Flux Jumps Research Articles

Barkhausen Noise as A Magnetic Nondestructive Testing Technique

Magnetic Barkhausen Noise (MBN) is a magnetic-based non-destructive electromagnetic testing method. Due to the electromagnetic working principle of MBN, it can be used for ferromagnetic materials, which consist of small magnetic fields discredited by domain walls and oriented in various directions. In an external magnetic field application, the fields turn to the magnetic direction, and the domain walls move and cause magnetic flux jumps. The jumps are named Barkhausen Noise (BN). The domain wall movements are sometimes pushed down by microstructure, composition, and defects. As the magnetic domain walls break away from the pinning sites produce MBN signal. MBN can be used for different material properties such as microstructure, composition, residual stress, and hardness. The paper's purpose is to analyze MBN as an improved NDT, clarify the relationship between material properties and MBN profile, and introduce MBN's applications and test equipment of MBN.

Electromechanical behavior of a rectangular bulk superconductor with an inhomogeneous critical current density under pulsed-field magnetization

Bulk high-temperature superconductors are widely used in various superconducting devices for their high critical current density and the ability to trap large magnetic field. In some applications, bulk superconductors can be arranged in an array structure to increase the magnetic field strength. However, rectangular bulk superconductors can be arranged more compactly than commonly used cylindrical bulk superconductors. The unique shape of rectangular bulk superconductors results in different distributions of electromagnetic fields, temperature, and stress under a pulsed-field magnetization (PFM) than for cylindrical bulk superconductors. In bulk superconductors, growth sector boundaries and growth sector regions have different critical current density, resulting in an uneven critical current density. Therefore, in this study, the electromagnetic and mechanical behavior of non-uniform rectangular bulk superconductors during the PFM process is investigated. The corresponding distribution and variation in the magnetic field, current, temperature, and stress in the bulk are calculated and analyzed. The influence of rectangle aspect ratio on the electromagnetic and mechanical behavior is discussed. The calculation results show that the magnetic flux jumps occur accompanied by sudden changes in the temperature and pressure. The effect of the aspect ratio of rectangular bulk superconductors on their electromagnetic and mechanical properties is analyzed. The influence of preexisting cracks in a non-uniform rectangular bulk superconductor on the simulation results is discussed. The numerical results indicate that the presence of an edge crack exacerbates the magnetic flux jump as well as the jumps in the temperature and stress. However, a central crack has a relatively small effect on the stability of a bulk superconductor.

Impact of local plastic deformation on thermo-magnetic instability of high-J c Nb3Sn strand

The future fusion reactor devices built by Institute of Plasma Physics, Chinese Academy of Science will be a compact burning plasma facility to fill the gap between ITER and the China Fusion Engineering Test Reactor, with the mission of studying the deuterium–tritium plasma in steady-state operation. The winding-package (WP) of its toroidal field coil is graded into high-field WP and low-field WP, and the high critical current density (J c) Nb3Sn strand will be applied to the high-field WP based on the current design. The thermo-magnetic instability is the main issue in the application of high-J c Nb3Sn strand, which may induce premature quenching in the low field regions. This issue can be improved by reducing the effective filament diameter (d eff) to suppress flux jumps and increasing the residual resistivity ratio (RRR) to enhance the release of heat generated by flux jumps. However, in the conductor manufacturing process, local plastic deformations (indentation) of strands can impact the sub-element layout and degrade the RRR of the strand, which would increase again the risk on instability. In this study, magnetization measurements and V–I tests were performed on samples with different indentation depths. The hysteresis loss and d eff of the indented sample was obtained from the test results. The impact of local plastic deformation on the thermo-magnetic instability of two types of Nb3Sn strand was confirmed by cross-sectional metallographic observation and quantitative microstructure analysis. It was shown that flux jumps were suppressed at indentation depths below 0.3 mm. Further indentation increase leads to severe flux jumps.

