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The Falcon Dipole (Future Accelerator post-LHC Cos-theta Optimized $\rm {Nb_3Sn}$ Dipole) is a single aperture $\rm {Nb_3Sn}$ cos-theta dipole short model in the framework of the Future Circular Collider (FCC) project. The Italian Institute of Nuclear Physics (INFN), in collaboration with CERN, is in charge of designing and constructing the magnet, which is a crucial step towards the construction of High Field $\rm {Nb_3Sn}$ magnets suitable for a post LHC collider. This paper recalls the electromagnetic design, the field quality and performances of the Falcon Dipole. The coil ends design has been implemented in a 3D FEM to study the peak field distribution on the magnet and influence on field quality. A special focus is given to the 2D analysis to study the effect of superconductor magnetization on field quality from the injection to the final energy and then to investigate the effectiveness of compensation methods.

In the challenging project concerning the realization of the CERN Future Circular Collider (FCC), Nb3Sn represents the best candidate material for the construction of high-field superconducting dipole magnets, since it is able to satisfy the requirements of Jc (non-Cu) = 1.5 kA/mm2 at 16 T and 4.2 K. In that context, a cluster layout of prototype internal tin Nb3Sn wires, developed by TVEL and the Bochvar Institute (Russia), was analyzed and compared to a standard layout produced by the same manufacturer. The main reason for dividing the sub-element into clusters is reducing the effective sub-element size (deff). The microstructural characterization of such a wire layout can provide fundamental contributions to steer the manufacturing processes towards higher performing wires. In particular, since the homogeneity in Sn concentration influences the superconducting properties, the effect of cluster and standard layouts on the Sn concentration gradient over the wire cross-section was evaluated. For this purpose, energy dispersive X-ray (EDX) spectroscopy was employed with both scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Finally, scanning Hall probe microscopy (SHPM) measurements were performed to understand how these cluster wire sub-elements, with their specific geometry, influence the local currents flowing through the wire cross-section on a microscopic scale. The comprehension of the correlation between the microstructural characteristics and superconducting performance is crucial for obtaining wires meeting the requirements of FCC dipole magnets.

The enhanced racetrack model coil and racetrack model magnet constitute the current R&D Nb3Sn magnets under development at CERN aiming to achieve dipole fields of 16-18 T, the design baseline of the Future Circular Collider (FCC). This article reports the mechanical behavior of their common support structure, which underwent three different levels of room-temperature preload (with the bladders and key method) and two cooldown cycles to 80 K. The structure was mounted using aluminum dummy blocks in lieu of the actual Nb3Sn coils. Strain gauges were placed in the external aluminum shell, tie-rods, and dummy coils. The measurements agree well with the results of the finite-element models (FEM). This work validates the FEM and a support structure for testing Nb3Sn accelerator magnets in the 16-T regime.

We present an analytic method to minimize the magnetic cross-talk in twin-aperture cos-theta dipoles. In the single-aperture cos-theta layout, the coil design can be performed with an analytic approach, based on a sector coil approximation. This method allows a fast evaluation of the field harmonics and an almost exhaustive scan on the positions and dimensions of the sectors, for coil layouts made of a different number of sectors. This increases the probabilities to find the coil shape which best fits the specifications. In a twin-aperture arrangement, the magnetic cross-talk can be not negligible and, to the aim of an analytic minimization of the unwanted multipoles, an extension of the single-aperture sector model is required. This is the case of the recombination dipole D2 for the High Luminosity LHC and of the 16-T bending dipole for the Future Circular Collider (FCC). This analytical method has been used to find alternative coil designs for both dipoles., Comment: 10 pages, 11 figures, 5 tables

High-temperature superconductor coatings have been proposed for the reduction of the beam coupling impedance for the future circular collider's hadron–hadron (FCC-hh) option. These coatings are, however, prone to hysteretic magnetization due to the ramp of the external magnet field. We present a mathematical formulation and implementation of Bean's model, which is a simplified, phenomenological model of persistent current loops and magnetization. After validating the model on simplified, analytically accessible examples, it is applied to the FCC setup under various conditions. The conclusion is that the magnetization might impair the magnetic field quality strongly for a complete coating, but a coating in the form of stripes can be a feasible tradeoff between field quality and impedance reduction.

