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(RE)-Ba-Cu-O ring bulks, used as trapped field magnets, show great promise as a compact and lightweight source for generating the magnetic fields required for nuclear magnetic resonance (NMR). The inhomogeneities introduced by the growth pro-cess of such bulks pose a challenge to the required field uniformity for NMR. In this study, we model a stack of ring bulks with varying ab-plane inhomogeneity and orientation to investigate the impact on the trapped field profile following field cooled magnetization. For a pair of rings, by offsetting the growth sector boundaries (GSBs), the inhomogeneity of the circumferential field at the mid-plane can be reduced by up to 65% compared with aligned GSBs, for less than 0.4% reduction in the central trapped field strength. Using two pairs of rings allows for the generation of a larger homogeneous region at the center of the bore, with a lower peak-peak variation across the measuring volume. The relative harmonic weighting of the field moves to higher orders, requiring more complex shimming coils to correct the residual field.

Funder: Engineering and Physical Sciences Research Council (EPSRC), Funder: W.D. Armstrong, When used as trapped field magnets (TFMs), single grain, bulk high-temperature superconducting (HTS) rings are promising candidates for the generation of strong, uniform magnetic fields for nuclear magnetic resonance. The pulsed field magnetisation (PFM) technique provides a low cost, compact and portable method to magnetise these samples as TFMs; however it has proven difficult to achieve high trapped fields in HTS rings using PFM. To date, a record field of only 0.60 T has been achieved for rings magnetised by single-pulse PFM—compared with over 4 T for disc-shaped HTS—and the reasons for this discrepancy are poorly understood. In this work, we use the finite element method to model the propagation of magnetic flux into HTS rings under quasi-static zero field cooled magnetisation and PFM, and validate the results analytically and experimentally. Magnetic flux is found to penetrate finite HTS rings from both the inner and outer surfaces, inducing a negative field at the inner face of the ring. This field is reversed as the applied field increases past the point of full penetration, locally dissipating magnetic energy and heating the sample. HTS rings are therefore more susceptible to local instabilities that severely limit their ability to trap a useful magnetic field. Consequently, thermomagnetic stability of HTS rings during single-pulse PFM can only be ensured by taking careful consideration of reducing flux movement through the bulk around the point at which the field is reversed. This may require more advanced PFM techniques like waveform control or multi-pulse stepwise-cooling to reduce local heating and increase the trapped field.

International audience; The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. It could be used, for example, to energise rotor windings in superconducting rotating machines without the need for connection to a power supply via current leads. A number of different numerical models have now been developed as useful and cost-efficient tools to further examine and explain experimental results, as well as optimise and improve flux pump design. To adequately compare the different modelling tools available, we propose a new benchmark numerical model for the HTS modelling community: the HTS dynamo. In this work, this benchmark problem is implemented using several different methods: (1) coupled H-A formulation, (2) H-formulation + shell current, (3) segregated H-formulation, (4) Minimum Electromagnetic Entropy Production (MEMEP), (5) coupled T-A formulation, (6) integral equation and (7) volume integral equation-based equivalent circuit. These different techniques are used to solve the benchmark problem and compared in terms of computational requirements, ease of use and the solutions obtained with reference to each other, as well as experimental measurements.

International audience; e have developed a 3D model for HTS ring shape magnets using homogenised 3D H formulation. Every ten HTS rings are homogenised into one domain in order to speed up the calculation. We have compared the simulation results to experiments performed using field cooling. The model agrees well with experimental results. We then use the model to guide the design of large HTS ring magnets for MRI application

International audience; The interactions between a permanent magnet (PM) and a coated conductor tape lies at the heart of several types of high-temperature superconducting (HTS) devices, including the HTS dynamo. The applied magnetic field from a PM is typically highly spatially inhomogeneous with large field gradients occurring near the edges of the PM. This situation differs substantially from the well known Brandt analytical model, which describes flux penetration and current behaviour of type-II supercon- ducting strips in a spatially-homogeneous applied magnetic field. The Brandt model also assumes the superconductor exhibits a constant critical current (Jc) throughout, and hence does not take into account the more complex behaviour of practical HTS tapes which exhibit an angular magnetic field-dependence of the critical current, Jc(B,θ). In this work, a finite-element model is developed to include such considerations and describe the interaction between a permanent magnet and an HTS coated-conductor wire at small flux gap distances similar to those used in the HTS dynamo. The effect of varying key parameters is studied including: (1) changing the critical current, (2) including an anisotropic magnetic field dependence to the critical current density, (3) changing the relative width of the PM to the coated conductor tape, and (4) changing the flux gap between the magnet and the HTS tape. The effects on the flux penetration and current behaviour of the HTS tape are calculated and compared to the Brandt model. Of particular interest are the key differences in the flux penetration profile which are observed when the magnet width is much smaller than the width of the coated conductor tape.

