Superconducting Accelerator Magnets Research Articles

Evaluation of the Parallel-Scheme Varistors as Energy-Extraction System for a Test Facility of Superconducting Accelerator Magnet

Evaluation of the Parallel-Scheme Varistors as Energy-Extraction System for a Test Facility of Superconducting Accelerator Magnet

Quench Heater Technology for HL-LHC Superconducting Accelerator Magnets

Quench Heater Technology for HL-LHC Superconducting Accelerator Magnets

Overview of Identified Challenges in the Development Process of Superconducting Accelerator Magnets

Development challenges in the domain of superconducting magnets are concentrated on technical problems in the current literature. Organizational, domain-specific challenges are often seen as secondary but must be considered with new holistic development approaches like Model-Based Systems Engineering (MBSE) becoming more popular. This work quantifies the domain challenges and gives the foundation to derive success criteria for design support in the future. A systematic literature review has been conducted to identify the overall domain challenges, and extensive interviews in the CERN technology department have been carried out to identify the development challenges on a practical level. Problems in knowledge management have been identified as a major challenge in the development process and the general literature. The paper concludes by picking up the most important challenges from the interviews and literature and puts them into the context of the authors’ knowledge of electrical magnet design.

Damage experiment with superconducting sample coils - experimental setup and observations during beam impact

The damage mechanisms and limits of superconducting accelerator magnets due to the impact of high-intensity particle beams have been subject to extensive studies in the past years at CERN. Recently an experiment with dedicated sample coils made from Nb–Ti and Nb3Sn strands was performed at CERN’s HiRadMat facility. This paper describes the design and construction of the sample coils as well as the results of their qualification before the beam impact. In addition, the experimental setup will be discussed. Finally, measurements during the beam experiment like the beam-based alignment, the observations during the impact of 440GeV protons on the sample coils and the achieved hot-spots and temperature gradients will be presented.

Magnetization in superconducting corrector magnets and impact on luminosity–calibration scans in the Large Hadron Collider

Superconducting accelerator magnets have a nonlinear dependence of field on current due to the magnetization associated with the iron or with persistent currents in the superconducting filaments. This also gives rise to hysteresis phenomena that create a dependence of the field on the powering history. Magnetization effects are of particular importance for luminosity–calibration scans in the Large Hadron Collider, during which a small number of Nb–Ti superconducting orbit correctors are excited at low field and with frequent flipping of the sign of the current ramp. This paper focuses on the analysis of special measurements carried out to estimate these nonlinear effects under the special cycling conditions used in these luminosity scans. For standard powering cycles, we evaluate the effect of the main magnetization loop; for complex operational schemes, magnetization-branch transitions occur that depend on the details of the current cycle. The modelling of these effects is not included in the magnetic field prediction software currently implemented in the LHC control system; here we present an approach to predict the transitions between the main magnetization branches. The final aim is to estimate the impact of magnetic hysteresis on the accuracy of luminosity-calibration scans.

Efficient multiscale investigation of mechanical behavior in Nb3Sn superconducting accelerator magnet based on self-consistent clustering analysis

The High Luminosity Large Hadron Collider (HL-LHC) is one of the large-scale projects currently being developed at the European Organization for Nuclear Research (CERN). Many Nb3Sn superconducting magnets are employed in this project, which exhibit complicated multiscale characteristics. The mechanical behaviors of magnets, which are directly related to the safety and stability of the overall structure, are affected by the electromagnetic–mechanical-thermal loading in actual service conditions. However, detailed modeling of magnets requires significant computing resources. A reduced-order method named self-consistent clustering analysis (SCA) has been proposed recently to reduce the cost. We have combined the SCA and finite element method (FEM) as an efficient multiscale framework, which is utilized to analyze the mechanical behaviors of accelerator magnets. Firstly, the computation results by presented framework are compared with direct numerical simulation (DNS) and existed experimental data to validate the accuracy and efficiency. Then, the FEM-SCA2 framework is utilized to study the mechanical behaviors of MQXFS accelerator magnet model under assembly, cool-down and excitation steps. The influences of material parameters, friction coefficient and stiffness degradation are also discussed. This paper provides an efficient multiscale analysis framework for investigating mechanical behavior in Nb3Sn accelerator magnet, which could be employed to study other magnets.