In the context of the Future Circular Collider (FCC) study, industrial and academic partners are developing novel Nb3Sn superconducting wires with a wide variety of layouts, production methods, and compositions, with the aim of achieving challenging performance targets including a non-copper critical current density of 1500 A mm–2 at 16 T and 4.2 K. There is a clear need for a systematic and quantitative approach to analyze these conductors, identifying correlations between performance, microstructure, and wire design, in order to optimize designs and heat treatments, and to identify the most promising directions for future trials. Image analysis methods have been developed to provide a quantitative description of key geometrical characteristics of a wire with an impact on Nb3Sn phase formation and superconducting performance. In this paper, these methods are introduced, examples are presented of their application to prototype conductors produced for the FCC study, and opportunities for improving the performance of these prototype conductors are identified. Finally, initial steps toward models of diffusion and phase transformations are reported, and the potential for establishing a quantitative, analytical approach to wire design is evaluated, identifying topics requiring further research.

The Future Circular Collider (FCC) project aims at producing a conceptual design of a post-Large Hadron Collider (LHC) particle collider, able to reach higher beam energy with higher luminosity both for proton-proton and electron-electron configurations. In the proton-proton configuration, the FCC must be able to circulate 50 GeV protons in a 100 km tunnel. A key role in this project is played by the R&D on superconducting magnets, which must be able to produce magnetic fields significantly higher than in the LHC. Beside the bending dipoles, which must produce a 16 T field, also the multiplets in the interaction regions represent a technological challenge: as an example, the recombination dipoles are expected to produce a field of 10 T and therefore Nb 3 Sn must be used. In this contribution, the preliminary design of a double aperture recombination dipole for the FCC will be presented in details. It features a two layers, cosine-theta design, in order to produce the required field of 10 T in the bore. The magnetic field has the same direction in both apertures, generating a not negligible crosstalk which is minimized using asymmetric coils. The magnetic design will be described, focusing on the main features of the Nb 3 Sn conductor. The winding configuration and the iron yoke shape have been optimized to achieve a suitable field quality. A solution for the mechanical design will also be presented: the necessary prestress will be given by the so-called “bladder and keys” concept, which avoids the collaring and allows to obtain, thanks to differential thermal contraction of the components, most of the prestress after the cool down, when the Nb 3 Sn is less brittle. The proposed solution fulfills all the standard requirements both from the magnetic point of view, i.e., field quality and current margin, and from the mechanical one, with a viable construction schema and reasonably low stress on conductor and support structures, during all the magnet operations.

The EuroCirCol project is part of the Future Circular Collider (FCC) study under the European Union leadership in the framework of a H2020 project. In particular, the Italian Institute for Nuclear Physics, in collaboration with CERN and other European laboratories, is developing the design of a cos theta ${{\rm Nb}_{3}{\rm Sn}}$ dipole magnet which will be part of the Conceptual Design Report of the FCC studies in 2019. The magnet, with an aperture diameter of 50 mm and a bore field of 16 T, will be able to bend the beams at final energies and within collider size constraints. Here we present an update of the electromagnetic design of the ${{\rm Nb}_{3}{\rm Sn}}$ cos theta dipole in double-aperture configuration, the 2-D mechanical analysis, and also the 3-D coil-ends study.

The future circular collider (FCC) will require 696 double-aperture lattice sextupoles, 9336 single-aperture sextupole corrector magnets, and 480 double-aperture octupoles. The tunnel length and the overall integrated field of the main dipoles have to be kept constant so that the FCC can both reach the specified center of mass collision energy and fit into the Geneva basin. Considering these criteria, any reduction in the length of the other magnets can be traded in exchange for a reduced dipole field, which would result in an overall cost saving for the FCC. However, to be able to reduce the length of these sextupole and octupole magnets, their local strength has to be maximized. Consequently, in this paper, we first explore the maximum achievable local strength for these different magnet types for both Nb-Ti and Nb3Sn wire technology taking into account circuit and protection criteria. We then select and present a preferred design based on an overall cost and complexity reduction for the FCC.

