High-temperature Superconductors Research Articles

Electromagnetic design of high-temperature superconducting electrodynamic suspension magnets

This paper introduces the electromagnetic design process for high-temperature superconducting (HTS) magnets used in electrodynamic suspension (EDS) systems. First, the winding process and detailed parameters of the magnets are described. Then, based on the full-field angle characteristic method, the critical current of the magnets is evaluated and the operating current is determined. Finally, the magnetic field distribution and charging delay of the magnets are assessed based on the design results. This paper provides a reference for the electromagnetic design of superconducting electromagnetic suspension magnets.

Numerical simulations on the AC loss of REBCO stacks under rotating magnetic fields

AC loss presents a significant challenge for high-temperature superconducting (HTS) rotating machines. To date, the behaviour of total AC loss (Qtol) (with current) and magnetization loss (Qm) (without current) in a single HTS tape under rotating magnetic fields (RF) have been explored. However, a research gap remains in understanding how these findings translate to the more complex HTS windings of rotating machines. Further exploration is needed to understand the loss behaviour of more complex HTS structures, such as HTS stacks. In this work, Qtol and Qm, in the HTS stacks under RF and a perpendicular AC standing wave magnetic field are numerically investigated. Two different RF models are considered: one is the Uni-RF model, characterized by a uniform field with equal field amplitudes and phases at each position, and the other is a non-uniform field created by a rotating Halbach array, referred to as the Hal-RF model. The dependence of AC loss on parameters such as the number of tapes in the stacks, tape width (2a), and the inclination angle (α) of tapes, which refers to the angle between the normal direction of the stack and the vertical direction, have been explored. The number of tapes in the stacks ranges from 1 to 16, α ranges from 0° to 90°, and the tape width includes 4 mm and 40 mm. Additionally, different rotating field directions are also considered. Interestingly, the analytical values from Brandt and Indenbom equation for Qm of a superconducting strip (BI-strip) are close to Qm results of the stacks under the standing wave at high fields, while they are over twice as high as those in the Hal-RF model at 1 T. This suggests the BI-strip equation is not reliable for predicting Qm under RF at high fields. We also show in the Hal-RF model that different rotation directions of the field lead to varying Qm and Qtol when asymmetric Jc (B, θ) data are applied. Moreover, it has been observed that the inclination angle has no impact on Qm under uniform RF while significantly impacts both Qm and Qtol in the Hal-RF model.

Prediction of potential high-temperature superconductivity in ternary Y–Hf–H compounds under high pressure

Compressed ternary alloy superhydrides are currently considered to be the most promising competitors for high-temperature superconducting materials. Here, the stable stoichiometries in the Y–Hf–H ternary system under pressure are comprehensively explored in theory and four fresh phases are predicted: Pmna-YHfH6 and P4/mmm-YHfH7 at 200 GPa, P4/mmm-YHfH8 at 300 GPa and P-6m2-YHfH18 at 400 GPa. The four Y–Hf–H ternary phases are thermodynamically and dynamically stable at corresponding pressure. In addition, structural features, bonding characteristics, electronic properties, and superconductivity of the four ternary Y–Hf–H phases are systematically calculated and discussed. As the hydrogen content and the density of states of H atoms at the Fermi level increase, the superconducting transition temperatures (Tc) of Y–Hf–H system are significantly enhanced. The P-6m2-YHfH18 with high hydrogen content exhibits a high calculated Tc value of 130 K at 400 GPa.

Advances in the Parameter Space Concept towards Picometer Precise Crystal Structure Refinement—A Resolution Study

The Parameter Space Concept (PSC) is an alternative approach to solving and refining (partial) crystal structures from very few pre-chosen X-ray or neutron diffraction amplitudes without the use of Fourier inversion. PSC interprets those amplitudes as piecewise analytic hyper-surfaces, so-called isosurfaces, in the Parameter Space, which is spanned by the spatial coordinates of all atoms of interest. The intersections of all isosurfaces constitute the (possibly degenerate) structure solution. The present feasibility study investigates the La and Sr split position of the potential high-temperature super-conductor (La0.5Sr1.5)MnO4, I4/mmm, with a postulated total displacement between La and Sr of a few pm by theoretical amplitudes of pre-selected 00l reflections (l=2,4,…,20). The revision of 15-year-old results with state-of-the-art computing equipment enhances the former simplified model by varying the scattering power ratio fLa/fSr, as exploitable by means of resonant scattering contrast at synchrotron facilities, and irrevocably reveals one of the two originally proposed solutions as being a “blurred” pseudo-solution. Finally, studying the resolution limits of PSC as a function of intensity errors by means of Monte-Carlo simulations shows both that the split can only be resolved for sufficiently low errors and, particularly for the resonant scattering contrast, a theoretical precision down to ±0.19 pm can be achieved for this specific structural problem.

