Magnetothermal Instabilities Research Articles

Dependence of thermomagnetic instability on strong nonlinear <i>E</i>-<i>J</i> models in superconducting films

The <inline-formula><tex-math id="M4">\begin{document}$E\text{-}J$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M4.png"/></alternatives></inline-formula> relationship in conventional conductor generally satisfies the linear Ohm's law. However, the <inline-formula><tex-math id="M5">\begin{document}$E\text{-}J$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M5.png"/></alternatives></inline-formula> model in superconductors presents strong nonlinear characteristics, which is significantly different from that of the conventional conductor. According to the nonlinear <inline-formula><tex-math id="M6">\begin{document}$E\text{-}J$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M6.png"/></alternatives></inline-formula> power law of superconducting materials, we quantitatively investigate the relationship between the magnetic-thermal stability and the nonlinear constitutive characteristic of superconducting films at different temperatures, magnetic field ramp rates, and critical current densities by using the fast Fourier transform method (FFT). We find that the strong nonlinear electromagnetic constitutive model plays a crucial role responsible for the onset and morphology (tree-like and finger-like) of the magneto-thermal instability of superconducting thin films. In addtion, the reason why similar magneto-thermal instabilities cannot be observed in conventional conductors is also explained. It can be found that the magnetic field on the border of the superconducting film increases rapidly for a larger creep exponent due to the enhancement of diamagnetism, which results in a large magnetic pressure and easily triggering off flux avalanches. Therefore, the threshold field of flux avalanches in the superconducting film decreases with flux creep exponent increasing. Finally, we present the curves that can clearly divide the <inline-formula><tex-math id="M7">\begin{document}$n_0\text{-}j_{c0}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M7.png"/></alternatives></inline-formula> plane and <inline-formula><tex-math id="M8">\begin{document}$n_0\text{-}\dot {H}_a$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20-20220285_M8.png"/></alternatives></inline-formula> plane into magneto-thermal stability region and magneto-thermal instability region for superconducting thin film with different levels of nonlinearity.

Legolas: A Modern Tool for Magnetohydrodynamic Spectroscopy

Abstract Magnetohydrodynamic (MHD) spectroscopy is central to many astrophysical disciplines, ranging from helio- to asteroseismology, over solar coronal (loop) seismology, to the study of waves and instabilities in jets, accretion disks, or solar/stellar atmospheres. MHD spectroscopy quantifies all linear (standing or traveling) wave modes, including overstable (i.e., growing) or damped modes, for a given configuration that achieves force and thermodynamic balance. Here, we present Legolas, a novel, open-source numerical code to calculate the full MHD spectrum of one-dimensional equilibria with flow, balancing pressure gradients, Lorentz forces, centrifugal effects, and gravity, and enriched with nonadiabatic aspects like radiative losses, thermal conduction, and resistivity. The governing equations use Fourier representations in the ignorable coordinates, and the set of linearized equations is discretized using finite elements in the important height or radial variation, handling Cartesian and cylindrical geometries using the same implementation. A weak Galerkin formulation results in a generalized (non-Hermitian) matrix eigenvalue problem, and linear algebraic algorithms calculate all eigenvalues and corresponding eigenvectors. We showcase a plethora of well-established results, ranging from p and g modes in magnetized, stratified atmospheres, over modes relevant for coronal loop seismology, thermal instabilities, and discrete overstable Alfvén modes related to solar prominences, to stability studies for astrophysical jet flows. We encounter (quasi-)Parker, (quasi-)interchange, current-driven, and Kelvin–Helmholtz instabilities, as well as nonideal quasi-modes, resistive tearing modes, up to magnetothermal instabilities. The use of high resolution sheds new light on previously calculated spectra, revealing interesting spectral regions that have yet to be investigated.