The CERN SRF infrastructure was originally set up for Nb on Cu-coated cavities for large electron positron collider (LEP) and later for large hadron collider (LHC). Today, Superconducting RF has become a vital technology not only for LHC but also for high intensity and energy upgrade of isotope separator on line device (HIE-ISOLDE) and the high luminosity (HL)-LHC project. More superconducting cavities will be needed for a potential high energy (HE)-LHC or for any of the future circular collider options, which are currently under study. To meet these demands, CERN has improved its SRF infrastructure over the recent years and has started several R&D lines including improved thin film coating techniques, high-power couplers, cold-test diagnostics, etc. This paper will give an overview of CERN's SRF activities today, and the challenges of future projects.

Nb3Sn magnets with a nominal operation field of ∼15 T are being considered for the large hadron collider (LHC) energy upgrade high-energy large hadron collider (HE-LHC) and a post-LHC future circular collider. To demonstrate the feasibility of 15-T accelerator quality dipole magnets, the U.S. magnet development program is developing a single-aperture 15-T Nb3Sn dipole demonstrator based on a 4-layer graded cos-theta coil with 60 mm aperture and cold iron yoke. The main design challenges for 15-T accelerator magnets include large Lorentz forces at this field level. To counteract them, an innovative mechanical structure based on a vertically split iron yoke, locked by large aluminum IC-clamps and supported by a thick stainless steel skin, has been developed at Fermilab. To study the performance of the structure, a parametric multiphysics finite element analysis (FEA) model has been set up. This paper describes the numerical model as well as the results of a sensitivity analysis of the effect of geometrical tolerances and assembly parameters.

The future circular collider or FCC is a study aimed at exploring the possibility to reach 100 TeV total collision energy that would require 16 T dipoles. Upon the conclusion of the high luminosity upgrade, the US LHC accelerator upgrade project in collaboration with CERN will have an extensive Nb3Sn magnet fabrication experience. This experience includes robust Nb3Sn conductor and insulation scheming, 2-layer cos 2θ coil fabrication, and bladder-and-key structure and assembly. By making improvements and modification to existing technology, the feasibility of a two-layer 16 T dipole is investigated. Preliminary designs indicate that fields up to 16.6 T are feasible with conductor grading while satisfying the HE-LHC and FCC specifications. Key challenges include accommodating high-aspect ratio conductor, narrow wedge design, Nb3Sn conductor grading, and especially quench protection of a 16 T device.

For the Future Circular Collider (FCC), a 100-TeV post Large Hadron Collider machine, 750 main quadrupoles with a gradient of around 400 T/m are required. This paper presents an electromagnetic design optimization of a double aperture Nb3Sn quadrupole, fulfilling the specifications and a structural design of a single aperture configuration towards a prototype.

As a part of the future circular collider conceptual design study for hadron-hadron physics (FCC-hh), conceptual designs of detector magnets are being developed to facilitate the measurement of particle products resulting from the 100-TeV collisions. This paper discusses the design evolution leading from a 65-GJ twin solenoid with forward dipoles design to the present baseline design that features three superconducting solenoids. The central magnet produces 4 T over a free bore of 10 m and a length of 20 m. The forward solenoids provide additional bending power to facilitate tracking of high-pseudo-rapidity particles. The combined stored energy of this system is 13.8 GJ. This design is discussed in terms of powering and quench protection, conductor composition, mechanical properties of the cold masses and vacuum vessels, stray fields, and heat loads. In addition, alternative designs are discussed, including an ultrathin superconducting solenoid concept with comparatively low stored magnet energy. Like the ATLAS central solenoid, this solenoid provides a magnetic field to the tracker, and particles have to tunnel through the solenoid before reaching the calorimeters. An iron yoke returns the flux, thus providing bending power for muon tagging and giving complete magnetic shielding.

We revisit the classical rigid-fluxon model which describes the effect of an applied magnetic flux on the RF surface resistance of a superconductor and discuss explicit formulations for a few limit cases. As an application, we discuss the role of magnetic flux on the enhanced surface resistance of RF accelerating cavities based on niobium, depending on its material properties. We also assess the conditions for the use of high-temperature superconductors for carrying the beam image RF currents in future high-energy circular hadron colliders such as the future circular collider being studied at CERN.

