Fast and efficient critical state modelling of field-cooled bulk high-temperature superconductors using a backward computation method

Abstract: 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

Influence of inner diameter and height of ring-shaped REBaCuO bulks on trapped field and mechanical stress during field-cooled magnetization

In this paper, the trapped field, Bz, thermal hoop stress, σθcool, by cooling from 300 to 50 K and electromagnetic hoop stress, σθFCM, during field cooled magnetization (FCM) from Bapp = 6.3 and 9.4 T are investigated numerically for ring-shaped REBaCuO bulks with various inner diameters (I.D.) and heights (H) and reinforced by an Al alloy ring. For simplicity, an identical critical current density, Jc(B), which is a typical value at 50 K, is assumed in the simulation. The Bz value at the center of the ring bulk changes depending on the I.D. and H values of the ring bulk, which results from the different distribution of the superconducting current. As a result, the total hoop stress, σθtotal, (= σθcool + σθFCM) also changes for each ring bulk and for each Bapp due to the variation of the σθcool and σθFCM values. The maximum σθ total value, which affects the bulk fracture at Bapp = 9.4 T, increases with decreasing the height of ring bulk. These results can present guidelines for designing a trapped-field magnet using ring bulks

Numerical optimisation of mechanical ring reinforcement for bulk high-temperature superconductors

The finite element method has been used extensively in recent years to solve various problems related to applied superconductivity and provides a useful tool for analysing and predicting experimental results. Based on a recently-developed modelling framework, implemented in the finite element software package COMSOL Multiphysics, investigations on the minimum ring reinforcement required to prevent mechanical failure in bulk high-temperature superconducting magnets have been carried out. Assuming homogeneous J$_{c}$(B,T) across the bulk sample irrespective of its dimensions, the maximum magnetic stresses experienced, and the minimum ring thickness required to prevent the hoop and radial stresses from exceeding the tensile strength of the bulk superconductor have been determined for varying values of the Young\u27s modulus, radius, height and temperature of a representative single-grain Ag-containing Gd-Ba-Cu-O bulk sample. This comprehensive analysis details the influence each of these key parameters has on the magnetic stress and hence their impact on the necessary ring thickness to prevent mechanical failure in any given system, i.e., for any combination of material properties and sample dimensions

Numerical optimisation of mechanical ring reinforcement for bulk high-temperature superconductors

Abstract: The finite element method has been used extensively in recent years to solve various problems related to applied superconductivity and provides a useful tool for analysing and predicting experimental results. Based on a recently-developed modelling framework, implemented in the finite element software package COMSOL Multiphysics, investigations on the minimum ring reinforcement required to prevent mechanical failure in bulk high-temperature superconducting magnets have been carried out. Assuming homogeneous Jc (B,T) across the bulk sample irrespective of its dimensions, the maximum magnetic stresses experienced, and the minimum ring thickness required to prevent the hoop and radial stresses from exceeding the tensile strength of the bulk superconductor have been determined for varying values of the Young’s modulus, radius, height and temperature of a representative single-grain Ag-containing Gd-Ba-Cu-O bulk sample. This comprehensive analysis details the influence each of these key parameters has on the magnetic stress and hence their impact on the necessary ring thickness to prevent mechanical failure in any given system, i.e., for any combination of material properties and sample dimensions

Reliable 4.8 T trapped magnetic fields in Gd-Ba-Cu-O bulk superconductors using pulsed field magnetization

Abstract A robust and reliable in-situ magnetization method is essential for exploiting the outstanding magnetic flux trapping ability of bulk superconductors in practical applications. We report a 4.8 T peak trapped magnetic field, B T, achieved at 30 K in a 36 mm diameter GdBa2Cu3O7-δ –Ag bulk superconductor using pulsed field magnetization (PFM). To realize this, we have developed a reliable two-step multi-pulse PFM process based on understanding and exploiting the avalanche-like flux jump phenomenon observed in these materials. The magnitude of the applied pulsed magnetic field (B a) necessary to trap 4.8 T was merely 5.29 T, corresponding to a remarkable magnetization efficiency (B T/B a) of 90%.This study was supported by the Engineering and Physical Sciences Research Council (No. EP/P00962X/1), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB25000000), the National Key R&D Program (2016YFF0101701) and the project (6140923050202). M D Ainslie would like to acknowledge financial support from an Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellowship, EP/P020313/

Fully-staggered-array bulk Re-Ba-Cu-O short-period undulator: large-scale 3D electromagnetic modelling and design optimization using A-V and H-formulation methods

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

Modelling higher trapped fields by pulsed field magnetisation of composite bulk MgB 2 superconducting rings

Funder: EPSRCAbstract: The recent results of Hirano et al (2020 Supercond. Sci. Technol. 33 085002) reported a high trapped field of 1.61 T in a composite MgB2 ring comprising copper plates and and a soft iron yoke magnetised by pulsed field magnetisation (PFM). Inspired by these results, an investigation using systematic modelling methods was conducted to investigate the key parameters leading to the success of Hirano et al. Our results indicate that composite structures of MgB2 rings present a viable method of trapping high magnetic fields when magnetised with PFM. Leveraging a finite element method modelling framework with a commercial software package (COMSOL Multiphysics), we have successfully modelled the experimental data with excellent agreement. We have paid careful attention to the assumptions regarding the thermal physics, which enabled the successful and accurate modelling of the experiment. Exploiting the flexibility of computational modelling, we extend our studies to investigate the influence of the constituent elements of the composite bulk on the electromagnetic and thermal behaviour, and discuss in detail how each can enhance the trapped field performance of the bulk. Aided by the models, it is shown how the number of copper layers influences the elongation of the applied pulse, reducing the field penetration and the maximum temperature rise of the bulk. The addition of the iron yoke significantly increases the trapped field, by concentrating flux during and after the pulse