Analysis of a passive vibration damper for high-speed superconducting magnetic bearings

Superconducting magnetic bearings (SMB) based on a combination of high temperature superconductors and permanent magnets enable the realization of self-stabilized high-speed devices with significantly reduced friction. However, external vibration might couple in the bearing resulting in large amplitude oscillations due to a resonance case. A dedicated eddy current damper (ECD) might be used to eliminate these oscillations for a stable operation. The influence of such damping elements was studied for a frictionless SMB twisting system designed to speed up the conventional ring spinning process. Therefore, conductive copper rings with different thicknesses were implemented at different positions into the bearing setup as ECD. Afterward, the SMB setup was analyzed during acceleration using an array of laser distance sensors to record the displacement of the levitating permanent magnet ring in radial and axial direction, respectively. Simultaneously, a numerical model was developed to investigate the influence of the ECDs on the dynamic and static behavior of the SMB in more detail. It was shown that the simulated damping coefficients are in good agreement with the measured values, which allows further optimization of the ECD with the developed numerical model.

Evidence of strong and mode-selective electron–phonon coupling in the topological superconductor candidate 2M-WS2

The interaction between lattice vibrations and electrons plays a key role in various aspects of condensed matter physics — including electron hydrodynamics, strange metal behavior, and high-temperature superconductivity. In this study, we present systematic investigations using Raman scattering and angle-resolved photoemission spectroscopy (ARPES) to examine the phononic and electronic subsystems of the topological superconductor candidate 2M-WS2. Raman scattering exhibits an anomalous nonmonotonic temperature dependence of phonon linewidths, indicative of strong phonon–electron scattering over phonon–phonon scattering. The ARPES results demonstrate pronounced dispersion anomalies (kinks) at multiple binding energies within both bulk and topological surface states, indicating a robust and mode-selective coupling between the electronic states and various phonon modes. These experimental findings align with previous calculations of the Eliashberg function, providing a deeper understanding of the highest superconducting transition temperature observed in 2M-WS2 (8.8 K) among all transition metal dichalcogenides as induced by electron–phonon coupling. Furthermore, our results may offer valuable insights into other properties of 2M-WS2 and guide the search for high-temperature topological superconductors.

Quench protection for high-temperature superconductor cables using active control of current distribution

Superconducting magnets of future fusion reactors are expected to rely on composite high-temperature superconductor (HTS) cable conductors. In presently used HTS cables, current sharing between components is limited due to poorly defined contact resistances between superconducting tapes or by design. The interplay between contact and termination resistances is the defining factor for power dissipation in these cables and ultimately defines their safe operational margins. However, the current distribution between components along the composite conductor and inside its terminations is a priori unknown, and presently, no means are available to actively tune current flow distribution in real-time to improve margins of quench protection. Also, the lack of ability to electrically probe individual components makes it impossible to identify conductor damage locations within the cable. In this work, we address both problems by introducing active current control of current distribution between components using cryogenically operated metal-oxide-semiconductor-field-effect transistors (MOSFETs). We demonstrate through simulation and experiments how real-time current controls can help to drastically reduce heat dissipation in a developing hot spot in a two-conductor model system and help identify critical current degradation of individual cable components. Prospects of other potential uses of MOSFET devices for improved voltage detection, AC loss-driven active quench protection, and remnant magnetization reduction in HTS magnets are also discussed.

