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

Abstract

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.

Nonlinear dynamics of 3D superconducting maglevs with six degrees of freedom: dependence on magnetization strategy and disturbance type

“…It should be noted that the thermomagnetic instability may take place in a bulk SC during magnetization, which is closely dependent on the SC size, the ambient temperature, and the sweep rate, direction, and uniformity of the external magnetic field [29]. For the maglev system, the impact of local temperature variations on the dynamic levitation performance seems to be negligible, due to the infinitely long geometry for the PMs and the relatively large size for the SC immersed in liquid nitrogen.…”

“…η 3 and η 4 , are derived from experiments [44]. For the singular point (u 1 , u 2 ) = (0, 0), with the help of equations ( 28), (29) and table 1, we obtain that the eigenvalues λ = −0.014 ± 16.38i, −0.017 ± 19.40i, and −0.020 ± 21.73i In order to intuitively understand the translational motion stability, we choose different initial conditions for equation (26) and show the calculated translational motion phase portrait in figure 16, where the comparison between the calculated curve and the fitting curve of the guidance force, i.e. equation (24), is also displayed.…”

“…In fact, pinning of flux lines mainly affects the hysteretic magnetic force, and thermal depinning of flux lines is related to the force relaxation and levitation drift. Motivated by these experiments, many numerical studies have been performed to understand the effect of flux motion on the vibration and drift phenomena for maglevs in recent years [24][25][26][27][28][29][30][31][32][33]. The dynamics with two degrees of freedom, including levitation drift and resonance behavior, and the strategies to improve the dynamic levitation performance were studied using a 2D model based on the A − V formulation in [26,27].…”

“…Furthermore, magnetic flux lines generated by the guideway will periodically move in and out as the SC vibrates, which causes the alternating current (AC) loss and further affects the superconductivity. Recently, we have developed a 2D thermal-electromagnetic model in terms of the A − V formulation to analyze the thermal and rotational effects on the dynamics, as well as the levitation force jumping phenomenon caused by thermomagnetic instability [28,29]. Based on the H formulation, Deng et al and Yang et al have built a 3D electromagnetic-thermal model to analyze the vibration behavior of maglevs in the vertical and lateral directions caused by guideway random irregularity [30][31][32][33].…”