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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., Comment: 10 pages, 11 figures

Accelerators magnets must have minimal magnetic field imperfections to reduce particle-beam instabilities. In the case of coils made of high-temperature superconducting (HTS) tapes, the magnetization due to persistent currents adds an undesired field contribution, potentially degrading the magnetic field quality. In this paper we study the use of superconducting screens based on HTS tapes for reducing the magnetic field imperfections in accelerator magnets. The screens exploit the magnetization by persistent currents to cancel out the magnetic field error. The screens are aligned with the main field component, such that only the undesired field components are compensated. The screens are self-regulating, and do not require any externally applied source of energy. Measurements in liquid nitrogen at 77 K show for dipole-field configurations a significant reduction of the magnetic field error up to a factor of four. The residual error is explained via numerical simulations accounting for the geometric defects in the HTS screens, achieving satisfactory agreement with experimental results. Simulations show that if screens are increased in width and thickness, and operated at 4.5 K , field errors may be eliminated almost entirely for the typical excitation cycles of accelerator magnets.

After the occurrence and detection of a short circuit to ground in the LHC main dipole circuit, a fast power abort is triggered and the current in the circuit starts decaying semi-exponentially from a maximum value of 11.85 kA to zero, with a time constant of 103 s. If a short to ground occurs, the current flows through the fuse that is present in the grounding subcircuit. Depending on the value of the thermal load, the fuse first enters a pre-arcing region where it starts intermittently blowing up, until the blow-up threshold is reached, after which it definitively blows up. A simulation scheme utilising a common interface between PSpice and Matlab is proposed in order to simulate the blow-up behaviour of the fuse and hence increase the accuracy of the circuit model for short circuits to ground. A parametric analysis of the short circuit to ground parameters is performed and a better understanding of the behaviour of the circuit under different conditions is obtained. The worst-case values of the voltage to ground in the LHC main dipole circuit are identified for both the case where the intermittent behaviour of the fuse is included in the model as well as for the case where the fuse is not modelled and a comparison between the two is given.

An energy of $362\:\text{MJ}$ is stored in each of the two LHC proton beams for nominal beam parameters. This will be further increased to about $700\:\text{MJ}$ in the future High Luminosity LHC (HL-LHC) and uncontrolled beam losses represent a significant hazard for the integrity and safe operation of the machine. In this paper, a number of failure mechanisms that can lead to a fast increase of beam losses are analyzed. Most critical are failures in the magnet protection system, namely the quench heaters and a novel protection system called Coupling-Loss Induced Quench (CLIQ). An important outcome is that magnet protection has to be evaluated for its impact on the beam and designed accordingly. In particular, CLIQ, which is to protect the new HL-LHC triplet magnets, constitutes the fastest known failure in the LHC if triggered spuriously. A schematic change of CLIQ to mitigate the hazard is presented. A loss of the Beam-Beam Kick due to the extraction of one beam is another source of beam losses with a fast onset. A significantly stronger impact is expected in the upcoming LHC Run III and HL-LHC as compared to the current LHC, mainly due to the increased bunch intensity. Its criticality and mitigation methods are discussed. It is shown that symmetric quenches in the superconducting magnets for the final focusing triplet can have a significant impact on the beam on short timescales. The impact on the beam due to failures of the Beam-Beam Compensating Wires as well as coherent excitations by the transverse beam damper are also discussed., Comment: 28 pages, 23 figures. To be published in Physical Review Accelerators and Beams

The Future Circular Collider (FCC-hh) project is a conceptual study whose goal is to design the successor of the Large Hadron Collider, increasing the collision energy from 14 to 100 TeV. The energy stored in the 16-T superconducting dipole magnets and the length of the sectors composing the 100-km FCC tunnel are considerably larger than those in present accelerators. This means that the energy stored in the FCC-hh dipole circuit is likely to be much higher than that in existing superconducting circuits. In the case of magnet quenches or faults, the circuit needs to be protected, i.e., its energy needs to be rapidly dissipated without inducing excessive voltages in the magnet chain. This article proposes a conceptual design for the FCC-hh dipole circuit, which satisfies the constraint of the maximum allowable voltage-to-ground and fulfills additional requirements related to the FCC-hh operation and tunnel layout. A compromise among the considered requirements leads to a relatively simple circuit layout and a large number of circuits for the entire machine. The behavior of the proposed circuit during the critical fast power abort phase is simulated through a numerical model, which covers the electrical circuit domain and the electrothermal magnet domain. Each FCC-hh dipole magnet is protected by means of the coupling-loss-induced quench (CLIQ) protection system, which also acts at the circuit level. The simulations predict severe voltage oscillations in the FCC-hh dipole circuits that may pose a problem for the quench detection system. The simulations also show that the severity of the oscillations is not due to the presence of CLIQ. This protection system can be integrated into the proposed circuit layout and represents an effective protection system for the entire string of FCC-hh dipole magnets. publishedVersion