Flux jump and mechanical response in inhomogeneous high-temperature superconductor under the pulsed-field magnetization

The high-temperature bulk superconductors with high critical current density are brittle, and can be damaged by large Lorentz forces and thermal stress during magnetization. Several studies have reported the failure of bulk superconductors during flux jumps. In this study, we analyzed the magnetization characteristics and mechanical response of the HTS bulk with inhomogeneous current density along the c-axis. The numerical simulation was consistent with the experimental results presented in the reference. Moreover, a flux jump occurred near the area of the pre-arrangement flux during the second pulsed field magnetization. The maximum temperature is lower than the critical temperature during the flux jump. In the mechanical analysis, the flux jump led to an abrupt change in the maximum stress of the bulk, and the maximum radial stress was significantly higher than the maximum hoop stress during the flux jump. The maximum radial stress increased with decreasing ambient temperature during the flux jump, and the maximum stress area was always near the seeded plane. Subsequently, the magnetization characteristics and mechanical response were studied for different locations of the seeded surface, two concentric superconducting bulks, and non-uniform fields.

Vortex Dynamics and Pinning in CaKFe4As4 Single Crystals from DC Magnetization Relaxation and AC Susceptibility

Among various “families” of iron-based superconductors, the quite recently discovered AeAFe4As4 (where Ae is an alkali-earth metal and A is an alkali metal) has high critical current density, a very high upper critical field, and a low anisotropy, and has recently received much interest for the possibility of high magnetic field applications at the liquid hydrogen temperature. We have performed DC magnetization relaxation and frequency-dependent AC susceptibility measurements on high-quality single crystals of CaKFe4As4 with the aim of determining the pinning potential U*. The temperature dependence of U* displays a clear crossover between elastic creep and plastic creep. At temperatures around 27–28 K, U* has a very high value, up to 1200 K, resulting in an infinitesimally small probability of thermally activated flux jumps. From the dependence of the normalized pinning potential on irreversible magnetization, we have determined the creep exponents in the two creep regimes, which are in complete agreement with theoretical models. The estimation of the pinning potential from multifrequency AC susceptibility measurements was possible only near the critical temperature due to equipment limitations, and the resulting value is very close to the one that resulted from the magnetization relaxation data. Magnetic hysteresis loops revealed a second magnetization peak and very high values of the critical current density.

The signature of refreshed shocks in the afterglow of GRB 030329

ABSTRACT GRB 030329 displays one clear and, possibly, multiple less intense fast-rising (Δt/t ∼ 0.3) jumps in its optical afterglow light curve. The decay rate of the optical light curve remains the same before and after the flux jumps. This may be the signature of energy injection into the shocked material at the front of the jet. In this study, we model the Gamma-ray Burst (GRB) ejecta as a series of shells. We follow the dynamical evolution of the ejecta as it interacts with itself (i.e. internal shocks) and with the circumburst medium (i.e. external forward and reverse shocks), and calculate the emission from each shock event assuming synchrotron emission. We confirm the viability of the proposed model in which the jumps in the optical afterglow light curve of GRB 030329 are produced via refreshed shocks. The refreshed shocks may be the signatures of collisions between earlier ejected material with an average Lorentz factor $\bar{\Gamma }\gtrsim 100$ and later ejected material with $\bar{\Gamma } \sim 10$ once the early material has decelerated due to interaction with the circumburst medium. We show that even if the late material is ejected with a spread of Lorentz factors, internal shocks naturally produce a narrow distribution of Lorentz factors (ΔΓ/Γ ≲ 0.1), which is a necessary condition to produce the observed quick rise times of the jumps. These results imply a phase of internal shocks at some point in the dynamical evolution of the ejecta, which requires a low magnetization in the outflow.

Multiquanta flux jumps in superconducting fractal

We study the magnetic field response of millimeter scale fractal Sierpinski gaskets (SG) assembled of superconducting equilateral triangular patches. Directly imaged quantitative induction maps reveal hierarchical periodic filling of enclosed void areas with multiquanta magnetic flux, which jumps inside the voids in repeating bundles of individual flux quanta Φ0. The number Ns of entering flux quanta in different triangular voids of the SG is proportional to the linear size s of the void, while the field periodicity of flux jumps varies as 1/s. We explain this behavior by modeling the triangular voids in the SG with effective superconducting rings and by calculating their response following the London analysis of persistent currents, Js, induced by the applied field Ha and by the entering flux. With changing Ha, Js reaches a critical value in the vertex joints that connect the triangular superconducting patches and allows the giant flux jumps into the SG voids through phase slips or multiple Abrikosov vortex transfer across the vertices. The unique flux behavior in superconducting SG patterns, may be used to design tunable low-loss resonators with multi-line high-frequency spectrum for microwave technologies.

