a quadrupole magnet. The promising results of this work encourage further investigation towards an updated simulation framework for next-generation accelerator magnets.

cs.CE↗