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A 6-around-1 transposed cable using superconducting STAR wires can be useful for future circular collider applications. We made three cable samples using single STAR wires with a diameter of 1.3 mm. The first two samples, made with a cabling machine, used STAR wires consisting of a 0.7 mm diameter Nb-Ti core. The third cable sample was manually wound and used a STAR wire made with a 0.81 mm diameter Cu core. The first sample showed severe degradation after the cable was bent to a 75 mm radius. The current-carrying capability of the innermost and outermost rebco tapes in the STAR wire degraded by 42% to 98% and the middle rebco tapes remained intact. This was also the case for the second and straight cable sample. After fabrication of the third cable sample, we observed only about 5% reduction in the current along the wire, measured at different locations inside the terminations. The results suggest that the differences in architecture or fabrication of the STAR wires could have caused differences in critical current retention after cabling.

To generate a dipole field above 20 T, we need high-temperature superconductors, including REBa2Cu3O 7 − x (RE = rare earth, rebco) coated conductors. However, the optimal architecture of a high-current flexible rebco cable is not yet settled for high-field magnet applications. Here we report a 6-around-1 cable concept based on the high-temperature superconducting star ® wires. We made two cable samples. One had a single star ® wire and the other had six star ® wires. The cable with six star ® wires was 1.5 m long. It had a diameter of 5.7 mm and a pitch length of 52 mm. The critical current of the cable before bending was 1448 A at 77 K, retaining at least 77% of the total critical current from individual star ® wires. The cable had a low n value around 4.5. At a bend radius of 30 mm, the critical current and n value remained the same as before bending. The total resistance of electrical terminations was 61 nΩ at 77 K. The flexible and transposed 6-around-1 star ® cable can provide another route toward practical rebco conductors for high-field accelerator and fusion magnet applications.

Abstract: A novel geometrical configuration to form a magnetic field perpendicular to an aperture, created by an asymmetric current distribution, within a single layer, and using a continuous ideal current line, named the uni-layer (UL) magnet, is here presented. The idea is compared to existing concepts in superconducting magnets, namely, the cos θ sector magnet, stress managed cos θ and canted cos θ . The UL magnet allows for a design with a continuous unit length (no layer jump), and an increased minimum bending radius of the conductor in relation to traditional cos θ and canted cos θ designs. The specific characteristics of the UL design are especially advantageous for strain-sensitive and prone to winding degradation high-temperature superconductors, in very high field accelerator magnet applications, in which, high efficiency in the use of conductor, and a small aperture are required. The advantages with regard to the design and fabrication of UL magnets in relation to other concepts are also discussed.

The US HL-LHC Accelerator Upgrade Project (AUP) is building Nb3Sn quadrupole magnets, called MQXFA, with plans to install 16 of them in the HL-LHC Interaction Regions. Variability in coil size must be dealt with at the assembly level, which requires timely and repeatable measurement of each coil. In this paper we will present the methodology used for coil measurements and the geometrical size data for the coils that have been measured thus far. We will also show the coil measurements of 8 coils before and after cold test. The Leica AT960-MR laser tracker with Spatial Analyzer software acquired to achieve these measurements has been used elsewhere in the project to great effect.

By the end of October 2022, the US HL-LHC Accelerator Upgrade Project (AUP) had completed fabrication of ten MQXFA magnets and tested eight of them. The MQXFA magnets are the low-beta quadrupole magnets to be used in the Q1 and Q3 Inner Triplet elements of the High Luminosity LHC. This AUP effort is shared by BNL, Fermilab, and LBNL, with strand verification tests at NHMFL. An important step of the AUP QA plan is the testing of MQXFA magnets in a vertical cryostat at BNL. The acceptance criteria that could be tested at BNL were all met by the first four production magnets (MQXFA03-MQXFA06). Subsequently, two magnets (MQXFA07 and MQXFA08) did not meet some of the criteria and were disassembled. Lessons learned during the disassembly of MQXFA07 caused a revision to the assembly specifications that were used for MQXFA10 and subsequent magnets. In this article, we present a summary of: 1) the fabrication and test data for all the MQXFA magnets; 2) the analysis of MQXFA07/A08 test results with characterization of the limiting mechanism; 3) the outcome of the investigation, including the lessons learned during MQXFA07 disassembly; and 4) the finite element analysis correlating observations with test performance.