Inverse analysis of critical current density in a bulk high-temperature superconducting undulator

In order to optimise the design of undulators using high-temperature superconductor (HTS) bulks we have developed a method to estimate the critical current density (Jc) of each bulk from the overall measured magnetic field of an undulator. The vertical magnetic field was measured along the electron-beam axis in a HTS bulk-based undulator consisting of twenty Gd-Ba-Cu-O (GdBCO) bulks inserted in a 12-T solenoid. The Jc values of the bulks were estimated by an inverse analysis approach in which the magnetic field was calculated by the forward simulation of the shielding currents in each HTS bulk with a given Jc. Subsequently the Jc values were iteratively updated using the pre-calculated response matrix of the undulator magnetic field to Jc. We demonstrate that it is possible to determine the Jc of each HTS bulk with sufficient accuracy for practical application within around 10 iterations. The pre-calculated response matrix, created in advance, enables the inverse analysis to be performed within a practically short time, on the order of several hours. The measurement error, which destroys the uniqueness of the solution, was investigated and the points to be noted for future magnetic field measurements were clarified. The results show that this inverse-analysis method allows the estimation of the Jc of each bulk comprising an HTS bulk undulator.CHART (Swiss Accelerator Research and Technology Collaboration); EPSRC Early Career Fellowship, EP/P020313/

The independent effects of hypovolemia and pulmonary vasoconstriction on ventricular function and exercise capacity during acclimatisation to 3800 m

We aimed to determine the isolated and combined contribution of hypovolemia and hypoxic pulmonary vasoconstriction in limiting left ventricular (LV) function and exercise capacity under chronic hypoxemia at high altitude. In a double‐blinded, randomized and placebo‐controlled design, twelve healthy participants underwent echocardiography at rest and during submaximal exercise before completing a maximal test to exhaustion at sea level (SL; 344 m) and after 5–10 days at 3800 m. Plasma volume was normalised to SL values, and hypoxic pulmonary vasoconstriction was reversed by administration of Sildenafil (50 mg) to create four unique experimental conditions that were compared with SL values; high altitude (HA), Plasma Volume Expansion (HA‐PVX), Sildenafil (HA‐SIL) and Plasma Volume Expansion with Sildenafil (HA‐PVX‐SIL). High altitude exposure reduced plasma volume by 11% (P < 0.01) and increased pulmonary artery systolic pressure (19.6 ± 4.3 vs. 26.0 ± 5.4, P < 0.001); these differences were abolished by PVX and SIL respectively. LV end‐diastolic volume (EDV) and stroke volume (SV) were decreased upon ascent to high altitude, but were comparable to sea level in the HA‐PVX. LV EDV and SV were also elevated in the HA‐SIL and HA‐PVX‐SIL trials compared to HA, but to a lesser extent. Neither PVX or SIL had a significant effect on the LV EDV and SV response to exercise, or the maximal oxygen consumption or peak power output. In summary, at 3800 m both hypovolemia and hypoxic pulmonary vasoconstriction contribute to the decrease in LV filling, however, restoring LV filling does not confer an improvement in maximal exercise performance

Pulsed-field magnetisation of Y-Ba-Cu-O bulk superconductors fabricated by the infiltration growth technique

Funder: King Abdulaziz City for Science and Technology; doi: http://dx.doi.org/10.13039/501100004919Abstract: Bulk high temperature superconductors based on the rare-earth copper oxides can be used effectively as trapped field magnets capable of generating large magnetic fields. The top-seeded infiltration growth (TSIG) processing technique can provide a more homogeneous microstructure and therefore more uniform superconducting properties than samples grown using conventional melt growth processes. In the present investigation, the properties of bulk, single grain superconductors processed by TSIG and magnetised by the pulsed-field magnetisation technique using a copper-wound solenoid have been studied. A trapped field of ∼3 T has been achieved in a 2-step buffer-assisted TSIG-processed Y-Ba-Cu-O (YBCO) sample at 40 K by magnetising the bulk superconductor completely via a single-pulse magnetisation process. Samples were also subjected to pulsed-field magnetisation at 65 K and by conventional field-cooled magnetisation at 77 K for comparison. Good correlation was observed between the microstructures, critical current densities and trapped field performance of bulk samples fabricated by TSIG and magnetised by pulsed-field and field-cooled magnetisation. The homogeneous distribution of Y2BaCuO5 inclusions within the microstructure of bulk YBCO samples fabricated by the 2-step buffer-assisted TSIG process reduces inhomogeneous flux penetration into the interior of the sample. This, in turn, results in a lower temperature rise of the bulk superconductor during the pulsed-field magnetisation process and a more effective and reliable magnetisation process