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Stainless steel vessels see widespread use in superconducting magnets for particle accelerator applications. Their function varies in different magnet designs: they always provide the necessary liquid helium containment, but in some cases are also used to provide azimuthal prestress and can also be welded to the magnet end plate to provide additional longitudinal stiffness. A magnet designed with the bladder and key technology does not rely on the structural role of the vessel. They are structurally supported using azimuthally prestressed aluminum shells, and the longitudinal constraint by rods. In this case, the magnet designer would generally like to minimize the interaction between the magnet and the stainless-steel vessel and to minimize the coil stress variation due to the vessel. The stress state in the vessel and in the coil is a function of the circumferential interference, defined as the vessel azimuthal length minus the magnet circumference. The vessel and the magnet azimuthal length machining tolerances are relatively large resulting in significant stress variations in the superconducting coils. In this paper we introduce an interference-control shim, which can significantly limit the stress variation of the coils for a given variation of the interference. The effectiveness of the interference-control shim is evaluated numerically on the MQXF, the low-β quadrupole for the High Luminosity LHC.

Superconducting magnets experience significant thermo-mechanical loads throughout their life cycle. These are introduced by the electro-magnetic forces during powering, but also by the prestress applied in many magnet designs. Further to this, the large thermal excursion that components of different materials experience can generate significant internal forces. The loads are also experienced by the superconducting coils, whose critical current can decrease as a consequence of the applied strain. It is then crucial to predict the overall mechanical behavior and conservatively design a magnet, avoiding failure of the mechanical components and of the superconducting coils. Finite Element Analysis (FEA) is generally used to perform these tasks, but its results rely heavily on the material properties and models used. This is in particular true for the coil composite, which is simplified to allow reasonable model sizes in full magnet models. In this paper, we present the state-of-art knowledge of the mechanical properties of the materials mostly used in superconducting magnet construction. We review elastic and plastic properties at room and cryogenic temperature, thermal contraction, and summarize the state-of-art failure criteria for these materials. Finally, the paper summarizes the present understanding of the mechanical behavior and limits of Nb3Sn coils. For the first time, an orthotropic failure criteria is proposed.

High energy physics research will need more and more powerful circular accelerators in the next decades. It is therefore desirable to have dipole magnets able to produce the largest possible magnetic field, in order to keep the machine diameter within a reasonable size. A 20 T dipole is considered a desired achievement since it would allow the construction of an 80 km machine, able to circulate 100 TeV proton beams. In order to reach 20 T, a hybrid Low-Temperature Superconductor (LTS) - High-Temperature Superconductor (HTS) magnet is needed, since LTS technology is presently limited to ∼16 T for accelerator magnet applications. In this paper, we present the design of a 6 layers 20 T hybrid dipole magnet using Nb3Sn (LTS) and Bi2212 (HTS). We show that it is possible to achieve this magnetic field with accelerator field quality, with sufficient margin on a realistic conductor, keeping the stresses within safe limit, avoiding conductor degradation.

A test facility dipole is being developed at LBNL, targeting a 16 T field in a 144 mm wide aperture. The magnet uses a block design, with two double-pancake coils. In order to minimize motion under the large Lorentz forces, the coils are preloaded against a thick aluminum shell and iron yoke using bladder and key technology. It is then crucial to verify that the performance of the magnet is not degraded due to strain induced on the Nb3Sn conductor during assembly, cool-down and powering. The critical current of extracted strands was measured in a varying background magnetic field and as a function of the applied longitudinal strain. Finite element analysis was used to extract the strain state inside the superconducting strands during magnet assembly and operation. This strain was then compared to the measurements to evaluate potential reversible and irreversible effects on the magnet performances. The results suggest that the magnet can reach 16 T with sufficient margin, with no irreversible degradation in the high field region.

High-temperature superconducting REBa{2} Cu{3}O{7-x} (rebco) conductors have the potential to generate a high magnetic field over a broad temperature range. The corresponding accelerator magnet technology, still in its infancy, can be attractive for future energy-frontier particle colliders such as a multi-TeV muon collider. To help develop the technology, we explore the requirements and potential characteristics of a rebco magnet, operating at 4.2 or 20 K, with a dipole field of 8-10 T in a clear aperture of 150 mm. We use the canted \cos \theta magnet configuration to reduce the electromagnetic stresses on the conductors. We present the resulting dipole fields, field gradients for combined-function cases, conductor stresses, magnet dimensions and conductor lengths. We also discuss the conductor performance that is required to achieve the target dipole field at 4.2 and 20 K. The information can provide useful input to the development of rebco magnet and conductor technology for collider-ring magnets in a muon collider.