The use of high-field superconducting magnets has furthered the development of medical diagnosis, fusion research, accelerators, and particle physics. High-temperature superconductors enable magnets more powerful than those possible with Nb-Ti (superconducting transition temperature Tc of 9.2 K) and Nb3Sn (Tc of 18.4 K) conductors due to their very high critical field Bc2 of greater than 100 T near 4.2 K. However, the development of high-field accelerator magnets using high-temperature superconductors is still at its early stage. We report the construction of the world's first high-temperature superconducting Bi2Sr2CaCu2Ox (Bi-2212 with Tc of ∼82 K) accelerator dipole magnet. The magnet is based on a canted-cosine-theta design with Bi-2212 Rutherford cables. A high critical current was achieved by an overpressure processing heat treatment. The magnet was constructed from a nine-strand Rutherford cable made from industrial 0.8 mm wires. At 4.2 K, it reached a quench current of 3600 A and a dipole field of 1.64 T in a bore of 31 mm. The magnet did not exhibit the undesirable quench training common in Nb-Ti and Nb3Sn accelerator magnets. It quenched a dozen times without degradation. The magnet exhibited low magnetic field hysteresis (

A dipole magnet generating 20 T and beyond will require high-temperature superconductors such as Bi2Sr2CaCu2O 8 − x and REBa2Cu3O 7 − x (RE = rare earth, rebco). Symmetric tape round (star®) wires based on rebco tapes are emerging as a potential conductor for such a magnet, demonstrating a whole-conductor current density of 580 A mm−2 at 20 T, 4.2 K, and at a bend radius of 15 mm. There are, however, few magnet developments using star® wires. Here we report a subscale canted cos θ dipole magnet as an initial experiment for two purposes: to evaluate the conductor performance in a magnet configuration and to start developing the magnet technology, leveraging the small bend radius afforded by star® wires. The magnet was wound with two star® wires, electrically in parallel and without transposition. We tested the magnet at 77 and 4.2 K. The magnet reached a peak current of 8.9 kA, 78% of the short-sample prediction at 4.2 K, and a whole-conductor current density of 1500 A mm−2. The experiment demonstrated a minimum viable concept for dipole magnet applications using star® wires. The results also allowed us to identify further development needs for star® conductors and associated magnet technology to enable high-field rebco magnets.

High-temperature superconductors such as REBa2Cu3O7-x (REBCO, RE = rare earth) can generate strong magnetic fields that are promising for applications in particle accelerators and compact fusion reactors. Traditionally, voltage taps are installed in superconducting magnets to measure the voltage signals due to resistive transitions. The voltage-tap-based diagnostics is important for the development of magnet technology as it can help pinpoint the locations in the magnet windings that limit the magnet performance. The architecture of the multi-tape REBCO cable such as CORC wires, however, makes it difficult to apply the voltage-tap-based diagnostics to identify the locations of resistive transitions. Distributed fiber optic sensing (DFOS) has the potential to address this issue. In this paper, we report the measurements of thermal strain along a CORC wire based on optical frequency domain reflectometry with a maximum spatial resolution of 0.65 mm and a temporal resolution of 10 Hz. The optical fiber is co-wound with the CORC wire that is epoxy impregnated. During the test, current was increased until a resistive transition occurred in the conductor. The spectrum shift of the reflected light along the fiber was recorded. The results suggested that with proper thermal isolation from the cryogen, DFOS can be used to identify the locations of resistive transitions in CORC wires and magnets. The results will allow a better understanding of the causes of resistive transitions in REBCO conductors and magnets, which will help improve the REBCO magnet technology.

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.

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.

HD3 is the latest magnet of a series of block-type Nb3Sn dipole model magnets developed by the Superconducting Magnet Program at Lawrence Berkeley National Laboratory. The magnet is 1 m long with a clear aperture of 43 mm. As a model magnet designed with accelerator-quality features, each coil has flared ends to provide a clear bore for a beam tube. The magnet design was also optimized to minimize the geometric and saturation field errors. In 2013, HD3b reached a peak dipole field of 13.4 T at 4.4 K. As part of the magnet test, we measured field quality using rotating coils with lengths of 26 and 130 mm developed by Fermi National Accelerator Laboratory. Here, we report and analyze the measured static and dynamic field errors. We discuss the insight provided by the field quality study of HD3, which can be useful for the development of high-field block-type dipole magnets for next-generation circular colliders.

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.

