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The concept of a high-gradient trapped field magnet (HG-TFM), which incorporates a hybrid system of two (RE)BaCuO superconducting bulk components with different functions, was proposed in 2021 by the authors based on the results of numerical simulations. The HG-TFM as a desktop-type magnet can be a more effective way to generate a higher magnetic field gradient product of Bz · dBz /dz (>−1400 T2 m−1, as calculated for a pure water), which can realize a quasi-microgravity space applicable for Space Environment Utilization on a laboratory scale. In this study, to validate the quasi-microgravity space in the HG-TFM, a prototype HG-TFM apparatus has been built using a slit-bulk TFM and stacked full-TFM (without slits) with inner diameters of 36 mm. After field-cooled magnetization from 8.60 T at 21 K, a trapped field of B T = 8.57 T was achieved at the center (i.e. at the bottom of a room temperature bore of 25 mm diameter outside the vacuum chamber), and consequently, a maximum Bz · dBz /dz = −1930 T2 m−1 was obtained at the intermediate position between the slit-bulk TFM and the stacked full-TFM. Magnetic levitation was demonstrated successfully for bismuth particles and a pure water drop, which validates the quasi-microgravity environment in the HG-TFM. Based on numerical simulation results of the trapped field profile, it is concluded that the reason for the instability of the levitated targets is because of the repulsive magnetic force applied along the horizontal plane. The levitating state can be controllable, for example, by changing the operating temperature, which would allow objects to levitate statically along the central axis.

Funder: EPSRC, 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.

The concept of a hybrid trapped field magnet lens (HTFML) was recently proposed by the authors, which consists of a trapped field magnet (TFM) cylinder exploiting the “vortex pinning effect,” combined with a superconducting bulk magnetic lens exploiting the “diamagnetic shielding effect.” This HTFML can generate, within its bore, a magnetic field higher than the applied magnetic field, even after external field decreases to zero. In this paper, a design optimization of the inner GdBaCuO magnetic lens within the GdBaCuO TFM cylinder was carried out using numerical simulations based on the finite-element method, in order to maximize the concentrated magnetic field. The HTFML with an optimized shape and size achieved a concentrated magnetic field of B c = 5.6 and 12.8 T at the center of the lens for applied magnetic fields of B app = 3 and 10 T, respectively. A maximum tensile stress of +135 MPa exists in the outer GdBaCuO TFM cylinder during the magnetizing process for B app = 10 T, which exceeds the fracture strength of the bulk. This result suggests that mechanical reinforcement is necessary to avoid mechanical fracture under such high magnetic field conditions.

In this work, we propose a new concept of a high gradient trapped field magnet (HG-TFM). The HG-TFM is made from (RE)BaCuO bulk superconductors, in which slit ring bulks (slit-TFMs) are tightly stacked with TFM cylinders (full-TFMs), and state-of-the-art numerical simulations were used to investigate the magnetic and mechanical properties in detail during and after magnetization. A maximum value of the magnetic field gradient product of B z ��� d B z / d z = 6040 T2 m���1 was obtained after conventional field cooled magnetization (FCM) with an applied field, B app, of 10 T of the HG-TFM with 60 mm in outer diameter and 10 mm in inner diameter. This value may be the highest value ever reported compared to any other magnetic sources. The B z ��� d B z / d z value increased with decreasing inner diameter of the HG-TFM and with increasing B app during FCM. The electromagnetic stress in the HG-TFM during the FCM process mainly results from the hoop stress along the circumferential direction. The simulations suggested that there is no fracture risk of the bulk components during FCM from 10 T in a proposed realistic configuration of the HG-TFM where both TFM parts are mounted in Al-alloy rings and the whole HG-TFM is encapsulated in a steel capsule. A quasi-zero gravity space can be realized in the HG-TFM with a high B z ��� d B z / d z value in an open space outside the vacuum chamber. The HG-TFM device can act as a compact and cryogen-free desktop-type magnetic source to provide a large magnetic force and could be useful in a number of life/medical science applications, such as protein crystallization and cell culture., JSPS KAKENHI Grant No. 19K05240 Adaptable and Seamless Technology transfer Program through Target-driven R&D (A-STEP) from Japan Science and Technology Agency (JST), Grant Nos. VP30218088419 and JPMJTM20AK

The recent results of Hirano et al. (Supercond. Sci. Technol. 33, 085002 (2020)) 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. We continue to discuss in detail how these materials influence the bulk thermal and electromagnetic behaviour.

