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It is necessary to fabricate (RE)BCO bulk high temperature superconductors in the form of individual single grains in order to maximise the length scale over which current flows, and hence the trapped magnetic field. However, inherent difficulties in the grain growth process place limitations on the diameter and height of the single grain that may be achieved by existing melt processes. A practical approach to increase the height of the sample and the trapped field at its surface is by assembling individual single grains in a stack formation with their ab planes aligned parallel, primarily to avoid the expensive process of fabricating large, individual monoliths. The trapped fields observed at the top and bottom surfaces of a single grain sample are frequently different since both the superconducting and physical properties of single grain (RE)BCO samples are generally non-uniform. This leads to challenges in determining how to spatially arrange stacks of single grain samples to generate the largest and most uniform trapped field overall. In this study, we report the optimisation of two-stack configurations involving a total of 8 individual GdBCO/Ag single grains. The samples were arranged in four pairs and configured with different surfaces in contact in the assembly of the stack. The primary superconducting properties for trapped field and total flux distributions were measured at 77 K and compared for each stack arrangement. The initial results indicate that surfaces with inferior flux trapping properties (measured in terms of the overall trapped field value) of a two-sample stack should be positioned at the middle of the assembly to achieve the best overall trapped field and higher total flux at the external, and therefore, usable surface of the stack sample. A numerical modelling method that incorporates different Jc-B characteristics for the top and bottom layers of a single grain to take account of the variability in physical properties and spatial non-uniformity confirmed the optimised experimental arrangement of the stacked bulk samples. Furthermore, the optimisation of single grains of ring geometry to achieve a longer and wider uniform magnetic field zone inside the bore was also performed.

One potential application of magnetized RE-Ba-Cu-O (where RE = rare earth or Y) bulk superconductors is as a high-field alternative to conventional permanent magnets in desktop NMR and MRI systems. Pulsed field magnetization (PFM) is one of the most promising practical methods of magnetizing such bulks. However, the trapped fields obtained by PFM are much lower than those obtained using quasi-static methods like field-cooling magnetization (FCM) due to heating during PFM. Furthermore, bulk superconducting rings have proved more difficult to magnetize via PFM than discs. The reported trapped fields in single bulk superconducting rings magnetized by PFM are less than 0.35 T at the centre of the bore due to thermomagnetic instabilities. In this work, systematic PFM measurements on a bulk Gd-Ba-Cu-O ring were carried out and a trapped field of 1.3 T at 55 K was achieved using a multi-pulse, stepwise cooling (MPSC) method. In the MPSC method, a sequence of pulsed fields is used to magnetize the ring bulk. The pulsed field is increased in small increments and the sample temperature is decreased sequentially. Consequently, as some field is already trapped after the first pulse, the motion of the flux for subsequent pulses will be reduced, leading to less heat generated in the bulk sample. This greatly improves the thermomagnetic stability of the PFM process, enabling larger trapped fields.

MgB₂ in bulk form shows great promise as an inexpensive, light-weight alternative to bulk (RE)-Ba-Cu-O materials to act as trapped field magnets (TFMs), which can replace permanent magnets in applications such as desktop high-field magnet systems and rotating machines. In this paper, we investigate the thickness dependence of the trapped magnetic field in bulk MgB₂ superconductors. Two bulk MgB₂ samples, 20 mm in diameter and 10 mm in thickness, were fabricated using the powder-in-closed-tube (PICT) technique. The trapped field was then measured after field-cooled magnetisation for thicknesses of approximately 20 mm (both bulks stacked), 10 mm (single bulk), and then 7.5, 5, 4, 3, 2, 1.5 and 1 mm, for which the sample was machined down to the designated thickness using an automated-wet-polishing technique. A 2D axisymmetric finite-element model based on the H-formulation is used to simulate the experimental results and explain the observed thickness dependence of the trapped field. The numerical results assume a Jc(B) dependence based on the measured characteristics of small specimens taken from the bulk before and after machining. The Jc(B) measurements suggested a degradation of Jc occurred as the bulk was machined thinner and thinner: a decrease in Jc(0 T) of ~35% was observed between the pre- and post-machining specimens. Taking this into account in the models, by assuming a linear reduction in Jc with each machining process, reproduced the experimental results with very good agreement. Consistent trapped field measurements on the top and bottom surfaces suggest this degradation occurred globally, rather than local to the machined surface.

