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Superconducting magnets with noncircular aperture are desired for accelerators and many other high-field applications. This paper presents new methods for the analytic design of elliptic bore superconducting accelerator magnets. Part 1 of this work shares the derivation of current to field relations between a sheet current density on an elliptic cylinder and the magnetic field harmonics inside the aperture. This result is explored in the general context of elliptic bore magnet design with relevant scaling laws compared between elliptic and circular bore magnets. In part 2, this approach is applied to the specific geometry of canted-cosine-theta (CCT) accelerator magnets, enabling analytic winding design for single or mixed circular harmonics within elliptic aperture CCT magnets.

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 QCD axion is a leading dark matter candidate that emerges as part of the solution to the strong CP problem in the Standard Model. The coupling of the axion to photons is the most common experimental probe, but much parameter space remains unexplored. The coupling of the QCD axion to the Standard Model scales linearly with the axion mass; therefore, the highly motivated region 0.4-120 neV, corresponding to a GUT-scale axion, is particularly difficult to reach. This paper presents the design requirements for a definitive search for GUT-scale axions and reviews the technological advances needed to enable this program.

The most effective way to achieve very high collision energies in a circular particle accelerator is to maximize the field strength of the main bending dipoles. In dipole magnets using Nb-Ti superconductor the practical field limit is considered to be 8-9 T. When Nb3Sn superconductor material is utilized, a field level of 15-16 T can be achieved. To further push the magnetic field beyond the Nb3Sn limits, High Temperature Superconductors (HTS) need to be considered in the magnet design. The most promising HTS materials for particle accelerator magnets are Bi2212 and REBCO. However, their outstanding performance comes with a significantly higher cost. Therefore, an economically viable option towards 20 T dipole magnets could consist in an 'hybrid' solution, where both HTS and Nb3Sn materials are used. We discuss in this paper preliminary conceptual designs of various 20 T hybrid magnet concepts. After the definition of the overall design criteria, the coil dimensions and parameters are investigated with finite element models based on simple sector coils. Preliminary 2D cross-section computation results are then presented and three main layouts compared: cos-theta, block, and common-coil. Both traditional designs and more advanced stress-management options are considered.

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

The multi-pass recirculating proton linac can significantly improve the usage efficiency of rf superconducting cavities by accelerating the proton beam through the same cavity multiple times. However, in order to achieve acceleration for different energy proton beams, longitudinal phase synchronous conditions among these beams have to be satisfied. In this paper, we propose a fixed field phase shifter system based on two superconducting bending magnets with an optimized field distribution to meet the synchronous conditions. Such a phase shifter provides both longitudinal phase delay and transverse focusing of multiple energy beams. Self-consistent macroparticle simulations including space-charge effects through the system show that the proton beam emittances can be well preserved after the phase shifter for multiple energy beams.

Although the high-temperature superconducting (HTS) REBa2Cu3O x (REBCO, RE-rare earth elements) material has a strong potential to enable dipole magnetic fields above 20 T in future circular particle colliders, the magnet and conductor technology needs to be developed. As part of an ongoing development to address this need, here we report on our CORC® canted cosθ magnet called C2 with a target dipole field of 3 T in a 65 mm aperture. The magnet was wound with 70 m of 3.8 mm diameter CORC® wire on machined metal mandrels. The wire had 30 commercial REBCO tapes from SuperPower Inc. each 2 mm wide with a 30 µm thick substrate. The magnet generated a peak dipole field of 2.91 T at 6.290 kA, 4.2 K. The magnet could be consistently driven into the flux-flow regime with reproducible voltage rise at an engineering current density between 400-550 A mm-2, allowing reliable quench detection and magnet protection. The C2 magnet represents another successful step towards the development of high-field accelerator magnet and CORC® conductor technologies. The test results highlighted two development needs: continue improving the performance and flexibility of CORC® wires and develop the capability to identify locations of first onset of flux-flow voltage.