Modeling the Effect of Thermal Field in Formation of Magnetic Flux Avalanches in Hard Superconductors

Magnetothermal instabilities are one of the uncharacteristic phenomena of interest in conventional type-II as well as in high-T c superconductors. Historically, some authors undertake to analyze the nature and origin of the magnetothermal instabilities of the critical state and flux jumps phenomena in superconductors in the light of theoretical and experimental results (Wipf, Phys. Rev. 161:404, 1967; Wipf, Cryogenics 31:936, 1992; Lee at al., J. Appl. Phys. 107:013902, 2010) [1, 2]. In contrast to previous reported works which had studied the magnetic flux avalanches in hard superconductors postulating an instability criterion, in this paper, we report the development of a theoretical model for describing the magnetization curves of type-II superconductors considering the fact that the jumps should arise naturally, i.e., without the need to impose a priori conditions of instability. The model developed is applied to make numerical calculations in order to get magnetization curves of MgB2 as well as to calculate and analyze the impact of changes in the thermal field and functions that describe the critical current. We investigate the effect of initial magnetic state on generation of magnetic flux avalanches. The initial state determines the evolution of the magnetization curves and their jumps. The results obtained with the application of this model allow us to reproduce the experimental conditions with greater accuracy than that achieved with models based on unstable conditions; further, the model predicts the impact of initial nonzero fields in the formation of avalanches.

Impact of the Residual Resistivity Ratio on the Stability of ${\rm Nb}_{3}{\rm Sn}$ Magnets

The CERN Large Hadron Collider (LHC) is envisioned to be upgraded in 2020 to increase the luminosity of the machine. The major upgrade will consist in replacing the NbTi quadrupole magnets of the interaction regions with larger aperture magnets. The Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn technology is the preferred option for this upgrade. The critical current density J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn strands have reached sufficiently high values (in excess of 3000 at 12 T and 4.2 K) allowing larger aperture/stronger field magnets. Nevertheless, such large J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> values may cause magneto-thermal instabilities that can drastically reduce the conductor performance by quenching the superconductor prematurely. In Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn magnets, a relevant parameter for preventing premature quenches induced by magneto-thermal instabilities is the Residual Resistivity Ratio (RRR) of the conductor stabilizing copper. An experimental and theoretical study was carried out to investigate how much the value of the RRR affects the magnet stability and to identify the proper conductor specifications. In this paper the main results are presented and discussed.

Magnetothermal and magnetorotational instabilities in hot accretion flows

In a hot, dilute, magnetized accretion flow, the electron mean-free path can be much greater than the Larmor radius, thus thermal conduction is anisotropic and along magnetic field lines. In this case, if the temperature decreases outward, the flow may be subject to a buoyancy instability (the magnetothermal instability, or MTI). The MTI amplifies the magnetic field, and aligns field lines with the radial direction. If the accretion flow is differentially rotating, the magnetorotational instability (MRI) may also be present. Using two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate the interaction between these two instabilities. We use global simulations that span over two orders of magnitude in radius, centered on the region around the Bondi radius where the infall time of gas is longer than the growth time of both the MTI and MRI. Significant amplification of the magnetic field is produced by both instabilities, although we find that the MTI primarily amplifies the radial component, and the MRI primarily the toroidal component, of the field, respectively. Most importantly, we find that if the MTI can amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$, then when the MTI and MRI are both present, the magnetic energy can be amplified by a factor of $F_t \cdot F_r$. We therefore conclude that amplification of the magnetic energy by the MTI and MRI operates independently. We also find that the MTI contributes to the transport of angular momentum, because radial motions induced by the MTI increase the Maxwell (by amplifying the magnetic field) and Reynolds stresses. Finally, we find that thermal conduction decreases the slope of the radial temperature profile. The increased temperature near the Bondi radius decreases the mass accretion rate.

Magneto-Thermal Stability in LARP ${\rm Nb}_{3}{\rm Sn}$ TQS Magnets

In the framework of the US LHC Accelerator Program (LARP), three US laboratories BNL, FNAL and LBNL are developing Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn quadrupole magnets for the Large Hadron Collider (LHC) luminosity upgrade. At present CERN is supporting this activity by testing some of the LARP 1 m long 90 mm aperture magnets. Recently two magnets using a shell based key and bladder technology (TQS) have been tested at CERN. These magnets (TQS02c, TQS03a) share the same mechanical structure and use a 27 strand Rutherford cable based on the 0.7 mm RRP strand. The main difference between the two magnets is the strand sub-element layout (54/61 in TQS02c versus 108/127 in TQS03a) and the strand critical current. The TQS03a wire has a lower (18%) critical current, a larger amount of copper stabilizer, and a larger number of superconducting sub-elements with respect to the TQS02c strand. The tests show that TQS02c was stable between 4.3 K and 2.7 K while it was limited by the self-field instability at lower temperatures. TQS03a was not limited by magneto-thermal instabilities and reached 93% of the short sample limit both at 4.3 K and 1.9 K. In this paper the results are summarized and compared with the stability measurements performed at CERN on individual strands.

