Accelerator Dipole Research Articles

A Novel Modular Cascaded H-Bridge High-Power Accelerator Dipole Magnet Pulse Power Supply for HIRFL-CSRm

A Novel Modular Cascaded H-Bridge High-Power Accelerator Dipole Magnet Pulse Power Supply for HIRFL-CSRm

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.

Computing the Non-Uniform Current Effects on the Magnetic Field in Sector Coil Dipoles

In this study, we extend the previous ‘Segmentation method’, which was originally suggested to calculate harmonic coefficients of solenoid magnets, to apply to high temperature superconductor (HTS) accelerator dipole magnets. The key idea of the segmentation method is to divide the current flowing domain into several segments to find its equivalent loop currents, by whose magnetic fields or corresponding field quality can be analytically calculated. This paper formulates an equation to calculate the multipole coefficients by segmented loop currents which represents the current densities of a sector-coil dipole magnet. The extended segmentation method is validated by comparison with analytic and inverse method through the multipole coefficient calculation. Second, the segmentation method is applied on an example model of a dipole magnet whose non-uniform current densities which are calculated by using the H-formulation based finite element method. The multipole coefficient calculation results and magnetic field are compared between the uniform and non-uniform current density using the segmentation method. Finally, a case study of extending the obtained 2D current density profile to 3D space is conducted with several assumptions.

Conceptual Design of 20 T Hybrid Accelerator Dipole Magnets

Hybrid magnets are currently under consideration as an economically viable option towards 20 T dipole magnets for next generation of particle accelerators. In these magnets, High Temperature Superconducting (HTS) materials are used in the high field part of the coil with so-called insert coils, and Low Temperature Superconductors (LTS) like Nb3Sn and Nb-Ti superconductors are used in the lower field region with so-called outsert coils. The attractiveness of the hybrid option lays on the fact that, on the one hand, the 20 T field level is beyond the Nb3Sn practical limits of 15-16 T for accelerator magnets and can be achieved only via HTS materials; on the other hand, the high cost of HTS superconductors compared to LTS superconductors makes it advantageous exploring a hybrid approach, where the HTS portion of the coil is minimized. We present in this paper an overview of different design options aimed at generating 20 T field in a 50 mm clear aperture. The coil layouts investigated include the Cos-theta design (CT), with its variations to reduce the conductor peak stress, namely the Canted Cos-theta design (CCT) and the Stress Management Cos-theta design (SMCT), and, in addition, the Block-type design (BL) including a form of stress management and the Common-Coil design (CC). Results from a magnetic and mechanical analysis are discussed, with particular focus on the comparison between the different options regarding quantity of superconducting material, field quality, conductor peak stress, and quench protection.

Design, fabrication, and characterization of a high-field high-temperature superconducting Bi-2212 accelerator dipole magnet

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 ${T}_{c}$ of 9.2 K) and ${\mathrm{Nb}}_{3}\mathrm{Sn}$ (${T}_{c}$ of 18.4 K) conductors due to their very high critical field ${B}_{c2}$ 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 ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{x}$ (Bi-2212 with ${T}_{c}$ of $\ensuremath{\sim}82\text{ }\text{ }\mathrm{K}$) 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 ${\mathrm{Nb}}_{3}\mathrm{Sn}$ 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 $0.54\text{ }\text{ }\mathrm{T}/\mathrm{s}$ without quenches. This work validates the canted-cosine-theta Bi-2212 dipole magnet design, illustrates the fabrication scheme, and establishes an initial performance benchmark.

Proof-of-Principle Design of a High-Field Overpass/Underpass Nb3Sn Dipole

A block coil geometry is appealing in the body of particle accelerator dipole or quadrupole magnets, but less so in the ends of conventional designs, because conductors near the midplane of the beam tube must be bent in the hard direction to cross over to the other side of the tube. To avoid damage to brittle conductors such as Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn or HTS, the bend must be very gradual, resulting in undesirably long magnet ends. An alternative design - “overpass/underpass” or “cloverleaf” - can ramp the conductor within a short length with bending only in the easy direction. Described here is a proof-of-principle design and analysis of an “overpass/underpass” coil geometry for a block coil dipole of 11 T or more.

