Hot Spot Stimulated Transition in YBCO Coated Conductors: Experiments and Simulations

Heat equations can estimate the thermal distribution and phase transformation in real-time based on the operating conditions and material properties. Such wonderful features have enabled heat equations in various fields, including laser and electron beam processing. The integral transform technique (ITT) is a powerful general-purpose semi-analytical/numerical method that transforms partial differential equations into a coupled system of ordinary differential equations. Under this category, Fourier and non-Fourier heat equations can be implemented on both equilibrium and non-equilibrium thermo-dynamical processes, including a wide range of processes such as the Two-Temperature Model, ultra-fast laser irradiation, and biological processes. This review article focuses on heat equation models, including Fourier and non-Fourier heat equations. A comparison between Fourier and non-Fourier heat equations and their generalized solutions have been discussed. Various components of heat equations and their implementation in multiple processes have been illustrated. Besides, literature has been collected based on ITT implementation in various materials. Furthermore, a future outlook has been provided for Fourier and non-Fourier heat equations. It was found that the Fourier heat equation is simple to use but involves infinite speed heat propagation in comparison to the non-Fourier heat equation and can be linked with the Two-Temperature Model in a natural way. On the other hand, the non-Fourier heat equation is complex and involves various unknowns compared to the Fourier heat equation. Fourier and Non-Fourier heat equations have proved their reliability in the case of laser–metallic materials, electron beam–biological and –inorganic materials, laser–semiconducting materials, and laser–graphene material interactions. It has been identified that the material properties, electron–phonon relaxation time, and Eigen Values play an essential role in defining the precise results of Fourier and non-Fourier heat equations. In the case of laser–graphene interaction, a restriction has been identified from ITT. When computations are carried out for attosecond pulse durations, the laser wavelength approaches the nucleus-first electron separation distance, resulting in meaningless results.

Extensive applications of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{YBa}_{2}\hbox{Cu}_{3}\hbox{O}_{7 - {\rm x}}$</tex></formula> (YBCO) tapes require a comprehensive knowledge of their behavior in every possible operating condition. In this paper, the thermal stability behavior of a conduction-cooled pancake coil wound with commercial YBCO coated conductors is reported from both the experimental and numerical point of view. The coil stability against heat disturbances is studied in terms of minimum quench energy and normal zone propagation velocity (NZPV) for different values of the coil currents at different temperatures. The quench dynamics of the tape is compared between experiment and the numerical analysis, obtaining a reasonable agreement for voltage traces, NZPV, and temperatures. The model allows a wide range of case studies that can be used to suggest appropriate solutions for the design of detection and protection systems.

The minimum quench energy ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MQE</i> ) and normal zone propagation velocity ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NZPV</i> ) of three kinds of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Al superconductors fabricated by the rapid heating, quenching and transformation (RHQT) process were measured under various conditions of applied magnetic field (10-14 T), temperature (7-11 K), and transport current (80-95% of the critical current), while cooled by a cryocooler for developing the over 20-T class cryogen-free magnet. As a result, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MQE</i> values were related to the critical current density ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ); high MQE was obtained for low <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> . It is assumed that <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> has a stronger influence on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MQE</i> than specific heat, thermal conductivity, resistivity, and other parameters of the composite superconductor including the matrix and the stabilizer. <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NZPV</i> was mainly proportional to the transport current density varying with applied field and temperature. The second contribution to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">NZPV</i> is assumed to be heat capacity depending on the wire configuration.

This paper mainly focuses on the thermal stability performance, such as minimum quench energy (MQE) and normal zone propagation velocity (NZPV), of a quasi-isotropic strand (Q-IS) with three different configurations made from 2G high-temperature superconducting (HTS) tapes in the adiabatic approximation. Due to the anisotropic performance of thermal conductivity in 2G HTS tapes, the tensor form of the heat conduction equation was used instead of conventional isotropic forms. We first measured the MQE and NZPV of three strands in the adiabatic approximation. Subsequently, the experimental results were verified by finite element analysis and compared with the values of MQE and NZPV in a liquid nitrogen (LN2) bath. Finally, the effect of a metal sheath on the current distribution and generation of Joule heat during the quench process were analyzed through simulation. The results show that the arc-shaped aluminum filler brings slightly higher thermal stability of Q-IS while the copper sheath largely improves stability. Moreover, compared with the thermal stability of the strand fully exposed to the LN2 bath, for the strand in the adiabatic approximation, the MQE decreases a lot while the maximum of NZPV is increased by 2–3 times.

Minimum quench energy and normal zone propagation velocity in MgB 2 superconducting tape

Copper-stabilized second generation high-temperature superconductor (HTS) coated conductors were modified to enhance their normal zone propagation velocity (NZPV). Experimental results, supported by numerical simulations, indicate that adding copper on the substrate side instead of adding it on the HTS side increases the NZPV by a factor of 2–3. Furthermore, a novel tape architecture, called hybrid-current flow diverter (CFD), was investigated. This hybrid-CFD tape was designed with the goal of having a very long current transfer length, which is the key to enhance the NZPV. Results show that it is possible to fabricate an HTS tape with double stabilizer thickness in comparison to a bare tape, while accelerating the NZPV by a factor of three. With the same approach, a ten-fold increase of the NZPV can be expected for a tape with a 40 µm thick copper-stabilizer.