Self Field Instability in High-${\rm J}_{\rm c}$${\rm Nb}_{3}{\rm Sn}$ Strands With High Copper Residual Resistivity Ratio

High critical current density (Jc) Nb3Sn conductor is the best candidate for next generation high field (>10 T) accelerator magnets. Although very promising, state of the art high-Jc Nb3Sn strands suffer magneto-thermal instabilities that can severely limit the strand performance. Recently it has been shown that at 1.9 K the self field instability is the dominating mechanism that limits the performance of strands with a low (<10) residual resistivity ratio (RRR) of the stabilizing copper. In this paper the self-field instability is investigated in high-Jc Nb3Sn strands with high RRR. At CERN several state of the art rod re-stack process (RRP) and powder in tube (PIT) Nb3Sn strands have been tested at 4.2 K and 1.9 K to study the effects on strand stability of: RRR, strand diameter and, strand impregnation with stycast. The experimental results are reported and discussed. A new 2-D finite element model for simulating magneto-thermal instabilities and its preliminary results are also presented. The model, which describes the whole development of the flux jump in the strand cross section taking into account the heat and current diffusion in the stabilizing copper, is in good agreement with the experimental data.

Magnetic instability in irradiated MgB2 dense samples

High density magnesium diboride samples were irradiated with low dosages of γ-rays, protons, and electrons. They were investigated by magnetization and thermal studies in order to determine if the irradiation increases the flux pinning and consequently the critical current density Jc. Zero field cooled magnetic susceptibility and specific heat measurements confirm the bulk transition temperature (Tc) with diamagnetic signal at ∼38.5 K. Magnetic instabilities were observed in the superconducting hysteresis loop at temperatures between 2 and 23 K in all studied polycrystalline MgB2 dense samples. The occurrence of flux jumps depended of the type of irradiation and the number of jumps decreases as temperature increases. The critical current density Jc, estimated from the magnetization hysteresis using the Bean’s model, is improved for gamma irradiated sample at H=0 and T=2 K. At low temperature, the Jc decreases and several steep drops in Jc are observed as a function of applied magnetic field. Furthermore, it is observed that the influence of crystalline defects plus local disorder, induced by hot isostatic pressure and irradiation with energetic atoms, increase the Jc but at the same time the magnetothermal instabilities increase in a broad range of temperature.

Self-Field Effects in Magneto-Thermal Instabilities for Nb-Sn Strands

Recent advancements in the critical current density of conductors, coupled with a large effective filament size, have drawn attention to the problem of magneto-thermal instabilities. At low magnetic fields, the quench current of such high strands is significantly lower than their critical current because of the above-mentioned instabilities. An adiabatic model to calculate the minimum current at which a strand can quench due to magneto-thermal instabilities is developed. The model is based on an dasiaintegralpsila approach already used elsewhere . The main difference with respect to the previous model is the addition of the self-field effect that allows to describe premature quenches of non-magnetized strands and to better calculate the quench current of strongly magnetized strands. The model is in good agreement with experimental results at 4.2 K obtained at Fermilab using virgin Modified Jelly Roll (MJR) strands with a low residual resistivity ratio (RRR) of the stabilizing copper. The prediction of the model at 1.9 K and the results of the tests carried out at CERN, at 4.2 K and 1.9 K, on a 0.8 mm Rod Re-Stack Process (RRP) strand with a low RRR value are discussed. At 1.9 K the test revealed an unexpected strand performance at low fields that might be a sign of a new stability regime.

Magnetothermal instabilities and melting of vortex lattice in κ-(BEDT-TTF)2Cu(NCS)2

We have measured the magnetothermal e..ect of κ-(BEDT-TTF)2Cu(NCS)2in a wide field range, and clearly observed the temperature spikes due to the flux jumps and the quasi-periodic temperature oscillations before the flux jumps in the two dimensional (2D) vortex lattice phase. The temperature dependence of the magnetothermal e..ect suggests that the melting transition from the 2D vortex lattice to the vortex liquid phase in low temperature is driven by quantum fluctuations rather than thermal one.

