Cosine Theta Research Articles

Conceptual Mechanical Structure Analysis of A 16 T Canted Cosine Theta (CCT) Magnet

Conceptual Mechanical Structure Analysis of A 16 T Canted Cosine Theta (CCT) Magnet

Test Results of the First Wax-Impregnated Nb-Ti Canted Cosine Theta Septum Magnet “SuShi”

Test Results of the First Wax-Impregnated Nb-Ti Canted Cosine Theta Septum Magnet “SuShi”

A Field Quality Modeling in Canted Cosine Theta Dipole Magnets Wound Using REBCO Cables

A Field Quality Modeling in Canted Cosine Theta Dipole Magnets Wound Using REBCO Cables

Conceptual Design of an HTS Canted Cosine Theta Dipole Magnet for Research and Hadron Therapy Accelerators

Conceptual Design of an HTS Canted Cosine Theta Dipole Magnet for Research and Hadron Therapy Accelerators

Training-free demonstration of a 5.4 T Nb3Sn Canted–Cosine–Theta accelerator dipole impregnated with paraffin wax

Lawrence Berkeley National Laboratory is pursuing stress-managed Nb3Sn Canted–Cosine–Theta (CCT) magnet technology for high field accelerator magnets. Although promising results have been reported, improvements in the training performance are desired. This work describes the fabrication and testing campaigns of two subscale Nb3Sn CCT magnets; a baseline impregnated with National High Magnetic Field Laboratory Mix-61 and a magnet impregnated with paraffin wax. The paraffin magnet reached the short sample limit of the conductor, to within the measurement uncertainty, with no training quenches inside the magnet. In contrast, the baseline magnet reached 80% of the short sample limit after approximately 20 quenches and exhibits some loss of memory after thermal cycles. Inter-layer flexible quench antennas combined with voltage tap data show that all quenches appear identical and originate from a region corresponding to the location of peak field in the cable. Although this success should be replicated at higher fields, these first test results demonstrate the potential for training free Nb3Sn accelerator magnets operating near the short-sample limit.

Training-free performance of the wax-impregnated SuShi septum magnet

In the framework of the Future Circular Collider Study a new septum magnet concept, nicknamed ‘SuShi’ has been developed, and a prototype was built at Wigner Research Center for Physics, and tested at the FREIA facility of Uppsala University in April 2023. The concept uses a canted cosine theta (CCT)-like superconducting magnet and a passive superconducting shield to create a zero-field and high-field region within its aperture. SuShi is the first CCT magnet with both of its winding layers simultaneously impregnated with wax. This paper describes the first powering test of the empty magnet at 4.2 K, without the shield being inserted in its aperture. The performance of the magnet, including the observation of quench-back, estimation of hot-spot temperatures and the fraction of energy dissipated in the magnet are presented, and most interestingly the absence of any quench during the entire testing period is reported. Sushi reached its nominal +5% peak field of 3.64 T at 450 A, which corresponds to 80% of the calculated short sample limit along the load line, without training.

Magnet Technology and Design of Superconducting Magnets for Heavy Ion Gantry for Hadron Therapy

Various initiatives in Europe have been launched to study superconducting magnets for a rotatable gantry suitable to deliver up to 440 MeV/A carbon ions for hadron therapy. One initiative is led by INFN inside an agreement with CERN, CNAO, and MedAustron aiming at designing and manufacturing a strongly curved cos θ dipole rated for 4 T central field and with a ramp rate of 0.15-0.4 T/s. Here we explore the suitability of dipole technology derived from HEP collider for a rotatable gantry that poses severe conditions on the thermal design (indirectly cooled coils). A second one is in the frame of the European program H2020-HITRIplus-WP8, aimed at exploring the feasibility of using the novel Canted Cosine Theta (CCT) concept to produce a superconducting dipole with similar characteristics. The scope is to design and built one or two prototypes with Nb-Ti rope, to see if this route could be a viable alternative. Finally in the European collaboration H2020-I. FAST-WP8 we are exploring both CCT in combined function design (dipole + quadrupole, in Nb-Ti) and the use of HTS (REBCO tapes) with CCT dipole layout, pursuing the design manufacture of small prototypes with European Industry. If HTS will be found successful, it will be a great benefit for the cryogenic design of the magnet system.