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.

Bulk high-temperature superconducting materials can trap magnetic fields up to an order of magnitude larger than conventional permanent magnets. Recent advances in pulsed field magnetization (PFM) techniques now provide a fast and cost-effective method to magnetize bulk superconductors to fields of up to 5 T. We have developed a portable, desktop bulk high-temperature superconducting magnet system by combining advanced PFM techniques with state-of-the-art cryocooler technology and single-grain, RE-Ba-Cu-O [(RE)BCO, where RE is a rare-earth element or yttrium] bulk superconducting materials. The base temperature of the system is 41 K and it takes about one hour for the system to cool down to 50 K from room temperature. A capacitor bank, combined with easily-interchangeable, solenoid- or split-type copper magnetizing coils and an insulated bipolar gate transistor acting as a high-speed switch, allows magnetic pulses to be generated with different pulse profiles. The system is capable of trapping magnetic fields of up to ~3 T. In this work, we report the results of the magnetization of a range of single-grain Y-Ba-Cu-O (YBCO), Eu-Ba-Cu-O (EuBCO) and Gd-Ba-Cu-O (GdBCO), bulk superconducting discs using this system. A higher trapped field was recorded using a split coil incorporating iron yokes at temperatures of 65 K and above, whereas at lower temperatures, a higher trapped field was obtained using the solenoid coil. The GdBCO sample achieved the highest trapped field for both single-pulse (SP) and two-stage-multi-pulse (TSMP) methods using the solenoid coil. Maximum trapped fields of 2.26 T at 55 K and 2.85 T at 49 K were recorded at the centre of the top surface of the GdBCO sample for the SP and TSMP methods, respectively. The PFM process is substantially an adiabatic process so, therefore, the thermal contact between the sample and sample holder is of critical importance for cooling the bulk sample during application of the pulse. The design of the sample holder can be modified easily to enhance the thermal stability of the sample in order to achieve a higher trapped field.

One of the potential applications of ring-shaped, single grain RE-Ba-Cu-O bulk superconductors is in desktop magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) systems as an alternative to conventional permanent magnets. The higher magnetic field available from magnetized bulk superconductors could significantly improve the performance of such systems, as well as reduce their size and increase portability. The pulsed field magnetization (PFM) method provides a fast, compact and cost-effective method for magnetizing these materials as trapped field magnets. However, bulk superconducting rings are very suscep-tible to thermomagnetic instabilities during the PFM process, and thus, to date, the reported trapped fields in ring bulks magnet-ized by PFM are less than 0.35 T at the centre of single rings. In this work, we demonstrate that the trapped field in a super-conducting ring bulk can be enhanced significantly by optimizing the waveform of the magnetizing pulse used in the PFM method. This optimization can be achieved easily by using an Insulated Gate Bipolar Transistor as a fast-switching device with a control-lable switching frequency in the pulse-generating electric circuit. Our findings represent a key step forward in utilizing bulk, sin-gle-grain superconducting rings magnetized by PFM in portable magnet systems.

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

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.

GdBa 2 Cu 3 O 7-δ bulk superconductors are a route to higher magnetic fields in rotating machines. Here, we examine the resistance of pulse-field magnetized bulks to the demagnetization fields they may experience in such a system. The bulks were magnetized at 77 K, after which several thousand cycles of AC field were applied. Subsequently, the decay of the trapped field was characterized. We found that the decay per cycle decreases with frequency and is, normalized to the initial trapped field, largest at the edge of the bulk. At 77 K, the reduction in trapped field proved significant (25% in the center for 150 mT (peak) AC field at 6 Hz), however, reducing below 1% when lowering the temperature to 60 K. We explain this observation as being due to increased flux pinning strength at low temperatures. When applying an AC field, we found a temperature rise that increased with applied field amplitude and frequency. However, when applying an AC field of amplitude 45 mT with a frequency of 48 Hz, we found an increase of the bulk temperature of only 100 mK. Therefore, we conclude that the temperature rise within the analyzed AC field frequency and amplitude range does not contribute significantly to the decay of trapped field.

