Racetrack Coils Research Articles

3D homogenization of the T-A formulation for the analysis of coils with complex geometries

The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing improvements, and computing quantities that are not easy to calculate with an analytical approach. For instance, the estimation of losses in HTS is fundamental during the design stage since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D finite element analysis is used to calculate AC losses in HTS, due to the lack of analytical solutions that can accurately represent complex operating conditions, such as AC transport current and AC external applied magnetic field in coils. These 2D models are usually a representation of an infinitely long arrangement. Therefore, they cannot be used to analyze end effects and complex 3D configurations. In this publication, we use the homogenization of the T-A formulation in 3D for the analysis of superconducting coils with complex geometries where a 2D approach cannot provide accurate analyses and verification of assumptions. The modeling methodology allows an easier implementation in commercial software (COMSOL Multiphysics) in comparison with the currently available 3D H homogenization, despite the complexity of the geometry. This methodology is first validated with a racetrack coil (benchmark case) by comparing the results with the well-established H formulation. Then, the electromagnetic behavior of coils with more complex geometries is analyzed.

Measurement of AC loss down to 25 K in a REBCO racetrack coil for electrical aircraft motor

The development of full superconducting motors for electric distributed aircraft propulsion requires to test the stator coils at the operation temperature, usually between 20 and 40 K. Here, we study the AC loss of a test racetrack coil made of REBCO tape. We developed a measurement system within a non-metallic cryostat where a cryocooler cools the test coil in combination with liquid or solid nitrogen. We present transport AC loss measurements by electrical means down to 25 K for current amplitudes up to 140 A and frequency 18–576 Hz. The AC loss increased with second power with current, and did not depend on frequency or temperature. Later, we measured the AC parallel magnetization loss in a stack of tapes made of the same material as the coil, and in a stack of tapes without superconducting layer. The results in both samples is almost identical and presents the same behavior as the coil. We conclude that the main contribution to the AC loss in the tape stack and in the coil was from the magnetism of the Hastelloy substrate or buffer layers. Therefore, researchers need to take this into account in tape production and in superconducting motor design.

REBCO Trapezoidal Armature Windings for Superconducting Induction Motors

For extensive use in electric vehicles, electric airplanes, and other such applications, superconducting motors are designed to be lightweight and have a high power density. Rare-earth barium copper oxide (REBCO) tapes are considered a potential material for use in these motors because of their high critical current density. Because REBCO can be modeled into tape shapes, motors with racetrack coils as armature windings have been studied. However, racetrack coils are inferior in terms of increasing the interlinkage flux to the rotor compared with distributed windings. In this study, we propose trapezoidal REBCO tape coils for shaping armature windings into distributed windings. Next, 2 kW-class induction motors using two types of coils—the trapezoidal and racetrack coils—were designed to compare the characteristics of the two motors. The JMAG-Designer software was used to perform electromagnetic simulations on the two models. The results revealed that the motor with trapezoidal coils required less REBCO tapes and exhibited a lower vertical component of magnetic flux density than the racetrack coils did. Therefore, the AC loss of the trapezoidal coils becomes lower than that of the racetrack coils, and the trapezoidal coils weigh less than racetrack coils.

Design and Optimization of the Superconducting Quadrupole Magnet Q1a in CEPC Interaction Region

To study the properties of Higgs, scientists from the Institute of High Energy Physics have proposed to build the Circular Electron Positron Collider (CEPC) and published a conceptual design report in 2018. In order to improve the collision luminosity of CEPC, the upgrade of the final focus system in the interaction region is on-going. According to the latest physical requirements of superconducting magnets in the CEPC interaction region, a high gradient, double-aperture quadrupole magnet Q1a is required, which is 1.9 m from the interaction point. In this paper, we present the magnetic design of superconducting quadrupole magnet Q1a, and discuss the advantages and disadvantages of the three kinds of quadrupole coil structures, including cos2θ coil, CCT coil, and racetrack coil. Low-temperature superconductor NbTi is used in our magnet design process. In addition, optimization is performed to greatly reduce the weight of the magnet.