A Method to Improve the Field Quality of the Curved Canted–Cosine–Theta Dipole

A Method to Improve the Field Quality of the Curved Canted–Cosine–Theta Dipole

Design and Test of a Curved Canted–Cosine–Theta Superconducting Dipole Magnet for Next Generation Ion Therapy

The curved superconducting dipole magnet is the core component of the next generation ion therapy device. The superconducting dipole magnet prototype with a physical bend angle of 90°, a magnetic bend angle of 45°, a bend radius of 800 mm, and a bore of 98 mm diameter is developed in China based on a novel type of Canted–Cosine–Theta (CCT) coil structure. The magnet design and manufacturing, and the quench protection system are reported first, and then testing process of this curved CCT superconducting magnet, which reached the nominal current of 610 A and generated the magnetic field of 2.018 T after five quench trainings in liquid helium test is reported, meeting the design indicators. A set of technical routes is explored through the development of the curved CCT magnet, providing support for the future ion therapy.

Canted Cosine Theta Dipole Magnet Wound Using REBCO CORC Cables–The Effect of Magnetization on Magnetic Field Quality

This paper presents the results of FEM analysis of the effect of REBCO CORC cable magnetization on the field quality of a canted cosine theta (CCT) dipole magnet. The magnetic properties of the CORC cable were the results of our measurements of its <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> ) curves at 4.2 K and magnetic fields up to 8 T. This magnetization data was used to calculate the field error for a CCT experimental magnet developed by LBNL. The results of analysis and experiment were compared. To make the computation less “expensive”, we modelled only a section of 10 or 8 turns of the magnet central part and calculated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b₁</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b₃</i> fields on a circle 2/3 of the innermost layer center line. Calculated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b₃</i> fields were compared with experimentally obtained values on the dipole operating in self-field mode. Reasonable agreement of the numerical and experiment values was achieved. The work continued with calculating of field errors for a 7 double layer version of that design.

Straight and Curved Canted Cosine Theta Superconducting Dipoles for Ion Therapy: Comparison Between Various Design Options and Technologies for Ramping Operation

Canted Cosine Theta layout for accelerator magnets is a very attractive since such magnets can be manufactured and assembled without big tooling, and with a relatively modest number of parts and tools. In the frame of European Horizon2020 funds, two collaborations, HITRI <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plus</i> and I.FAST, are developing a CCT design, of 80 mm free bore, 4 T central dipole field, and 0.4 T/s ramp-rate. This magnet is expected to be the bending element of a gantry, to control the beam delivery in therapy with ions (hadrontherapy). The paper illustrates first a comparison between CCT and more classical cosine theta layout, followed by the comparison between Nb-Ti, Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn, MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and HTS tapes coils. Relevant requirement for the magnets of this study is to be operated at low current, to limit the heat generation, in sight of a liquid-free cooling system. The results of the comparison is then applied to the design of two magnet demonstrators. Both adopt a low-losses Nb-Ti rope, consistently with the need for keeping the heat generation as low as possible. The first is a straight combined function dipole-quadrupole, while the second is a curved CCT dipole. The paper concludes with the first manufacturing tests for the CCT formers, for which aluminium -bronze, stainless steel and charged PEEK polymer are being explored as basic material.

Investigation on nonuniform current density and shape deformation affecting the magnetic field performance of a saddle-shaped no-insulation HTS cosine–theta dipole magnet

High magnetic fields are desirable for discovering new particles in particle accelerators. Dipole magnets using superconductors have played a key role in creating the required field intensity and uniformity. In contrast, high temperature superconductor (HTS) dipole magnets have recently been spotlit because of their ability to generate higher magnetic fields compared to their low temperature superconductor counterpart. Similar needs have emerged in other fields using magnets, and no-insulation (NI) technology is considered a feasible option to reach high magnetic fields by overcoming the disadvantages of HTS magnets. However, research has rarely been carried out on the utilization of NI HTS magnet technology for dipole magnets in high-field accelerators. Here we show the design, fabrication, and test results of an NI HTS dipole magnet with numerical analysis results. This paper aims to investigate the effect of nonuniform current density and undesirable shape deformation on the magnetic field distribution of a saddle-shaped NI HTS dipole magnet. The magnet is designed and constructed considering the ‘constant perimeter winding’ technique and tested in liquid nitrogen. The field mapping process is also performed along a designated mapping trajectory to obtain the magnetic field distribution. A T-A formulation-based simulation model, named the ‘sequential simulation model,’ is suggested to reproduce the measurements and employed considering the current distribution and shape deformation. As a result of quantitative analysis of the transverse direction measurements, the magnetic field error decreased by 0.02 percent point (pp) when the nonuniform current density is considered. It decreased by 0.13 pp when the shape deformation is considered. Moreover, the critical current calculated through an additional numerical analysis shows an error of up to 10%. In conclusion, the saddle-shaped NI HTS dipole magnet can produce a sufficient magnetic field level for particle accelerator research, even though the field distribution shows a uniformity of 0.37% within this study.