Intelligent surrogate model of a high-temperature superconducting cable for reliable energy delivery: short-circuit fault performance

High-temperature superconducting (HTS) cables are promising solutions for electric power transmission of renewable energy resources, where their fault performance study is vital to avoid power interruptions in the grid. In this study, a fast intelligent surrogate model was presented to estimate the fault performance of a 22.9 kV/50 MW HTS cable to make fast fault performance analysis of the HTS cables possible during the design stage. Different fault scenarios were considered under different fault durations, fault resistances, and types of faults. Then, the fault energy, fault current, fault type, fault duration, and fault resistance were fed into the surrogate model as inputs. The outputs were the temperature of the rare-earth barium copper oxide (ReBCO) tapes, the former temperature, the ReBCO layer current, and the total resistance of each phase. For surrogate modelling, cascade forward neural networks (CFNNs) were used. The results show that the CFNN-based model estimated the fault performance of the cable with an average accuracy of 99.1%. Finally, the impact of considering fault energy, fault current, and both, as the inputs of the models, on the final accuracy were explored. The results show that by considering the fault energy, the accuracy of the surrogate model can be increased.

High performance one-step grown half-moon shaped YBCO bulk superconductors

High-temperature superconducting (HTS) undulator exploiting the high trapped field of HTS bulk superconductors enables the design of extremely short-period insertion devices for synchrotron light sources and free electron lasers. In such a promising application the trapped field performance and the uniformity of the HTS bulk superconductors are essential. In this study, the half-moon shaped YBa2Cu3O7−δ (YBCO) single-grain superconductors have been directly grown by the top-seeded melted-growth method. Half-moon shaped samples directly grown from preforms with four different type of seed crystal arrangements were compared with that cut from larger cylindrical bulk superconductors in regarding to the trapped magnetic fields and correspondingly the distribution. We found that the arrangement of seed crystals greatly affects the melt-growth process and hence the homogeneity of the samples. The one-step grown half-moon shaped samples show higher trapped field (B trap), 0.542 T for a 24 mm and 0.785 T for a 32 mm diameter sample, and better uniformity of trapped field distribution compared to that obtained from machining with B trap of 0.427 T and 0.528 T. It was found that the growth sectors would be restricted when the seed crystal was placed at the edge of a preform, and the angle of the seed crystal, parallel or 45° to the long edge would influence the melt growth as well.

Superconductivity in pressurized trilayer La4Ni3O10-δ single crystals.

The pursuit of discovering new high-temperature superconductors that diverge from the copper-based model1-3 has profound implications for explaining mechanisms behind superconductivity and may also enable new applications4-8. Here our investigation shows that the application of pressure effectively suppresses the spin-charge order in trilayer nickelate La4Ni3O10-δ single crystals, leading to the emergence of superconductivity with a maximum critical temperature (Tc) of around 30 K at 69.0 GPa. The d.c. susceptibility measurements confirm a substantial diamagnetic response below Tc, indicating the presence of bulk superconductivity with a volume fraction exceeding 80%. In the normal state, we observe a strange metal behaviour, characterized by a linear temperature-dependent resistance extending up to 300 K. Furthermore, the layer-dependent superconductivity observed hints at a unique interlayer coupling mechanism specific to nickelates, setting them apart from cuprates in this regard. Our findings provide crucial insights into the fundamental mechanisms underpinning superconductivity, while also introducing a new material platform to explore the intricate interplay between the spin-charge order, flat band structures, interlayer coupling, strange metal behaviour and high-temperature superconductivity.

The Nature of Pointer States and Their Role in Macroscopic Quantum Coherence

This article begins with an interdisciplinary review of a hydrodynamic approach to understanding the origins and nature of macroscopic quantum phenomena in high-temperature superconductivity, superfluidity, turbulence and biological systems. Building on this review, we consider new theoretical insights into the origin and nature of pointer states and their role in the emergence of quantum systems. The approach includes a theory of quantum coherence underpinned by turbulence, generated by a field of pointer states, which take the form of recirculating, spin-1/2 vortices (toroids), interconnected via a cascade of spin-1 vortices. Decoherence occurs when the bosonic network connecting pointer states is disrupted, leading to their localisation. Building further on this work, we explore how quantum particles (in the form of different vortex structures) could emerge as the product of a causal dynamic process, within a turbulent (fractal) spacetime. The resulting particle structures offer new insights into intrinsic spin, the probabilistic nature of the wave function and how we might consider pointer states within the standard “point source” representation of a quantum particle, which intuitively requires a more complexed description.

Tunneling Spectroscopy at Megabar Pressures: Determination of the Superconducting Gap in Sulfur.