A compact gantry delivering 70-220 MeV protons with fixed field in the superconducting magnets could reduce the cost and improve the adoption of proton therapy. While a number of magnet and cryogenics designs have been proposed, the combined capital and operating costs of state-of-the-art superconducting materials have not been analyzed. In response, we develop a thermoeconomic model of a multi-stage, conduction cooled gantry lattice and analyze the cryocooler operating cost, cryocooler capital cost and conductor capital cost for Nb-Ti, Nb3Sn, REBCO and Bi-2223 over a continuous range of magnet temperatures, and a differential evolution algorithm is used to identify the optimal combination of thermal intercept temperatures. Although Nb3Sn yields the lowest Net Present Value (NPV) of $111.7k at a magnet temperature of 9.4 K, the optimized Bi-2223 design at 12.8 K approaches the realm of commercial feasibility by offering improved thermal stability and forgoing the need for costly conductor heat treatment and magnet quench training. Furthermore, it was found that Nb3Sn was more cost effective than Nb-Ti and that REBCO was not economically viable for the parameters of this investigation. The thermoeconomic model developed herein can optimize conductor choices, magnet temperatures and thermal staging which has value for any conduction-cooled superconducting magnet.

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

The U.S. Magnet Development Program (MDP) collaboration is designing a utility mechanical structure for testing various high-field superconducting dipole coils. The design uses a shell-based structure concept, which allows applying preload in two steps: During a room temperature assembly and during a cool down to a cryogenic temperature. The structure is designed to accommodate various coil designs - including Nb3Sn Cosine Theta (CT) and Canted CT magnets as well as hybrid magnets with high temperature superconductor cables. Superconducting coils, enclosed by bolted pads to form an octagonal coil pack, will be inserted into a reusable yoke-shell subassembly and precisely preloaded during the assembly using a bladder-and-key technology. Due to a differential thermal contraction between an external aluminum shell and the magnet core, the coil preload increases during the cool down up to level required for 17-T excitation. Such a reusable structure will serve as a testing fixture supporting goals of the MDP program, decreasing cost and simplifying coil performance testing at different preload levels. We present a finite-element analysis of the structure preloading various coil designs and examine the predicted coil stress at each step of the magnet assembly and excitation.

The U.S. Magnet Development Program (MDP) is exploring the possibility of combining low-and higherature superconductor technologies, using cosine-theta and canted-cosine-theta (CCT) Nb3Sn dipole magnets together with Bi-2212 CCT inserts, with the ultimate goal of constructing a 20-T dipole. The MDP short-term goal is a Bi-2212 CCT insert capable of reaching 5 T in the bore when operating as a stand-alone and 3 T when operating under a background field of 15 T. This paper reports on the fabrication of our BIN4 dipole magnet and our BIN5a and BIN5b coils, designed and built at the Lawrence Berkeley National Laboratory to address potential fabrication issues of Bi-2212 coils and verify the design of our 18-20-T dipole magnet. BIN4 is a two-layer 50-cm-long CCT magnet that uses a nine-strand Rutherford cable made with 0.8-mm-diameter Bi-2212 strands. Its goal is to investigate critical current, insulation integrity, manufacturing challenges, and quench protection issues after heat treating both layers together under oxygen at standard atmosphere (1 bar). BIN5a and BIN5b are two identical coils, similar to the outer layer of BIN4, with the difference that the length is 39 cm, and they will undergo 50-bar overpressure processing heat treatment. BIN5 coils are made from the state-of-the-art strand with an engineering critical current density of 1150 A/mm2 at 4.2 K and 5 T.

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 Nb3Sn 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.

The critical current density of Bi-2212 round wires has seen significant improvement over the past two years. We present the magnetic design and stress analysis of two Bi-2212 dipoles based on Canted-Cosine-Theta (CCT) technology using the state-of-the-art wires. The first design, based on a 19-strand Rutherford cable of θ0.8mm strands, is a two-layer dipole with a bore diameter of 40 mm and an outer diameter of 98.4 mm; it generates 5.4Twhen operating in stand-alone configuration and 18.9T in 15 T background field. The second design, based on a 13-strand Rutherford cable of θ0.8mm strands, is also a two-layer dipole with a bore diameter of 40 mm and an outer diameter of 81 mm; it generates 4.0 T when operating in stand-alone configuration and 17.8 T in 15 T background field. Normal stresses on the conductor in these magnets do not exceed 35 MPa when working under background field.Moreover, we propose a novel approach for increasing the efficiency of CCT magnets using keystoned Rutherford cable while removing the midplane ribs. with this method, it is possible to increase the efficiency of small radius CCT coils by 20%. We conclude that Bi-2212 can be used to increase the limit of accelerator magnet dipole fields beyond 15 T while managing stresses in the coils to acceptable levels.

