Optical fibre based quench detection in HTS applications using machine learning classifiers

A. Akbar; N. Riva; B. Dutoit 

A Mach-Zehnder Interferometer (MZI) based optical fibre sensing technique, developed and patented by EPFL, is an efficient and economical way to detect hotspots in High Temperature Superconductor (HTS) applications. Due to the MZI sensitivity being a composite of strain sensitive and temperature sensitive contributions, the MZI gives an instantaneous response to a quench (within 10 ms), because of the quick strain transfer to the optical fibre. However, the MZI output signal also manifests the environmental noise caused by mechanical vibrations, bubbling in the cryostat and temperature variations, along with the response to the quench. This presents the problems of false alarms and indiscernible response to a quench. Discrete wavelet transform (DWT) has been proven to be a useful tool for feature extraction in different fields requiring signal categorization and hence holds the potential to enable quench recognition in the MZI output. This paper proposes an effective approach of performing DWT based feature extraction on experimental data and subsequently using the extracted features for the MZI response classification using two machine learning based classification techniques: k-nearest neighbours (KNN) and Artificial Neural Network (ANN). For this manuscript, experiments were performed using MZI for quench detection in an HTS tape. Feature extraction was then implemented on these experimental measurements using discrete wavelet coefficients extracted at different decomposition levels from the MZI output; these features were then used to train the KNN and ANN models for identifying quench in the MZI signal. This method could be a valuable supplement to the MZI technique by enabling the development of a real time application that can process the MZI output data as well as eliminate the occurrences of false alarms; thereby facilitating reliable quench detection. With this development, the MZI technique would become an even more attractive solution for the health monitoring of HTS applications.

Optimization Method for Extracting Stabilizer Geometry and Properties of REBCO Tapes

N. Riva; F. Grilli; F. Sirois; C. Lacroix; A. Akbar et al. 

A good knowledge of material properties is a critical aspect for modeling high-temperature superconductor (HTS) devices. However, the knowledge of the electrical resistivity of coated conductors above the critical current is limited. The major challenge in characterizing this regime lies in the fact that for I > I-c, heating effects and thermal instabilities can quickly destroy the conductor if nothing is done to protect it. In previous work we extracted overcritical current data, obtained by combining fast pulsed current measurements with finite element analysis (Uniform Current (UC) model). In this work, we assessed the impact of the uncertainties of the input parameters on the quantities calculated with the UC model (temperature, current in each layer of the tape and resistivity of HTS). Firstly, sensitivity and uncertainty analyses were performed and it was found that the input parameters that mostly affect the accuracy of the UC model are the electrical resistivity and the thickness of the silver layer. Afterwards, an optimization method was developed to correctly estimate the geometry and the resistivity of the silver layer. This method combines experimental measurements of resistance R(T) of the tape and pulsed current measurements. The development of this strategy allowed us to determine the parameters that significantly impact the results of the UC model and helped to minimize their uncertainties. This enables a more accurate estimation of the resistivity in the overcritical current regime.

Design of the First HTS Single-Coil Demonstrator of GaToroid Toroidal Gantry for Hadron Therapy

E. Felcini; J. Harray; T. Lehtinen; D. Perini; J. C. Perez et al. 

The design and construction of compact and lightweight gantries for hadron therapy are essential steps toward wider accessibility to this cancer treatment. The use of a high-field steady-state toroidal gantry, i.e., GaToroid, represents an attractive alternative to the state-of-the-art with the potential of significantly reducing size and weight of present installations. It is interesting to conceive the use of High-Temperature Superconductors (HTS) conductors to reach magnetic fields beyond 8 T at relatively high temperatures, decreasing the beam bending radius and, at the same time, avoiding complex cryogenics systems in the hospitals. The construction of such a machine requires several steps of prototyping and this manuscript presents the design of the first GaToroid single-coil demonstrator, wound with ReBCO conductors. The demonstrator is a scaled version of a full-scale GaToroid coil, with the conductors spaced into four planar windings, i.e., grades, and wound as a double pancake. Two operating regimes are foreseen to test the demonstrator at different temperatures, currents and magnetic fields. The cable geometry, composed of four ReBCO non-twisted tapes, was validated through 1D quench propagation studies in both regimes, and the hot spot temperature is well below 100 K. Furthermore, three-dimensional mechanical simulations allowed to estimate the stress state on the conductor, as well as to define the impregnation strategy of the demonstrator. The answers provided by the manufacturing, powering and test of the proposed demonstrator can provide valuable insights for the future construction of full-scale GaToroid coils.