Sawh et al. recently reported experimental results that showed, in the case of a partially-magnetized bulk superconductor, magnetized using zero-field-cooling, that flux creep resulted in a reduced field measured at the center of the top surface of the bulk. The authors reported that this may suggest magnetic flux vortices, in this case, move against the Lorentz force, contravening commonly-accepted theory. In this paper, we report the results of numerical simulations explaining the observed measurements, and show that the vortices do indeed move with the Lorentz force, but that geometric effects from the finite geometry of the bulk and the form of the resulting induced supercurrent flowing within the bulk play a key role in this observed phenomenon. As a result, the relaxation of the magnetic flux can result in a measured magnetic field above the bulk superconductor that could be perceived as magnetic flux moving against the Lorentz force, when applying a simple Bean model (infinite slab) analysis to the problem.

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.

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.

Large, single-grain bulk high-temperature superconducting materials can trap high magnetic fields in comparison with conventional permanent magnets, making them ideal candidates to develop more compact and efficient devices, such as actuators, magnetic levitation systems, flywheel energy storage systems and electric machines. However, macrosegregation of Y-211 inclusions in melt-processed Y-Ba-Cu-O (YBCO) limits the macroscopic critical current density of such bulk superconductors, and hence, the potential trapped field. A new fabrication technique using graded precursor powders has recently been developed by our research group, which results in a more uniform distribution of Y-211 particles, in order to further improve the superconducting properties and trapped field capability of such materials. Large, single-grain bulk high-temperature superconducting materials can trap high magnetic fields in comparison with conventional permanent magnets, making them ideal candidates to develop more compact and efficient devices, such as actuators, magnetic levitation systems, flywheel energy storage systems and electric machines. However, macrosegregation of Y-211 inclusions in melt-processed Y-Ba-Cu-O (YBCO) limits the macroscopic critical current density of such bulk superconductors, and hence, the potential trapped field. A new fabrication technique using graded precursor powders has recently been developed by our research group, which results in a more uniform distribution of Y-211 particles, in order to further improve the superconducting properties and trapped field capability of such materials.

Design requirements of next generation electric aircraft place stringent requirements on the power density required from electric motors. Future prototype planned in the scope of European project “Advanced Superconducting Motor Experimental Demonstrator” ASuMED considers a permanent magnet synchronous motor, where the conventional ferromagnets are replaced with superconducting trapped field magnets, which promise higher flux densities and thus higher output power without adding weight. Previous work has indicated that stacks of tape show lower cross-field demagnetisation rate to bulk (RE)BCO whilst retaining similar performance for their size, however the crossed-field demagnetisation rate has not been studied in the temperature, magnetic field and frequency range that is relevant for the operational prototype motor. This work investigates crossed-field demagnetisation in 2G HTS stacks at temperatures below 77 K and frequency range above 10 Hz. This information is crucial in developing designs and determining operational time before re-magnetisation could be required.

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.

This paper presents a proof-of-concept of the idea of using bulk high-temperature superconducting (HTS) materials as quasi-permanent magnets that would form, in the future, an integral part of an advanced Lorentz Force Velocimetry (LFV) system. The experiments, calculations and numerical simulations are performed in accordance with the fundamental theory of LFV, whereby a moving metal rod passes through a static magnetic field, in our case generated by the bulk HTSs. The bulk HTS magnet system (MS) consists of two Y-Ba-Cu-O samples in the form of bulk cylindrical discs, which are encapsulated in an aluminium holder and wrapped with styrofoam. The aluminium holder is designed to locate the bulk HTS magnets on either side of the metal rod. After fi eld cooling (FC) magnetisation with an applied fi eld of 1.5 T at 77 K, the bulk HTS MS provides a quasi-permanent magnetic field over 240 s, enabling Lorentz force measurements to be carried out with a constant velocity of the metal rod. Two sets of Lorentz force measurements with copper and aluminium rods with velocities ranging from approximately 54 to 81 mm·s-1 were performed. The obtained results, which are validated using a numerical model developed in COMSOL Multiphysics, demonstrate the linear relationship between the Lorentz force and velocity of the moving conductor. Finally, the potential of generating very high magnetic fi elds using bulk HTS that would enable LFV in even weakly conducting and slow-flowing fuids, e.g., glass melts, is discussed.