3-D Modeling of Current Decay in a Closed HTS Racetrack Coil Under Traveling Magnetic Fields

High temperature superconducting (HTS) magnets working in persistent current mode (PCM) have shown a superior potential in electrodynamic suspension (EDS) train applications. When exposed to the external traveling magnetic fields generated by the propulsion coils, the on-board HTS coils used as the secondary of synchronous motor will suffer a non-negligible loss resulting from dynamic resistance which is much larger than caused by joint resistance. In this work, we build a 3-D finite element model of a real scale HTS racetrack coil to predict its behaviour. In the modeling, homogenization technique and the symmetry plane are adopted for accelerating computation, and the proper boundary conditions are used for field-cooling excitation as well as applying traveling fields. Firstly, the effectiveness of the model has been validated by comparing with experimental results of a small prototype. Then based on the method, a real scale HTS racetrack magnet model with the symmetry modified as to adapt the EDS scenario is built for investigating the current decay property varying with the external fields. Moreover, the effect mechanism of the instantaneous AC loss on the current attenuation is deeply analyzed.

3D Conceptual Design of R2D2, the Research Racetrack Dipole Demonstrator

R2D2, the Research Racetrack Dipole Demonstrator, is a short model being developed within a collaboration between CEA Paris-Saclay and CERN. The goal of the program is to develop key technologies for future high field 16 T Nb3Sn magnets for particle colliders. In the particular case of block-coil designs, two different cable grades are wound in the same coil layer, in order to maximize the current density, therefore to minimize the size of the magnet and the use of superconductor. One of the most challenging technologies with this grading concept, is the connection between two cables grades. CEA Paris-Saclay has proposed a concept of external joints, for which the cable exits are guided outside of the coil to perform the connections between the cable grades. The R2D2 project is aimed at demonstrating this technology in a representative demonstrator magnet, while simplifying and reducing the risks when possible, as an intermediate step towards 16 T magnets. In particular, the magnet is composed of single-layer racetrack coils, mainly to reduce the use of conductor and simplify some fabrication steps. However, the complexity inherent to the external joints requires a special focus in the design of the coil ends. To do so, the design of the magnet has been performed using a combination of CAD (Computer Aided Design), magnetic and mechanical 3D FEM (Finite-Elements Models). This paper will explain the design choices leading to a safe operation of the magnet in terms of peak fields and peak stresses.

Modeling and Characteristic Analysis of Air-Cored Linear Synchronous Motors With Racetrack Coils for Electrodynamic Suspension Train

Air-cored linear synchronous motor (LSM) consisting of racetrack coils is a core part of electrodynamic suspension (EDS) as it propels train to realize high-speed running. Considering operating conditions, a precise and fast analysis of LSM is essential to investigate and optimize EDS system. An analytical model is proposed to calculate the magnetic field and 3-D forces of LSM with considering the sectional power supply of the primary and multi-degree-of-freedom (DOF) motions of EDS train. Afterward, the influence of sectional power supply was studied to acquire the ideal feeding position of balancing the stable thrust against the efficiency. The effects of multi-DOF motions on electromagnetic characteristics of LSM were analyzed by the proposed model and finite element model. The obtained results indicate that the lateral displacement of multi-DOF motions should be limited to ±28 mm and this model can simulate realistic operating conditions of superconducting LSM. Furthermore, the analytical model reduces the computation time by 96% with high accuracy compared with 3-D finite element model. Finally, experiments were performed to confirm the proposed model with measured magnetic field and forces.

Flux Creep in a Bi-2212 Rutherford Cable for Particle Accelerator Applications

Bi-2212 superconducting cables are being considered for use in the high field magnets needed for the next generation of particle accelerators. Magnetization in these cables and the decay of that magnetization lead to field error and field-error drift, respectively, which need to be compensated. To study this, a segment of the winding pack was extracted from a racetrack coil made from Bi-2212 Rutherford cable. Using a Hall probe measurement technique, we measured the response of the cable's magnetization and its magnetization decay to changes in the applied magnetic field. The effect of adjustments to the cycling of the magnetic field was studied, intended to simulate the preinjection cycles of an accelerator magnet. Three <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> vs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> loops were constructed by sweeping the magnetic field applied to the sample from 0 to 2.5 T, then to a preinjection field “x” (where x = 0, 0.25, 0.75 T), and finally up to 1 T. The applied field was then held at 1 T for 1500 s, and the magnetization decay was measured. The decay was found to vary from 8% to 14% after 1500 s, depending on the preinjection field cycle.