Superconductors for power applications: an executable and web application to learn about resistive fault current limiters

N. Riva; F. Grilli; B. Dutoit 

High-temperature superconductors (HTS) can be superconducting in liquid nitrogen (77 K) at atmospheric pressure, which holds immense promises for our future such as nuclear fusion, compact medical devices and efficient power applications. In a power system, high short-circuit currents can exceed the operational current by more than ten times, putting at risk many parts of the system. Superconducting fault current limiters (SFCL) can limit the prospective fault current without disconnecting the power system, and are thus becoming increasingly attractive for future grids. With a growing interest in modeling and commercializing SFCL, the question of how to teach and to explain their operation to students has arisen. In order to help students visualize the potential use and benefits of a SFCL, we created an executable and a web application using COMSOL Multiphysics. This executable allows students to investigate the electro-thermal response of a resistive SFCL. The executable solves a 1D electro-thermal model of the SFCL under AC fault conditions, evaluating important figures of merit such as the limited current, the prospective current and the maximum temperature reached within the tape. Finally, the geometrical parameters as well as the superconducting properties of the device can be modified. The importance of the amount of silver stabilizer necessary to protect the device from over-heating occurring during a fault current can be investigated. In addition, the effects of having a sharp nonlinear transition from the superconducting to the normal state (intrinsic property of the superconductor) to obtain a current limitation can be well explored. The executable allows the users to learn about the consequences of superconductors in real-life applications, without the prerequisite of extensive modeling or experimental setup. The executable can be downloaded from the HTS modeling website and run on the most commonly used operating systems.

Fast Hotspot Detection in SFCLs by Exploiting Strain Response in Optical Fiber Sensing

A. Akbar; N. Riva; Z. Yang; L. Thevenaz; B. Dutoit 

Superconducting fault current limiters (SFCLs) can be used to limit fault currents in both meshed DC and AC grids by transitioning from superconducting to resistive state, in the presence of high currents. While the device is theoretically a great way to protect grids, the inherent inhomogeneity of critical current along the superconductor length can lead to localized heating, called hotspots, and ultimately destruction of the SFCL device. At EPFL under the European Union project Fastgrid, an extremely efficient Mach-Zehnder interferometer (MZI) based optical fiber sensing technique has been developed and patented that can detect even singular hotspots within 15 ms to protect SFCLs. The MZI response is characterized by a strain sensitive as well as a temperature sensitive contribution. This paper outlines an investigation by means of FEM modeling into the response sensitivity. A 2-D thermal model of the superconducting tape and optical fiber was made to study thermal transfer to the optical fiber from the REBCO tape. The simulation results showed that temperature rise observed in the optical fiber is slower than the MZI response time, proving a strain sensitive response in the experiment measurements. Sound mechanical coupling between the optical fiber and the superconductor tape can enhance strain transfer to the optical fiber and hence reduce hotspot detection time. With this improved performance, the health monitoring for SFCLs can be much more efficient and reliable.