An Open-Source Finite Element Quench Simulation Tool for Superconducting Magnets

An open-source Finite Element Quench Simulator (FiQuS) is being developed as part of the STEAM framework following CERN's open science policy [1]. The tool is based solely on open-source software and uses Python to generate geometries and meshes with Gmsh, and compute solutions with GetDP. FiQuS scripts have a modular structure in order to accommodate a broad range of geometries and simulation requirements with the main focus on superconducting accelerator magnets. The tool, at its advanced stage, will be capable of 1D, 2D, and 3D geometry generation of superconducting elements such as bus bars, multi-pole, solenoid, and canted-cos-theta (CCT) magnets. It already has the capability for parametrized mesh control and subsequent model generation of 2D multi-pole and 3D CCT magnets. It will be possible to perform either electromagnetic (EM), thermal (TH), or coupled EM-TH simulations for static or transient analysis. The focus is on aspects related to the powering and quench transients, enabling parametric analyses and co-simulations to support comprehensive quench protection studies. In this contribution, we lay the foundation of FiQuS by presenting its structure and three specific capabilities that represent the basis upon which the future modules will be built. These capabilities showcase the integration of FiQuS with software developed at CERN, at other national laboratories, and within the STEAM framework. The first capability is the integration with the STEAM framework, which enables cooperative simulations with the other tools of the framework, the automatization of multi-step studies, and the Single Source Of Truth (SSOT) practice through the centralization of model and material data. The second capability is the integration with the magnet design software ROXIE via a dedicated input files parser, which seamlessly integrates magnet design details around a single input file. Examples of magnetostatic solutions obtained in FiQuS are shown for the 2D cross-section of LHC magnets based on ROXIE input files. The third capability is the integration with the parametric analysis software Dakota developed by Sandia National Laboratories. An example is shown of multi-objective optimization of the model mesh to minimize the error of the computed magnetic field.

Model-Based System Engineering Framework for Superconducting Accelerator Magnet Design

The design specification of future high-field accelerator magnets require innovation in and integration of multiple disciplines. Numerical models underpin each step of the design. In this paper, we present a methodology for collaborative modeling based on relevant concepts of model-based systems engineering. The methodology is composed of three pillars: encapsulated computing environments with service query interface, model notebooks with auto-generated model views, and model query interface with results caching. The methodology aims at a de-centralized approach to multi-model and multi-scale collaboration that maintains the cornerstones of traceability and reproducibility. It is demonstrated with a multi-model coil design optimization of a high-field superconducting magnet.

HTS Dipole Magnet Model for the Persistent Current Operation

Recent advances in the fabrication of high-temperature superconducting (HTS) coils allow the design of superconducting accelerator magnets that work in a persistent current mode. Many various, rather low-field magnets in particle accelerators operate in the DC current mode. Fermilab designed, fabricated, and tested an HTS dipole magnet model that has 20-mm air gap and a magnetic field up to 0.5 T. The magnet has a primary copper coil that for a short period pumps the energy in the short-circuited secondary HTS coil. The current paper presents the design, fabrication, and testing of this magnet at liquid-nitrogen temperature.

Record High Ramping Rates in HTS Based Superconducting Accelerator Magnet

We report results of experimental test of the High Temperature Superconductor (HTS) based fast-cycling prototype accelerator magnet capable to operate up to about 300 T/s field ramping rate with some 0.5 T B-field in the magnet gap. The measured upper limit for the cryogenic cooling power required to support magnet conductor operation at high ramping rates indicates great potential for such type of magnets in rapid cycling synchrotrons for neutrino research or acceleration of very short-lived muons. The test magnet design, construction and supporting cryogenic and power systems are briefly described. The magnet's power test results are discussed in terms of a possible upgrade of this magnet design to 2 T B-field, a maximum feasible with super-ferric magnet.

Quasi-3D Magneto-Thermal Quench Simulation Scheme for Superconducting Accelerator Magnets

To tackle the multi-scale problem in the quench simulation of superconducting accelerator magnets, this work proposes a hybrid numerical method which uses two-dimensional first-order finite-elements in the magnet cross-section and one-dimensional higher-order orthogonal polynomials in longitudinal direction.