Trapped Fields of Hot-Pressed MgB2 for Applications in Liquid Hydrogen

The development of hydrogen energy and, in particular, high-performance submersible liquid hydrogen (LH) pumps requires superconducting bearings which can trap magnetic fields up to 1 T at 20 K. MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is hence a promising candidate for this application. The superconducting properties and microstructure of differently prepared MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> were compared and the ability of different composite materials to trap magnetic fields was studied. Hollow cylinders of the same geometry were manufactured from hot pressed (under 30 MPa) blocks prepared from Mg:2B with Ti, TiC and Ti-O additives as well as from melt-textured YBCO ceramics. The high critical current densities and critical magnetic fields should ensure high trapped fields in all these materials. Indeed all materials demonstrated the required performance; however, flux jumps are a serious issue in MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> even in crack free cylinders and impeded higher trapped fields.

Properties of superconducting MgB2 spherical shells deposited on 2 mm and 1 mm diameter Si3N4 spheres

Superconducting spherical shells may not only provide an appealing platform for exploring superconductivity in three-dimensional (3D) geometries with curved surfaces, but also be practically applied in important fields, such as in gyroscopes and gravimeters. In inertial confinement fusion (ICF), the perturbation on the target capsule caused by traditional contact support methods is recognized as one of the major contributors to performance degradation in ICF implosions. It was proposed recently that coating the capsule with a thin superconducting MgB2 spherical shell to realize non-contact support by means of magnetic levitation at the required temperatures K might offer a promising solution to this longstanding problem. To simulate the coating of ICF capsules, we deposited MgB2 spherical shells onto polycrystalline Si3N4 spheres (diameter d = 2 mm and 1 mm) via a hybrid physical–chemical vapour deposition technique. For both diameters, the spherical shells, of about 1 µm in thickness and covering the whole spheres completely, were polycrystalline with thin plate-shaped MgB2 crystallites oriented randomly and closely connected. The spherical shells exhibited superconducting transition at a zero resistance temperature of 38.5–39.4 K in four-probe resistance measurements and ideal diamagnetism at low temperatures in magnetization measurements, suggesting the good crystallinity and homogeneity of the shells. The upper critical field , the irreversibility field and the lower critical field were characterized and showed similar magnitudes and temperature dependencies for the d = 2 mm and 1 mm shells, yielding of 7–8 T and of 7–12 mT at 20 K. The superconducting critical current density values, evaluated from the magnetization hysteresis loops, were A cm−2 and A cm−2 at 20 K under zero and 2 T applied field, respectively, for the d = 1 mm shell. The occurrence of small flux jumps was observed at low temperatures up to 12 K and in low fields below 0.3 T. The results demonstrate the feasibility of fabricating MgB2 spherical shells with properties applicable to potential areas employing magnetic levitation such as in ICF and that MgB2 spherical shells may be exploited as an experimental system to study superconductivity in 3D curvilinear geometry.

Significant reduction in the low-field magnetization of Nb3Sn superconducting strands using the internal oxidation APC approach

Nb3Sn superconductors are promising for building accelerator magnets for future energy-frontier circular colliders. A critical factor for this application is the low-field persistent-current magnetization because it leads to several critical issues: e.g. low-field instability (including flux jumps), hysteresis loss, and field errors in magnet bores. Suppression of low-field magnetization requires reduction of low-field critical current density (J c) or effective subelement size (d eff). However, reduction of d eff of state-of-the-art Nb3Sn conductors—the restacked-rod-process (RRP®) type—below 40–50 μm without a pronounced decrease in high-field J c is difficult. On the other hand, the internal oxidation method which forms artificial pinning centers (APC) in Nb3Sn offers an alternative approach to reducing the low-field magnetization. Compared with a conventional Nb3Sn conductor whose flux pinning force versus field (F p–B) curve peaks at ∼20% of its irreversibility field (B irr), the F p–B curve peaks of APC conductors shift to higher fields due to the point pinning effect, leading to flattening of the J c–B curves. The goal of this paper is to quantitatively study how much the APC approach can reduce the low-field magnetization. We measured the J c–B curves of an RRP® conductor and two APC conductors (reacted at 700 °C) from zero field to B irr using a high-field vibrating sample magnetometer. The results showed that the APC conductors have higher non-Cu J c at high fields (e.g. 32%–41% higher at 16 T) and simultaneously lower non-Cu J c at low fields (e.g. 28%–34% lower at 1 T) compared with the RRP®. This effect is due to a competition between their Nb3Sn layer fraction ratios and layer F p ratios. Suppose they reach the same 16 T non-Cu J c, then the 1 T non-Cu J c and magnetization of the APC conductors are only half or even less compared with the RRP® conductor.