Optimization Method for Extracting Stabilizer Geometry and Properties of REBCO Tapes

N. Riva; F. Grilli; F. Sirois; C. Lacroix; A. Akbar et al. 

A good knowledge of material properties is a critical aspect for modeling high-temperature superconductor (HTS) devices. However, the electrical resistivity of coated conductors above the critical current is limited. The major challenge in characterizing this regime lies in the fact that for I > Ic, heating effects and thermal instabilities can quickly destroy the conductor if nothing is done to protect it. In our previous works we proposed the overcritical current model, obtained by combining fast pulsed current measurements with finite element analysis (Uniform Current (UC) model). In this work, we assessed the impact of the uncertainties of the input parameters on the quantities calculated with the UC model (temperature and current in each layer of the tape). Firstly, sensitivity and uncertainty analyses were performed and it was found that the input parameters that mostly affect the UC model are the electrical resistivity and the thickness of the silver layer. Afterwards, an optimization method to correctly estimate the geometry and the resistivity of the silver layer was developed. This method combined experimental measurements of resistance R(T) of the tape and pulsed current measurement. The development of this strategy allowed us to determine the parameters that significantly impact the UC model and helps to minimize their uncertainties. This can enable a precise estimation of the overcritical current resistivity. 10%

Delivery, Beam and Range Monitoring in Particle Therapy in a Highly Innovative Integrated Design

L. Bottura; E. Felcini; V. Ferrero; E. Fiorina; V. Monaco et al. 

The design of a particle therapy system that integrates an innovative beam delivery concept based on a static toroidal gantry and an imaging configuration suitable for beam and online range monitoring is proposed and discussed. Such approach would provide a compact and cost-effective layout, with a highly flexible and fast beam delivery, single particle counting capability for fast measurement of beam fluence and position and a precise real time verification of the compliance between the treatment delivery and its prescription. The gantry configuration is discussed, presenting an analysis of the residual magnetic field in the bore and of the feasibility of irradiating a realistic target volume. Moreover, the expected performance of the PET-based range monitor is assessed through Monte Carlo simulations, showing a precision in the reconstruction of the activity distribution from a clinical treatment plan better than the state-of-the-art devices. The feasibility of the proposed design is then discussed through an assessment of the technological improvements required to actually start the construction and commissioning of a system prototype.

Resistivity of REBCO tapes in overcritical current regime: impact on superconducting fault current limiter modeling

N. Riva; F. Sirois; C. Lacroix; W. T. B. de Sousa; B. Dutoit et al. 

A detailed knowledge of the resistivity of high-temperature superconductors in the overcritical current regime is important to achieve reliable numerical simulations of applications such as superconducting fault current limiters. We have previously shown that the combination of fast pulsed current measurements and finite element analysis allows accounting for heating effects occurring during the current pulses. We demonstrated that it is possible to retrieve the correct current and temperature dependence of the resistivity data points of the superconductor material. In this contribution, we apply this method to characterize the resistivity vs. current and temperature of commercial REBCO tapes in the overcritical current regime, between 77 K and 90 K and in self-field conditions. The self-consistency of the overcritical resistivity model rho_OC is verified by comparing DC fault measurements with the results of numerical simulations using this model as input. We then analyze by numerical simulation to what extent using therho_OC model instead of the widely used power-law model rho_PWL affects the thermal and electrical performance of the tapes in the practical case of a superconducting fault current limiter. A remarkable difference is observed between the measured overcritical current resistivity model rho_OC and the power-law resistivity model rho_PWL. In particular, the simulations using the power-law model show that the device quenches faster than with the overcritical resistivity model. This information can be used to optimize the architecture of the stabilizer in superconducting fault current limiters.

An Algorithm for Toroidal Field Harmonics Computation in Arbitrary Magnetic Configurations

L. Gambini; M. Breschi; E. Felcini; A. Cristofolini; L. Bottura 

Toroidal magnetic configurations are widely exploited in industry and scientific research, involving a vast spectrum of applications, such as thermonuclear fusion, particle detectors, SMES systems and medical devices. To properly design and analyse these sys-tems, it is crucial to determine the magnetic field generated by dif-ferent configurations. The multipole expansion theory can be ap-plied to the analysis of toroidal configurations, by solving the La-place equation for the magnetic scalar potential in toroidal coor-dinates. Contrarily to the case of accelerator magnets with straight axis, in this case the correlation between the current dis-tribution and the field harmonics cannot easily be identified. This paper proposes a methodology for the computation of field har-monics in toroidal coordinates, which is validated by comparison with the results obtained through the Biot-Savart law. This work was carried out in the frame of the GaToroid project ongoing at CERN.