The cross-sectiondesign of cos (θ) superconducting magnets is historically developed in a two-step process: initially, the coil geometry is defined on the basis of magnetic optimizations; then, the structure is designed around the coil. The first step searches for the best coil cross-section maximizing the magnetic field, margin, field quality and conductor efficiency. The latter step aims at limiting the coil stresses and deformations. However, the coil design, defined with the initial magnetic optimization, can influence the mechanical behaviour of the magnet, altering, for example, the peak stress during operation. As the critical current is a function of the applied strain, the mechanical implications of the coil cross-section design can limit the achievable performance. In this paper we propose an integrated optimization process that targets the peak stress on the conductor in addition to the magnetic objectives. The results are presented for a sample high-field Nb3 Sn dipole: a 4-layer design aiming at ultimate conductor performance.

The High Luminosity LHC (HL-LHC) Project is planning to install 16 cold-masses made with Nb3Sn quadrupole magnets in the LHC Interaction Regions to significantly increase its luminosity. Half of these cold masses are fabricated at BNL, FNAL, and LBNL under the US Accelerator Research Program (AUP). Each cold mass includes two identical Nb3Sn quadrupole magnets, called MQXFA with a magnetic length of 4.2 m. Currently, the AUP project has completed the fabrication and test of the first 5 pre-series magnets, and is working on the following 16 magnets for the series production. The brittleness and strain sensitivity of the Nb3Sn superconducting material requires a careful definition of the allowable maximum stress in the windings during magnet assembly and pre-load, and a tight control of their variation within the whole coil length. Therefore, a series of assembly and pre-load specifications have been defined with the goals of minimizing the risk of conductor degradation and providing the mechanical support required to reach the nominal current during powering. In this paper we present the specifications defined for the MQXFA magnets and applied during the different assembly phases and during the pre-load process of the first 5 pre-series magnets.

The Electron Ion Collider (EIC) will require large aperture quadrupole magnets for the Hadron beam in the insertion region. Key requirements include high field, compact size, and tight control of the fringe fields. A 120 mm aperture, 308.4 mm outer diameter actively shielded Nb3Sn quadrupole model is under development to support these goals. This work is being carried out by a collaboration of BNL, JLAB and LBNL. A compact shell-based structure preloaded with a bladder and key system was developed for this project. In this paper, the effect of the compact structure on the mechanical behavior was investigated. In particular, the impact of the assembly tolerances and coil size variations on the actual coil stresses and bladder pressures was computed and compared with results from larger bladder and key structures developed for the LHC IR. The longitudinal preload is provided by stainless steel rods. Differently from other bladder and key magnets, the rods are first preloaded axially before coil axial load is applied. This new design aims to increase the overall stiffness of the system and reduce the longitudinal coil displacement during powering. Based on the results of a 3D mechanical analysis, the preliminary pre-load targets for the EIC quadrupole assembly will be reviewed and discussed.

Numerous experiments have shown that the loads applied to Nb3Sn strands and cables can reduce their critical current. Experiments, performed on uniaxially loaded strands, allowed to define clear laws to describe the evolution of the critical surface as a function of the applied current, field, temperature and strain. It is, however, still unclear how these laws can be applied to superconducting magnets. The present paper proposes a methodology to estimate the critical current and temperature margin reduction on superconducting magnets due to stress on the superconducting material. The methodology is tested on the MQXF magnets, a quadrupole developed for the High Luminosity LHC project, and successfully validated by comparing computed strain with data from strain gauge measurements. Results suggested that, because of the stresses arising in winding during assembly, cool-down and powering, the current limit of the magnet is lower than the expected short sample limit, and that the most critical region does not coincide with the peak field location.

For the Large Hadron Collider luminosity upgrade, two of the NbTi 8.3 T main bending dipoles will be replaced by two shorter Nb3Sn 11.2 T dipoles to create space for the installation of collimators in the dispersion suppression region. With the aim to verify the design features, several 2 m long 11 T models have been constructed and tested at CERN. During the fabrication and assembly of, so far, seven single and two double aperture short model magnets, several challenges were identified and tackled. These include reproducibility in coil fabrication and assembly procedure, as well as control of mechanical stresses in the conductor and surrounding structure. In order to limit coil over-compression and improve reproducibility, the cable insulation was re-optimized. In addition, a review of the collaring procedure of the 11 T magnet was launched with the goal of reducing the risk of conductor degradation due to excessive stress. In this paper, the main fabrication and assembly steps are described, including the description of the actions taken to resolve the identified weakness.