A high-Tc superconducting (HTS) dynamo enables the injection of large DC currents into a superconducting circuit, without the requirement for current leads. In this work, we attempt to explain the frequency dependence of such dynamos/flux pumps reported in the literature, where it is observed that the rate at which the open-circuit DC voltage increases reduces with increasing frequency, in contrast to the expected linear behaviour. Heat generated in the HTS wire has been the common explanation given to date for this phenomenon. Here we offer an alternative explanation: the interaction between and current flow in the different layers of the HTS wire as the frequency of the dynamo increases. Our claim is based on numerical analysis using a segregated H-formulation finite-element model of the HTS dynamo benchmark problem that is extended to include the full HTS wire architecture and coupled with a thermal model. This framework enables us to efficiently model the relative movement between the rotating room-temperature permanent magnet and the stationary HTS wire and to study the impact of the frequency of rotation and temperature on the open-circuit DC voltage of the dynamo.

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. A critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model., 22 pages, 7 figures, 2 tables

A backward computation method has been developed to accelerate modelling of the critical state magnetization current in a staggered-array bulk high-temperature superconducting (HTS) undulator. The key concept is as follows: i) a large magnetization current is first generated on the surface of the HTS bulks after rapid field-cooling (FC) magnetization; ii) the magnetization current then relaxes inwards step-by-step obeying the critical state model; iii) after tens of backward iterations the magnetization current reaches a steady state. The simulation results show excellent agreement with the H-formulation method for both the electromagnetic and electromagnetic-mechanical coupled analyses, but with significantly faster computation speed. Solving the FEA model with 1.8 million degrees of freedom (DOFs), the backward computation method takes less than 1.4 hours, an order of magnitude or higher faster than other state-of-the-art numerical methods. Finally, the models are used to investigate the influence of the mechanical stress on the distribution of the critical state magnetization current and the undulator field along the central axis., 12 pages, 7 figures

Dynamic resistance is observed in type-II superconductors carrying a DC transport current while simultaneously exposed to an alternating magnetic field. The appearance of a non-zero resistance is attributed to the interaction between the transport current and moving fluxons. This effect is relevant to many superconductor applications such as high-temperature-superconductor (HTS) flux pumps, DC/AC magnets, synchronous machines, and persistent current switches. Here, we present a finite element method (FEM) analysis of both the time averaged dynamic resistance and the instantaneous current sharing behaviour in a cable comprised of a stack of four YBCO thin films connected in parallel. Numerical modelling was performed using the H -formulation method implemented in the commercial software COMSOL. The model employs experimentally measured values of the angular dependence of the critical current I c( B, θ ) and the flux creep exponent n ( B, θ ). A single threshold field is observed, above which a finite dynamic resistance is observed in all tapes simultaneously. The time-averaged dynamic resistance of individual tapes tends to be larger for the exterior tapes than the interior tapes, but this difference decreases as the total transport current in the cable increases. We attribute this to shielding currents flowing in the exterior tapes during the majority of the cycle, which displace net DC current into the interior tapes. However, the relative proportion of DC transport current flowing in the exterior and interior tapes is also observed to vary periodically once per half cycle of the applied field. This is due to the periodic trapping of return screening currents in the interior tapes.

Contributed talk at the European Conference on Applied Superconductivity (EUCAS) 2019, Glasgow, UK.

The development of a new hard x-ray beamline I-TOMCAT equipped with a 1-meter-long short-period bulk high-temperature superconductor undulator (BHTSU) has been scheduled for the upgrade of the Swiss Light Source (SLS 2.0) at the Paul Scherrer Institute (PSI). The very hard x-ray source generated by the BHTSU will increase the brilliance at the beamline by over one order of magnitude in comparison to other state-of-the-art undulator technologies and allow experiments to be carried out with photon energies in excess of 60 keV. One of the key challenges for designing a 1-meter-long (100 periods) BHTSU is the large-scale simulation of the magnetization currents inside 200 staggered-array bulk superconductors. A feasible approach to simplify the electromagnetic model is to retain five periods from both ends of the 1-meter-long BHTSU, reducing the number of degrees of freedom (DOFs) to the scale of millions. In this paper, the theory of the recently-proposed 2D A-V formulation-based backward computation method is extended to calculate the critical state magnetization currents in the ten-period staggered-array BHTSU in 3D. The simulation results of the magnetization currents and the associated undulator field along the electron beam axis are compared with the well-known 3D H-formulation and the highly efficient 3D H-{\phi} formulation method, all methods showing excellent agreement with each other as well as with experimental results. The mixed H-{\phi} formulation avoids computing the eddy currents in the air subdomain and is significantly faster than the full H-formulation method, but is slower in comparison to the A-V formulation-based backward computation. Finally, the fastest and the most efficient A-V formulation in ANSYS 2020R1 Academic is adopted to optimize the integrals of the undulator field along the electron beam axis by optimizing the sizes of the end bulks., Comment: 19 pages, 12 figures