Charging Characteristics of 2G HTS Coils With Insulation, Metal-Insulation, Non-Insulation, and Smart-Insulation Using Circuit Simulations

This study aimed to compare and analyze the output characteristics of second-generation high-temperature superconducting racetrack coils with insulation, metal-insulation (MI), non-insulation (NI), and smart-insulation (SI). First, the output characteristics of each coil were experimentally validated, and circuit equations were examined to analyze these characteristics. The output characteristics were found to be affected by the turn-to-turn resistance. Circuit analysis was used to identify the nature of dependence of output characteristics on turn-to-turn resistance in addition to internal behavior and other mechanisms. In particular, an equation relating the output characteristics of the SI coil with temperature change was derived, and each coil model was simulated using the circuit equation. Then, the simulation results were analyzed, the advantages and disadvantages of each insulation method were discussed, and the validity of the simulation was confirmed. The circuit simulation proposed in this study is expected to facilitate advanced predictions in smart insulation material candidate groups.

Characteristics of 300-Turn Smart Insulation Race-Track Coil in External Fluctuating Magnetic Field

Experiments and finite-element analyses were conducted to investigate the characteristics of a 300-turn smart insulation (SI) coil coated with vanadium trioxide (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) placed in an external fluctuating magnetic field. The external fluctuating magnetic field generator was designed to allow sliding insertion through a fabricated non-rotating liquid-nitrogen tank inside the stator of a 1-MW superconducting rotating machine. The 300-turn SI coil was fabricated in a two-layer design with 150-turn windings in each layer. Experiments were conducted in such a manner that the SI coil did not rotate during the generation of the external fluctuating magnetic field owing to the rotating magnetic field of the stator. The SI coil with many turns showed no magnetic field delay because of the ramping time,thereby demonstrating controllability equivalent to that of a normal insulated coil. The stability of the SI coil was confirmed via repeated overcurrent tests, with and without an external fluctuating magnetic field.

An efficient HTS electromagnetic model combining thin-strip, homogeneous and multi-scale methods by T-A formulation

Recently, combination models, in which two or more advanced methods are employed, have been studied to explore various approaches to simulating large-scale ReBCO coils efficiently. However, modeling the combinations could be more complex if the methods are not integrated well. In this paper, an ingenious combination of thin-strip, homogeneous and multi-scale methods is presented. In particular, we build the thin strips as both the analyzed HTS tapes and the boundaries of the homogeneous bulks where the non-analyzed tapes are merged. Thus, the coil geometry is re-constructed with several bulks, but the bulks’ boundaries and domains are tackled with different electromagnetic properties, and solved by T and A formulations, respectively. Firstly, we introduce the modeling process and highlight the differences and advantages over the previous models. Then, the accuracy of the proposed model is validated by comparing the results with those from the reference model based on a 2000-turn coil. The distributions of normalized current density, magnetic flux density and hysteresis losses from the two models are highly consistent, and the error of the total loss is less than 1%. Besides, the combination model is the most time-saving among all the advanced models. Furthermore, the proposed method can be applied in 3D simulations, and the high accuracy and efficiency are validated by simulating a 50-turn racetrack coil. The study shows that the combination method is a feasible approach to simulating large-scale HTS coils, and can be a powerful tool to design and optimize HTS systems.

Thermal and electrical design of superconducting demonstrator for magnetic density separation

In this paper the focus is on thermal and electrical design aspects of a NbTi-based demonstrator magnet for magnetic density separation (MDS) that is being constructed at the University of Twente. MDS is a recycling technology that allows the separation of non-magnetic particles based on their mass density, using a vertical magnetic field gradient and a ferrofluid. To minimize the distance between the planar array of racetrack coils and the ferrofluid bath, the system is conduction-cooled. First the thermal design is presented, which shows that the coils can operate below 4.5 K with sufficient margin using a single cryocooler. High-purity aluminium heat drains enable a low thermal gradient across the cold mass. The current path is introduced, as well as the adopted protection scheme. The magnet’s stored energy can safely be dumped in the coils. Diodes are placed (anti-)parallel to the coils in the cold to prevent high terminal voltages. In the case of a quench in the superconducting part of the current leads or an external anomaly, a switch is opened and the current is forced through a resistor in series with the diodes, causing a deliberate transition of the coils to the normal state and thus a fast ramp-down.