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.

Large, single-grain bulk high-temperature superconductors (HTS) can trap magnetic fields over 17 T below 30 K and up to 3 T at 77 K, and have significant potential to replace permanent magnets, the fields from which are limited to significantly less than 2 T. Therefore, bulk HTS samples are ideal candidates to develop more compact and efficient devices, such as actuators, magnetic levitation systems, flywheel energy storage systems and electric machines. In electric machines, in particular, the higher flux density improves the power density of the machine, resulting in smaller, lighter devices. However, in a real electric machine environment, bulk HTS samples can be exposed to AC magnetic field fluctuations that can affect the distribution of the supercurrent in the material and attenuate the trapped field, leading to a reduction in the magnetic loading of the machine, and in some cases, full demagnetisation. In this paper, the variation of trapped field with the frequency and magnitude of an external time-varying magnetic field is analysed numerically, and the mechanisms of the attenuation of the trapped field in HTS bulks are investigated using a two-dimensional (2D) axisymmetric finite-element model based on the H-formulation, considering both the electromagnetic and thermal behaviour of the bulk sample.

The multi-seeding process has the potential to enlarge the sample size of (RE)BCO (where RE = rare earth or Y) single-grain, bulk superconductors with improved fabrication speed, and in previous studies on multi-seeding, a significant improvement was made in the alignment of the seeds in such samples using a novel bridge-seeding technique. In this paper, we report the experimental measurements of the pulsed field magnetization (PFM) of a 0°-0° bridge-seeded Y-Ba-Cu-O (YBCO) sample. The PFM is carried out using a solenoid coil, as well as a split coil arrangement with an iron yoke, at temperature of 65, 40 and 20 K, and the resultant trapped fields and magnetic flux dynamics for these two PFM techniques are compared. It is shown that such bridge-seeded bulk YBCO can be fabricated that performs as a bulk magnet with trapped fields comparable to or better than standard, single-seeded high-$J_\text{c}$ samples, with the potential of enlarging the sample size. Furthermore, the split coil arrangement with an iron yoke is useful to enhance the trapped field and has a positive effect on the maximum temperature rise in the sample, which increases at lower temperatures and seriously impacts the achievable trapped field from PFM.

Investigating, predicting and optimising practical magnetisation techniques for charging bulk superconductors is a crucial prerequisite to their use as high performance ‘psuedo’ permanent magnets. The leading technique for such magnetisation is the pulsed field magnetisation (PFM) technique, in which a large magnetic field is applied via an external magnetic field pulse of duration of the order of milliseconds. Recently ‘giant field leaps’ have been observed during charging by PFM: this effect greatly aids magnetisation as flux jumps occur in the superconductor leading to magnetic flux suddenly intruding into the centre of the superconductor. This results in a large increase in the measured trapped field at the centre of the top surface of the bulk sample and full magnetisation. Due to the complex nature of the magnetic flux dynamics during the PFM process, simple analytical methods, such as those based on the Bean critical state model, are not applicable. Consequently, in order to successfully model this process, a multi-physical numerical model is required, including both electromagnetic and thermal considerations over short time scales. In this paper, we show that a standard numerical modelling technique, based on a 2D axisymmetric finite-element model implementing the $H$-formulation, can model this behaviour. In order to reproduce the observed behaviour in our model all that is required is the insertion of a bulk sample of high critical current density, $J_c$. We further explore the consequences of this observation by examining the applicability of the model to a range of previously reported experimental results. Our key conclusion is that the ‘giant field leaps’ reported by Weinstein $\textit{et al}$ and others need no new physical explanation in terms of the behaviour of bulk superconductors: it is clear the ‘giant field leap’ or flux jump-assisted magnetisation of bulk superconductors will be a key enabling technology for practical applications.