Over-critical current resistivity characterization of ReBCO commercial coated conductors: modified E-J curves

N. Riva; F. Sirois; C. Lacroix; F. Grilli; B. Dutoit 

Magnetic Design of a Superconducting Toroidal Gantry for Hadron Therapy

E. Felcini; L. Bottura; J. van Nugteren; G. de Rijk; G. Kirby et al. 

Hadron and proton therapy are cutting edge techniques for cancer treatment and a great development of specialized medical centers and research facilities is foreseen in the next decades. One of the main obstacles to the penetration of the use of charged particles for therapy is the construction of complex and expensive accelerating structures and rotating transfer lines, i.e. gantries, able to bend and focus the beam down to the patient. GaToroid is a novel concept of a fixed toroidal gantry, able to deliver the dose at discrete angles in the whole range of treatment energies in steady-state configuration. The steady-state current and magnet-ic field are appealing features, implying simplified demands on stability, powering, mechanics and cooling, as well as for the clinical perspective, allowing rapid variations of beam energy and treatment angle. In this work, we present the magnetic design of the toroidal coils composing the first instance of GaToroid, focusing the analysis on an option for a proton machine with an energy range of 70 MeV to 250 MeV. To create a proper magnetic field distribution, the coils have been designed with peculiar asymmetric shape and the windings have been graded. An initial winding geometry was obtained with an optimization aiming at maximum energy acceptance of the gantry. We are now progressing to the detailed engineering design. We describe here the over-all magnet design, coil and conductor layout (LTS and HTS options), and mechanical studies involving the general torus structure. Quench protection is evaluated for LTS (Nb-Ti) configuration, as well as more innovative HTS (REBCO) options. Finally, we present the design and the construction of a scaled-down demonstrator, intended as the proof of principle of winding procedure and mechanical coil structure.

Resistivity of HTS tapes in overcritical current regime: Impact on Superconducting Fault Current Limiter

N. Riva; B. Dutoit; F. Grilli; F. Sirois; C. Lacroix 

Status of the European Union Project FASTGRID

P. Tixador; M. Bauer; C-E. Bruzek; A. Calleja; G. Deutscher et al. 

High voltage direct current super-grids are one attractive solution for the transmission of bulk power of renewable electricity over long distances. Their protection is still an issue and superconducting fault current limiters (SCFCL) offer attractive perspectives. However, the actual superconducting tapes are not yet properly designed for operation at high voltages (>100 kV): The electric field developed during the current limitation is still too low (approximately 50 V/m for 50 ms) and the limiter requires too long lengths of tape. The European project FASTGRID aims at improving the properties of the REBCO tapes to enhance significantly (by 2-3 times) the electric field limit and so the economical SCFCL attractiveness. We use advanced THEVA tapes. Substantial improvements are also planned on the stabilizer (shunt) layer. Several shunt ways are under investigations. Other improvement on the tape properties will be carried out, namely the increase of the normal zone propagation velocity by at least one order of magnitude, with the help of the innovative current flow diverter architecture. The optimized conductor will be used in a SCFCL module (approximate to 1.5 kA-50 kV) tested at 65 K. We will monitor the temperature along the conductor using an attached optical fibre. FAST-GRID will also develop innovative tapes based on sapphire substrate, which can tolerate very high electric fields, in the range of kilovolts per meter. Validated on the laboratory scale, this game-changing technology needs to be implemented at long lengths with an industrial process. We will provide an overview of the project and its first results.