Enhancement of the Unidirectional Radiation Pattern of Shear Horizontal Ultrasonic Waves Generated by Side-Shifted Periodic Permanent Magnets Electromagnetic Acoustic Transducers With Multiple Rows of Magnets

Shear horizontal (SH) guided waves are widely used in non-destructive evaluation and can be generated by permanent magnet electromagnetic acoustic transducer (PPM EMATs). PPM EMATs generate SH waves that propagate both forwards and backwards. This is often an undesirable characteristic. Unidirectional generation can be achieved by the interference mechanism produced by two independent sources. This, however, is non-feasible for the conventional PPM EMATs due to the arrangement of PPM array and racetrack coil. Recently, we presented a design of an SH EMAT with side-shifted PPM arrays that generates SH waves nominally in a single direction. Due to the shift of the produced wavefronts from each array, that design produced side-lobes in the backward semi-plane. In this paper, we enhance the unidirectional generation of SH waves with side-shifted PPM EMATs by evaluating the effect of the separation between individual arrays as well as the number of rows of magnets in each array. An analytical model is used to calculate the radiation pattern. The amplitude of the backward side-lobes decreases either with increasing the number of magnets rows or decreasing the lateral gap between rows. This behaviour is explained by the amount of wavefront misalignment introduced by each design. Increasing the number of magnets rows also increases the directivity and the energy of the forward generated waves. Twelve different configurations were fabricated, with a reasonably short wavelength of 12 mm, and experimentally evaluated, agreeing with the theoretically calculated radiation pattern. The magnitude of the backward side-lobes was roughly halved when compared with the original design.

Charging Optimization of a YBCO Racetrack Coil With a Linear-Motor Type Flux Pump for an HTS Synchronous Motor

This paper presents the preliminary charging test results of an high temperature superconducting (HTS) no-insulated (NI) double racetrack coil with the linear-motor type flux pump. The racetrack coil is designed and manufactured for the rotor field winding of a 16.9-kW-class HTS synchronous motor. This HTS synchronous motor was designed to employ a contactless static excitation device (CSED), i.e., the linear-motor type flux pump, which can charge the racetrack coil installed in the rotating machine in contactless manner. In the experiment, the major components of the 16.9-kW-class HTS synchronous motor, such as the racetrack coil and the CSED, had been manufactured, tested and optimized. The charging performance was tested in 77 K. In particular, we optimize the CSED of the HTS synchronous motor by testing different wavelengths of flux pumps and different superconducting stator wires, so as to select the appropriate wavelength of the flux pump and stator wire to optimize the operation of the synchronous motor.

Ramping Loss Analysis of No-Insulation HTS Coil Under External Field Using an Improved Equivalent Circuit Model

This article is to study the ramping loss of no-insulation (NI) high temperature superconducting (HTS) racetrack coil under different external magnetic fields during the charging process. An improved equivalent circuit electromagnetic coupling model for the HTS racetrack coil is introduced with good computational speed and accuracy. The simulation results show that the turn-to-turn loss and the change of the lowest critical current position are obviously influenced by the external field that have not been mentioned from our knowledge base. During the rising time of the power supply current, there is little difference in current distribution under different external fields. But after that, steady state of charging process is deeply influenced by the external field. A larger external field will lead to a lower charging current and the external bypass phenomenon. Another result is that the relationship between direction of external field and orientation of coils will influence the lowest critical current amount and position. The relationship between turn-to-turn resistivity of co-winding materials and ramping loss is also discussed in the paper. The distributed unevenness and value of the turn-to-turn loss change with the increase of turn-to-turn resistivity.

HTS Flux Pump Charging an HTS Coil: Experiment and Modeling

An HTS flux pump is an effective device to compensate the field decay in HTS magnets running in persistent mode. This paper contains updates to the model for the travelling wave HTS electromagnetic flux pump, in which the magnetization system is modelled as an L-R circuit. In this paper we consider the various sources of resistance. There are three components, joint resistance, resistance of superconductor and dynamic resistance. Joint resistance is treated as a constant. The superconducting resistance is derived from the E-J model and finally the dynamic resistance is a function of applied field strength and frequency. In addition the model includes the electromotive force which is a function of the applied field, frequency and surface area of the tape. This is a calculated value based on the φ model we built. In order to test the model, a series of experiments were performed in which an HTS coil was actuated using our flux pump. The flux pump test rig was made from 4-pair rectangular copper solenoids with laminated iron cores, which were fixed on the supporting iron frame. This rig was used to magnetize a double layer HTS racetrack coil at 77 K. The induced current in superconducting coil can reach more than 90% of critical current. Our model was found to be a good fit to the experimental data.

