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.

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.

Cable and magnet applications require bending REBa2 Cu3O 7-δ (REBCO, RE = rare earth) tapes around a former to carry high current or generate specific magnetic fields. With a high aspect ratio, REBCO tapes favor the bending along their broad surfaces (easy way) than their thin edges (hard way). The easy-way bending forms can be effectively determined by the constant-perimeter method that was developed in the 1970s to fabricate accelerator magnets with flat thin conductors. The method, however, does not consider the strain distribution in the REBCO layer that can result from bending. Therefore, the REBCO layer can be overstrained and damaged even if it is bent in an easy way as determined by the constant-perimeter method. To address this issue, we developed a numerical approach to determine the strain in the REBCO layer using the local curvatures of the tape neutral plane. Two orthogonal strain components are determined: the axial component along the tape length and the transverse component along the tape width. These two components can be used to determine the conductor critical current after bending. The approach is demonstrated with four examples relevant for applications: a helical form for cables, forms for canted cos θ dipole and quadrupole magnets, and a form for the coil end design. The approach allows us to optimize the design of REBCO cables and magnets based on the constant-perimeter geometry and to reduce the strain-induced critical current degradation.

The superconducting electron cyclotron resonance (ECR) source magnet for the facility for rare isotope beams at Michigan State University was designed and built by the Superconducting Magnet Group at Lawrence Berkeley National Laboratory (LBNL) in 2017. The 28 GHz NbTi ion source magnet features a sextupole-in-solenoids configuration which is comparable to the VENUS ECR magnet operated at LBNL. However, the mechanical design of this magnet utilizes a shell-based support structure which allows fine adjustments to the sextupole preload and reversibility of the magnet assembly process. The magnet has been assembled and tested to operational currents at LBNL. This paper describes the mechanical analyses performed to estimate the sextupole's and solenoids' preloads. We will report on the 3-D finite element analysis during room temperature assembly, cool-down, and magnet excitation, and then describe the magnet preload operations. Finally, we will describe the performance of the support structure during the quench training.

The superconducting ECR source magnet for the Facility for Rare Isotope Beams at Michigan State University was designed and built by the Superconducting Magnet Group at Lawrence Berkeley National Laboratory (LBNL). The 28-GHz NbTi ion source magnet features a sextupole-in-solenoids configuration, which is comparable to the VENUS ECR magnet operated at LBNL. A shell-based support structure using bladders and keys has been incorporated into the design to allow for adjustments of the preload and reversibility of the magnet assembly process. The magnet has been assembled and successfully tested to operational currents at LBNL. This paper describes the basic design of the magnet and the passive quench protection system. The test results are also presented, including the quench behavior of the magnet, the training performance, and the magnetic measurement results.

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.

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 (<0.1%) as measured by a cryogenic Hall sensor. It was fast cycled to 1.47 T at 0.54 T/s without quenches. This work validates the canted-cosine-theta Bi-2212 dipole magnet design, illustrates the fabrication scheme, and establishes an initial performance benchmark.

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.

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.