Accelerator Magnets Research Articles

Improving critical current density of Nb3Sn by optimizing pinning potential of grain boundary and grain size

Nb3Sn superconductor is of significant interest for applications in constructing high-field magnets beyond the limit of NbTi. However, its critical current density decreases rapidly at high magnetic fields (12 T) and the state-of-the-art level of Nb3Sn superconductors still cannot meet the requirements of the planned future accelerator magnets. The primary flux pinning centers for Nb3Sn wire mainly arise from the grain boundaries (GBs). In the present paper, we theoretically investigate, through time-dependent Ginzburg-Landau theory and with graphics-processing unit parallel technique, the vortex pinning and the critical current density in large-scale polycrystalline Nb3Sn superconductor by varying the pinning potential of GB and grain size at various magnetic fields. Unlike the conventional dot-like pinning systems, it is found that the critical current is not a monotonous function by suppressing the superconductivity of the GBs. The optimal pinning potential of GB for maximum critical current density strongly depends on magnetic fields. Furthermore, we find that the critical current density can be significantly enhanced by reducing grain size at low magnetic fields, while increase of critical current density cannot always be observed at high magnetic fields. Actually, critical current density even decreases by reducing grain size, which depends on the superconductivity of GBs. The findings in the paper provide theoretical foundations to achieve further improvement of Nb3Sn with optimizing the flux pinning.

Using additive manufacturing technologies in high-field accelerator magnet coils

Recent advances with additive manufacturing (AM) technologies using various materials allow them to be considered for the manufacture of precise and complicated metal parts of the magnet coils of high field accelerator magnets from aluminum bronze, titanium alloy, stainless steel, etc. The 3D printing technology is also being used to fabricate prototype models of real parts to test and optimize their geometry. This paper discusses the designs of the complex stress-management coil parts developed at Fermilab, their fabrication using AM technologies, and quality control methods and results.

Improved training in paraffin-wax impregnated Nb3Sn Rutherford cables demonstrated in BOX samples

Resin-impregnated high-field Nb3Sn type of accelerator magnets are known to require extensive training campaigns and even may exhibit performance-limiting defects after thermal or electromagnetic cycling. In order to efficiently explore technological solutions for this behaviour and assess a wide variety of impregnation material combinations and surface treatments, the BOnding eXperiment (BOX) sample was developed. BOX provides a short-sample test platform featuring magnet-relevant Lorentz forces and exhibits associated training. Here we report on the comparative behaviour of BOX samples comprising the same Nb3Sn Rutherford cable but impregnated either with common resins used in high-field magnets, or with less conventional paraffin wax. Remarkably, the two paraffin wax-impregnated BOX samples reached their critical current without training and are also resilient to thermal and mechanical cycling. These rather encouraging results strongly contrast to those obtained with resin impregnated samples, which show the characteristic extensive training and at best barely reach their critical current value.

Application of high order symplectic integration methods with forward integration steps in beam dynamics

The Hamiltonian describing particle motion in an accelerator belongs to a large class of systems, the members of which can be integrated with a new set of high order symplectic integrators. One benefit of these integrators is their strong numerical stability, which results from the inclusion of only forward integration steps, independent of the order of accuracy. Using these integrators, the transfer map of any multipolar accelerator magnet is derived and presented here. From these maps, the Hamiltonian flow in different lattices is simulated and benchmarked against other well established integration schemes in the accelerator community. By comparing quantities such as the linear phase advance and action invariant, the chromaticity, as well as the working point and the tune spread with amplitude, the superiority of the novel symplectic integrators is demonstrated with respect to accuracy and integration cost.

Multi-scale nonlinear stress analysis of Nb3Sn superconducting accelerator magnets

A multi-scale nonlinear procedure to analyze the stress in Nb3Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets—the issue of stress management. The study demonstrates that gasket materials (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb3Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb3Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb3Sn coil was simulated, in three orthongonal axes, using the combined properties of the gasket materials (insulation layers) and Hill materials (resin-impreganted cable). The procedure makes very few assumptions with regard to material properties because it incorporates actual measured stress–strain curves in the analysis. The coil was simulated to the level of detail of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb3Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb3Sn magnets, this versatile procedure can also be employed in the design of LTS, HTS, and room temperature magnets or of any structures ultilizing composite materials; specifically, it can be used to manage the stress and strain of HTS fusion magnets.