Characterization of Candidate Insulation Resins for Training Reduction in High Energy Physics Magnets

Superconducting magnets are critical components in particle accelerators and are used to generate and sustain the large magnetic fields needed for High Energy Physics programs. One significant issue with current epoxy insulated Nb3Sn magnets is the long training process required before stable magnet performance can be realized. It is believed that training can be significantly reduced by addressing magnet quenching through improvements in the epoxy electrical insulation. In this work, two approaches for insulation modification have been undertaken: (1) addition of thermally conductive fillers to help with quench management and (2) development of insulation resins with high strain capability at cryogenic temperatures. This paper will discuss the characterization of these insulation systems to verify their performance prior to evaluation in subscale Nb3Sn canted cosine theta accelerator dipole magnets.

Transverse-pressure susceptibility of high-Jc RRP and PIT types of Nb3Sn Rutherford cables for accelerator magnets

In the frame of the High-Luminosity Large Hadron Collider construction and Future Circular Collider development program, the magnetic field in the accelerator dipole magnets is being enhanced to 11 T, and 15 T to 16 T level, respectively. Advanced Nb3Sn superconductors with a non-copper critical current density exceeding 2500 A mm−2 at 4.2 K and 12 T, are being developed using the Restacked-Rod-Process (RRP) and Powder-In-Tube (PIT) wire technologies. However, since Nb3Sn is extremely brittle, it is a significant challenge to construct the high-field dipole magnets with such very strain-susceptible superconductor. The high-level of stress acting on the wide face of the Rutherford cables in the coils of 120 MPa to 200 MPa generated by the Lorenz’ force, causes initially a reversible reduction and eventually at some stress level followed by permanent degradation of the critical current when strain goes to high. This study sets out to examine the critical current and upper critical field performance of state-of-the-art RRP and PIT Nb3Sn Rutherford cables in terms of transverse pressure. The variation of the critical current and upper critical field due to the thermal- and mechanical load-cycling was investigated as well. For reference, the critical current of witness wires characterized on standard ITER type barrels were also measured. The results indicate that the RRP type of Nb3Sn Rutherford cables, when fully impregnated with epoxy resin, are able to withstand a transverse stress of 170 MPa to 250 MPa without noticeable irreversible critical current reduction. For the transverse pressure limit for present PIT type of Nb3Sn Rutherford cables somewhat lower values are found at the level of 50 MPa to 120 MPa. Therefore, given the present cables, the high-field dipole magnet construction can be realized using the RRP Nb3Sn Rutherford cables, while for PIT type cables more cable development is requested to enhance the onset of irreversible degradation. The reversible critical current reduction in RRP type of cables of 10% at 150 MPa to 250 MPa needs to be taken into account when predicting magnet performance. Finally, extreme care needs to be taken into account for Nb3Sn coil fabrication, since the experimental results show significant critical current reduction due to stress concentrations already at 0.2° misalignment angles between the pressure applying surface and the surface of the impregnated cable.

Development of a compact and fast trimmable FeCo magnet for medical gantries

In the frame of the Tulip project, an application for accelerator technology to radiation therapy, supported by a CERN Knowledge Technology Fund, the design, manufacture and test of a compact, fast trimmable iron cobalt (FeCo) accelerator dipole magnet prototype has been performed and completed at CERN. The aim of this project is to illustrate the benefits of a FeCo magnet for medical gantries in which weight and size are critical. The prototype is a 250 mm long dipole providing a central field of up to 1.8 T, the field can be trimmed in the percent range at frequencies of up to 200 Hz. The experimental results clearly demonstrate that FeCo magnets can be interesting alternatives for medical gantries because of their linear behavior up to high fields and their compact nature.

Superconducting Accelerator Magnets Based on High-Temperature Superconducting Bi-2212 Round Wires

Superconducting magnets are an invaluable tool for scientific discovery, energy research, and medical diagnosis. To date, virtually all superconducting magnets have been made from two Nb-based low-temperature superconductors (Nb-Ti with a superconducting transition temperature Tc of 9.2 K and Nb3Sn with a Tc of 18.3 K). The 8.33 T Nb-Ti accelerator dipole magnets of the large hadron collider (LHC) at CERN enabled the discovery of the Higgs Boson and the ongoing search for physics beyond the standard model of high energy physics. The 12 T class Nb3Sn magnets are key to the International Thermonuclear Experimental Reactor (ITER) Tokamak and to the high-luminosity upgrade of the LHC that aims to increase the luminosity by a factor of 5–10. In this paper, we discuss opportunities with a high-temperature superconducting material Bi-2212 with a Tc of 80–92 K for building more powerful magnets for high energy circular colliders. The development of a superconducting accelerator magnet could not succeed without a parallel development of a high performance conductor. We will review triumphs of developing Bi-2212 round wires into a magnet grade conductor and technologies that enable them. Then, we will discuss the challenges associated with constructing a high-field accelerator magnet using Bi-2212 wires, especially those dipoles of 15–20 T class with a significant value for future physics colliders, potential technology paths forward, and progress made so far with subscale magnet development based on racetrack coils and a canted-cosine-theta magnet design that uniquely addresses the mechanical weaknesses of Bi-2212 cables. Additionally, a roadmap being implemented by the US Magnet Development Program for demonstrating high-field Bi-2212 accelerator dipole technologies is presented.