This paper presents several magnetic designs for a 16-T 50-mm aperture Nb 3 Sn dipole based on the common coil design for a future circular collider. It has an aperture-to-aperture spacing of 250 mm, a yoke outer diameter of 700 mm, and uses a similar or less conductor amounts than cosine theta or block designs. All field harmonics are about an order of magnitude better than specified at the design field and well below the specification in the entire range of operation. Initial results of mechanical design and analysis are also encouraging. They indicate that the proposed structure is able to support the pole coil blocks against the vertical Lorentz forces and that the maximum stresses in all coils remain generally below 150 MPa. Given several inherent advantages of the common coil design, the development presented here should make this approach a leading candidate for very high field magnets in future colliders.

High-field superconducting accelerator magnets are a key technology of the future circular collider. In order to master the technical challenges and achieve the performance targets, CERN has launched a technology development program. The first step of the program is to explore the Nb3Sn performance limits at 18 T field level and high stress, simplifying to the maximum the coil geometry. The first magnet to be built, the enhanced racetrack model coil (ERMC), aims at a mid-plane field of 16 T with 10% margin on the load line at 4.2 K. The ERMC is composed of two flat racetrack coils with no bore. To further develop the block-coil geometry, a second magnet, the racetrack model magnet (RMM), will be composed of two ERMC coils and a middle coil with a 50-mm closed cavity, addressing the issue of the design of an inner support to compensate for the preload forces. The RMM aims at a central field of 16 T in a 50-mm cavity, with 10% margin at 4.2 K. The next step is to develop a more compact and cost-effective design using two cable sizes, and therefore two different current densities. The coils will be assembled in a shell-based support structure using bladders and keys, which allows a precise control of the stress with minimal spring back and conductor overstress. This paper describes the magnetic and mechanical design of the ERMC and the RMM.

International audience; A future circular collider (FCC) with a center-of-mass energy of 100 TeV and a circumference of around 100 km, or an energy upgrade of the LHC (HE-LHC) to 27 TeV require bending magnets providing 16 T in a 50-mm aperture. Several development programs for these magnets, based on Nb$_3$Sn technology, are being pursued in Europe and in the U.S. In these programs, cos-theta, block-type, common-coil, and canted-cos-theta magnets are explored; first model magnets are under manufacture; limits on conductor stress levels are studied; and a conductor with enhanced characteristics is developed. This paper summarizes and discusses the status, plans, and preliminary results of these programs.

Accelerator magnets for future particle accelerators are designed to work with as high energy densities as possible to achieve high fields and compact magnet designs. A key factor limiting the energy density is given by the protection in case of a quench: If a quench occurs, the stored energy must be first absorbed by the windings, and the magnet temperature shall not exceed a given limit. In this paper, we present a back-of-the-envelope method for estimating the magnet's maximum temperature after a quench based on its stored energy. The method combines the existing concepts of MIIT (Mega*current*current*time), time margin, and protection delay to allow for an easy and direct calculation of the hot-spot temperature. We apply the proposed method to several Nb 3 Sn dipole and quadrupole magnets developed for the high luminosity Large Hadron Collider and the Future Circular Collider for hadron-hadron collisions and compare the results to a more detailed simulation. The proposed energy density method is a useful tool for fast feedback in the early magnet design phase to ensure that the magnet is not impossible to protect.

Three different 16 T dipole magnet options for the Future Circular Collider (FCC) have been designed within the H2020 EuroCirCol collaboration, namely a cosθ-, a block-, and a common-coil -type of magnet. All magnets were designed using the same constraints related to magnetic field, cable parameters, mechanics, and quench protection. The quench protection analysis during the magnet design was centralized and done for all the options using the same tools and methods. This paper summarizes the final conceptual protection schemes. They are based either on the novel CLIQ-technology (Coupling Loss Induced Quench) or on traditional quench heaters. We compare the performance of the protection systems and show that while both can protect the magnet at nominal operation current, CLIQ is more efficient in reducing peak temperatures than heaters, and the system operation is simpler due to smaller amount of protection units. Therefore, CLIQ has been chosen as the baseline protection option for the FCC dipole magnets. The future development of heaters is considered as a back-up option. acceptedVersion