Pulsed field magnetization of a rectangular Y–Ba–Cu–O bulk, single grain superconductor assembly

The practical magnetization of arrays of multiple single grain, bulk high temperature superconductors is essential for practical applications, such as trapped flux rotating machines, magnetic resonance imaging and nuclear magnetic resonance. We report a systematic investigation of the pulsed field magnetization (PFM) of a bulk assembly consisting of two rectangular Y–Ba–Cu–O bulk single grains, in close proximity, at various temperatures. The measurements of the dynamic variation of the magnetic flux density, supported by numerical analysis, reveal that the induced screening currents during the rise of a pulsed field may greatly enhance the flux density in the region of the junction leading to uneven flux penetration and to an increased likelihood of flux jumps in this region. Such coupling between field and current promotes magnetic flux penetration and improves the peak trapped field from 3.01 T for a bulk single grain to 3.11 T for the bulk assembly at 30 K, improving the magnetization efficiency from 80% to 90%. The peak trapped field was further enhanced to 3.39 T and 3.31 T for the single bulk single grain and the bulk assembly, respectively, by employing a two-step multi-pulse PFM process.

Determination of the Temperature in a Homogeneous Half-Plane with an Inclined Rectilinear Crack Approaching the Boundary of the Half-Plane According to the Magnitude of the Heat Flux Through the Boundary of the Half-Plane and the Magnitude of the Temperature and Heat Flux Jumps on the Crack

Statement of the problem. The study is devoted to determining the temperature in a homogeneous half-plane with a finite rectilinear crack approaching the boundary of the half-plane, provided that the magnitude of the heat flux through the boundary of the half-plane as well as the jumps in temperature and heat flux on the crack are known. Results. A mathematical model is set forth that describes the stationary distribution of heat in a homogeneous half-plane with a rectilinear crack approaching the boundary of the half-plane, for the case when the magnitude of the heat flux through the boundary of the half-plane and the jumps in temperature and heat flux on the crack are known. The mathematical correctness of the proposed model is proved; a technique for constructing a solution to the model, as well as a whole class of related problems, is shown; a formula for representing the solution of the model is obtained. Conclusions. The formula obtained in the article can be used to study the temperature distribution in a material with a crack, including in the vicinity of a crack, as well as to determine what effect the presence of a crack has on the heat distribution.

CoolPINNs: A physics-informed neural network modeling of active cooling in vascular systems

Emerging technologies like hypersonic aircraft, space exploration vehicles, and batteries avail fluid circulation in embedded microvasculatures for efficient thermal regulation. Modeling is vital during the design and operational phases of these engineered systems. However, many challenges exist in developing a modeling framework. What is lacking is an accurate framework that (i) captures sharp jumps in the thermal flux across complex vasculature layouts, (ii) deals with oblique derivatives (involving tangential and normal components), (iii) handles nonlinearity because of radiative heat transfer, (iv) provides a high-speed forecast for real-time monitoring, and (v) facilitates robust inverse modeling. This paper addresses these challenges by availing the power of physics-informed neural networks (PINNs). We develop a fast, reliable, and accurate Scientific Machine Learning (SciML) framework for vascular-based thermal regulation—called CoolPINNs: a PINNs-based modeling framework for active cooling. The proposed mesh-less framework elegantly overcomes all the mentioned challenges. The significance of the reported research is multi-fold. First, the framework is valuable for real-time monitoring of thermal regulatory systems because of rapid forecasting. Second, researchers can address complex thermoregulation designs since the approach is meshless. Finally, the framework facilitates systematic parameter identification and inverse modeling studies, perhaps the most significant utility of the current framework.