The recent discovery of high-temperature, high-pressure superconductors, such as hydrides and nickelates, has opened exciting avenues in studying high-temperature superconductivity. The primary superconducting properties of these materials are well characterized by measuring various electrical and magnetic properties, despite the challenges posed by the high-pressure environment. Experimental microscopic insight into the pairing mechanism of these superconductors is even more challenging, due to the lack of direct probes of the superconducting gap structures at high pressure conditions. Here, we have developed a planar tunnel junction technique for diamond anvil cells and present ground-breaking tunneling spectroscopy measurements at megabar pressures. We determined the superconducting gap of elemental sulfur at 160GPa, a key constituent of the high-temperature superconductor H_{3}S. High quality tunneling spectra indicate that β-Po phase sulfur is a type II superconductor with a single s-wave gap with a gap value 2Δ(0)=5.6 meV. This technique is compatible with superconducting compounds synthesized in diamond anvil cells and provides insight into the pairing mechanism in novel superconductors under high-pressure conditions.

3D electromagnetic assessment of bended CORC® cables

Conductor on round core (CORC®) cables have emerged as a leading contender in high-temperature superconducting (HTS) cable designs, offering exceptional performance with current densities surpassing 300 A/mm2 and the ability to withstand high axial tensile and compressive strain. Despite their remarkable properties, optimizing CORC® cables remains a challenge, particularly in accurately estimating their AC losses under real-world conditions, which necessitates advanced numerical modeling techniques. Building upon recent advancements in simulating straight CORC® cables, where Bean’s-like current profiles were observed across the actual thickness of wound superconducting tapes, we introduce a tailored computational approach to enhance the processing speed of three-dimensional (3D) finite element models of wound HTS tapes. This tailored approach is specifically designed to address the complexities of bent CORC® cables, which exhibit helicoidal winding and are subjected to varying mechanical strain. We focus on analyzing their electromagnetic performance by transitioning from idealized straight-former designs to more realistic scenarios where cable-formers are bent to accommodate flexible cable routing or coil configurations. Our simulations consider a typical cable design comprising three 4 mm-wide SuperPower tapes (SCS4050) with a twist pitch of 40 mm. We demonstrate the capability to accurately model the full electromagnetic behavior of bent CORC® cables without the reduction of degrees of freedom, providing valuable insights into their performance under bending conditions. Our findings contribute to the ongoing optimization of CORC® cable designs for a wide range of practical applications in high-current and high-magnetic field environments.

A platform to study defect-induced behavior in high-temperature superconductor cables

High-temperature superconductor (HTS) cables and magnets are enabling a range of high-current and high-field applications, including compact fusion devices aiming to achieve net energy. Defects in HTS pose manufacturing, cost, and operational challenges. A rigorous understanding and predictive capability for defect-induced behavior at relevant scale has not been established. To address this shortcoming, we have developed a cable-level defect characterization experimental platform coupled to high-fidelity computational modeling. The cable ( Ic∼ 438 A at 77.4 K, self-field) comprises a non-twisted 70 cm-long copper former containing a soldered stack of five rare-earth barium copper oxide (REBCO) tapes (each with Ic = 115.7 A/4 mm-w at 77.4 K, self-field), which can contain a variety of induced defects. Spatially-resolved electric fields are measured with a high-density voltage tap array and absolute current distribution with six custom-wound embedded Rogowski coils. 3D circuit modeling uses nodal analysis and self-consistently accounts for the magnetic field dependence of critical current. The model successfully predicts the experimentally measured spatial and operating current dependencies of electric field and current distribution with no defects, one defect, and two defects, validating the defect characterization platform as a tool for improving the design, cost, fabrication, and operation of REBCO cables.

Study on the response of the winding direction of multi-layer CORC cable to its electromagnetic characteristics

A Conductor on Round Core (CORC) cable wound with a high-temperature superconductor is an important cable concept for high-current density applications. It is widely used in large power systems because of its advantages of good flexibility and high engineering current density. However, the complex design structure of CORC cable makes it very difficult to understand its electromagnetic properties (such as AC loss). In particular, the different winding directions of each layer in multi-layer cable have a great influence on its electromagnetic characteristics. In this paper, the H-method is used to solve the electromagnetism and mechanics equations. The influence of the winding direction of CORC cable on its electromagnetic field distribution characteristics, AC loss, and mechanical variation under the action of external magnetic field is investigated. The AC loss study of single-layer cable reveals that when the applied magnetic field is increased from 0.01 to 0.02 and 0.03 T, the AC loss peak of the cable increases by 107 and 103 orders of magnitude, respectively, indicating that the effect of low applied magnetic field on the AC loss of the cable is more significant. For multi-layer cables, cables with opposite winding directions have a greater depth of current density penetration than cables with the same winding direction. In addition, the mechanical variations of multi-layer cables with different winding orientations are explored. The results show that the Mises stress in the cable with the same winding direction is about 32% higher than that of the cable with the opposite winding direction, which indicates that the method of winding the cable in the opposite direction between adjacent layers of tape can avoid excessive mechanical stress.