During quasi-static magnetization of bulk superconductors using field-cooled magnetization (FCM) from high fields at low temperatures, such bulks are sometimes broken, which is believed to be mainly due to an electromagnetic force—and subsequent stress—larger than the fracture strength. However, a ring bulk can break, even during pulsed field magnetization (PFM), from relatively lower pulsed fields and at relatively higher temperatures. Previous simulation results suggest that the ring bulk should not break due to the electromagnetic force during PFM. In this paper, taking experimental and numerical results into consideration, we propose the possibility of mechanical fracture of a ring bulk during PFM due to thermal stress induced by local heat generation, which has not been considered and investigated to date. Two numerical models with different sizes of heat-generating region were constructed for the ring bulk with a relatively large inner diameter (60 mm outer diameter, 36 mm inner diameter, 17 mm height). For Model-1, with a large heat region, the bulk fracture due to the thermal stress results from the tensile stress along the radial direction in the neighboring heat region. The risk of bulk fracture is enhanced at the inner or outer edges of the bulk surface, compared with that inside the bulk. For Model-2, with a small heat region inside the bulk, the bulk fracture due to the thermal stress results from the compressive stress along the radial direction in the neighboring heat region. These results strongly suggest the possibility of mechanical fracture of an actual ring bulk due to thermal stress induced by local heat generation. This idea is also applicable more generally to the fracture mechanism during FCM of superconducting bulks.

Funder: King Abdulaziz City for Science and Technology; doi: http://dx.doi.org/10.13039/501100004919, 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.

© 2002-2011 IEEE. In this paper, the trapped field properties of GdBaCuO disk bulk superconductors of various diameters during pulsed-field magnetization (PFM) using an identical split coil at 65 K have been investigated both experimentally and numerically. The maximum trapped field, BTmax, of the φ43-mm bulk was larger than that of the φ30-mm bulk. However, BTmax of the φ65-mm bulk was smaller than that of the φ43-mm bulk and the trapped field profile exhibited a distorted 'C-shaped' profile. Using the numerical simulation, these results for the φ65-mm bulk can be explained by an inhomogeneous temperature profile and the larger generated heat, Q, due to the lower cooling power of the refrigerator compared to the generated heat. The important issues to achieve higher and homogeneous trapped fields are discussed when using split-coil PFM for larger bulks.

We have investigated the trapped field properties of a GdBaCuO disk bulk during single- and double- pulsed field magnetization (PFM) using a split-type coil for various pulse sequences for the first time. It is well known that the multi-PFM technique using a solenoid-type coil and the single-PFM technique using a split-type coil are effective to enhance the trapped field due to a lower tem-perature rise. However, it was found, in this work, that the trapped field by double-PFM using the split-type coil was not en-hanced in spite of lower temperature rise. We analyzed the mag-netizing process using two parameters, the “magnetic flux pene-tration ratio”, Rin, and the “magnetic flux residual ratio”, Rout, for various pulse sequences for the split-type and solenoid-type coils. The Rin value was decreased by the double-PFM for both coils, and the Rout value was improved only by the double-PFM using the solenoid-type coil. As a result, the trapped field for single-PFM using the split-type coil, which has a higher Rin, reduced af-ter the double-PFM due to a decrease of Rin and no enhancement of Rout. These results are in clear contrast to those using the sole-noid-type coil.