Differential geometry method for minimum hard-way bending 3D design of coils with ReBCO tape conductor

The use of tape conductor poses design challenges for superconducting magnets. Due to its very high aspect ratio, it is hardly possible to bend the conductor over its thin edges (hard-way bending) rather than over its wide side (easy-way bending). Overstraining the conductor causes critical current degradation. In this paper, we propose a new design approach to three-dimensional coil layouts and coil end geometries with tape conductor, which considers the tape’s geometrical limitations. To geometrically describe the conductor surface, we use the thin strip model, also referred to as constant perimeter geometry. To prevent conductor degradation, new optimization criteria valid for three-dimensional geometries are presented, which are prevention of conductor creasing, minimization of overall bending energy, and prevention of over-straining the conductor. We will apply this to two 3D coil designs called helix and canted cosine theta. For the design of the coil ends, we propose a new design method using Bézier splines, which allows for much greater design flexibility than previous methods. Two examples of coil end geometries generated with Bézier splines are presented: the so-called cloverleaf and cosine-theta.

DCT&amp;CCT Superconducting Multiplets for HIAF-HFRS

HIAF (High Intensity heavy ion Accelerator Facility) is the new generation heavy ion accelerator under construction in China. The HFRS (FRagment Separator of HIAF) is a fragment separator and also a transfer-line between the Booster Ring and the Spectrometer ring, which has magnetic rigidity up to 25 Tm. HFRS magnet system is composed of 11 superconducting dipoles and 13 sets of triplets. Several multipole magnets (an octupole coil, a quadrupole coil, and a sextupole coil) are nested together to compact the length of the HFRS-line. All of them feature high field gradients (13 T/m, 25 T/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , 105 T/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) and large bores (320 mm). To reduce the cold mass and ensure the field quality, the whole multipole magnets are all designed with coil-dominated magnets of CCT (Canted Cosine Theta) and DCT (Discrete Cosine Theta). This paper will introduce the general design process of an HFRS multipole module. The development process and test results of the prototype will be presented.

Structure Design and Test of a Fast Ramp Multilayer Canted Cosine Theta (CCT) Magnet

A fast ramp superconducting dipole magnet based on the Canted-Cosine-Theta (CCT) type coil with a magnetic field of 2 T, ramping rate of 3 T/s and a bore diameter of 60 mm has been designed for the compact synchrotron. The fast ramp magnet is comprised of four-layers of CCT coils embedded in the formers with high efficiency cooling channel and layer by layer pre-tightening structure to ensure structural reliability and thermal stability. This paper presented the main mechanical structure de-sign, analyze and measurements of the fast ramp CCT magnet. Based on the finite element method (FEM) model with ANSYS, a detailed analysis of the CCT magnet mechanical behavior during cool-down and excitation has been studied. Finally, the magnetic field and strain measurements are measured from a cryogenic test bath cooled with liquid helium, during which the magnet reached the expected goal. Comparisons of the strain measurements with 3D finite element model results are also reported in this paper.

The Superconducting Shield (SuShi) Septum Magnet Prototype

The Future Circular Collider proton-proton ring would require a high-field septum magnet with a blade as thin as possible for the extraction of the 50 TeV proton beam from the ring. One of the two baseline concepts in the conceptual design report is the “superconducting shield” (nicknamed as SuShi) septum, utilizing a zero field cooled, passive superconducting shield in order to create a zero-field channel for the circulating beam inside the bore of a 3 Tesla canted cosine theta (CCT) type superconducting magnet. Besides the overview of the magnet design, progress in the construction of the prototype is presented.