Fractal flux jumps in an organic superconducting crystal

Angle dependant torque magnetization measurements have been carried out on the organic superconductor, κ-(ET) 2Cu(NCS) 2 at extremely low temperatures (25–300 mK). Magneto-thermal instabilities are observed in the form of abrupt magnetization (flux) jumps for magnetic field sweeps of 0–20 T. A fractal analysis of the flux jumps indicate that the instabilities do show a self similar structure with a fractal dimension of varying between 1.15 and 1.6. The fractal structure of the flux jumps in our sample shows a striking similarity to that of MgB 2 thin film samples, in which magneto-optical experiments have recently shown that the small flux jumps are due to the formation of dendritic flux structures. These smaller instabilities act to suppress the critical current density of the thin films. The similarity of the flux jump structure of our samples suggests that we may also observing the dendritic instability, but in a bulk sample rather than a thin film. If true, this is the first observation of the dendritic instability in a bulk superconducting sample, and is likely due to the layered nature of κ-(ET) 2Cu(NCS) 2, which results in a quasi-two dimensional flux structure over the majority it's mixed state phase diagram.

Paramagnetic reentrance ofacscreening: Evidence of vortex avalanches inPbthin films

We have studied the influence of a square array of pinning centers on the dynamics of vortex avalanches in $\mathrm{Pb}$ thin films by means of $\mathrm{ac}\text{\ensuremath{-}}$ and $\mathrm{dc}\text{\ensuremath{-}}$magnetization measurements. Close to the superconducting transition ${T}_{c}$, the commensurability between the vortex lattice and the pinning array leads to the well known local increments of the critical current. As temperature $T$ decreases, matching features progressively fade out and eventually disappear. Further down in temperature, vortex avalanches develop and dominate the magnetic response. These avalanches manifest themselves as jumps in the $\mathrm{dc}$ magnetization and produce a lower $\mathrm{ac}$ shielding, giving rise to a paramagnetic reentrance in the $\mathrm{ac}$ screening ${\ensuremath{\chi}}^{\ensuremath{'}}(T)$. Within the flux-jump regime, two subregimes can be identified. Close to the boundary where vortex avalanches develop, the field separation between consecutive jumps follows the periodicity of the pinning array and a field- and temperature-dependent screening is observed. In this regime, the response also depends on frequency $f$ in agreement with theoretical models for magnetothermal instabilities. At low enough temperatures and fields, the screening saturates to a constant value independent of $T$, $H$, and $f$, where jumps are randomly distributed. We have also found that vortex instabilities occupy a larger portion of the $H\text{\ensuremath{-}}T$ diagram in patterned samples than in films without nanoengineered pinning sites. Finally, we discuss the possible origin of the vortex avalanches and compare our results with previous experimental and theoretical studies.

Flux Jumps and H-T Diagram of Instability for MgB2

We present a study of magneto-thermal instabilities in polycrystalline MgB2 superconductor, by magnetic hysteresis loop measurements and by investigations of magnetic flux dynamics with a miniature Hall probe. Temperature and magnetic field ranges where the flux jumps may be observed have been determined. On the basis of measurements of the magnetic flux dynamics, an average magnetic diffusivity describing the process of the flux jump is estimated. This parameter is compared with the thermal and magnetic diffusivities calculated on the basis of available data for thermal conductivity, heat capacity and resistivity. It is shown that the estimated value of the field of the first flux jump is influenced significantly by the field dependence of specific heat. In order to explain the observed phenomenon, the temperature reached by the sample during the flux jump at different magnetic fields is calculated.

The critical state in κ-(BEDT-TTF) 2Cu(NCS) 2

Angle-dependent torque magnetization measurements, in the temperature range 25–200 mK, are used to investigate the rich dynamical process by which magnetic flux penetrates the mixed state of the extreme type-II organic superconductor κ-(BEDT-TTF) 2Cu(NCS) 2. Magneto-thermal instabilities are observed in the form of dramatic flux jumps. Our previous work [M. Mola et al., Phys. Rev. Lett. 86 (2001) 2130] has shown that the cessation of these flux jumps is associated with a melting transition from a two-dimensional vortex solid phase to a liquid state. In this study, we analyze the field and temperature dependence of the flux jumps themselves, thus providing access to considerable information concerning dissipation and the collective behavior of vortices within the mixed state of the title compound.