© 2017 EU. Canted-cosine-theta (CCT) technology has been studied for its suitability for a future-circular-collider (FCC) main dipole in terms of magnetic and mechanical performance, elec-trothermal protectability, as well as efficiency. In this paper, we present lessons learnt from our search for efficient CCT solutions by means of two-dimensional (2-D) magnetic and mechanical simulations, discuss the 3-D periodic mechanical model, as well as 3-D electromagnetic analysis of the end regions. Temperature and voltage distributions during a quench under simplifying assumptions are discussed, and the magnet’s efficiency is compared to that of other contenders in the FCC design study. The results qualify the CCT design as a contender for the FCC main dipole.

The Canted–Cosine–Theta is a design option for the next generation of high field superconducting dipoles being pursued within the US Magnet Development Program. This paper presents new modeling techniques developed for design and analysis of CCT magnets. For mechanical modeling in ANSYS, three approaches with increasing accuracy are compared: 2-D symmetry models; 3-D periodic symmetry models; and full 3-D models. Methods for the static and transient magnetic simulation using ANSYS are presented with a focus on circuit-coupled models for predicting magnet behavior following quench. Where applicable, simulation results are compared to data from CCT magnet tests at Berkeley.

The Canted-Cosine-Theta (CCT) technology has the potential, by its intrinsic stress-management, to lower coil stresses in high-field accelerator magnets. This is especially relevant for Nb3Sn magnets, which may be subject to irreversible degradation if the coil stresses exceed critical values. The internal structure of CCT coils, however, dilutes the engineering current density. For an efficient design, the internal structure, therefore, needs to be reduced to the limit given by the computer-numerical-control machining capabilities. In that case, however, additional mechanical stiffness must be provided by an external mechanical structure. The mechanical structure for the Paul Scherrer Institut (PSI) CCT program, which is described in this paper, is based on the bladder and key concept. The CCT-specific deviations from the prevalent bladder and key implementations are discussed. In addition, a two-dimensional and three-dimensional analysis in all stages of loading, cooling, and powering of the first PSI magnet prototype, as well as a tolerance analysis, is reported.

Recent studies have shown that strong, alternating focusing magnets can be used to greatly increase the momentum acceptance of hadron therapy gantries. With the high gradients achievable with superconducting magnets a level of momentum acceptance can be reached which may have significant implications to medical gantries and to the introduction of superconducting technology in this area. The design of such a superconducting magnet system for a proton therapy gantry will be presented. The Canted-Cosine-Theta concept is extended to a curved magnet system generating the desired bending and alternating focusing fields for the achromatic optics. Magnetic, structural, and thermal analysis of this design is presented along with preliminary efforts towards fabrication and assembly of the curved magnet.

A four-layer canted-cosine-theta 16-T dipole has been designed as a possible candidate for future hadron colliders. The design maintains part of the future-circular-collider magnet requirements, i.e., a 50 mm clear bore and 16 T operating at 1.9 K. The magnet intercepts Lorentz forces with an internal structure of ribs and spars, minimizes conductor, and reduces the number of layers and magnet size by using wide cables. The role of iron and its impact on field and magnet size is discussed. A three-dimensional magnetic analysis was carried out for 1-in-1 and 2-in-1 designs including a structural analysis for the 1-in-1 case. Thoughts on future improvements during winding are also discussed.

We present a design of superconducting magnets, optimized for application in a gantry for proton therapy. We have introduced a new magnet design concept, called an alternating-gradient canted cosine theta (AG-CCT) concept, which is compatible with an achromatic layout. This layout allows a large momentum acceptance. The 15 cm radius of the bore aperture enables the application of pencil beam scanning in front of the SC-magnet. The optical and dynamic performance of a gantry based on these magnets has been analyzed using the fields derived (via Biot-Savart law) from the actual windings of the AG-CCT combined with the full equations of motion. The results show that with appropriate higher order correction, a large 3D volume can be rapidly scanned with little beam shape distortion. A very big advantage is that all this can be done while keeping the AG-CCT fields fixed. This reduces the need for fast field ramping of the superconducting magnets between the successive beam energies used for the scanning in depth and it is important for medical application since this reduces the technical risk (e.g., a quench) associated with fast field changes in superconducting magnets. For proton gantries the corresponding superconducting magnet system holds promise of dramatic reduction in weight. For heavier ion gantries there may furthermore be a significant reduction in size.