The future upgrades of the CERN accelerator chain along with the future high-energy colliders, notably the future circular collider (FCC), will require high gradient quadrupoles. As part of the High Luminosity Large Hadron Collider (HL-LHC) project, the 11 T dipole was designed to be compatible with accelerator requirements and industrial production. It is based on the “pole-loading” concept. This allows shimming at the pole and uses the collars more efficiently for creating the coil prestress. MKQXF is a further application of the “pole-loading” concept for Nb3Sn quadrupoles. The pole region of the coils is identical to the 11 T dipole and the collared coil is based on dipole-type collars. This concept can be extended to any length and applied on both 1-in-1 and 2-in-1 configurations. For benchmarking purposes and to compare with the present base-line design of the HL-LHC IR quadrupole MQXF, based on the bladder-and-key concept, this conceptual study was made with identical coils and quasi-identical magnetic characteristics. The design features 140 T/m gradient in 150 mm coil aperture. This paper describes the design concept of MKQXF and the multiphysics finite element model, including the end regions. The design is described and the optimized assembly parameters and the effect of the manufacturing tolerances are presented.

After LHC will be turned off, a new, more energetic machine will be needed in order to explore unknown regions of the high-energy physics. For this reason, the project Future Circular Collider (FCC) has started, with the goal of developing a 100 km circumference collider of 50 TeV proton beams. The Eurocircol collaboration is part of the FCC study under the European Community leadership, and it aims to develop a conceptual design of FCC within 2019. One of the main targets is to design a bending dipole able to reach 16 T operation magnetic field, in order to accomplish the size and energy constraints. Such a magnetic field can be reached using Nb$_{3}$Sn conductors at their highest performance. One option under exploration is the Cosθ dipole, by INFN of Milano and Genova. One of the aspects to be taken into consideration is the amount of conductor needed, because of the relatively high cost of superconducting cables involving Nb$_{3}$Sn. The amount of superconductor in the cross-section conductor area is a discriminant element for the choice of the magnet lay-out. At the same time enough copper stabilizer must be included in order to limit the Joule dissipation in case of quench. For these reasons, together with the very high stored energy, quench protection is one of the most challenging aspects of the design. In this paper, the quench protection of the cosθ design is presented. A standard quench protection study is accompanied by a less conservative study which includes AC effects on the power dissipation inside the coils and on the magnet inductance, in order to not exclude preventively more convenient designs, and to develop a more performing magnet as possible.

Within the future circular collider study, a 100-km long circular hadron collider is being designed for 100 TeV center-of-mass collision energies. The design of the 16 T Nb3Sn bending dipole magnets is carried out within the EuroCirCol collaboration. Three different type of dipole designs have been developed, each aiming to be as compact as possible, accounting for the design criteria. Quench protection a critical aspect of the magnet design and potentially limits the magnet compactness. The EuroCirCol magnets were designed assuming a protection system with significantly improved efficiency compared to the present LHC dipole protection. In this paper, we consider present state-of-the-art quench protection technologies, such as quench heaters and CLIQ, and apply them into the designed 16 T Block-type dipole. Two different simulation models are used to estimate the magnet hotspot temperature and voltages after a quench and consequently estimate the suitability of the different methods. acceptedVersion

With the Large Hadron Collider (LHC) up and running, studies have started for its successor. Under study is the Future Circular Collider (FCC), which has a circumference of about 100 km, aiming at a proton-proton collision energy of 100 TeV. Consequently, the main bending dipole magnets have to operate at a magnetic field of 16 T. As a first step towards its realization, this paper presents the results of a parametric study of the cross-sectional layout for dipole magnets with a field in the range of 13-17 T using Nb-Ti and Nb3Sn superconductors. The principal layouts included are the classical Cosine-Theta, the Canted Cosine-Theta, and the Block type. Conductor cost can be reduced significantly when a graded hybrid solution is chosen. Optimizing such complex magnet layouts requires an iterative algorithm, which arranges the positions of the various blocks of coil windings in the coil cross section, thereby finding the thickness of the coil layers. The iterative algorithm is coupled to an adiabatic quench model, which finds an optimal copper-to-superconductor fraction for each of the layers. Outside the iterative cycle, a pattern search algorithm is applied to find a cost optimal distribution of the magnetic field generated by each coil layer.