The Nb3Sn quadrupole MQXF is being developed as a part of the large hadron collide (LHC) High Luminosity upgrade. The magnet design was tested on 1.5-m-long short models, sharing the same cross section with the full-length magnets. Various azimuthal and longitudinal preloads were applied, studying the impact on the magnet training and on its mechanical performances. The experiments demonstrated the possibility to control the magnet prestress. However, various factors, coil size among the others, may affect the stress variation between and within each winding. This variation could prevent the magnets from reaching the magnet performances, as for example as a result of the critical current reduction of the Nb3Sn strands. This paper analyzes the mechanical performances of the short models, studying in particular the stress variation on different coils. The measured coil size was used as input in the numerical simulations, and the results were then compared with the strain gauge measurements. Finally, the short model experience was used to evaluate the feasibility of a loading operation that does not rely on the strain measurements.

High field superconducting magnets for particle accelerators often exhibit premature quenches. Once a normal zone is generated within the conductor, the quench may propagate causing temperature and resistive voltage rise along the coil. The resulting thermal gradients can potentially cause new peak stresses that might exceed the tolerable limits, degrading the conductor. The computation of the strain state in the coils during quench then becomes of paramount importance for magnet design, and requires a complete three-dimensional (3-D) analysis of quench phenomena. The objective of this paper is to present the first multiphysics modeling activities towards a new full 3-D methodology for the analysis of magnet mechanics during quench. As a first step, a 3-D thermal-electric finite element model of a Nb3Sn superconducting coil is developed and explained here. The model uses direct coupled-field elements to solve the system of thermal and electrical equations. A solving algorithm has also been implemented in order to investigate the physics behind quench transients. The output from this model, built in ANSYS APDL, can be easily coupled in a later stage to a mechanical model in order to estimate the strain state in the coil windings. A very good agreement has been observed between the numerical results and experimental tests performed in individual superconducting cables and real superconducting magnets.

For the high luminosity upgrade of the CERN large hadron collider, lower β∗ quadrupole magnets based on advanced Nb3Sn conductors will be installed on each side of the ATLAS and compact muon solenoid (CMS) experiment insertion zones. As part of the technological developments needed to achieve the required field gradient of 132.6 T/m within a 150-mm aperture, short length model magnets, named MQXFS, are tested both at the CERN SM18 and Fermilab test facilities. The model magnets rely on two types of Nb3Sn conductors (restack rod process (RRP) and powder-in-tube (PIT)) and on an innovative bladders and keys design to provide mechanical support against the Lorentz forces. In 2016 and 2017, the powering tests of the first two models MQXFS3 (RRP) and MQXFS5 (PIT) proved that nominal performance (16.5 kA) could be reached with excellent memory of the quench current after thermal cycle. However both magnets showed a slow training behavior with clear observations of voltage disturbances before the quench. Besides, only MQXFS5 could reach ultimate current (17.9 kA) whereas erratic behavior was observed on MQXFS3 due to conductor local degradation at the head of one of the coils. In 2018, this limiting coil was changed and the applied azimuthal prestress increased. While ultimate current could then be reached, no stable current could be maintained due to identified defect on the outer layer of the new coil. Finally the outcome of the test of the new model MQXFS4, featuring the final RRP conductors that will be used for the series production and variation on the inner layer quench heater designs are here reported in details.

The high-luminosity upgrade of the Large Hadron Collider (HL-LHC) requires new high-field and large-aperture quadrupole magnets for the low-beta inner triplets (MQXF). The U.S. HiLumi-LHC Accelerator Upgrade and CERN are jointly developing a 150-mm aperture Nb3Sn magnet. Due to the large beam size and orbit displacement in the final focusing triplet, MQXF has challenging field quality targets at collision energy. Magnetic measurements have been performed both at ambient and cryogenic temperatures in the four short models that were built and tested. This paper presents the magnetic analysis, comparing field measurements with the expectations and the field quality requirements. The analysis is focused on the geometrical harmonics and iron saturation effect, including three-dimensional effects and transfer function repeatability. Persistent currents and dynamic effects are also discussed.