Overcritical Current Resistivity of YBCO-Coated Conductors Through Combination of PCM and Finite-Element Analysis

N. Riva; S. Richard; E. Sirois; C. Lacroix; B. Dutoit et al. 

Understanding the electro-thermal behavior of high-temperature superconductor (HTS) materials is a critical aspect for designing efficient and reliable applications. In order to optimize cost and performance, one needs to understand the role played by the various layers of an HTS tape during a quench. On one hand, the electrical and thermal properties of the materials used in the manufacturing of those tapes (e.g., alloy substrate, silver, and copper) are well known. Knowledge of the functional dependence of the superconductor’s resistivity rho(J, T) above the critical current in 2G HTS CCs is very limited. In the flux creep or normal state regime, the resistivity can be approximated by empirical laws. In the flux-flow regime, it is difficult to extract rho(J, T) due to the presence of Joule heating. In this contribution, using finite-element analysis, we present a method to retrieve the overcritical current resistivity, by estimating the amount of current, temperature, and heat present in the various layers.

Stability modeling of the LHC Nb-Ti Rutherford cables subjected to beam losses

L. Bottura; M. Breschi; E. Felcini; A. Lechner 

The Large Hadron Collider (LHC) at CERN is being prepared for its full energy exploitation during Run III, i.e. an increase of the beam energy beyond the present 6.5 TeV, targeting the maximum discovery potential attainable. This requires an increase of the operating field of the superconducting dipole and quadrupole magnets, which in turn will result in more demanding working conditions due to a reduction of the operating margin while the energy deposited by particle loss will increase. Beam-induced magnet quenches, i.e. the transition to normal conducting state, will become an increasing concern, because they could affect the availability of the LHC. It is hence very important to understand and be able to predict the quench levels of the main LHC magnets for the required values of current and generated magnetic fields. This information will be used to set accurate operating limits of beam loss, with sufficient but not excessive margin, so to achieve maximal beam delivery to the experiments. In this study we used a one dimensional, multi-strand thermal-electric model to analyze the maximum beam-losses that can be sustained by the LHC magnets, still remaining superconducting. The heat deposition distribution due to the beam losses is given as an input for the stability analysis. Critical elements of the model are the ability to capture heat and current distribution among strands, and heat transfer to the superfluid helium bath. The computational model has been benchmarked against energy densities reconstructed from beam-induced MB (Main Bending) dipole quenches during LHC operation at 6.5 TeV. The model was then used to evaluate the stability margin of both MB and MQ (Main Quadrupole) magnets at different beam energies, up to the expected ultimate operating energy of the LHC, 7.5 TeV. The comparison between the quench levels underlines how the increase of beam energy implies a substantial reduction of magnets stability and will require much stricter setting on the allowable beam losses to avoid resistive transitions during operation.

Modeling of Beam Loss Induced Quenches in the LHC Main Dipole Magnets

M. Breschi; E. Felcini; P. P. Granieri; A. Bevilacqua; E. Bergonzoni et al. 

The full energy exploitation of the Large Hadron Collider (LHC), a planned increase of the beam energy beyond the present 6.5 TeV, will result in more demanding working conditions for the superconducting dipoles and quadrupoles operating in the machine. It is hence crucial to analyze, understand, and predict the quench levels of these magnets for the required values of current and generated magnetic fields. A one-dimensional multi-strand electro-thermal model has been developed to analyze the effect of beam-losses heat deposition. Critical elements of the model are the ability to capture heat and current distribution among strands, and heat transfer to the superfluid helium bath. The computational model has been benchmarked against experimental values of LHC quench limits measured at 6.5 TeV for the Main Bending dipole magnets.

Quench behavior of High-Temperature Superconductor tapes for power applications: Isothermal Resistivity Curves of HTS Coated Conductors – A Synergy Between Experiment and Simulation

N. Riva; B. Dutoit; F. Grilli; F. Sirois; S. Richard et al. 

Modeling The Hyperloop With COMSOL Multiphysics® : On The Design Of The EPFLoop Pressurized Systems