A multilayer high field dipole magnet has been designed for future particle accelerators. The magnet has eight layers of a Nb3Sn outsert coil and four layers of a Bi-2212 insert coil (see Figs. 1 and 2). The layers are graded, delivering a short-sample field of 17.7 T in a 40-mm bore. The coil layers are of a canted cosine-theta design - with ribs and spars that guide and support the coil windings, shape the field, intercept Lorentz forces, and minimize conductor prestress. We present a general overview of the concept and report on the magnetic and mechanical design including an initial cost estimate and construction plan.

Canted-Cosine-Theta (CCT) magnet is an accelerator magnet that superposes fields of nested and tilted solenoids that are oppositely canted. The current distribution of any canted layer generates a pure harmonic field as well as a solenoid field that can be cancelled with a similar but oppositely canted layer. The concept places windings within mandrel's ribs and spars that simultaneously intercept and guide Lorentz forces of each turn to prevent stress accumulation. With respect to other designs, the need for pre-stress in this concept is reduced by an order of magnitude making it highly compatible with the use of strain sensitive superconductors such as Nb3Sn or HTS. Intercepting large Lorentz forces is of particular interest in magnets with large bores and high field accelerator magnets like the one foreseen in the future high energy upgrade of the LHC. This paper describes the CCT concept and reports on the construction of CCT1 a "proof of principle" dipole.

The Canted-Cosine-Theta (CCT) magnet design offer significant reductions in conductor stress by using mandrels t prevent the accumulation of operating Lorentz forces. Each mandre consists of a cylindrical spar with ribs guiding the conductor These ribs intercept the turn-To-Turn accumulation of forces b transferring them to the spar. Design studies of a layered CC coil pack coupled to a shell-based structure are shown. The us of a 3-D periodic symmetry region to reduce the problem size fo finite element modeling is detailed along with a discussion of axia boundary conditions. ANSYS calculation results for a two laye NbTi dipole being constructed at LBNL (CCT1) are presented ANSYS calculations show the Lorentz force induced stress i CCT1 at the single turn level, demonstrating interception an suggesting investigation of CCT design with minimal structur external to the coil pack.

The Superconducting Magnet Group, at Lawrence Berkeley National Laboratory (LBNL), has been developing a canted cosine-theta (CCT) superconducting dipole coil as well as the coil's supporting magnet structure. This contribution reports on the progress in the development of the coil's winding mandrel and its fabrication options. A comprehensive study of the coil's Lorentz forces was performed to validate the winding mandrel's "stress interception" attributes. The design of the external structure and the application of the "Bladder & Key" technology is also discussed. Additionally, the application of these studies to a curved ion-therapy CCT dipole magnet is reported.

The size and weight of ion-beam cancer therapy gantries are frequently determined by a large aperture, curved, ninety degree, dipole magnet. The higher fields achievable with superconducting technology promise to greatly reduce the size and weight of this magnet and therefore also the gantry as a whole. This paper reports advances in the design of winding mandrels for curved, canted cosine-theta (CCT) magnets in the context of a preliminary magnet design for a proton gantry. The winding mandrel is integral to the CCT design and significantly affects the construction cost, stress management, winding feasibility, eddy current power losses, and field quality of the magnet. A laminated mandrel design using a minimum symmetry in the winding path is introduced and its feasibility demonstrated by a rapid prototype model. Piecewise construction of the mandrel using this laminated approach allows for increased manufacturing techniques and material choices. Sectioning the mandrel also reduces eddy currents produced during field changes accommodating the scan of beam energies during treatment. This symmetry concept can also greatly reduce the computational resources needed for 3D finite element calculations. It is shown that the small region of symmetry forming the laminations combined with periodic boundary conditions can model the entire magnet geometry disregarding the ends. © 2013 Elsevier B.V.