Among the components to be upgraded in LHC interaction regions for the HiLumi-LHC projects are the inner triplet (or low-β) quadrupole magnets, denoted as Q1, Q2a, Q2b, and Q3. The new quadrupole magnets, called MQXF, are based on Nb3Sn superconducting magnet technology and operate at a gradient of 132.6 T/m, with a conductor peak field of 11.4 T. Q1 and Q3 are composed of magnets (called MQXFA) fabricated by the U.S. Accelerator Upgrade Project (AUP), with a magnetic length of 4.2 m. Q2a and Q2b consist of magnets (called MQXFB) fabricated by CERN, with a magnetic length of 7.15 m. After a series of short models, constructed in close collaboration by the US and CERN, the development program is now entering in the prototyping phase, with CERN on one side and BNL, FNAL, and LBNL on the other side assembling and testing their first long magnets We provide in this paper a description of the status of the MQXF program, with a summary of the short model test results, including quench performance, and mechanics, and an update on the fabrication, assembly, and test of the long prototypes.

For the Large Hadron Collider luminosity upgrade, two of the NbTi 8.3 T main bending dipoles will be replaced by two shorter Nb3Sn 11.2 T dipoles to create space for the installation of collimators in the dispersion suppression region. With the aim to verify the design features, several 2 m long 11 T models have been constructed and tested at CERN. During the fabrication and assembly of, so far, seven single and two double aperture short model magnets, several challenges were identified and tackled. These include reproducibility in coil fabrication and assembly procedure, as well as control of mechanical stresses in the conductor and surrounding structure. In order to limit coil over-compression and improve reproducibility, the cable insulation was re-optimized. In addition, a review of the collaring procedure of the 11 T magnet was launched with the goal of reducing the risk of conductor degradation due to excessive stress. In this paper, the main fabrication and assembly steps are described, including the description of the actions taken to resolve the identified weakness.

The Nb 3 Sn low-β quadrupole MQXF is being developed as a part of the High-Luminosity large hadron collider (LHC) upgrade project. The magnet will be produced in two different configurations, sharing the same cross section but with different lengths. A 7.2-m mechanical model of MQXFB was recently assembled at european organization for nuclear research (CERN) with one copper coil, two low-grade coils, and one rejected coil. Coil dimensions were measured with a portable coordinate measurement machine. The coil pack shimming was designed in order to optimize the field quality and the contacts between the coils and the collars. The azimuthal preload target was defined using the short models experience. The mechanical behavior during loading was monitored by means of strain gauges. The results demonstrated that the structure can provide the required prestress to the coils.

In the framework of the high-luminosity upgrade of the Large Hadron Collider, the U.S. LARP collaboration and CERN are jointly developing a 150 mm aperture Nb3Sn quadrupole for the LHC interaction regions. Due to the large stored energy density and the low copper stabilizer section, the quench protection of these magnets is particularly challenging, relying on a combination of quench heaters attached to the coil surface and coupling loss induced quench (CLIQ) units electrically connected to the coils. This paper summarizes the performance of the quench heater strips in different configurations relevant to machine operation. The analysis is focused on the inner layer quench heaters, where several heater strips failed during powering tests. Failure modes are discussed in order to address the technology issues and provide guidance for future tests.

The high-luminosity Large Hadron Collider (HL-LHC) project aims at allowing to increase the collisions in the LHC by a factor of ten in the decade 2025-2035. One essential element is the superconducting magnet around the interaction region points, where the large aperture magnets will be installed to allow to further reduce the beam size in the interaction point. The core of this upgrade is the Nb3Sn triplet, made up of 150-mm aperture quadrupoles in the range of 7-8 m. The project is being shared between the European Organization for Nuclear Research and the US Accelerator Upgrade Program, based on the same design, and on the two strand technologies. The project is ending the short model phase, and entering the prototype construction. We will report on the main results of the short model program, including the quench performance and field quality. A second important element is the 11 T dipole that replaces a standard dipole making space for additional collimators. The magnet is also ending the model development and entering the prototype phase. A critical point in the design of this magnet is the large current density, allowing increase of the field from 8 to 11 T with the same coil cross section as in the LHC dipoles. This is also the first two-in-one Nb3Sn magnet developed so far. We will report the main results on the test and the critical aspects.

The development of Nb3Sn quadrupole magnets for the High-Luminosity LHC upgrade is a joint venture between the US LHC Accelerator Research Program (LARP)∗ and CERN with the goal of fabricating large aperture quadrupoles for the LHC interaction regions (IR). The inner triplet (low-β) NbTi quadrupoles in the IR will be replaced by the stronger Nb3Sn magnets boosting the LHC program of having 10-fold increase in integrated luminosity after the foreseen upgrades. Previously, LARP conducted successful tests of short and long models with up to 120 mm aperture. The first short 150 mm aperture quadrupole model MQXFS1 was assembled with coils fabricated by both CERN and LARP. The magnet demonstrated a strong performance at Fermilab's vertical magnet test facility reaching the LHC operating limits. This paper reports the latest results from MQXFS1 tests with changed prestress levels. The overall magnet performance, including quench training and memory, ramp rate, and temperature dependence, is also summarized.