Analysis of critical current inhomogeneity in r–z plane of GdBCO superconducting bulk and simulation of flux jumps during pulsed field magnetization

In pulsed field magnetization (PFM), the phenomenon of flux jump is capable of driving magnetic flux vortexes into the GdBCO superconducting bulk center to aid full magnetization. Various homogeneous critical current density (J c) models have been implemented to reproduce flux jumps, but the simulated multi-physical responses differ from experimental observations. This paper proposes a modified J c model to consider r–z plane J c inhomogeneity, and simulates flux jumps under experimental conditions by solving a 2D axisymmetric electromagnetic-thermal coupled model. A numerical treatment is developed to reflect the breaking of shielding current during flux jumps. The accuracy of our model is verified by comparisons of the calculated results for trapped magnetic fields (B T) and the PFM and field-cooling experimental results. On this basis, we investigate the improvement of the inhomogeneous J c model and obtain multi-physical responses that show better agreement with the experimental results compared to the homogeneous J c model. Moreover, to further test the ability of the inhomogeneous J c model to predict the anisotropy of the spatial magnetic field distribution, the simulated B T profiles at the top and bottom surfaces of the high-temperature superconductor (HTS) bulk at 77 K are compared to the experiments. This study may provide a new approach for modeling the inhomogeneity of J c characteristics and a useful analysis tool for industrial devices using HTS bulk magnets.

Similarity of magnetization and magnetic flux jumps evolution with the magnetic field direction relative to the plane of the superconducting niobium plate

The magnetization M(H) of the superconducting niobium plate was measured for a series of angles α between the direction of the magnetic field and the plane of the sample. It was found that: (1) M(H) at α = 0° and α = 90° differ significantly; (2) the jumps in the magnetic flux, which are observed on M(H) at low temperatures, also differ significantly for α = 0° and α = 90°; (3) in a wide range of angles, the form of the dependences M(H) and the flux jumps, characteristic of α = 90°, are retained when the magnetic field deviates from the normal of the sample. The same is observed at a deviation from α = 0°, but in a smaller range of angles.

Fast time-varying current triggering flux jumps of multi-filamentary Nb3Sn wire exposed to oblique magnetic field

Due to the oblique magnetic field and rapid time-varying current, the electromagnetic response and thermomagnetic instabilities of high-field superconducting dipole magnets are quite different from the solenoid coils. In this work, we theoretically investigate the flux jump of composite multi-filamentary Nb3Sn wire with high critical current density exposed to an oblique magnetic field and fast transport current. The thermomagnetic stability/instability regions are obtained with respect to flux creep factor and oblique ratios of magnetic field. It is found that the parallel component of the oblique magnetic field can suppress the flux jump. Unlike slow current, it is interesting to find that the fast variations of self-field by high ramp current can trigger flux jumps in Nb3Sn wire. The fast current triggering flux jumps can be tuned by the static oblique magnetic field. Furthermore, we demonstrate that current-like distribution is more likely to trigger quenches, while the magnetic field-like distribution is more likely to trigger flux jumps. The findings of this work are helpful for the optimization of the superconducting coils exposed to oblique magnetic field and fast time-varying current.

Modelling and mitigating flux jumps in bulk high-temperature superconductors during quasi-static, high-field magnetisation

(RE)-Ba2Cu3O bulk superconductors acting as permanent trapped field magnet analogues have been shown to trap fields in excess of 17 T. However, the occurrence of thermomagnetic instabilities during their magnetisation process can limit their performance. In 2019, Naito et al trapped 15.1 T in a (Y)-BaCuO bulk pair under applied fields of up to 22 T (2019 J. Appl. Phys. 126 243901), whilst also documenting the mechanical failure of the bulks due to a flux jump. Here, we accurately numerically model this experiment and the observed flux jump, providing insight into the experimental results, such as the role of heating, the presence of thermal gradients, and a possible reason for the location of the bulk-pair fracturing. Extending the study with an investigation into the role of enhanced cooling of the bulk-pair, the influence of cooling power on the calculated trapped field and flux jump is explored. Finally, we propose and numerically investigate a new composite bulk configuration, consisting of stacks of (Y)-BaCuO bulk and interspaced metallic discs, to enhance the thermal stability of the bulk pair, to ultimately improve the trapped field performance.