A comprehensive study of the quench properties of single laminated wires having a double-layered superconducting structure is presented. In particular, we have focused on the influence of the angle and intensity of an external magnetic field perpendicular to direction of the applied current on the minimum quench energy (MQE) and normal zone propagation velocity (NZPV) values. We conclude that strong changes on the NZPV are mainly determined by the intensity of the applied current, while the orientation and magnitude of the applied field have a less but not negligible impact on the resulting NZPV. The quench parameters are also reported for the case when the applied current is considered as a constant parameter in which case the MQE has been found to reach a maximum value when the in-field critical current is the largest.

This study examined the effects of external pressures on the thermal and electrical stabilities of stacked GdBCO CCs through quench tests. The minimum quench energies and two-dimensional normal zone propagation velocities of stacked GdBCO CCs connected electrically in series under various external pressures were examined. The quench test results showed that the minimum quench energy increased with increasing the external pressure. Longitudinal normal zone propagation velocities were greater than transverse normal zone propagation velocities. Moreover, normal zone propagation velocities increased with increasing applied pressure implying that applied pressure resulted in increased layer-to-layer thermal contact that allowed hot spots to dissipate more easily.

Insulated high temperature superconducting (HTS) magnets are still widely used in low field applications, such as HTS motors and generators. In this paper, a two-dimensional/three-dimensional (2D/3D) mixed electrothermal model and a homogeneous 3D electrothermal model are employed to study the influence of inter-turn contact stress on the minimum quench energy (MQE), longitudinal and transverse normal zone propagation velocity (NZPV) of insulated YBCO magnets for the temperature range 30 K – 60 K. This temperature range is of interest usually in applications, such as HTS motors, generators and transformers, because it allows the use of low cost cooling system. It is found that MQE increases significantly with increasing inter-turn contact stress. The inter-turn contact stress has small influence on the longitudinal NZPV of insulated YBCO pancake magnet. However, the transverse NZPV rises significantly with the increase of inter-turn contact stress. The transverse NZPV is nearly proportional to the inter-turn contact stress. The 3D homogeneous model gives results that are in agreement with those of 2D/3D mixed model, especially for the temperature range 45 K – 60 K; however, the MQE and transverse NZPV given by the two models are different for the temperature range 30 K – 45 K. That means for insulated HTS YBCO pancake magnets operating at the temperature range 45 K – 60 K, the 3D homogeneous electro-thermal model can be a good replacement of the 2D/3D mixed model to study the quench behavior, which can achieve better computational efficiency without significant loss of accuracy.

REBCO-coated conductor is widely used in various HTS power applications. The HTS coils for power applications are generally impregnated with epoxy resin to enhance their mechanical stability, and the coil conductors would be subjected to transverse compressive loading in these applications. Although the effect of various operating conditions on the quench characteristics of REBCO-coated conductor have been investigated, the effects of compressive stress on quench characteristics of epoxy-impregnated REBCO-coated conductor has rarely been reported. This study examined the effects of transverse compressive loading on the minimum quench energy (MQE) and normal zone propagation velocities (NZPV) of epoxy-impregnated REBCO-coated conductor. The critical current of the conductor shows little degradation when transverse compressive stress is applied up to 80 MPa. Under the same compressive stress, the MQE decreases but the NZPV increases with the transport current. For fixed transport current, compressive stress increases the thermal contact conductance between conductor and epoxy which allows the heater energy of the conductor dissipating faster towards the surrounding epoxy, resulting in the increase of MQE and decrease of NZPV when increasing transverse compressive stress. The results indicate that higher compressive stress is helpful to decrease the quench damage of the conductor.

Self-field quench behaviours of YBa2Cu3O7−δ coated conductors with different stabilizers are studied. Samples include one with Cuon both sides (Cu–Cu), one with stainless steel on both sides (SS–SS), and onewith Cu on one side and stainless steel on the other (Cu–SS). The measurementsof the minimum quench energy (MQE) and normal zone propagation velocity(NZPV) are taken at various temperatures (30–75 K), and transport currents (30%Ic to 90%Ic) at a typicalpressure of 10−5 Pa. Of the three samples, the Cu–Cu sample has the highest MQE while theSS–SS one has the lowest MQE at the same temperature and percentage ofIc; the NZPV in the SS–SS sample is found to be the highest while those of the Cu–Cu andCu–SS samples are similar. The normal zone voltage and the hot-spot temperature are alsocompared. Both the classic adiabatic quench propagation model and the interfaceresistance model are used to explain the NZPV and MQE differences between the samples.The implications for conductor design and quench detection and protection are discussed.