To achieve the goal of increased luminosity, two out of eight main dipole circuits of the accelerator will be reconfigured in the coming LHC upgrade by replacing one standard 14.3-m long, Nb-Ti-based, 8.3 T dipole magnet by two 5.3-m long, Nb 3 Sn-based, 11.2 T magnets (MBH). The modified dipole circuits will contain 153 Nb-Ti magnets and two MBH magnets. The latter will be connected to an additional trim power converter to compensate for the differences in the magnetic transfer functions. These modifications imply a number of challenges from the point of view of the circuit integrity, operation, and quench protection. In order to assess the circuit performance under different scenarios and to validate the circuit quench protection strategy, reliable and accurate numerical transient simulations have to be performed. We present the field/circuit coupling simulation of the reconfigured main dipole magnet chain following the introduction of the MBH magnets. 2-D distributed LEDET models of the MBH's have been created to simulate the electrothermal transient occurring during a quench event, whereas the full electrical circuit of the main dipole chain, containing the 11 T magnets and their trim circuit, is simulated in PSpice. These two models are coupled through the STEAM cosimulation framework, calculating the electromagnetic and thermal transients in the magnets and circuit. The field/circuit coupling simulations performed with STEAM evaluate how the complex circuit affects the quenching magnet and vice versa. The results show a safe fast power abort of the system in the event of a quench in one of the MBH magnets, and support the validation of the correct functioning of the reconfigured main dipole circuit.

In recent years, the superconducting Nb3Sn cable material became the privileged mature candidate for the high-field magnets in new projects like high-luminosity LHC (HL-LHC) accelerator at CERN, Geneva, Switzerland. The technology in 2017–2021 needs to be deployed through an unprecedented magnet series production with dedicated online quality control. The key fabrication stage of the vacuum pressure impregnation (VPI) after the heat treatment reaction of Nb3Sn coils, as on the new 11-T dispersion region dipole, enhances both the structural integrity and the dielectric strength of the winding packs. The global vacuum impregnation pressure method exhibits various merits in insulation performance and high dielectric strength reliability, which is strongly dependent on the success of the resin filling cycle. This online capacitive measurement method enables one to derive comparative master trend curves of various impregnated coils and possibly optimize the curing cycle. Ultimately, a combination of the above methods with a dielectric frequency response can bring insights on the impregnation process, the impacts from the resin choice and insulation material quality on the degree of curing, and the coil assembly geometry. The frequency impedance measurement of the first short dipole models DP101-102 provides the distributed lumped circuit fitting electrical parameters for the transient characterization of produced magnets.

Transient effects occurring in a superconducting accelerator circuit can be correctly simulated only if the models consistently account for the electrothermodynamic coupling between the magnets, the protection systems, and the remaining network. We present a framework based on the idea of cosimulation. The core component is a coupling interface exchanging information between the independent models. Within the framework, we simulate selected parts of a magnet and the electrical network, combining appropriately different commercial tools. This modularity gives the possibility of integrating new tools in the framework, to provide further insights on different physical domains as mechanics or fluid dynamics. The workflow is applied to the field-circuit coupling of an LHC main dipole magnet.

Quench heaters are an essential part of the protection of all high-current large hadron collider (LHC) superconducting circuits. About 2000 dipole and quadrupole magnets are equipped with quench heaters in order to protect them against development of excessive voltage and overheating after a resistive transition. The quench heaters are made of stainless steel foil partially plated with copper and connected to 900 V capacitor bank discharge power supplies. During Hardware Commissioning campaigns and machine operation every quench heater discharge event is carefully analysed to detect a possible failure or a precursor of a failure, which could lead to damage of the heater or to the superconducting coils in subsequent discharges. This paper will briefly describe two different ways of quench heater data analysis and will present the heaters performance during the years 2008-2015. A summary of the quench heater fatigue test performed on a spare LHC main dipole magnet will also be given.