Stacks of superconducting (RE)BCO tape are gaining popularity as a potential alternative for superconducting bulks for trapped field applications. This is partly due to versatility and uniformity of the starting material, allowing for more deterministic prediction of field profile and magnitude. However, most FEM models of trapped field magnets do not incorporate parameters such as critical current and n-value dependence on the angle of applied magnetic field, leading to only qualitative modeling results. More quantitative results can be obtained from incorporating more data for superconductivity and thermal properties of the material. Such models can be used as a starting point for most geometries and both trapped field and current transport modeling problems. An FEM model of a stack of tapes was constructed using the H formulation, incorporating goniometric critical current and n-value measurements. The modeling results were compared to field cooling experiments for stacks of different heights. The experiment and modeling show good agreement.

Large, single-grain high-temperature superconducting (HTS) bulks have significant potential to replace permanent magnets in various engineering applications. However, based on our previous research, the trapped field in a bulk superconductor can be attenuated or even erased when a bulk is subjected to a time-varying, external magnetic field. Therefore, it is important to develop a method to protect bulks from demagnetization by (a) improving the thermal conduction of the bulk and/or (b) reducing AC losses. Improvement in the thermal conduction of bulks involves modification of the material fabrication process, which may have a detrimental effect on its superconducting properties. Employing shielding materials around a bulk helps to decrease the AC losses, but also provides a durable way to maintain the original material properties. In this paper, two shielding cases are proposed and evaluated numerically: ring-shaped shielding with a copper coil, and surface shielding with a ferromagnetic material. Based on the numerical modelling results, the ring-shaped coil works well for externally applied AC fields of larger magnitude and higher frequency. However, the ferromagnetic material was preferable for surface shielding for relatively lower fields. Finally, an optimal shield design is presented.

Investigating and predicting the magnetization of bulk superconducting materials and developing practical magnetizing techniques is crucial to using them as trapped field magnets (TFMs) in engineering applications. The pulsed field magnetization (PFM) technique is considered to be a compact, mobile and relative inexpensive way to magnetize bulk samples, requiring shorter magnetization times (on the order of milliseconds) and a smaller and less complicated magnetization fixture; however, the trapped field produced by PFM is generally much smaller than that of slower zero field cooling (ZFC) or field cooling (FC) techniques, particularly at lower operating temperatures. In this paper, the PFM of two, standard Ag-containing Gd-Ba-Cu-O samples is carried out using two types of magnetizing coils: 1) a solenoid coil, and 2) a split coil, both of which make use of an iron yoke to enhance the trapped magnetic field. It is shown that a significantly higher trapped field can be achieved using a split coil with an iron yoke, and in order to explain these how this arrangement works in detail, numerical simulations using a 2D axisymmetric finite element method based on the H-formulation are carried to qualitatively reproduce and analyse the magnetization process from both electromagnetic and thermal points of view. It is observed that after the pulse peak significantly less flux exits the bulk when the iron core is present, resulting in a higher peak trapped field, as well as more overall trapped flux, after the magnetization process is complete. The results have important implications for practical applications of bulk superconductors as such a split coil arrangement with an iron yoke could be incorporated into the design of a portable, high magnetic field source/magnet to enhance the available magnetic field or in an axial gap-type bulk superconducting electric machine, where iron can be incorporated into the stator windings to 1) improve the trapped field from the magnetization process, and 2) increase the effective air-gap magnetic field.

The trapped magnetic field profile of stacks of GdBa2Cu3O7−x superconducting tape was investigated. Angled stacks of superconducting tape were magnetized and found to produce very uniform trapped field profiles. The angled stacks were made of 12 mm × 24 mm solder coated tape pieces and were bonded together following a brief consolidation heat treatment. Layering multiple stacks together and adding a ferromagnetic plate beneath the samples were both found to enhance the magnitude and uniformity of the trapped field profiles. Stationary and time-dependent critical state finite element models were also developed to complement the experimental results and investigate the magnetization process. The size and shapes possible with the angled stacks make them attractive for applications requiring uniform magnetic fields over larger areas than can be achieved with existing bulk rings or tape annuli.