YBa2Cu3O7- x (YBCO) coated conductors (CCs) are now capable of carrying very high transport critical current density Jc over a broad range of magnetic field and temperature space, and as a result, they are receiving significant interest for a wide range of applications. While many of these applications take advantage of the high-temperature performance of YBCO CCs, because the YBCO CC is typically produced on a high-strength substrate and carries very high Jc at very high magnetic field, there is now growing interest in using YBCO CCs at 4.2 K to generate very high magnetic fields. The transition from high-field conductor to high-field superconducting magnet, however, requires that some challenging issues be addressed. One of the most important challenges remaining is to better understand the stability and quench behavior at 4.2 K, so that an effective quench protection system can be developed. Here, we report on measurements of the stability and quench behavior of short YBCO CC at 4.2 K by inducing a quench via a heat pulse from a heater mounted on the conductor surface. Through gradually increasing heater pulse amplitude, the transition from stable to unstable (i.e., recovery to quench) is observed through voltage and temperature measurements. Using these data, the minimum quench energy (MQE) and normal zone propagation velocity (NZPV) are determined. It is found that, for the same fraction of critical current (I/Ic), YBCO CCs have similar MQE and NZPV as Ag-alloy-clad Bi2Sr2CaCu2Ox wires and significantly higher MQE and lower NZPV than those of MgB2 round wires of similar Ic (4.2 K). Furthermore, the voltage and temperature versus time data are correlated to better understand the quench onset behavior at 4.2 K. It is determined that a normal temperature gradient exists from the CC surface to the YBCO layer within the conductor, as well as a directly measured longitudinal temperature gradient. After the heater pulse has ended but while the transport current continues, the temperature gradient along the length becomes dominant. Nevertheless, voltage and temperature measurements remain problematic for quench detection in large magnets because of the slow longitudinal propagation velocity. Thus, new approaches to quench detection and/or protection of high-field YBCO magnets are needed.

Due to the limited current-carrying capacity of a single high-temperature superconducting (HTS) tape, multiple tapes are often connected in parallel for high-field applications. Therefore, investigating the quench propagation characteristics of HTS stacks is crucial for ensuring the safe operation of HTS devices. Compared with liquid nitrogen immersion cooling, conduction-cooled quench tests are performed in a quasi adiabatic environment, minimizing environmental effects and allowing the results to more accurately reflect the intrinsic quench characteristics of the HTS stack. In this study, we investigate the quench propagation characteristics of REBCO stacks under conduction-cooled conditions. The stacks were fabricated using 4 mm-wide REBCO tapes, and a conduction cooled quench test platform was built based on a GM cryocooler to perform measurements under near-adiabatic conditions. Potential taps were placed continuously along the length of the sample to monitor quench propagation, while thermocouples were attached to measure the temperature distribution. The minimum quench energy (MQE) and normal zone propagation velocity (NZPV) of the REBCO stacks were measured at ambient temperatures ranging from 60 K to 77 K. The experimental results are compared with those of a single tape sample. To verify the thermal behavior of the REBCO stack, a numerical analysis of the temperature trace was performed using the Finite Element Method (FEM). The numerical simulation results were compared with the experimental data to verify the validity of the experimental data. The results indicate that differences in the coefficient of thermal expansion between the solder and the tapes during the cooling process led to a reduction in the critical current of the REBCO stack. As the temperature increases, both types of samples exhibit a decrease in MQE and a slowdown in NZPV. The heat absorption of the solder during quench increases the MQE of the stacked HTS tapes. Meanwhile, it also enhances the Joule heating power within the normal zone, and accelerates the NZPV.

The ability of second-generation YBCO coated conductor (CC) tapes to transport high current densities at high temperature, i.e., up to 77 K, and at very high magnetic fields, i.e., above 20 T, are pushing the use of these tapes in various applications, from magnet to power system technologies. An accurate study of their quench behavior is mandatory for the design and safe use of cables and magnets manufactured with this ceramic superconducting material. A new 2-D finite-element method (FEM) numerical quench model, which is called anisotropic model of YBCO CCs, was built for this purpose in the COMSOL Multiphysics environment. One of the most difficult issues in the modeling of the YBCO tapes with the FEM is their high aspect ratio due to the very small thickness of the YBCO layer, about 1 μm. In the model developed, the problem of the high aspect ratio of the tape is tackled by multiplying the tape thickness by a constant factor and then compensating the heat and electrical balance equations through the introduction of material anisotropic properties. The FEM model is validated by comparison with literature experimental data on minimum quench energy and normal zone propagation velocity.

In experimental studies of HTS quench behaviors, different experimental protocols, especially heater configurations, including heater pulse duration and magnitudes, can lead to inconsistent measured results. In this work, mainly based on experimental measurements, the quench characteristics of REBCO samples, including minimum quench energy (MQE) and normal zone propagation velocities (NZPV), are investigated with various heater configurations. The relations between the measured quench characteristics and the heater configurations demonstrated that the measured MQE increased with the increasing heater pulse duration employed in the quench experiments, and the heater pulse duration had better be smaller than the diffusion time constant over minimum propagation zone; and the heater pulses adopted in the quench measurements for the stacks can be longer than that for the single tape.