Designs and Prospects of Bi-2212 Canted-Cosine-Theta Magnets to Increase the Magnetic Field of Accelerator Dipoles Beyond 15 T

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 $\emptyset {\text{0.8}}\,{\text{mm}}$ strands, is a two-layer dipole with a bore diameter of 40 mm and an outer diameter of 98.4 mm; it generates 5.4 T when operating in stand-alone configuration and 18.9 T in 15 T background field. The second design, based on a 13-strand Rutherford cable of $\emptyset {\text{0.8}}\,{\text{mm}}$ 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.

Optimization of an E${}^3$SPreSSO Energy-Extraction System for High-Field Superconducting Magnets

High-temperature superconducting magnets (HTS) suffer from slow quench propagation and have in large fraction high thermal margin. Due to the high thermal margin, quench protection systems (QPS) based on initiating large normal zones, with, e.g., quench protection heaters or CLIQ, are not effective with HTS, and energy extraction is needed. In large magnets, energy extraction with a single dump is not effective and new solutions are looked for. Recently, a concept E ${}^3$ SPreSSO for HTS magnet protection has been presented in the scope of European project EuCARD-2. E ${}^3$ SPreSSO utilizes a series-connected bifilar HTS or LTS coil. In this work, we present a methodology to design QPS based on E ${}^3$ SPreSSO for HTS magnets. Then, we utilize this methodology to design and analyze the suitability of such QPS for a 20 T HTS accelerator dipole.

Investigation of Adopting Shrink-Fit Multilayered Aluminum Shell in High-Field Common-Coil Accelerator Dipole Magnet

This paper presents the shrink-fit multilayered aluminum shell (SMAS) used for withstanding large Lorentz force in a 20-T shell-based common-coil accelerator dipole magnet. Finite element analysis (FEA) is carried out to optimize the required shell thickness when a single layer aluminum shell is used to support the 20-T dipole magnet. Also, FEA is carried out to study the performance of a three-layer SMAS used in the same dipole magnet. The analyzed results indicate that the three-layer SMAS with thickness of 75 mm can help us to reduce the peak shell stress significantly compared to a 75-mm-thick single layer aluminum shell when they provide the same preload to the coils. Some preliminary experiments have been carried out which prove that the initial stress distribution in the SMAS can be well controlled after the assembly. Hopefully, the outer diameter of the twin-aperture 20-T common-coil dipole magnet can be restricted to 900 mm if we use a three-layer SMAS as the support structure.

Partially Insulated Twisted Stacked Cable for HTS Insert of a Particle Accelerator

High Tc superconducting (HTS) insert in combination with low Tc superconducting (LTS) outsert is the only possibility today to go above 16 T for future high-energy particle accelerator dipoles. These HTS inserts will feature large operating current (≥ 10 kA) and high background fields (≥ 13 T) leading to severe operating conditions. In our 46-turns HTS insert, a 4 × 4 mm twisted stacked cable composed of 20 tapes and carrying 10.4 kA is used. It is simple to manufacture and enables a partial transposition. The designed insert can generate 5 T with good field homogeneity, assuming a homogeneous current density in the cable. However, a half twist per turn applied in the magnet ends of a 15-m-long insert makes it difficult to obtain both low magnetization and uniform current distribution in the cable. Three twisted stacked cables solutions are numerically studied: noninsulated cable, insulated cable, and partially insulated cable. The simulated HTS insert is first submitted to the external field of the outsert then the current is ramped up to nominal value. The partially insulated twisted stacked cable compounds both advantages of noninsulated and insulated cables, and thus appear to be the best solution for the HTS insert.

Optimized Field/Circuit Coupling for the Simulation of Quenches in Superconducting Magnets

In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial differential model and an electrical lumped-element circuit. Such a multi-physics, multi-rate and multi-scale problem requires a consistent formulation and a dedicated framework to tackle the challenging transient effects occurring at both circuit and magnet level during normal operation and in case of faults. We derive an equivalent magnet model at the circuit side for the linear and the non-linear settings and discuss the convergence of the overall scheme in the framework of optimized Schwarz methods. The efficiency of the developed approach is illustrated by a numerical example of an accelerator dipole magnet with accompanying protection system.