Construction and Test of the Enhanced Racetrack Model Coil, First CERN R&D Magnet for the FCC

Racetrack model coils (RMC) have been built at CERN during the past decade, as an R&D tool to qualify conductors and technologies developed for high field superconducting accelerator magnets (Perez <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2016). RMC, assembled in a dipole magnet configuration, proved to be an efficient instrument reducing cost and feed-back time while developing new magnets. In a similar way, as for the High-Luminosity Large Hadron Collider (HL-LHC) project, CERN has designed the enhanced RMC (eRMC) made of two flat coils using 40 (1 mm diameter) Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strand cable produced with Rod Restack Process (RRP) technology. This conductor geometry, originally designed and produced to build the block coil dipole magnet FRESCA2 (Rochepault <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2019), was chosen to reduce the production time and shorten the road towards the feasibility demonstration to reach 16–18 T magnetic fields in a dipolar configuration. Like previous model coils built at CERN (Short model coils (SMC) & RMC), eRMC1a has been built using the “bladders and keys” type mechanical structure. This paper describes the main construction steps and the powering test results. At 1.9 K the magnet produced 16.5 T peak field in the conductor, the highest ever for a dipole magnet of this configuration.

Development of a Roebel structure transposed cable with in-plane bending of REBCO tapes

A compact High Temperature Superconductor (HTS) cable that can carry large current is crucial for developing high field superconducting accelerator magnets. Herein, we are reporting a high current and low AC loss REBCO cable that adopts the Roebel structure, but it is implemented by in-plane bending stacked REBCO tapes directly to realize the transposition, instead of by punching REBCO tapes to the desired shape. The cable maximizes the utilization of the original REBCO tapes, so that the material cost is significantly reduced comparing with the present “Roebel” REBCO cable. Recently, a prototype cable has been successfully fabricated. The critical current of each REBCO tape after cabling shows no degradation, and the cable’s measured critical current is 1939.8 A at 77 K and self-field, which is very close to the predicted critical current by simulation. Calculations also show that the AC loss of the cable is lower compared with that of a simple REBCO stack with the same cross-section and current-carrying capacity. In this paper, we first introduce the fabrication process of the cable. What follows is the measurement of the in-plane bending performance of REBCO tapes. Then, we present the design and fabrication of the prototype cable together with current-carrying performance tests. Finally, the AC loss calculation and analysis of the cable are reported.

Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

A multi-scale nonlinear procedure to analyze the stress in Nb3Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets—the issue of stress management. The study demonstrates that gasket materials (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb3Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb3Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb3Sn coil was simulated, in three orthongonal axes, using the combined properties of the gasket materials (insulation layers) and Hill materials (resin-impreganted cable). The procedure makes very few assumptions with regard to material properties because it incorporates actual measured stress–strain curves in the analysis. The coil was simulated to the level of detail of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb3Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb3Sn magnets, this versatile procedure can also be employed in the design of LTS, HTS, and room temperature magnets or of any structures ultilizing composite materials; specifically, it can be used to manage the stress and strain of HTS fusion magnets.

Hybrid modeling: towards the next level of scientific computing in engineering

The integration of machine learning (Keplerian paradigm) and more general artificial intelligence technologies with physical modeling based on first principles (Newtonian paradigm) will impact scientific computing in engineering in fundamental ways. Such hybrid models combine first principle-based models with data-based models into a joint architecture. This paper will give some background, explain trends and showcase recent achievements from an applied mathematics and industrial perspective. Examples include characterization of superconducting accelerator magnets by blending data with physics, data-driven magnetostatic field simulation without an explicit model of the constitutive law, and Bayesian free-shape optimization of a trace pair with bend on a printed circuit board.

Study on Internal Strain Distribution of the High-Field Nb₃Sn Superconducting Accelerator Magnets With Homogenization Theory