A large aperture Nb 3 Sn dipole is proposed to replace the magnet assembly of EDIPO, which was irreversibly damaged in 2016. The goal is to generate a background field of 15 T at 4.2 K in a clear aperture of approximately 100×150 mm 2 and over a uniform length of 1000 mm in order to test superconducting cables for both fusion and high-energy physics applications. The magnet features a block-type coil design wound with wide Rutherford cable (two alternative coil cross sections are considered) and supported by a mechanical structure based on keys-and-bladders technology. In the end regions, the coils tilt up (flare) through a hard-way bend of the cables to provide room for the test well, following a layout already adopted in the LBNL HD2 and CERN-CEA FRESCA2 magnets. The two considered coil design alternatives aim at minimizing the mechanical stress in the coil windings. One coil pack design makes the use of two double pancake coils per pole, whereas the other alternative features three double pancakes per pole. Both design options are presented focusing on the results of numerical computations carried out with finite-element models to investigate peak stresses in the coils during room-temperature pre-loading, cool down, and powering.

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.

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.

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.

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.

A next step of energy increase of hadron colliders beyond the LHC requires high-field superconducting magnets capable of providing a dipolar field in the range of 16 T in a 50-mm aperture with accelerator quality. These characteristics could meet the requirements for an upgrade of the LHC to twice the present beam energy or for a 100-TeV center of mass energy future circular collider. This paper summarizes the activities and plans for the development of these magnets, in particular within the 16 T Magnet Technology Program, the WP5 of the EuroCirCol, and the U.S. Magnet Development Program.

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.

Advances in the performance of low- and high-temperature superconductors enable the development of advanced magnets for a range of applications, including tokamaks for fusion energy, dipoles, and quadrupoles for hadron colliders, and solenoids for nuclear magnetic resonance studies. The capability of testing prototype cables and insert coils at high field is critical to these developments. We present here the conceptual design of a test facility dipole with features suitable to support the advanced magnet development efforts of both Fusion and HEP communities. In particular, a background field of 15 T is provided over a minimum homogeneous length of 1000 mm, and the magnet clear bore of approximately 144 × 94 mm can accommodate large fusion conductors as well as prototype coils for high field dipoles, along with flexible cryogenic and mechanical provisions for sample characterization. Two technical solutions are considered. The first uses a forced flow cable-in-conduit conductor and follows the design developed by EFDA for the EDIPO magnet. The second uses a bath cooled Rutherford cable and follows a block-coil design similar to the CERN FRESCA2 dipole, and the LBNL HD and LD1 dipoles. Following a comparison between the two approaches, we present two designs for the Rutherford cable approach including performance objectives, key parameters, and preliminary magnetic, mechanical and quench protection analysis.

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 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.

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.

The US LHC Accelerator Research Program is constructing prototype interaction region quadrupoles as part of the US in-kind contribution to the Hi-Lumi LHC project. The low-beta MQXFA Q1/Q3 coils have a 4-m length and a 150 mm bore. The design was previously validated on short, one meter models (MQXFS) developed as part of the longstanding Nb3Sn quadrupole R&D by LARP in collaboration with CERN. In parallel, facilities and tooling are being developed and refined at BNL, LBNL, and FNAL to enable long coil production, assembly, and cold testing. Long length scale-up is based on the experience from the LARP 90-mm aperture (TQ-LQ) and 120-mm aperture (HQ and Long HQ) programs. A 4-m long MQXF practice coil was fabricated to verify procedures, parts, and tooling. In parallel, the first complete prototype coil (QXFP01a) was fabricated and assembled in a long magnetic mirror, MQXFPM1, to provide early feedback on coil design and fabrication following the successful experience of previous LARP mirror tests.

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.

The Large Hadron Collider Luminosity upgrade (HiLumi) program requires new low-β triplet quadrupole magnets, called MQXF, in the interaction region to increase the LHC peak and integrated luminosity. The MQXF magnets, designed and fabricated in collaboration between CERN and the U.S. LARP, will all have the same cross section. The MQXF long model, referred as MQXFA, is a quadrupole using the Nb3Sn superconducting technology with 150 mm aperture and a 4.2 m magnetic length and is the first long prototype of the final MQXF design. The MQXFA magnet is based on the previous LARP HQ and MQXFS designs. In this paper, we present the baseline design of the MQXFA structure with detailed three-dimensional (3-D) numerical analysis. A detailed tolerance analysis of the baseline case has been performed by using a 3-D finite element model, which allows fast computation of structures modeled with actual tolerances. Tolerance sensitivity of each component is discussed to verify the actual tolerances to be achieved by vendors. Tolerance stack-up analysis is presented in the end of this paper.