Future accelerator magnets are pushed to their limits in terms of magnetic field, mechanical strength and from the quench protection point of view. This forces the magnet designers to re-think the quench modelling. One issue that has not so far been largely explored is the mechanical behaviour of the superconducting coils during a quench. This can cause limitations to the design of high field accelerator magnets. This paper focuses on mechanical behavior in the event of a quench of a Nb3Sn 16 T dipole magnet currently developed in the framework of the EuroCirCol project in view of the Future Circular Collider conceptual design study. The thermo-mechanical analysis is performed through finite element modeling. The analysis takes into account the Lorentz force and the thermal stress due to the non-uniform temperature distribution in the winding during a quench. acceptedVersion

In the framework of the EuroCirCol project, the development of a conceptual design of the Future Circular Collider main dipole is performed. Here is described the status of the study focusing on the block coil layout. An electromagnetic investigation carried out in a double aperture configuration is reported. This study is followed by a preliminary investigation of the magnet performance in three-dimensional (3-D) taking into consideration the integrated field quality as well as the peak field in the coil ends. Finally, a 2-D mechanical analysis of the bladder and key structure is detailed. This study clearly shows that the design reaches the limit of the material properties.

After LHC is turned off, a new accelerator machine will be needed in order to explore unknown regions of high-energy particle physics. For this reason, the project Future Circular Collider (FCC) has started at CERN, with the target of studying the feasibility of a very large hadron collider with 50-TeV proton beams in a 100-km circumference. The EuroCirCol project is part of the FCC study under European Community leadership. In particular, it has the outcome of producing a conceptual design of the FCC within 2019. One of the main activities is the development of 16-T superconducting dipole able to produce a bore field, in order to bend the beams within energy and size constraints. Here, we present the conceptual design of a Nb3Sn cos θ dipole in double-aperture configuration (LHC-style). We show that it is possible to produce a bore field of 16 T with a good field quality, with reasonable assumptions on the conductor features, and with a reasonable amount of cable. A bladders and keys mechanical structure is also presented, proving that the electromagnetic forces can be maintained, keeping the stress in the coils within a safe limit. Finally, we present a preliminary quench study, showing that the magnet can be protected using well-known technologies.

After the large hadron collider (LHC), a higher energy range must be explored to address the open questions in particle physics. A new generation of colliders will be necessary, able to accelerate both leptons and hadrons to energy higher than previous machines. The EuroCirCol European collaboration, in the framework of the future circular collider (FCC) project, has the aim to provide a design for a hadron collider that is able to accelerate protons to 50 TeV in a 80-100 km circumference tunnel. One of the most challenging task is the design of the bending dipole, which must be able to produce magnetic field as high as 16 T. In this paper, the state of art of the cos θ option for the 16 T dipole for FCC is presented. In particular, the mechanical design will be described, showing that promising solutions have been found.

International audience; EuroCirCol is a conceptual design study for a post-LHC research infrastructure based on an energy-frontier 100 TeV circular hadron collider. In the frame of the high field accelerator magnet design work package of this study, three different layouts for double-aperture dipole magnets made of Nb3Sn conductors and providing a field of 16 T in a 50-mm aperture are being considered: block-coils, common-coils, and cosine-theta. All options are being explored and will be compared based on the same assumptions, in particular with regards to conductor performance, operating temperature and margin. This paper details the block-option presently under development at CEA. After an exploratory phase of various block-coils possibilities (cable dimensions, number of layers, cable grading) the design converged to a four layer magnet. An internal grading-two different geometries of cables are used in the coil-driven by a conductor saving is required. An electromagnetic analysis of the magnet cross-section in a 2-in-1 configuration is performed, coupled to a protection investigation. Preliminary results of a mechanical study on a bladder-and-key single aperture magnet are also reported.