In this paper, the trapped field B z , thermal hoop stress σ θ cool by cooling from 300 to 50 K, and electromagnetic hoop stress σ θ FCM during field-cooled magnetization (FCM) from B app = 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 J c (B), which is a typical value at 50 K, is assumed in the simulation. The B z 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 σ θ total (= σ θ cool + σ θ FCM ) also changes for each ring bulk and each B app because of the variation of the σ θ cool and σ θ FCM values. The maximum σ θ total value, which affects the bulk fracture at B app = 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.

In this paper, simultaneous measurements of the electromagnetic strains along both the circumferential (θ) and radial (r) directions are reported for a large single-grain EuBaCuO ring bulk reinforced by an Al alloy ring during field-cooled magnetization (FCM) from 5 T at 50 K using several strain gauges adhered to the surface. To verify the experimental results and to understand the complex stress–strain behavior, mechanical analyses were carried out using a three-dimensional finite element model that closely represents the experimental setup. The simulation results of the electromagnetic strains along both directions showed excellent qualitative and quantitative agreement with the experimental ones. These results strongly suggest that the numerical model must include the exact same structure (size, shape and materials) of the mechanical support structure as the experimental setup in order to reproduce the experimental results both qualitatively as well as quantitatively. This also explains our previous research (SuST 2019 32 015007), where the measured circumferential strains were about 50% smaller those in the numerical simulation. Furthermore, the electromagnetic stresses along both directions during the FCM process are estimated from the obtained experimental strains. As a result, the estimated stresses were fairly consistent with those obtained by the numerical simulations, suggesting that our stress–strain simulation technique is both qualitatively and quantitatively reliable and useful to clarify the possibility of mechanical fracture of bulk superconductors.

The magnetic field trapping capability of a bulk superconductor is essentially determined by the critical current density, J c (B, T), of the material. With state-of-the-art bulk (RE)BCO (where RE = rare earth or Y) materials it is clear that trapped fields of over 20 T are potentially achievable. However, the large Lorentz forces, F L = J × B , that develop during magnetisation of the sample lead to large mechanical stresses that can result in mechanical failure. The radial forces are tensile and the resulting stresses are not resisted well because of the brittle ceramic nature of (RE)BCO materials. Where fields of more than 17 T have been achieved, the samples were reinforced mechanically using resin impregnation and carbon-fibre wrapping or shrink-fit stainless steel. In this paper, two-dimensional (2D) axisymmetric and three-dimensional (3D) finite-element models based on the H -formulation, implemented in the commercial finite element software package COMSOL Multiphysics, are used to provide a comprehensive picture of the mechanical stresses in bulk superconductor magnets with and without mechanical reinforcement during field-cooled magnetisation. The chosen modelling framework couples together electromagnetic, thermal and structural mechanics models, and is extremely flexible in allowing the inclusion of various magnetisation processes and conditions, as well as detailed and realistic properties of the materials involved. The 2D model - a faster route to parametric optimisation - is firstly used to investigate the influence of the ramp rate of the applied field and any heat generated in the bulk. Finally, the 3D model is used to investigate the influence of inhomogeneous J c (B, T) properties around the ab-plane of the bulk superconductor on the developed mechanical stress.

A hybrid trapped field magnet lens (HTFML) is a promising device that is able to concentrate a magnetic field higher than the applied field continuously, even after removing an external field, which was conceptually proposed by the authors in 2018. This paper presents, for the first time, the experimental realization of the HTFML using a GdBaCuO magnetic lens and MgB2 trapped field magnet cylinder. A maximum concentrated magnetic field of B c = 3.55 T was achieved at the central bore of the HTFML after removing an applied field of B app = 2.0 T at T = 20 K. For higher B app, the B c value was not enhanced because of a weakened lens effect due to magnetic flux penetration into the bulk GdBaCuO material comprising the lens. The enhancement of the trapped field using such an HTFML for the present experimental setup is discussed in detail.