As part of the High-Luminosity Large Hadron Collider (LHC) Project, a set of Nb3Snquadrupoles are being developed, aiming to enhance the performance of the inner triplets. The new magnets, identified as MQXFA and MQXFB, will share the same cross section with two different lengths, 4.2 and 7.2 m, respectively. During the magnet development, three short models were tested, along with a number of mechanical models, demonstrating the capability of the magnet cross section to achieve the specified performances. The same performances are now required for the full-length magnets. To ensure this, the authors studied the impact of the magnet length on the capability of the structure to provide an adequate support to the coils. Finite element and simplified analytical models were used to evaluate the impact of the magnet length on the stresses in the magnet ends and coil elongation during powering. The models were calibrated using the results from the short model tests, and used to provide an indication on the required prestress and its foreseen impact on the magnet performance.

During the development of MQXF, the new Nb3Sn quadrupole to be used in the large hadron collider (LHC) inner triplets for the High Luminosity upgrade, three short models were tested: MQXFS1, MQXFS3, and MQXFS5. These models differ in the use of thin or thick laminations for the iron components, in the coil design, and in the superconductive strands, rod restack process (RRP) or powder in tube (PIT). In the MQXF design, the azimuthal prestress is provided at room temperature by means of the bladder-key technology, and it is further increased during the cooldown by the differential thermal contraction of the various components. Four aluminum rods provide the longitudinal prestress. Both systems allow for a flexible control of the amount of prestress applied. As a consequence, it was possible to test the models exploring different azimuthal and longitudinal prestress conditions, in an attempt to understand their impact on the magnet performances. This paper studies the mechanical behavior of these short models, also providing the strain and stresses measured by means of strain gauges installed on the aluminum shell, on the winding poles and on the rods. Finally, the paper compares the measures with the results from finite element (FE) models.

In the framework of the high-luminosity upgrade of the large hadron collider, the U.S. LARP collaboration and CERN are jointly developing a 150-mm aperture Nb3Sn quadrupole for the Large Hadron Collider (LHC) interaction regions. Due to the large beam size and orbit displacement in the final focusing triplet, MQXF has challenging targets for field quality at nominal operation conditions. Three short model magnets have been tested and around 30 coils have been built, allowing a first analysis of the reproducibility of the coil size and turns positioning. The impact of the coil shimming on field quality is evaluated, with special emphasis on the warm magnetic measurements and the correlation to field measurements at cold and nominal field. The variability of the field harmonics along the magnet axis is studied by means of a Monte-Carlo analysis and the effects of the corrective actions implemented to suppress the low-order unallowed multipoles are discussed.

The LHC accelerator research program (LARP), in collaboration with CERN and under the scope of the high luminosity upgrade of the Large Hadron Collider, is in the prototyping stage in the development of a 150 mm aperture high-field Nb3Sn quadrupole magnet called MQXF. This magnet is mechanically supported using a shell-based support structure, which has been extensively demonstrated on several R&D models within LARP, as well as in the more recent short (1.2 m magnetic length) MQXF model program. The MQXFA magnets are each 4.2 m magnetic length, and the first mechanical long model, MQXFA1M (using aluminum surrogate coils), and MQXFAP1 prototype magnet (the first prototype with Nb3Sn coils) have been assembled at the LBNL. In this paper, we summarize the tooling and the assembly processes, and discuss the mechanical performance of these first two assemblies, comparing strain gauge data with finite element model analysis, as well as the near-term plans for the long MQXF magnet program.

In the framework of the High-Luminosity Large Hadron Collider, the installation of a new generation of quadrupole magnets is foreseen on each side of ATLAS and CMS experiments. The new magnets are based on Nb3Sn technology and shall be able to reach an ultimate current of 17.9 kA with a peak field of 12.3 T in the coil. In 2016 and 2017, the first two short models, called MQXFS3 and MQXFS5, have been tested at 4.2 and 1.9 K in the two new test benches at the European Organization for Nuclear Research. This paper presents the result of the quench performance of the two models; the first magnet reached nominal but failed to reach ultimate, showing detraining in one coil. MQXFS5 reached ultimate performance without any detraining phenomena, validating the PIT conductor used for the first time in this magnet program.