A backward computation method has been developed to accelerate modelling of the critical state magnetization current in a staggered-array bulk high-temperature superconducting (HTS) undulator. The key concept is as follows: (i) a large magnetization current is first generated on the surface of the HTS bulks after rapid field-cooling (FC) magnetization; (ii) the magnetization current then relaxes inwards step-by-step obeying the critical state model; (iii) after tens of backward iterations the magnetization current reaches a steady state. The simulation results show excellent agreement with the H -formulation method for both the electromagnetic and electromagnetic-mechanical coupled analyses, but with significantly faster computation speed. The simulation results using the backward computation method are further validated by the recent experimental results of a five-period Gd–Ba–Cu–O (GdBCO) bulk undulator. Solving the finite element analysis (FEA) model with 1.8 million degrees of freedom (DOFs), the backward computation method takes less than 1.4 h, an order of magnitude or higher faster than other state-of-the-art numerical methods. Finally, the models are used to investigate the influence of the mechanical stress on the distribution of the critical state magnetization current and the undulator field along the central axis.

The development of a new hard x-ray beamline I-TOMCAT equipped with a 1 m long short-period bulk high-temperature superconductor undulator (BHTSU) has been scheduled for the upgrade of the Swiss Light Source at the Paul Scherrer Institute. The very hard x-ray source generated by the BHTSU will increase the brilliance at the beamline by over one order of magnitude in comparison to other state-of-the-art undulator technologies and allow experiments to be carried out with photon energies in excess of 60 keV. One of the key challenges for designing a 1 m long (100 periods) BHTSU is the large-scale simulation of the magnetization currents inside 200 staggered-array bulk superconductors. A feasible approach to simplify the electromagnetic model is to retain five periods from both ends of the 1 m long BHTSU, reducing the number of degrees of freedom to the scale of millions. In this paper, the theory of the recently-proposed 2D A -V formulation-based backward computation method is extended to calculate the critical state magnetization currents in the ten-period staggered-array BHTSU in 3D. The simulation results of the magnetization currents and the associated undulator field along the electron beam axis are compared with the well-known 3D H -formulation and the highly efficient 3D H -ϕ formulation method, all methods showing excellent agreement with each other as well as with experimental results. The mixed H -ϕ formulation avoids computing the eddy currents in the air subdomain and is significantly faster than the full H -formulation method, but is slower in comparison to the A -V formulation-based backward computation. Finally, the fastest and the most efficient A -V formulation, implemented in ANSYS 2020R1 Academic, is adopted to optimize the integrals of the undulator field along the electron beam axis by optimizing the sizes of the end bulks.

The development of a new hard x-ray beamline I-TOMCAT equipped with a 1-meter-long short-period bulk high-temperature superconductor undulator (BHTSU) has been scheduled for the upgrade of the Swiss Light Source (SLS 2.0) at the Paul Scherrer Institute (PSI). The very hard x-ray source generated by the BHTSU will increase the brilliance at the beamline by over one order of magnitude in comparison to other state-of-the-art undulator technologies and allow experiments to be carried out with photon energies in excess of 60 keV. One of the key challenges for designing a 1-meter-long (100 periods) BHTSU is the large-scale simulation of the magnetization currents inside 200 staggered-array bulk superconductors. A feasible approach to simplify the electromagnetic model is to retain five periods from both ends of the 1-meter-long BHTSU, reducing the number of degrees of freedom (DOFs) to the scale of millions. In this paper, the theory of the recently-proposed 2D A-V formulation-based backward computation method is extended to calculate the critical state magnetization currents in the ten-period staggered-array BHTSU in 3D. The simulation results of the magnetization currents and the associated undulator field along the electron beam axis are compared with the well-known 3D H-formulation and the highly efficient 3D H-{\phi} formulation method, all methods showing excellent agreement with each other as well as with experimental results. The mixed H-{\phi} formulation avoids computing the eddy currents in the air subdomain and is significantly faster than the full H-formulation method, but is slower in comparison to the A-V formulation-based backward computation. Finally, the fastest and the most efficient A-V formulation in ANSYS 2020R1 Academic is adopted to optimize the integrals of the undulator field along the electron beam axis by optimizing the sizes of the end bulks.