A novel positioning method for Hall magnetic field measurement of heavy ion accelerator

In the magnetic field measurement of accelerator magnets, the precise positioning of the magnetic field measurement system and the magnet is a basic and very important part. By analyzing the mechanical structure and working principle of Hall magnetic field measurement system, a novel positioning method is proposed in this research for the high-precision and fast positioning of magnet and Hall magnetic field measurement system. By measuring the geometric elements of the magnetic field measurement system and the calibration benchmark of the magnet, the geometric relationship between the magnetic field measurement system and the magnet is established, so as to quickly locate the magnet to the position and attitude required by the magnetic field measurement. The mechanical structure of the Hall probe of the magnetic field measurement system is optimized. Two special ceramic reflectors are installed on the vertical and horizontal axes corresponding to the center of the Hall sensor, and the two ceramic reflectors installed on the Hall probe is monitored with a laser tracker. In this way the Hall sensor can be intuitively positioned at the geometric center of the magnet with an accuracy better than 0.05 mm. In the measurement process, the magnetic field measurement trajectory of Hall sensor in the magnet can also be detected by monitoring the coordinates of ceramic reflector in real time. The practical application in Space Environment Simulation and Research Infrastructure (SESRI) magnet magnetic field measurement show that, compared with the traditional positioning method, the proposed positioning method not only improves the repeatability of Hall magnetic field measurement integral field by nearly 10 times, but also improves the positioning efficiency of magnetic field measurement. These results have verified the practicability and effectiveness of the proposed positioning method.

Hybrid modeling: towards the next level of scientific computing in engineering

The integration of machine learning (Keplerian paradigm) and more general artificial intelligence technologies with physical modeling based on first principles (Newtonian paradigm) will impact scientific computing in engineering in fundamental ways. Such hybrid models combine first principle-based models with data-based models into a joint architecture. This paper will give some background, explain trends and showcase recent achievements from an applied mathematics and industrial perspective. Examples include characterization of superconducting accelerator magnets by blending data with physics, data-driven magnetostatic field simulation without an explicit model of the constitutive law, and Bayesian free-shape optimization of a trace pair with bend on a printed circuit board.

Tomography analysis tool: an application for image analysis based on unsupervised machine learning

We developed a graphical user interface (GUI) to analyse tomographic images of superconducting Nb3Sn wires designed for the next generation accelerator magnets. The Tomography Analysis Tool (TAT) relies on the k-means algorithm, an unsupervised machine learning technique which is widely used to partition images into separated clusters. The GUI is compatible with both Linux and Windows operating systems. The software reliability was tested by optical inspecting the tomographic images superimposed on the clustered image obtained by the k-means algorithm. TAT was proven to correctly segment the various components of the Nb3Sn superconducting wires with single pixel precision. Finally, this software can be a useful tool for the scientific community to segment and analyse quickly and reproducibly tomographic images.

Iron lamination and interlaminar insulation for high-frequency pulsed magnets.

In high-frequency pulsed magnets, such as kickers in particle accelerators, it is essential to reduce eddy currents that could be induced in the magnet core during excitation not to distort and attenuate the magnetic field pulse. A novel iron lamination scheme with additional interlaminar insulation is proposed for the magnet core of such pulsed magnets. A laminated steel sheet core is formed by alternately stacking thin steel and insulation sheets. For application to matched kicker magnets for accelerators, test magnets with the new and conventional iron lamination were designed, assembled, and extensively evaluated. The pulsed magnetic field waveforms of two test magnets with the new lamination successfully matched to below 0.1% over the entire pulse duration, which was significantly better than those with the conventional lamination. Among the applications of the developed high-frequency pulsed magnets, beam injection kickers for the coming next generation light sources and future colliders, where suppression of the transient stored-beam oscillation during beam injection is crucial, are considered to be promising.

Study on Internal Strain Distribution of the High-Field Nb₃Sn Superconducting Accelerator Magnets With Homogenization Theory

To fabricate 10–16 Tesla high-field accelerator magnets, the high-Jc Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn superconductor is one of the most practical choices. However, it is a brittle material and is strain-sensitive. To reduce the potential Jc degradation of the conductor, it is crucial to accurately evaluate the stress of the coils owing to the large Lorentz force during magnet excitation. In the traditional stress analysis of magnets, the coils are usually regarded as homogenized structures using isotropic material coefficients; however, most superconducting (SC) coils have hierarchical and complicated structures. To obtain a more accurate estimation, it is necessary to consider the detailed internal structure of the coils during stress analysis. In this study, the homogenization method was applied to multi-scale stress analysis of a high-field accelerator SC magnet. The effective material coefficients of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn coils were calculated using this method. Stress analysis of the magnet was performed using the effective material coefficients and isotropic material coefficients for comparison. Compared with the result obtained using isotropic material coefficients, the Von-Mises stress of the coil using effective material coefficients is larger at different load steps. The stress level of most Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments in the strand was higher than that of the coil. The maximum stress of the Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn filaments appeared in the strand contact regions. In addition, there was a significant difference in the average stress of all materials in the strand. These findings will help develop more accurate analysis and simulation models for high-field SC magnets.