JWST NIRCam Defocused Imaging: Photometric Stability Performance and How It Can Sense Mirror Tilts

We use JWST NIRCam short-wavelength photometry to capture a transit lightcurve of the exoplanet HAT-P-14 b to assess performance as part of instrument commissioning. The short-wavelength precision is 152 ppm per 27 s integration as measured over the full time series compared to a theoretical limit of 107 ppm, after corrections to spatially correlated 1/f noise. Persistence effects from charge trapping are well fit by an exponential function with short characteristic timescales, settling on the order of 5–15 minutes. The short-wavelength defocused photometry is also uniquely well suited to measure the real-time wave-front error of JWST. Analysis of the images and reconstructed wave-front maps indicates that two different hexagonal primary mirror segments exhibited “tilt events,” where they changed orientation rapidly in less than ∼1.4 s. In some cases, the magnitude and timing of the flux jumps caused by tilt events can be accurately predicted with a telescope model. These tilt events can be sensed by simultaneous longer-wavelength NIRCam grism spectral images alone in the form of changes to the point-spread function, diagnosed from the full width at half maximum. They can also be sensed with the fine guidance sensor instrument from difference images. Tilt events possibly from sudden releases of stress in the backplane structure behind the mirrors were expected during the commissioning period because they were found in ground-based testing. Tilt events have shown signs of decreasing in frequency but have not disappeared completely. The detectors exhibit some minor (less than 1%) deviations from linear behavior in the first few groups of each integration, potentially impacting absolute fluxes and transit depths on bright targets, where only a handful of groups are possible. Overall, the noise is within 50% of the theoretical photon noise and read noise. This bodes well for high-precision measurements of transiting exoplanets and other time variable targets.

Thermomagnetic instabilities in 3D network of superconducting lead nanofilaments in porous glass

Thermomagnetic instabilities in the lead-porous glass (Pb-PG) nanocomposite in superconducting state were studied, and a model was proposed that relates magnetization jumps and heat release spikes with average critical current density. The samples were created by filling porous glass (characteristic pore size d = 7 nm) with lead from a melt under pressure, which created a 3D multiply connected system of lead filaments. The critical temperature of superconducting transition in Pb-PG T c = 7.2 K is the same as for bulk lead and the critical magnetic field H c (0) ≈ 40 kOe is much higher than H c bulk (0) ≈ 800 Oe for bulk lead. Hysteresis and magnetic flux jumps were observed in the magnetization curves m(H) of the Pb-PG nanocomposite, which are connected with the formation of magnetic flux gradients in a system of interconnected contours. Magnetic flux jumps are thermomagnetic processes accompanied by heat release which was directly observed by measuring adiabatic temperature change in the sample during magnetic field sweep. The flux jumps in the magnetization and heat release events were almost periodic in the magnetic field. The period dependences on the magnetic field are similar to the calculated average critical current density dependence j c (H).

Thermomagnetic instability and accompanied stress intensity factor jumps in type-II superconducting bulks under various magnetization processes

For type-II superconducting bulks used as trapped-field magnets, the thermomagnetic instability, manifested as flux jumps and temperature spikes, frequently takes place, resulting in a large amount of energy dissipation in a short time and further the crack problem due to electromagnetic and thermal stresses. In this paper, based on the magnetic and heat diffusion equations and fracture theory, we develop a thermal-magnetic-mechanical coupling model to analyze the flux-jump and fracture behaviors in bulk samples of BiSrCaCuO under various magnetization processes. This model has an important advantage that the simulation domain can be restricted to the sample itself, without having to consider the air region around it, and its reliability is verified by the existing experimental and numerical results. The effects of the sample size, the ambient temperature, and the sweep rate, direction, and uniformity of the external magnetic field on the flux jumps, and Mode I and Mode II stress intensity factors are fully analyzed under different cooling conditions. It is found that as ambient temperature or field inclined angle increases or field sweep rate decreases, the first flux-jump field presents a trend of monotonically increasing for zero-field-cooling magnetization but it has an opposite trend for field-cooling magnetization. The flux jump can lead to the jump of temperature, electromagnetic force, and stress intensity factor. In addition, the sensitivity of flux-jump and fracture behaviors to different parameters and the influence of flux jump on the demagnetization behavior under crossed magnetic fields are discussed. We also find the levitation force jumping phenomenon when the bulk sample is magnetized in a nonuniform magnetic field. From the results obtained, we provide some general guidelines on how the system parameters of superconducting bulk magnets could be chosen to improve the thermal-magnetic-mechanical stability.