In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit. Such a multi-physics, multi-rate and multi-scale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both circuit and magnet level during normal operation and in case of faults. We derive an equivalent magnet model at the circuit side for the linear and the non-linear settings and discuss the convergence of the overall scheme in the framework of optimized Schwarz methods. The efficiency of the developed approach is illustrated by a numerical example of an accelerator dipole magnet with accompanying protection system., Comment: 8 pages, 7 figures

International audience; Part of the Future Circular Collider (FCC-hh) study is dedicated to the development of the 16 Tesla ${\rm Nb_3Sn}$superconducting dipole magnets. The design of the magnets was enabled by a cooperative effort of national research institutes, universities, and CERN. These actors tackled the problem from different sides, namely, the electromagnetic design, the mechanical design, the design of the quench protection systems, and the circuit design. The article deals with the design of the quench protection systems and provides solid motivations for the selection of the coupling-loss-induced quench (CLIQ) device as the baseline protection system for the FCC-hh main dipole magnets. The article shows that the design domains mentioned above are tightly interconnected and, therefore, the simulation of a quench event involves a complex multiphysics problem. The STEAM cosimulation framework, recently developed at CERN, is applied to address the complexity. The STEAM-SIGMA models are employed to simulate the CLIQ quench protection system applied to the FCC-hh dipole magnets. Dedicated CLIQ configurations are identified to protect the magnets in case of a quench. In addition, the possible implications of the CLIQ protection system on the mechanical design of the magnets are discussed. To this end, the article employs the co-simulation of different software platforms to calculate the mechanical stress during a quench. The results show that CLIQ does not produce additional stress.

International audience; The Nb$_3$Sn block coil dipole magnet FRESCA2 was developed within the framework of a collaboration between CEA Saclay and CERN, in the continuity of the European project EuCARD and EuCARD2. With an aperture of 100 mm and a target bore field of 13 T at 10.6 kA, the magnet is required for a new FRESCA2 cable test facility at CERN. In 2017, the magnet was pre-loaded to retain the forces while the magnet was powered to achieve 13.3 T in the magnet bore. Results of these tests were published. In 2018, the loading of the magnet has been increased for powering to higher current. In this paper, the updated results of the cold powering tests are discussed in terms of training, memory, and stable operation. The loading of the magnet and the mechanical measurements during cooldown are shown and compared to the earlier loading steps. The protection of the magnet is further reviewed and measured results are compared to the model simulations.

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., Comment: 14 pages, 18 figures

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., Comment: 7 pages, 14 figures

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., 5 pages, 6 figures

In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting its digital implementation, whereas a circuit simulation usually employs an adaptive time stepping scheme in order to account for a wide range of time constants within the circuit model. In order to maintain the characteristic of both models as well as to facilitate model replacement, we treat them separately by means of input/output relations and propose an application of a waveform relaxation algorithm. Furthermore, the maximum and minimum number of iterations of the proposed algorithm are mathematically analyzed. The concept of controller/circuit coupling is illustrated by an example of the co-simulation of a PI power converter controller and a model of the main dipole circuit of the Large Hadron Collider.

Dynamic simulation of superconducting magnets is critical for the design of quench protection systems to prevent potentially damaging temperatures and high voltage from developing after magnet quench. Modeling these scenarios is challenging due to the many multiscale phenomena which impact magnet behavior. These range from conductor scale effects of quench and interfilament coupling currents up to the behavior of the magnet in its powering and protection circuit. In addition, a strong coupling between electromagnetic and thermal domains is required to capture temperature and field dependent material properties and quench behavior. We present a finite element approach which integrates the various effects into the commercial software ANSYS by means of programming new element types. This is shown capable of simulating the strongly coupled transient electromagnetic, thermal, and circuit behavior of superconducting magnets required for quench protection studies. A benchmarking study is presented which shows close agreement between the new ANSYS elements and a COMSOL Multiphysics implementation developed at CERN for dump resistor and coupling loss induced quench based magnet protection of a Nb3Sn block dipole. Following this, the ANSYS implementation is shown reproducing strongly coupled quench back behavior observed during the test of a Nb3Sn superconducting undulator prototype at Lawrence Berkeley National Laboratory.