S. Zsofia; N. Riva; L. Benedetti 

The EPFLoop team from Ecole Polytechnique Fédérale de Lausanne has developed a capsule thanks to which it won the 3rd place in SpaceX’s Hyperloop Pod Competition in 2018. COMSOL Multiphysics was used to analyze and study the pressurized systems of the pod. Three pressure vessels (PVs) of different shape and structure are used to store electrical components in a pressurized environment at 1 bar, meanwhile the external environment is at 8 mbar. The PVs’ failure under load was studied using a stationary simulation and shell finite elements in order to represent the plies of carbon fiber-epoxy and foam. The load conditions were the maximum deceleration (2.6 g), the weight of the internal components and the internal pressure of 1 bar. The aim was to design the plies layering with a minimum Tsai-Wu safety factor of 2 everywhere. A parametric sweep was then performed to estimate the maximum allowable working pressure (MAWP, corresponding to a safety factor equal to 2) and the BURST pressure (pressure for which the safety factor is less equal than 1 and failure is imminent). To ensure the normal functioning of electronic components, analyses were done to ensure that the temperature inside the PVs wouldn’t be greater than 50°C due to internal electronic heat loads. This has been done by coupling the Heat Transfer in Solid Module with the Laminar Flow Module in order to take into account convection effects. The simulations were validated by measurements during experimental tests. Experimental results confirmed the design and analyses carried out using COMSOL Multiphysics®.

Quench Level of the HL-LHC Nb3Sn IR Quadrupoles

M. Breschi; E. Felcini; L. Bottura 

The scope of the Large Hadron Collider Hi-Lumi Project at CERN includes the installation of several superconducting magnets wound with Nb3Sn Rutherford cables. The quench level of these magnets (i.e. the maximum energy that a cable can tolerate without quenching) is a key value required to set magnet protection from beam losses, and is expected to be significantly different from the computed and measured levels of the LHC Nb-Ti magnets. In this work, we applied a one-dimensional numerical model of multi-strand Rutherford cables to simulate the electro-thermal instabilities caused by the heat released by the particle beam losses. Two models have been applied, one based on the analysis of the single strand, and the other accounting for all the strands in the multi-strand cable. The results of these two models are compared to analyze the effects of heat and current redistribution during quench. A comparison between the quench energy values obtained for the Nb3Sn conductor in the working conditions of the LHC Hi-Lumi inner triplet low-β quadrupole (MQXF) and those of the NbTi Rutherford cable of the LHC main quadrupole magnet (MQ) is presented. The differences and similarities in quench performance between the impregnated cables for Nb3Sn magnets and the non-impregnated ones for NbTi magnets at their respective typical working conditions in superconducting accelerator magnets are highlighted.

Insulation effect on thermal stability of Coated Conductors wires in liquid nitrogen

T. Rubeli; B. Dutoit; I. Martynova; A. Makarevich; A. Molodyk et al. 

Superconducting wires are not perfectly homogeneous in term of critical current as well as stabilization. In resistive fault current limiter applications this could lead to hot spots if the fault current is only slightly above the nominal current of the device. Increasing stabilization by using thicker silver coating for example may prevent this problem but this method implies longer wire length to maintain the same impedance during a fault. Very efficient cooling in another way to prevent hot spots, this can be achieved in nucleate boiling regime. Optimal insulation can be used to prevent film boiling regime, staying in nucleate boiling regime in a much broader temperature range. In this work a novel technique is used to monitor in real time the temperature of the wire during the quench. Using this method several increasing insulation thicknesses are tested, measuring for each the heat exchange rate to the nitrogen bath. Exchange rate measurements are made in quasistatic regime and during the re-cooling of the wire. SuperOx wires provided with different insulation thicknesses exhibit an excellent stability, far above a bare wire. On the other side, for very thick insulations the stability gain is lost. Re-cooling speeds dependency on insulation thicknesses is measured too.