In this work, we have verified experimentally an all-(RE)BaCuO hybrid trapped field magnet lens (HTFML) using only one cryocooler and a special technique named the ���loose contact method���. In the experimental setup, only the inner magnetic lens was tightly connected to the cold stage and cooled at all times, and the outer trapped field magnet (TFM) cylinder was loosely connected to the cold stage before the magnetizing process by introducing a gap between the outer TFM and cold stage of the cryocooler. As a result, the superconducting state for zero-field cooled magnetization of the inner magnetic lens and the non-superconducting (normal) state for field-cooled magnetization of the outer TFM cylinder can co-exist at the same time. A maximum concentrated field of B c = 9.8 T was achieved for the magnetizing process with an applied field of B app = 7 T in the present HTFML, consistent with the numerical estimation in our previous conceptual study. These results validate the HTFML concept as a compact and desktop-type magnet device that can provide 10 T-class magnetic field enhancement from the viewpoint of the magnetizing method. However, during magnetization with a higher B app of 10 T, thermal instability of the outer stacked TFM cylinder caused flux jumps to occur, resulting in mechanical fracture of multiple bulks. These results suggest that the further development of a practical cooling method that can realize a stable and controllable cooling process for each part of the HTFML is necessary based on fundamental studies relating to the thermal stability of the large stacked TFM cylinder., JSPS KAKENHI Grant No. 19K05240; - Adaptable and Seamless Technology transfer Program through Target-driven R&D (A-STEP) from Japan Science and Technology Agency (JST), Grant Nos. VP30218088419 and JPMJTM20AK; - Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellowship, EP/P020313/1

In this paper, a new concept of a hybrid trapped field magnet lens (HTFML) is proposed. The HTMFL exploits the “vortex pinning effect” of an outer superconducting bulk cylinder, which is magnetized as a trapped field magnet (TFM) using field-cooled magnetization (FCM), and the “diamagnetic shielding effect” of an inner bulk magnetic lens to generate a concentrated magnetic field higher than the trapped field from the TFM in the bore of the magnetic lens. This requires that, during the FCM process, the outer cylinder is in the normal state (T > superconducting transition temperature, Tc) and the inner lens is in the superconducting state (T < Tc) when the external magnetizing field is applied, followed by cooling to an appropriate operating temperature, then removing the external field. This is explored for two potential cases: 1) exploiting the difference in Tc of two different bulk materials (“case-1”), e.g. MgB2 (Tc = 39 K) and GdBaCuO (Tc = 92 K) or 2) using the same material for the whole HTFML, e.g., GdBaCuO, but utilizing individually-controlled cryostats, the same cryostat with different cooling loops or coolants, or heaters that keep the outer bulk cylinder at a temperature above Tc to achieve the same desired effect. The HTFML is verified using numerical simulations for “case-1” using an MgB2 cylinder and GdBaCuO lens pair and for “case-2” using a GdBaCuO cylinder and GdBaCuO lens pair. As a result, the HTFML could reliably generate a concentrated magnetic field Bc = 4.73 T with the external magnetizing field Bapp = 3 T in the “case-1, and a higher Bc = 13.49 T with higher Bapp = 10 T in the “case-2,” respectively. This could, for example, be used to enhance the magnetic field in the bore of a bulk superconducting NMR/MRI system to improve its resolution.

Pulsed field magnetisation (PFM) is the most practical method for magnetising bulk superconducting materials as trapped field magnets (TFMs), but the record trapped field achieved by PFM to date is still significantly less than the true trapped field capability of these materials. In this paper, a flexible numerical modelling technique based on the finite element method is used to provide a comprehensive and realistic picture of multi-pulse PFM, which has been shown to be effective in increasing the trapped field/flux over a single pulse. Firstly, the maximum trapped field capability of a representative sample is determined using two types of numerical model simulating field-cooling (FC) and zero-field-cooling (ZFC) magnetisation. Next, various sets of magnetic field pulses are applied to the bulk to analyse multi-pulse PFM. An increase in the trapped field can be achieved after a 2nd pulse and to do so an increased amplitude of applied field is required to maximize the trapped field fully. The numerical analysis shows that this occurs in subsequent pulses because it is more difficult for the magnetic flux to penetrate the sample and there is a lower temperature rise.