Large, single-grain (RE)BCO (where RE = rare earth or Y) bulk superconductors with complicated geometries are required for a variety of potential applications, such as rotating machines, magnetic bearings and magnetic separation. As a consequence, the top multi-seeded melt growth process has been studied over many years in an attempt to deliver large, single grains for practical applications. Among these techniques, the so-called bridge-seeding produces the best alignment of two seeds during melt processing of multi-seed samples. In this paper, the trapped field performance and magnetic flux dynamics of two bridge-seeded, multi-seed samples magnetized by pulsed field magnetization (PFM) are analysed: one with a 45⁰-45⁰ and another with a 0⁰-0⁰ bridge seed. Based on an analysis of the flux penetration across the seeds and in-between the seeds of the 45⁰-45⁰ multi-seed sample, an estimated Jc distribution over the ab-plane was determined, which provides the basis for further analysis via numerical simulation. A 3D finite-element model, developed to qualitatively reproduce and interpret the experimental results, was employed to investigate the influence of the length of the bridge seed for such multi-seed samples. The simulation results agree well with the observed experimental results, in that the multi-seed sample’s particular inhomogeneous Jc distribution acts to distort the trapped field profile from a traditional conical Bean’s profile, which is determined by the length and direction of the bridge seed on the bulk surface.

Bulk, high temperature superconductors have significant potential for use as powerful permanent magnets in a variety of practical applications due to their ability to trap record magnetic fields. In this paper, soft ferromagnetic sections are combined with a bulk, large grain Y-Ba-Cu-O (YBCO) high temperature superconductor to form superconductor/ferromagnet (SC/FM) hybrid structures. We study how the ferromagnetic sections influence the shape of the profile of the trapped magnetic induction at the surface of each structure and report the surface magnetic flux density measured by Hall probe mapping. These configurations have been modelled using a 2D axisymmetric finite element method based on the H-formulation and the results show excellent qualitative and quantitative agreement with the experimental measurements. The model has also been used to study the magnetic flux distribution and predict the behaviour for other constitutive laws and geometries. The results show that the ferromagnetic material acts as a magnetic shield, but the flux density and its gradient are enhanced on the face opposite to the ferromagnet. The thickness and saturation magnetization of the ferromagnetic material are important and a characteristic ferromagnet thickness d* is derived: below d*, saturation of the ferromagnet occurs, and above d*, a weak thickness-dependence is observed. The influence of the ferromagnet is observed even if its saturation magnetization is lower than the trapped flux density of the superconductor. Conversely, thin ferromagnetic discs can be driven to full saturation even though the outer magnetic field is much smaller than their saturation magnetization.

MgB_2 in bulk form shows great promise as trapped field magnets (TFMs) as an alternative to bulk (RE)BCO materials to replace permanent magnets in applications such as rotating machines, magnetic bearings and magnetic separation, and the relative ease of fabrication of MgB_2 materials has enabled a number of different processing techniques to be developed. In this paper, a comparison is made between bulk MgB_2 samples fabricated by the hot isostatic pressing (HIP), with and without Ti-doping, and infiltration growth (IG) methods and the highest trapped field in an IG-processed bulk MgB_2 sample, B_z = 2.12 at 5 K and 1.66 T at 15 K, is reported. Since bulk MgB_2 has a more homogeneous J_c distribution than (RE)BCO bulks, studies on such systems are made somewhat easier because simplified assumptions regarding the geometry and J_c distribution can be made, and a numerical simulation technique based on the 2D axisymmetric H-formulation is introduced to model the complete process of field cooling (FC) magnetization. As input data for the model, the measured J_c(B,T) characteristics of a single, small specimen taken from each bulk sample are used, in addition to measured specific heat and thermal conductivity data for the materials. The results of the simulation reproduce the experimental results extremely well: (1) indicating the samples have excellent homogeneity, and (2) validating the numerical model as a fast, accurate and powerful tool to investigate the trapped field profile of bulk MgB_2 discs of any size accurately, under any specific operating conditions. Finally, the paper is concluded with a numerical analysis of the influence of the dimensions of the bulk sample on the trapped field.