Quench position reconstruction through harmonic field analysis in superconducting magnets

The performances of superconducting magnets for particle accelerators are limited by instabilities or disturbances which lead to the transition of the superconducting material to the normal resistive state and the activation of the quench protection system to prevent damage to the magnet. To locate the position of the state transition, voltage taps or quench antennas are the most commonly used technologies for their reliability and accuracy. However, during the production phase of a magnet, the number of voltage taps is commonly reduced to simplify the construction process and quench antennas are generally used only for dipoles or quadrupoles to limit the antenna design complexity. To increase the accuracy in the reconstruction of the quench event position, a novel method, suitable for magnets with independent superconducting coils and quench protected without the use of quench heaters, is proposed in this paper. This method, based on standard magnetic measurement techniques for field harmonic analysis, can locate the position of the superconductor transition inside the magnet after the quench event when the magnet has been discharged. Analyzing the not allowed harmonics produced in the field quality at zero current, the position of the quenched coils can be retrieved for any magnet orders without increasing the complexity of the dedicated measurement technique.

Experimental Study On the Critical Current of CORC Cable Under Cyclic Bending-straightening

To develop the application potential of conductor on round core (CORC) cables in the next generation of fusion magnets and accelerator magnets, fully automatic mechanized winding technology is required for the long CORC cables manufacturing. Meanwhile, the manufacturing and usage of the CORC cable are both limited by the strain sensitivity of the wound ReBCO tape on the CORC cable, because the processes may cause the superconducting layer of the ReBCO tape damaged when the strain limit is exceeded. The strains can arise from the manufacturing, bending, cooling, and operation of the cable and magnet, especially for the needed cyclic bending-straightening procedure for a long and multilayer cable winding layer by layer. Thus in this manuscript, a 1-m-long 12-layer CORC cable was manufactured to study the influence of cyclic bending on the critical current carrying performance of the CORC cable. It is consisted of 28 ReBCO tapes from Fujikura with 4 mm width and 0.05mm substrate thickness. The central core has an outer diameter of 3.85 mm. The cyclic bending-straightening experiment was conducted with a bending diameter of 900 mm and 700 mm, the Ic was tested at 77 K and self-field. After the cyclic bending test, the sample was bended to a diameter of 95 mm, which is planned to be used for the following insert solenoid coil, and has been verified no influence on the critical current carrying performance if bended without cyclic bending-straightening treatment. The results show that the required diameter for the reel experiencing cyclic bending-straightening procedure for ReBCO cable winding is suggested to be larger than 700 mm, especially for the equipment used for multilayer cables winding.

Quasi-3-D spectral wavelet method for a thermal quench simulation

The finite element method is widely used in simulations of various fields. However, when considering domains whose extent differs strongly in different spatial directions a finite element simulation becomes computationally very expensive due to the large number of degrees of freedom. An example of such a domain are the cables inside of the magnets of particle accelerators. For translationally invariant domains, this work proposes a quasi-3-D method. Thereby, a 2-D finite element method with a nodal basis in the cross-section is combined with a spectral method with a wavelet basis in the longitudinal direction. Furthermore, a spectral method with a wavelet basis and an adaptive and time-dependent resolution is presented. All methods are verified. As an example the hot-spot propagation due to a quench in Rutherford cables is simulated successfully.

Cable Design and Development for the High-Temperature Superconductor Cable Test Facility Magnet

A large bore “High-Temperature Superconductor Cable Test Facility Magnet” for testing advanced cables and inserts in high transverse field is in its design phase. This magnet will be the core component of a facility for developing conductors and accelerator magnets operating above 15 T, an enabling technology for next-generation fusion devices using magnetic confinement of plasma and for future energy frontier colliders. The procurement of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn conductor, fabrication of cables, winding of coils, and assembly of the dipole magnet will be done at Lawrence Berkeley National Laboratory (LBNL) and the test pit and cryostat will be constructed at Fermi National Accelerator Laboratory. This article will present the conductor element of the LBNL project, specifically cable design parameters (based on the Bruker OST RRP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{\bigcirc \!\!\!\! {\hbox{R}}}$</tex-math></inline-formula> Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn superconducting wire) and the development phase cable fabrication experience. Challenges of the cable fabrication will be discussed. The wire and cable planned for this magnet are similar to those under study for the Future Circular Collider and other large facility magnets. The successful fabrication of the development cable has positive implications for these other projects.

Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

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.

High-temperature superconducting screens for magnetic field-error cancellation in accelerator magnets

Accelerators magnets must have minimal magnetic field imperfections to reduce particle-beam instabilities. In the case of coils made of high-temperature superconducting (HTS) tapes, the magnetization due to persistent currents adds an undesired field contribution, potentially degrading the magnetic field quality. In this paper we study the use of superconducting screens based on HTS tapes for reducing the magnetic field imperfections in accelerator magnets. The screens exploit the magnetization by persistent currents to cancel out the magnetic field error. The screens are aligned with the main field component, such that only the undesired field components are compensated. The screens are self-regulating, and do not require any externally applied source of energy. Measurements in liquid nitrogen at show for dipole-field configurations a significant reduction of the magnetic field error up to a factor of four. The residual error is explained via numerical simulations accounting for the geometric defects in the HTS screens, achieving satisfactory agreement with experimental results. Simulations show that if screens are increased in width and thickness, and operated at , field errors may be eliminated almost entirely for the typical excitation cycles of accelerator magnets.

Quench Detection and Protection for High-Temperature Superconductor Accelerator Magnets

High-temperature superconductors (HTS) are being increasingly used for magnet applications. One of the known challenges of practical conductors made with high-temperature superconductor materials is a slow normal zone propagation velocity resulting from a large superconducting temperature margin in combination with a higher heat capacity compared to conventional low-temperature superconductors (LTS). As a result, traditional voltage-based quench detection schemes may be ineffective for detecting normal zone formation in superconducting accelerator magnet windings. A developing hot spot may reach high temperatures and destroy the conductor before a practically measurable resistive voltage is detected. The present paper discusses various approaches to mitigating this problem, specifically focusing on recently developed non-voltage techniques for quench detection.

The Magnetization of Bi:2212 Rutherford Cables for Particle Accelerator Applications

High temperature superconductors, including Bi:2212, are being considered for high magnetic field magnets to be used in particle accelerators. A knowledge of HTS magnetization properties are needed for calculating field errors in such accelerator magnets. Here we present magnetic measurements of a 17 strand Bi:2212 Rutherford cable. The Bi:2212 strand was a Bruker OST PMM170123 non-twisted wire wound into a cable with dimensions 1.46 mm x 7.8 mm and cable pitch of 50.8 mm. M-H loop measurements were made with a Hall probe at 4.2 K. Two calibration methods were compared, (i) a flux exclusion approach, and (ii) a Ni replacement technique. The latter was found to be more reliable in this case. An effective filament diameter of 358 μm was calculated for the strand at 4.2 K and a perpendicular applied field of 3.33 T, significantly larger than the diameter of the filament bundle. Magnetization values at 1 T on the shielding branch were seen to be 100 kA/m when normalized to the total strand in the cable volume. The penetration field ≅ 0.4 T.

Progress on Tests on Splices Between Nb3Sn Rutherford Cables for Graded High-Field Accelerator Magnets

Future high-field accelerator magnets foresee the extensive use of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn, more expensive than the Nb-Ti of LHC. For projects involving the series production of magnets, conductor grading is mandatory in order to reduce the cost. To allow grading, a splice between higher and lower grade cables must be implemented. The internal splice option, i.e., embedded in the winding pack, is the one considered in this manuscript. The magnet technology is Wind&React (W&R). The target resistance is 1 nΩ at a background field of B≈10 T and ratio between operational and critical current I/I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ≈1/3, the one at which such Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn dipoles are expected to work. This manuscript reports progress on ultrasonically welded, soldered and diffusion-bonded splices. The feasibility studies on ultrasonic welding between Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn Rutherford cables and strands is presented. The potential corrosive effect of fluxing agents of impregnated soldered samples is examined. In the end, the design and test in SULTAN of bent diffusion-bonded splices is reported.

Application of CMM Technology in Accelerator Magnet Detection

Application of CMM Technology in Accelerator Magnet Detection