The influence of Sm[formula omitted]O[formula omitted] nanoparticles adding on some superconducting properties of Bi[formula omitted]Pb[formula omitted]Sr[formula omitted]Ca[formula omitted]Cu[formula omitted]O[formula omitted] ceramics

High-Temperature Superconductors Bi1.6Pb0.4Sr2Ca2Cu3O10+δ samples doped with Sm2O3 nanoparticles in different quantities (0.00, 0.02, 0.04 and 0.06), were synthesised. Solid state feedback technique was used to prepare the samples and then characterised. The morphology and structure of the specimens were deployed by scanning electron microscopy (SEM) and X-ray diffraction (XRD) examination. The spectroscopy of the energy dispersive X-ray (EDX) experiment was utilised to obtain the elemental composition of the samples. Resistivity versus temperature measurement in DC mode was employed to estimate the critical transition temperature of each sample. XRD with the Rietveld refinement process revealed that Bi2223 and Bi2212 stages exist mutually in specimens with orthorhombic crystal systems. The lowest percentage of volume fraction associated with the Bi2223 phase belonged to the sample with x=0.06 nanoparticle samarium doped. It was detected that with rising samarium content the volume division of the Bi2223 phase decreases but the Bi2212 stage increases compared with the pristine specimen. SEM showed that the shrinkage of grain size occurs when the amount of nano-sized Sm was added to x=0.02 sample with lower inter-coupling among superconducting granules. This effect might be verified by SEM and TEM images. EDX exhibited some peaks related to Sm and other elements of the Bi2223 structure. These patterns confirm that all elements associated with the compounds were introduced into the Bi2223 matrix. The critical temperatures such as Tconset, TcPeak and Tczero decreased for Sm doped samples compared with the pure sample. Adding Sm2O3 nanoparticles causes rising calculated density and hole carrier concentration. These outcomes can be interpreted as the allocation of additional positive charges to the CuO2 planes. It is worth mentioning that the superb properties such as high-Tc, high Jc, strong flux pinning, and good thermal stability, for Bi2223 and high breakdown electric field, high dielectric constant, and large bandgap for Sm2O3 are the issues to motivate the author to dope Bi2223 with Sm2O3 NPs. In brief, the electrical, mechanical and structural properties of Sm2O3 NPs doped Bi2223 play the main role in the applications, which drive the investigations to emphasise the synthesis of superconducting samples.

Electronic State-Regulated Magnetic Phenomena in Single-Crystal FeSe

In contrast to the observed high-temperature superconductivity in monolayer FeSe/SrTiO3 films, akin to CoSb/SrTiO3, the bulk counterpart, FeSe, does not exhibit superconductivity even under elevated pressure, and its magnetic characteristics remain subject to debate. This investigation delves into the electrical and magnetic attributes, alongside X-ray photoelectron spectroscopy (XPS) analysis, of FeSe mono-crystal. Magnetic and electrical transport assessments indicate that FeSe demonstrates characteristics of a Pauli paramagnetic metal within non-Fermi liquid traits. XPS analysis further reveals that the Fe and Se pair in FeSe exist in a zero-valence state, forming a predominantly metallic-bonded alloy. The Pauli paramagnetism observed in FeSe is ascribed to its itinerant electrons. The comprehension of the electronic states in FeSe mono-crystal not only clarifies its lack of magnetic characteristics but also paves the way for exploring potential high-temperature superconductivity.