Creeping instability in YBCO ceramics under non-isothermal superconducting transition

A high number of normal-superconductor transitions of sintered YBCO samples have been monitored by AC susceptibility measurements simultaneously in three different regions of samples, in the presence of strong thermal gradient. With this method, different accidental mesoscopic vortex structure instabilities have not only been observed but also located. Even if local magnetothermal instabilities of oscillatory nature (f=0.1–0.02 Hz) appear in strong thermal gradient fields, their evolution remains localized. However, when such instabilities appear in superposed temperature and electric (DC) potential gradient fields, they travel together with the mixed-state zone (v=0.06–0.1 mm s −1) along the macroscopic specimen. The interaction of transport currents with shielding current instabilities of the mixed-state — modifying some percolative network paths — can be considered as a possible macroscopic scenario for the traveling instabilities.

MAGNETO-THERMAL INSTABILITIES IN AN ORGANIC SUPERCONDUCTOR

Angle and temperature dependent torque magnetization measurements are reported for the organic superconductor κ-( ET)2Cu(NCS)2 , at extremely low temperatures (~ Tc /103). Magneto-thermal instabilities are observed in the form of abrupt magnetization (flux) jumps. We carry out an analysis of the temperature and field orientation dependence of these flux jumps based on accepted models for layered type-II superconductors. Using a simple Bean model, we also find a critical current density of 4 × 108 A/m 2 from the remnant magnetization, in agreement with previous measurements.

Quantum melting of the quasi-two-dimensional vortex lattice in kappa- (ET)2Cu(NCS)(2).

We report torque magnetization measurements in regions of the mixed state phase diagram ( B approximately mu(o)H(c2) and T(c)/10(3)) of the organic superconductor kappa-(ET)2Cu(NCS)(2), where quantum fluctuations are expected to dominate thermal effects. Over most of the field range below the irreversibility line ( B(irr)), magnetothermal instabilities are observed in the form of flux jumps. The abrupt cessation of these instabilities just below B(irr) indicates a quantum melting transition from a quasi-two-dimensional vortex lattice phase to a quantum liquid phase.

Magnetothermal instabilities in cylindrical melt-textured Y-Ba-Cu-O

The magnetothermal flux jump instabilities of the critical state in cylindrical melt-textured Y-Ba-Cu-O samples are investigated during the magnetization process. The flux jumps result in a drastic reduction of the magnetization accompanied by a strong heating of the sample. We determine the first flux jump field as function of the parameters, which influence the stability, such as the heat transfer coefficient between the surface of the sample and the surrounding, the sweep rate of the external field and the temperature of the sample. The comparison of the thermal and magnetic diffusivity of the melt-textured material indicates isothermal behavior of the flux jump scenario, supporting a dynamic stability criterion.

High-field flux jumps in BSCCO at very low temperature

Magnetization of single crystals of high- T c superconductor BSCCO-2212 comprises flux jumps (FJs) that differ qualitatively from well-studied magneto-thermal instabilities in conventional superconductors. FJs start above full penetration field, demonstrating clear periodicity in the slowly changing magnetic field. Magnetization process exhibits high reproducibility, which is, however, prone to sudden and uncontrollable breaks. Thin plate-like samples were examined in fields up to 17 T at temperatures down to 0.3 K, using magnetometric and calorimetric techniques.

Magnetothermal instabilities in type II superconductors: The influence of magnetic irreversibility

Complete magnetization and magnetostriction loops for type II superconductors were calculated in terms of the following pinned critical state models which incorporate the flux jump instability criterion: the Kim–Anderson model, the exponential model, the linear model, and the model with peak effect. These results were used for constructing magnetic field–temperature (H–T) diagrams of instability of these critical state models. Magnetothermal instabilities of superconductors with peak effect were investigated experimentally and theoretically. Regions in the H–T diagram where flux jumps occur were built and compared with experimental M(H) hysteresis loops. We have explained the phenomenon of “island” jumps. The influence of flux trapping on the flux jump regions of magnetic fields was studied.