This paper presents a topical review of the current state of the art in modelling the magnetization of bulk superconductors, including both (RE)BCO (where RE = rare earth or Y) and MgB2 materials. Such modelling is a powerful tool to understand the physical mechanisms of their magnetization, to assist in interpretation of experimental results, and to predict the performance of practical bulk superconductor-based devices, which is particularly important as many superconducting applications head towards the commercialisation stage of their development in the coming years. In addition to the analytical and numerical techniques currently used by researchers for modelling such materials, the commonly used practical techniques to magnetize bulk superconductors are summarised with a particular focus on pulsed field magnetization (PFM), which is promising as a compact, mobile and relatively inexpensive magnetizing technique. A number of numerical models developed to analyse the issues related to PFM and optimise the technique are described in detail, including understanding the dynamics of the magnetic flux penetration and the influence of material inhomogeneities, thermal properties, pulse duration, magnitude and shape, and the shape of the magnetization coil(s). The effect of externally applied magnetic fields in different configurations on the attenuation of the trapped field is also discussed. A number of novel and hybrid bulk superconductor structures are described, including improved thermal conductivity structures and ferromagnet-superconductor structures, which have been designed to overcome some of the issues related to bulk superconductors and their magnetization and enhance the intrinsic properties of bulk superconductors acting as trapped field magnets (TFMs). Finally, the use of hollow bulk cylinders/tubes for shielding is analysed.

The ability to generate a permanent, stable magnetic field unsupported by an electromotive force is fundamental to a variety of engineering applications. Bulk high temperature superconducting (HTS) materials can trap magnetic fields of magnitude over ten times higher than the maximum field produced by conventional magnets, which is limited practically to rather less than 2 T. In this paper, two large c-axis oriented, single-grain YBCO and GdBCO bulk superconductors are magnetized by the pulsed field magnetization (PFM) technique at temperatures of 40 and 65 K and the characteristics of the resulting trapped field profile are investigated with a view of magnetizing such samples as trapped field magnets (TFMs) in situ inside a trapped flux-type superconducting electric machine. A comparison is made between the temperatures at which the pulsed magnetic field is applied and the results have strong implications for the optimum operating temperature for TFMs in trapped flux-type superconducting electric machines. The effects of inhomogeneities, which occur during the growth process of single-grain bulk superconductors, on the trapped field and maximum temperature rise in the sample are modelled numerically using a 3D finite-element model based on the H-formulation and implemented in Comsol Multiphysics 4.3a. The results agree qualitatively with the observed experimental results, in that inhomogeneities act to distort the trapped field profile and reduce the magnitude of the trapped field due to localized heating within the sample and preferential movement and pinning of flux lines around the growth section regions (GSRs) and growth sector boundaries (GSBs), respectively. The modelling framework will allow further investigation of various inhomogeneities that arise during the processing of (RE)BCO bulk superconductors, including inhomogeneous Jc distributions and the presence of current-limiting grain boundaries and cracks, and it can be used to assist optimization of processing and PFM techniques for practical bulk superconductor applications.

The trapped field strength of HTSC stacks were measured in the temperature range T=4-80 K and dc magnetic fields up to 8 Т. A single 12 mm by 12 mm square samples were cut from commercial (RE)BCO tape 12 mm wide and then stacked together. The number of layers in the stacks was varied from n =5 to n =250. Trapped field strength was measured by means of Hall probe which was placed directly on the stacks surface. The dependences of remnant field strength B rem on number of layers in the stacks at different temperature B rem (n) as well as on temperature dependences B rem (T) at various n were obtained. It was found that B rem ( n ) dependences have a nonlinear character with a tendency to saturation for n > 60. The maximum remnant (trapped) field was found to be more than 2.5 Т at T=4 К. The relaxation of trapped field was studied also and it was determined that the rate of relaxation processes tends to decrease with the increase in a number of tapes in the stack. The correlation between dependency B rem ( n ) and dependency of magnetic levitation force measured at T=77 K at zero field cooling were found.