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About one hundred magnets of six different types shall be installed in the High Luminosity LHC (HL-LHC) in the years 2026-2028 at CERN. The magnets design, construction and test are based on CERN collaborations with institutes and industrial partners in USA, Spain, Italy, Japan and China. Three types of correctors are based on Nb‒Ti technology and feature conductor peak fields in the 2 to 4 T range: for all of them the prototype phase has been successfully completed. The production is well advanced for the superferric correctors, and is starting for the canted cosine theta correctors and for the nested correctors. The separation and recombination Nb‒Ti dipoles D1 and D2, with a 4.5-6 T bore field range, are both in the prototype phase after the completion of the short model program. The most challenging magnet, the Nb3Sn quadrupole with conductor peak field above 11 T, is in the prototype phase at CERN and halfway through the production phase in the USA. In this paper we will give, for each type of magnet, an overview of the main achievements obtained so far and we will outline the technical points still needing validation from the prototype program.

Under the U.S. High Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP), the 150 mm bore, high-field Nb3Sn low-β MQXFA quadrupole magnets are being fabricated, assembled and tested, in the context of the CERN Hi-Luminosity LHC (HL-LHC) upgrade. These magnets have 4.2 m magnetic length and 4.56 m long iron yoke. To date, eight MQXFA magnets have been tested. One of the magnets additionally underwent a successful endurance test with 40 triggered quenches, and two magnets did not perform as expected. This work summarizes for the first time the available strain gauge data from eight identical Nb3Sn MQXFA tested magnets, focusing on the endurance test, and on a possible cause of underperformance of the two magnets that did not pass the vertical test. We applied methods to prevent this from happening in future MQXFA magnets, which shown to be effective for last two tested magnets. Under the U.S. High Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP), the 150 mm bore, high-field Nb3Sn low-{̱e̱ṯa̱}̱ MQXFA quadrupole magnets are being fabricated, assembled and tested, in the context of the CERN Hi-Luminosity LHC (HL-LHC) upgrade. These magnets have 4.2 m magnetic length and 4.56 m long iron yoke. To date, eight MQXFA magnets have been tested. One of the magnets additionally underwent a successful endurance test with 40 triggered quenches, and two magnets did not perform as expected. This work summarizes for the first time the available strain gauge data from eight identical Nb3Sn MQXFA tested magnets, focusing on the endurance test, and on a possible cause of underperformance of the two magnets that did not pass the vertical test. We applied methods to prevent this from happening in future MQXFA magnets, which shown to be effective for last two tested magnets.

A superconducting dipole, designed for use as a sweeper magnet for nuclear physics experiments, is being constructed by the NHMFL for operation at the NSCL. The magnet operates at a peak mid-plane field of 3.8 T in a 140 mm gap. A multi-particle beam enters the magnet from the upstream side. The neutrons continue straight through to a neutron detector. The charged particles are swept 43 degrees on a one meter radius into a mass spectrometer. Extensive model-based computer analysis (MBA) have been applied for optimizing the coils and the stainless steel bobbin with regard to its shape while keeping the strain and the fraction of actual to critical current within reasonable limits. The structural FEM analysis had to address a variety of complex physical phenomena (composites with orthotropic material properties, cool down, surface-to-surface contacts, etc.) and the loads due to operation (Lorentz forces) had to be obtained from a parallel/coupled magnetic field analysis. One of the challenges magnet designers face in optimizing magnet systems is that the detail required to obtain reasonable accuracy is not well known. This paper presents results of the structural design optimization for the sweeper project and evaluates the adequacy of alternative modeling approaches. Also the final magnetic design of the system is summarized and progress toward fabrication is presented.

The muon collider is a new idea for lepton colliders. The ultimate energy of an electron ring is limited by synchrotron radiation. Muons, which have a rest mass that is 200 times that of an electron can be stores at much higher energies before synchrotron radiation limits ring performance. The problem with muons is their short life time (2.1 /spl mu/s at rest). In order to operate a muon storage ring large numbers of muons must be collected, cooled and accelerated before they decay to an electron and two neutrinos. As we see it now, high field superconducting solenoids are an integral part of a muon collider muon production and cooling systems. This report will describe the design parameters for superconducting and hybrid solenoids that are used for pion production and collection, RF phase rotations of the pions as they decay into muons and the muon cooling (reduction of the muon emittance) before acceleration.

The problem of optimizing the design of magnet systems to simultaneously satisfy a set of constraint equations for field, geometry, protection, and stability while minimizing the total system cost is considered. A mathematical description of the problem is given, along with details concerning possible constraint algorithms and cost functions. Rules for the optimal selection of magnet technology (potted, ventilated, and cable-in-conduit coils) are presented. The resulting sets of equations can be solved by different numerical methods; the final choice is based on considerations of functional form as well as computational speed and accuracy. Depending on the choice of constraint equations, the resulting problem may or may not be smooth, and may or may not admit multiple minima. The choice of minimization algorithm can be tailored to the situation at hand to yield optimal performance. We present results pertaining to an alternating-field solenoid system being considered by the MuCool collaboration. The system design requires consideration of field profile, magnet stability, magnet structure, and protection, as well as total cost. A key application of the optimization code is the analysis of cost trade-off with respect to the imposed constraints, and examples are given in the alternating-solenoid case.

The Muon-Electron Conversion experiment, to be built at Brookhaven National Laboratory, requires a complex set of solenoids to generate the required field profile. Field magnitude, gradient and oscillations must all be controlled along the /spl sim/27 meter curved beamline to allow for optimal capture of /spl pi/ and /spl mu/ particles, the sign and momentum selection of appropriate /spl mu/ particles, and their transport to the detector region. The solenoid system is designed to yield the required field profile in an efficient and cost-effective manner. A critical concern is the removal of field gradient reversals along the beamline. The system is decomposed into a large number of simple solenoids of equal current density, whose dimensions vary so as to obtain the required field contribution. Analysis of the field influence of cosmic ray shielding is provided, along with the field footprint of the entire system. Structural aspects are discussed, in particular relating to magnetic forces and cryostat requirements.

The design of multi-coil resistive magnets can be greatly improved by optimizing the numerous variables involved. We have developed a code that optimizes the design for maximum field. Maximum magnetic field at the center (the objective function) is sought under numerous geometric and mechanical constraints. We apply the penalty method to reduce the constrained problem to a sequence of unconstrained optimizations. The objective function and the majority of the constraints are nonlinear. The BFGS quasi-Newton method is used at the core of the optimization procedure. We give the mathematical problem formulation and describe the code implementation. The method is shown to be easily modified to account for new constraints. Examples of code results and typical nonlinear behavior of the function being minimized are shown.

It is pointed out that the optimum current density distribution for stress-limited, high-field, high-power magnets can be approached by magnets built up of many thin coils, to maximize their efficiency ('tesla per watt'). By optimizing the radial thickness and height of each subcoil, magnets consisting of only 8 Bitter coils can closely approximate the optimum. For instance with 24 MW such a magnet of inner and outer radii of 28 mm and 420 mm, respectively, could generate over 30 T. The authors therefore propose a new method of magnet construction, the Poly-Bitter magnet. >