Heat transfer monitoring between quenched high-temperature superconducting coated conductors and liquid nitrogen

T. Rubeli; D. Colangelo; B. Dutoit; M. Vojenčiak 

High-temperature superconducting coated conductors (HTS-CCs) are good candidates for resistive superconducting fault current limiter (RSFCL) applications. However, the high current density they can carry and their low thermal diffusivity expose them to the risk of thermal instability. In order to find the best compromise between stability and cost, it is important to study the heat transfer between HTS-CCs and the liquid nitrogen (LN2) bath. This paper presents an experimental method to monitor in real-time the temperature of a quenched HTS-CC during a current pulse. The current and the associated voltage are measured, giving a precise knowledge of the amount of energy dissipated in the tape. These values are compared with an adiabatic numerical thermal model which takes into account heat capacity temperature dependence of the stabilizer and substrate. The result is a precise estimation of the heat transfer to the liquid nitrogen bath at each time step. Measurements were taken on a bare tape and have been repeated using increasing Kapton® insulation layers. The different heat exchange regimes can be clearly identified. This experimental method enables us to characterize the recooling process after a quench. Finally, suggestions are done to reduce the temperature increase of the tape, at a rated current and given limitation time, using different thermal insulation thicknesses.

Impact of the Normal Zone Propagations Velocity of High Temperature Superconducting Coated Conductors on Resistive Fault Current Limiters

D. Colangelo; B. Dutoit 

The engineering critical current (Ic) of the high temperature superconducting coated conductors (HTS-CCs), today available on the market, is not a uniform parameter and varies significantly along the length of the conductors. Moreover, commercial HTS-CCs have a low normal zone propagation velocity (NZPV). This property, together with the Ic inhomogeneity, exposes the HTS-CCs to local thermal instabilities. A crucial challenge for the design of resistive fault current limiters (RFCLs) based on HTS-CCs is to avoid the thermal runaway of the conductors, and in this respect the enhancement of the NZPV is a promising solution. In the recent years, several methods have been proposed and many and various techniques are now available to enhance the NZPV. Whichever will be the best technical solution to improve NZPV of HTS-CCs, our aim is to quantify the impact the enhancement of NZPV will have on the design of RFCLs based on HTS-CCs. For this reason, we used numerical models to analyze the effects of the enhancement of NZPV on the limitation performance of a RFCL integrated in a medium voltage (MV) power grid. In this manuscript, we quantify the benefits the enhancement of the NZPV will have on the next generation of HTS-CC-based RFCLs for MV grids

Analysis of the influence of the normal zone propagation velocity on the design of resistive fault current limiters

D. Colangelo; B. Dutoit 

Commercial high-temperature superconducting coated conductors (HTS-CCs) have low thermal diffusivity and nonuniform critical current density. These two factors lead commercial HTS-CCs to a partial quench when they are subjected to a transport current around their average critical current (I-c.av). The consequence is the appearance of localized resistive zones, and a high risk of thermal runaway can arise when HTS-CCs are used for resistive fault current limiter (RFCL) purposes. The enhancement of the normal zone propagation velocity (NZPV) of HTS-CCs is a desirable solution for achieving sufficient thermal stability while keeping the cost of RFCLs under an acceptable threshold. Even though in recent years, several valid methods to increase the NZPV have been proposed, their impact on the design of RFCLs is not clear. For this reason, we developed a one-dimensional numerical model that enables us to simulate HTS-CCs with enhanced NZPV and to study the limitation performance of a HTS-CC-based RFCL in real operating conditions. Our preliminary re sults demonstrate that the NZPV enhancement can effectively limit the needed amount of HTS-CCs with important economic benefits for the design of RFCLs.

Indirect cooling of superconducting fault current limiter

M. Vojenciak; B. Dutoit; D. Colangelo 

Science and technology research and development in support to ITER and the Broader Approach at CEA

A. Becoulet; G. T. Hoang; J. Abiteboul; J. Achard; T. Alarcon et al. 

In parallel to the direct contribution to the procurement phase of ITER and Broader Approach, CEA has initiated research & development programmes, accompanied by experiments together with a significant modelling effort, aimed at ensuring robust operation, plasma performance, as well as mitigating the risks of the procurement phase. This overview reports the latest progress in both fusion science and technology including many areas, namely the mitigation of superconducting magnet quenches, disruption-generated runaway electrons, edge-localized modes (ELMs), the development of imaging surveillance, and heating and current drive systems for steady-state operation. The WEST (W Environment for Steady-state Tokamaks) project, turning Tore Supra into an actively cooled W-divertor platform open to the ITER partners and industries, is presented.