Design of CCT6: A Large Aperture, Nb$_3$Sn Dipole Magnet for HTS Insert Testing

We present the design of a four-layer, Canted Cosine Theta (CCT) Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_3$</tex-math></inline-formula> Sn dipole magnet as part of the general R&D program for high field superconducting magnets supported by the US Magnet Development Program (US-MDP). Future testing with High-Temperature Superconducting (HTS) inserts in a hybrid configuration motivates the design’s large clear aperture of 120 mm and target operating dipole field of 12 T at 4.2 K. First, we present a graded magnetic design utilizing existing Nb <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_3$</tex-math></inline-formula> Sn cables which results in 30% operating current margin at the target field. We then share results from a 2D mechanical analysis which makes use of an idealized external structure to provide initial guidance for design studies. This mechanical analysis is extended to demonstrate compatibility of the CCT6 design with a mechanical support structure, based on key and bladder technology, currently considered for use within multiple US-MDP high-field magnet programs.

Superconducting Curved Canted–Cosine–Theta (CCT) for the HIE-ISOLDE Recoil Separator Ring at CERN

The ISOLDE facility at CERN delivers the largest range of low-energy radioactive beams, exploited by several detector systems to investigate nuclear properties from the stable isotopes to the very exotic systems close to the neutron or proton drip lines. These studies can largely benefit from the use of a high-resolution fragment separator. To achieve this goal, an innovative spectrometer based on a compact superconducting (SC) ring, the Isolde Superconducting Recoil Separator (ISRS), is being studied. The ring will operate as an isochronous non-scaling fixed-field alternating-gradient (FFAG) system based on Canted-Cosine-Theta (CCT) magnets. These multifunction magnets have two alternating-gradient quadrupoles nested inside an outer dipole. According to preliminary beam dynamics studies, the dipole will need to generate a maximum field of 2.2 T. A maximum quadrupole gradient of approximately 14 T/m will guarantee orbit stability for heavy ions with a maximum kinetic energy of 10 MeV/u. Fine tuning of the CCT magnets and the FFAG optics will provide very large solid angles > 100 msr and momentum acceptances Δp/p > 20%. In this paper we present, the magnet designs and their optimisation. A cost-effective active stray field superconducting coil shield design has been introduced to be able to remove approximate 4000 kg of iron yoke and the complexity of building a tightly curved yoke.

Quench Protection of the HL-LHC Hollow Electron Lens Superconducting Solenoid Magnets

The High-Luminosity LHC (HL-LHC) project is an upgrade of the Large Hadron Collider (LHC) and comprises the installation of two Hollow Electron Lens (HEL) systems, each acting on one beam on both sides of LHC Point 4. The systems aim for a controlled depletion of hadron beam tails and an enhanced hadron beam halo collimation. Each HEL unit contains 22 circuits made up of solenoid, saddle coils and canted cosine theta corrector magnets. The largest magnet is a 1.6 m long solenoid, with a 180 mm bore diameter and central field of 5 T at 300 A and 4.5 K. This contribution focuses on the powering and protection strategy of the solenoid magnet circuits. The circuits are protected by active quench detection and a timely switch-off of the power converter. For the circuit with the largest stored energy, a study is performed on the efficiency of an energy extraction system. The quench simulations performed using the STEAM-LEDET code are combined with uncertainty quantification methods available in the DAKOTA software. Quench simulation input parameters related to the superconducting wire, magnet, circuit, and detection have been parametrized and randomly varied to calculate statistics of key output parameters. These are compared to the allowed limits, namely 500 V maximum peak voltage-to-ground and 120 K maximum coil temperature.

Study On Torsion Behavior of Superconducting Conductor On Round Core Cable

With high current-carrying capacity and strong mechanical properties, conductor on round core (CORC) cable is widely adopted in high-field magnet applications, for instance, in the form of solenoids, double pancakes and canted cosine theta coils. However, CORC cable may be twisted in the fabrication of magnet with complex structure, as well as suffering huge Lorentz force in the operation process, which could pose unpredictable strain on helical superconducting tape, arousing secondary damage. In this paper, single layer and double layer CORC samples were fabricated to test their torsion performance through both numerical and experimental methods. Critical twisting angle would be analyzed from the aspect of critical current degradation. Result shows that, compared to additional strain on tape, geometric distortion due to multi-layer structure of CORC cable is more harmful to current-carrying performance of cable. Conclusion obtained from this paper could provide important data for future optimization.