During the development of MQXF, the new Nb3Sn quadrupole to be used in the large hadron collider (LHC) inner triplets for the High Luminosity upgrade, three short models were tested: MQXFS1, MQXFS3, and MQXFS5. These models differ in the use of thin or thick laminations for the iron components, in the coil design, and in the superconductive strands, rod restack process (RRP) or powder in tube (PIT). In the MQXF design, the azimuthal prestress is provided at room temperature by means of the bladder-key technology, and it is further increased during the cooldown by the differential thermal contraction of the various components. Four aluminum rods provide the longitudinal prestress. Both systems allow for a flexible control of the amount of prestress applied. As a consequence, it was possible to test the models exploring different azimuthal and longitudinal prestress conditions, in an attempt to understand their impact on the magnet performances. This paper studies the mechanical behavior of these short models, also providing the strain and stresses measured by means of strain gauges installed on the aluminum shell, on the winding poles and on the rods. Finally, the paper compares the measures with the results from finite element (FE) models.

Multiplexing is a strategy to augment the transmission capacity of acommunication system. It consists of combining multiple signals over the samedata channel and it has been very successful in classical communications.However, the use of enhanced channels has only reached limited practicality inquantum communications (QC) as it requires the complex manipulation of quantumsystems of higher dimensions. Considerable effort is being made towards QCusing high-dimensional quantum systems encoded into the transverse momentum ofsingle photons but, so far, no approach has been proven to be fully compatiblewith the existing telecommunication infrastructure. Here, we overcome such atechnological challenge and demonstrate a stable and secure high-dimensionaldecoy-state quantum key distribution session over a 0.3 km long multicoreoptical fiber. The high-dimensional quantum states are defined in terms of themultiple core modes available for the photon transmission over the fiber, andthe decoy-state analysis demonstrates that our technique enables a positivesecret key generation rate up to 25 km of fiber propagation. Finally, we showhow our results build up towards a high-dimensional quantum network composed offree-space and fiber based links

The U.S. LHC Accelerator Research Program (LARP) and CERN combined their efforts in developing Nb3Sn magnets for the high-luminosity LHC upgrade. The ultimate goal of this collaboration is to fabricate large aperture Nb 3Sn quadrupoles for the LHC interaction regions. These magnets will replace the present 70-mm-Aperture NbTi quadrupole triplets for expected increase of the LHC peak luminosity up to 5 × 1034 cm-2s-1 or more. Over the past decade, LARP successfully fabricated and tested short and long models of 90 and 120-mm-Aperture Nb3Sn quadrupoles. Recently, the first short model of 150-mm-diameter quadrupole MQXFS was built with coils fabricated both by LARP and CERN. The magnet performance was tested at Fermilab's vertical magnet test facility. This paper reports the test results, including the quench training at 1.9 K, ramp rate and temperature dependence, as well as protection heater studies.

As part of the Large Hadron Collider Luminosity upgrade (HiLumi-LHC) program, the US LARP collaboration and CERN are working together to design and build 150-mm aperture Nb3Sn quadrupoles for the LHC interaction regions. A first series of 1.5-m-long coils were fabricated, assembled, and tested in the first short model. This paper presents the magnetic analysis, comparing magnetic field measurements with the expectations and the field quality requirements. The analysis is focused on the geometrical harmonics, iron saturation effect, and cold-warm correlation. Three-dimensional effects such as the variability of the field harmonics along the magnet axis and the contribution of the coil ends are also discussed. Moreover, we present the influence of the conductor magnetization and the dynamic effects.

In the framework of the Hi-Lumi LHC Project, CERN and U.S. LARP are jointly developing MQXF, a 150-mm aperture high-field Nb3Sn quadrupole for the upgrade of the inner triplet of the low-beta interaction regions. The magnet is supported by a shell-based structure, providing the preload by means of bladder-key technology and differential thermal contraction of the various components. Two short models have been produced using the same cross section currently considered for the final magnet. The structures were preliminarily tested replacing the superconducting coils with blocks of aluminum. This procedure allows for model validation and calibration, and also to set performance goals for the real magnet. Strain gauges were used to monitor the behavior of the structure during assembly, cool down and also excitation in the case of the magnets. The various structures differ for the shell partitioning strategies adopted and for the presence of thick or thin laminations. This paper presents the results obtained and discusses the mechanical performance of all the short models produced up to now.