On the steerability of phased array EMATs: The dipole element

Shear wave phased array EMATs have a range of properties that make them a desirable solution compared to their piezoelectric counterparts: They do not require direct contact with the specimen and they can operate at elevated temperatures. Shear wave phased array EMATs do not need a Perspex wedge or couplant, making them easy to deploy across industrial applications even at elevated temperatures. Nonetheless, they are not commonly used because of concerns over the strength of signal excitation and lack of knowledge about potential changes in the emitted wavefields as a result of changes in the magnetic properties of the inspected material. In this work, a shear wave phased array EMAT designed to induce shear waves into paramagnetic, diamagnetic, ferromagnetic and ferromagnetic and magnetostrictive metals without compromising its angle coverage or steerability is proposed. The phased array EMAT was designed based on a dipole element wave generation source. The proposed dipole element source is formed by the interaction of the bias magnetic field of the PA EMAT and the electromagnetic field induced by the race-track coils of the PA EMAT. For each race-track coil this results in a combined source that consists of two parallel and slightly separated shear line sources of opposite polarity. A detailed study of the wave generation based on the surface loads induced by the dipole element is presented. The surface loads of the three excitation mechanisms involved in the EMAT transduction -Lorentz force, magnetisation force and magnetostriction force-were estimated in a 2D finite element model. The waves generated by the induced surface loads were estimated in a second 2D finite element model. A shear wave steerability analysis of the phased array EMAT on different metallic materials based on the 2D finite element results is presented in combination with an experimental evaluation on Aluminium 6082 (diamagnetic), mild steel EN1A (ferromagnetic), stainless steel 316 (paramagnetic), stainless steel 304 (paramagnetic) and nickel 201 (ferromagnetic and magnetostrictive). The experimental results showed good agreement with the simulation study. The simulation and experimental results concluded that the angle coverage of the phased array EMAT is almost insensitive to the inspected metallic material.

Mechanical design of a superconducting demonstrator for magnetic density separation

The focus of this paper is on the mechanical design of a NbTi-based demonstrator magnet for magnetic density separation (MDS) that is being constructed at the University of Twente. MDS is a new recycling technology that allows the separation of non-magnetic particles based on their mass density, using a vertical magnetic field gradient and a ferrofluid. The unique mechanical design challenge for this type of magnet is the desired minimization of the distance between a sim1 m2 planar array of cryogenic racetrack coils and the ambient-temperature ferrofluid bath. The optimization of the magnet geometry results in a distance between the coils and ferrofluid of 50 mm. This is made possible by opting for conduction-cooling, for the inclusion of room-temperature rods that pass through the cold mass to support the cryostat, and for the geometry of the cassette that reacts to the Lorentz force.

3D finite element modelling on racetrack coils using the homogeneous T-A formulation

High temperature superconducting (HTS) coated conductors (CCs) hold a promising feature in use of manufacturing kinds of magnets, coils, cables and so on. Its advantage on large-current-transporting capacity makes it suitable in MW-class machines and other large power electrical applications. In most situations, corresponding simulations were modeled in a 2D architecture. While, more complicated influences on ends of machines have been ignored artificially due to the simplification on model dimensions and huge expanses on the computational time. Therefore, comprehensive and full-scale models, which cannot easily be simplified as 1D or 2D representations, are urgent to analyze their electromagnetic behaviors in the early-stage design with an acceptable speed. In this paper, we propose a homogeneous T-A formulation for the 3D racetrack coil for the first time, which is treated as an anisotropic bulk-like equivalent to be modeled. Only the superconducting layer of HTS CCs has been preserved and other layers are ignored while still retaining its electromagnetic characteristics. This method in this paper has been fully verified with the widely accepted H formulation. However, the computational expense in T-A model is more than that of H model. At last, AC loss of a manufactured HTS double racetrack coil of one synchronous generator was measured and its experimental results are in good agreements with numerical profiles. This work has a guiding significance to accelerate the pace of 3D model and simulation in HTS applications.

Stray-Capacitance As a Simple Tool for Monitoring and Locating Heat Generation Demonstrated in Three Superconducting Magnets

Real-time monitoring of heat loads in cryogenic systems is critical for many applications, particularly high field magnets. We demonstrated that by monitoring changes in the capacitance of local probes consisting of thin metal strips with a porous glass fiber dielectric, boiling helium from as little as 0.1 J of deposited heat can be located by an analysis of the response speed and amplitude in nearby probes. We further implemented stray-capacitance monitoring of a magnet's metal support structures, a more global probe of the magnet volumes, in three high temperature superconducting Bi-2212 magnet types. Global structural stray-capacitance monitoring was evaluated for a single racetrack coil, a common coil dipole, and a canted cosine theta winding, showing a quench response comparable to voltage signals without inductive effects. The response of the local and global probes was compared in the single racetrack coil with well-known quench properties. Monitoring the cool-down of the common coil dipole demonstrated the added benefit of the global stray-capacitance as a liquid level monitor. This simple method of monitoring the capacitance has proven to be a versatile and robust technique for monitoring and locating heat.