Exfoliated YBCO filaments for second-generation superconducting cable

The second-generation high temperature superconductor (2G HTS) wire is the most promising conductor for high-field magnets such as accelerator dipoles and compact fusion devices. The key element of the wire is a thin Y1Ba2Cu3O7 (YBCO) layer deposited on a flexible metal substrate. The substrate, which becomes incorporated in the 2G conductor, reduces the electrical and mechanical performance of the wire. This is a process that exfoliates the YBCO layer from the substrate while retaining the critical current density of the superconductor. Ten-centimeter long coupons of exfoliated YBCO layers were manufactured, and detailed structural, electrical, and mechanical characterization were reported. After exfoliation, the YBCO layer was supported by a 75 μm thick stainless steel foil, which makes for a compact, mechanically stronger, and inexpensive conductor. The critical current density of the filaments was measured at both 77 K and 4.2 K. The exfoliated YBCO retained 90% of the original critical current. Similarly, tests in an external magnetic field at 4.2 K confirmed that the pinning strength of the YBCO layer was also retained following exfoliation.

Mechanical Design of FECD1 at IHEP: a 12-T Hybrid Common-coil Dipole Magnet

A 12-T Nb3Sn/NbTi common-coil dipole magnet with the outer diameter of 720 mm is under development as the first R&D step towards the final 20-T accelerator dipole magnet which is required in the Super proton-proton Collider. This Flat End Common-coil Dipole magnet is based on the shell support structure with the bladder & key technology. The designed peak field is 12-T in the Nb3Sn inner coil at the operating current of 3,970 A, with a margin of 18.4% at 4.2 K. The coil structure is optimized to enhance the transfer efficiency of horizontal preload and the central magnetic field. The aluminum alloy tie rod is used to apply axial preload to the coils. The stress in the whole dipole magnet is below an acceptable level when the shell thickness is 60 mm and the friction coefficient is 0.2. The coil displacement after excitation is below 8 μm. Further analysis indicates that a larger shell thickness may increase the cold shrinking force and a larger friction coefficient value can lead to the rise of peak coil stress.

Magnetic and structural design of a 15 T Nb3Sn accelerator dipole model

Hadron Colliders (HC) are the most powerful discovery tools in modern high energy physics. A 100 TeV scale HC with a nominal operation field of at least 15 T is being considered for the post-LHC era. The choice of a 15 T nominal field requires using the Nb3Sn technology. Practical demonstration of this field level in an accelerator-quality magnet and substantial reduction of the magnet costs are the key conditions for realization of such a machine. FNAL has started the development of a 15 T Nb3Sn dipole demonstrator for a 100 TeV scale HC. The magnet design is based on 4-layer shell type coils, graded between the inner and outer layers to maximize the performance. The experience gained during the 11-T dipole R&D campaign is applied to different aspects of the magnet design. This paper describes the magnetic and structural designs and parameters of the 15 T Nb3Sn dipole and the steps towards the demonstration model.

2D Analytical Magnetic Optimizations for Accelerator Dipole Block Designs

A new magnetic design method, which optimizes the position of the conductors in the cross-section of a race-track-shaped magnet, has been set up. This method is based on the computation of analytical formulas of field, harmonics and forces. The conductors are modeled with rectangles, which is particularly well adapted to a block design. A first equation is used to calculate the contribution of the rectangles, as a function of their four spatial coordinates. All the block contributions are then added up to give the entire equation as a function of all the rectangles coordinates. Finally a non-linear optimization, using the analytical formulas, computes these coordinates to fulfill the magnet specifications. The objective can be either to maximize the central field, or to minimize a criterion, for instance the conductor volume, the harmonics, the electromagnetic forces. Various kinds of constraints can also be imposed: zeroed harmonics, blocks position and number, central field. Two magnets designs are proposed as practical examples: a 13 T Nb3Sn magnet and a 20 T graded magnet.

Design Study and Test Arrangement of HTS Transmission Line Power Cable for Fast Cycling Accelerator Magnets

Designs of the HTS transmission line power cable and the matching magnetic core for a fast-cycling accelerator dipole magnet are presented. The hysteretic and eddy currents induced power losses of the proposed HTS cable operating under various sweeping magnetic fields are projected and compared to those of the LTS cable in similar applications. The engineering design of the HTS power cable for the fast cycling dipole magnet is presented, and the test arrangement of a short-sample cable operating under the sweeping magnetic field is described.