To fabricate 10–16 Tesla high-field accelerator magnets, the high-Jc Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn superconductor is one of the most practical choices. However, it is a brittle material and is strain-sensitive. To reduce the potential Jc degradation of the conductor, it is crucial to accurately evaluate the stress of the coils owing to the large Lorentz force during magnet excitation. In the traditional stress analysis of magnets, the coils are usually regarded as homogenized structures using isotropic material coefficients; however, most superconducting (SC) coils have hierarchical and complicated structures. To obtain a more accurate estimation, it is necessary to consider the detailed internal structure of the coils during stress analysis. In this study, the homogenization method was applied to multi-scale stress analysis of a high-field accelerator SC magnet. The effective material coefficients of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn coils were calculated using this method. Stress analysis of the magnet was performed using the effective material coefficients and isotropic material coefficients for comparison. Compared with the result obtained using isotropic material coefficients, the Von-Mises stress of the coil using effective material coefficients is larger at different load steps. The stress level of most Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments in the strand was higher than that of the coil. The maximum stress of the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments appeared in the strand contact regions. In addition, there was a significant difference in the average stress of all materials in the strand. These findings will help develop more accurate analysis and simulation models for high-field SC magnets.

Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

Quench Detection and Protection for High-Temperature Superconductor Accelerator Magnets

High-temperature superconductors (HTS) are being increasingly used for magnet applications. One of the known challenges of practical conductors made with high-temperature superconductor materials is a slow normal zone propagation velocity resulting from a large superconducting temperature margin in combination with a higher heat capacity compared to conventional low-temperature superconductors (LTS). As a result, traditional voltage-based quench detection schemes may be ineffective for detecting normal zone formation in superconducting accelerator magnet windings. A developing hot spot may reach high temperatures and destroy the conductor before a practically measurable resistive voltage is detected. The present paper discusses various approaches to mitigating this problem, specifically focusing on recently developed non-voltage techniques for quench detection.

A methodology for the analysis of the three-dimensional mechanical behavior of a Nb3Sn superconducting accelerator magnet during a quench

The fast thermal and electromagnetic transients that occur in a superconducting magnet in case of a quench have the potential of generating large mechanical stresses both in the superconducting coils and in the magnet structure. While the investigation of such quench loads should generally be conducted to ensure a safe operation of the system, its importance is greatly enlarged in the case of high-field magnets based on strain sensitive superconductors. For these, a rigorous analysis of the magnet mechanics during a quench becomes critical. The scope of this work is hence to bring, for the first time, a detailed understanding of the three-dimensional mechanical behavior of a Nb3Sn accelerator magnet during a quench discharge. The study relies on the use of finite element models, where various multi-domain simulations are employed together to solve the coupled physics of the problem. Our analysis elaborates on the case study of the new MQXF quadrupole magnet, currently being developed for the high-luminosity upgrade of the LHC. Notably, we could find a very good agreement between the results of the simulation and experimental data from full-scale magnet tests. The validated model confirms the appearance of new peak stresses in the superconducting coils. An increase in the most relevant transverse coil stresses of 20–40 MPa with respect to the values after magnet cool-down has been found for the examined case.

A hybrid FPM/BEM scalar potential formulation for field calculation in nonlinear magnetostatic analysis of superconducting accelerator magnets

A new hybrid numerical method for the solution of nonlinear magnetostatic problems in accelerator magnets is proposed. The methodology combines the Fragile Points Method (FPM) and the Boundary Element Method (BEM). The FPM is a Galerkin-type meshless method employing for field approximation simple, local, and discontinuous point – based interpolation functions. Because of the discontinuity of these functions, the FPM can be considered as a meshless discontinuous Galerkin formulation where numerical flux corrections are employed for the treatment of local discontinuity inconsistencies. The FPM possesses the advantages of a mesh-free method, evaluates with high accuracy field gradients, and treats nonlinear magnetostatic problems by utilizing, for the same problem, fewer nodal points than the Finite Element Method (FEM). In the present work, the nonlinear ferromagnetic material of an accelerator magnet is treated by the FPM, while the BEM is employed for the infinitely extended, surrounding air space. The proposed hybrid scheme is based on the scalar potential formulation of Mayergouz et.al (1987), also used in the BEM/BEM and FEM/BEM schemes of Rodopoulos et al. (2019, 2020). The applicability of the method is demonstrated with the solution of representative 2-D magnetostatic problems and the obtained numerical results are compared to those provided by the FEM/BEM scheme of Rodopoulos et al. (2020), as well as by the commercial FEM package ANSYS. Finally, the magnetic field utilized for stable bending of the particles’ trajectory in a 16 Tesla dipole magnet design for the Future Circular Collider (FCC) project of CERN is accurately evaluated with the aid of the proposed here FPM/BEM scheme.