Epitaxial Growth of Nano‐Sized Pb Islands on SrTiO3 Substrate: Competition Between Electron Correlation and Enhanced Superconductivity

AbstractThe discovery of the interface‐enhanced superconductivity in the single‐layer film of FeSe epitaxially grown on SrTiO3 substrates has triggered a flurry of activity in the field of superconductivity. It raised the hope to find more conventional high transition temperature (Tc) superconductors that are purely driven by the electron‐phonon interaction at ambient pressure. Here the epitaxial growth of the Pb nano‐sized islands on SrTiO3 (001) substrates with the island volumes ranging from 286 to 4945 nm3 is reported by molecular beam epitaxy, followed by systematic scanning tunneling microscopic/spectroscopic (STM/S) investigation. The observed STS gap for the nanoscale islands highly dependent on the volumes of nano‐sized islands, can be divided into three regions. By performing a detailed spectroscopic investigation, it is founded that superconductivity in the volume above 3700 nm3 (Region I) has a zero temperature energy gap (Δ(0)) and Tc of 6.8 meV and 9.8 K obtained by BCS fitting, showing the largely‐enhanced Δ and slightly‐increased Tc by comparing to the bulk Pb (1.4 meV and 7.2 K). As the volume in the range from 1300 to 3700 nm3 (Region II), a large Coulomb gap induced by electron correlation emerged and shows a volume‐dependent behavior, suggesting the reduced size can enhance electron correlation in Pb islands. As the volume decreases down to Region III, enhanced electron correlation and Coulomb gap become more dominant and superconductivity is totally suppressed. The experiment reveals that an electron‐electron interaction in nano‐sized Pb islands can be significantly enhanced by reducing the island sizes and suppresses the superconductivity, thus demonstrates a competition between superconductivity and electron correlation as the volume varies.

Optimization of Nd-Fe-B permanent magnet guideways with high-temperature stability

High-temperature superconducting (HTS) pinning Maglev systems are advantageous due to their ability to achieve large-scale passive-stabilized levitation. Elevated temperatures can lead to a reduction in the magnetic characteristics of the permanent magnet guideway (PMG), which may pose a risk to the safe functioning of HTS Maglev trains. In order to guarantee the secure and dependable functioning of HTS Maglev trains, it is necessary to augment the high-temperature stability of the PMG. This study involves simulating the high-temperature stability of present PMGs and developing a new PMG that exhibits greater performance. Magnetic field simulation is employed to compute the demagnetization of permanent magnets (PMs) in several typical PMGs, encompassing both reversible and irreversible scenarios, in order to examine the factors contributing to demagnetization and evaluate the thermal stability of the PMGs at elevated temperatures. The grade, size, and magnetization direction of the Halbach-type PMG are subsequently optimized and compared to the original Halbach-type PMG. Following this, ideas for further optimization are provided. The optimized Halbach-type PMG reduces the overall decay ratio of the highest magnetic flux density Bz by 5.77% compared to the existing Halbach-type PMG. Additionally, the irreversible decay ratio is decreased by 6.13% at 85 ℃. The levitation force decay ratio on the HTS bulks above the optimized Halbach-type PMG is decreased by 8.11% compared to the existing Halbach-type PMG. Additionally, the irreversible decay ratio is reduced by 9% at 85 ℃. This study provides valuable insights for enhancing the efficiency and performance of PMGs and HTS Maglev trains over extended periods of operation.

Comparative calculations of trapped field and trapped magnetic flux with different multi-pulse magnetization methods for a bulk high-temperature superconductor

Bulk high-temperature superconductors (HTSs) can trap high magnetic field and are potentially useful for a variety of applications as pseudo-permanent magnets. The pulsed field magnetization (PFM) for bulk HTSs is cost effective and flexible in application compared with quasi-static field cooling and zero field cooling techniques. Many PFM methods have been proposed in many studies to achieve the excellent magnetization performances such as high trapped field and large trapped magnetic flux. In order to clarify the magnetization characteristics of bulk HTSs using different typical PFM methods, we comparatively analyze several typical PFM methods using a simulation model based on the H-formulation combining the thermal conductivity equation. The electromagnetic and thermal behaviors during the magnetization of a bulk HTS with different PFM methods are numerically achieved using the solenoid-type coil to magnetize the bulk. The calculations show that multi-pulse magnetization methods can effectively enhance the trapped field and trapped magnetic flux of the bulk, and different multi-pulse magnetization methods have different efficiencies enhancing these performances. Among all considered PFM methods in the study, the combination method of modified multi-pulse technique with step-wise cooling and iteratively magnetizing pulsed-field method with reducing amplitude has the largest improvement for the trapped magnetic field and the trapped flux simultaneously.