Electrical and Thermal Characterization of Commercial Superconducting YBCO Coated Conductors

G. Angeli; D. Colangelo; M. Bocchi; B. Dutoit; L. Martini 

This paper reports on experimental and modelling activities aimed to identify E(I,T) characteristics of commercial YBCO High Temperature Superconductor Coated Conductors (HTS-CCs). The aforesaid approach is applied to investigate the HTS-CCs behavior in the different regimes: superconducting state, flux-creep, flux-flow and normal state. In order to thoroughly represent the HTS-CCs behavior, parameterized analytical formulations of E(I,T) characteristics have been assumed and then validated through fitting methodologies. Numerical calculation of the electric field as a function of the temperature and of the current density in the HTS-CC, is fundamental to the development of models suitable to design devices based on HTS-CCs. In fact it allows improving the dedicated-software calculation accuracy. This is particularly important for the simulation of Superconducting Fault Current Limiters (SFCL) behavior against short-circuits and/or overloads events, because during the SFCL limitation the HTS-CCs performance strongly depends on the different above mentioned regimes. As matter of fact, numerical simulations are somewhat simpler for high prospective currents as compared to intermediate conditions as for overload or low short-circuit currents.

Modelling of the quench behaviour of HTS-CCs for RFCLs

D. Colangelo; B. Dutoit 

Study of the quench phenomenon is crucial for the design of Resistive Fault Current Limiters (RFCLs) based on high temperature superconducting coated conductors (HTS-CCs). An optimal stabilization of the tape is required to achieve both an economic device and a safe quench. In this context we developed an electro-thermal model that describe the HTS-CCs quench behavior for different degrees of inhomogeneity, both in terms of critical current and of thickness stabilizer. The critical current inhomogeneity for long lengths of tape has been modeled with Gaussian distributions. The mathematical expressions that define the superconducting-to-normal state transition are supported by experimental measurements. Our model allows optimizing the tape design leading to economic and safe limiting performance.

MV Power Grids Integration of a Resistive Fault Current Limiter Based on HTS-CCs

D. Colangelo; B. Dutoit 

Due to the energy demand growth and distributed generation (DG) units penetration, a substantial increase of the rated short-circuit current of the electrical lines is expected. As a consequence, the electrical grid infrastructure needs to be extended or drastically renovated. In this context, resistive superconducting fault current limiters (RFCLs) based on high temperature superconducting coated conductors (HTS-CCs) represent a promising technology to limit the upgrading costs. Thanks to recent improvements on HTS-CCs performances, RFCLs are now close to commercial applications. However, as they are novel devices, their real impact on the electricity network remains an open issue. In particular, the subject of this research is to study the grid integration of the RFCL designed within the European project ECCOFLOW [1]. The device has been simulated in two applications in two different typologies of existing medium voltage grids: RFCL used as busbars coupler and RFCL used as transformer feeder. This contribution is the continuation of previous works [2], [3], where the effects of symmetrical and unsymmetrical short-circuits on inhomogeneous HTS-CCs have been extensively analyzed.

Inhomogeneity effects in HTS coated conductors used as resistive FCLs in medium voltage grids

D. Colangelo; B. Dutoit 

For resistive fault current limiters (RFCLs) based on high temperature superconducting coated conductors (HTS-CCs), inhomogeneity, in terms of critical current and geometrical imperfections such as stabilizer and substrate thicknesses, plays a very important role and it may limit the penetration of such devices into the electrical market. This paper presents an electrothermal model, developed in SimPowerSystem™, able to describe the transient response of HTS-CC candidates with different degrees of inhomogeneity, both in terms of critical current and of stabilizer thickness. Critical current inhomogeneity has been modeled with Gaussian distributions. The layer thicknesses used in the simulations have been chosen by fitting the temperature dependence of real tape resistances. Our approach considers relative inhomogeneity positions as well as thermal conduction along the HTS-CC length. The model is tuned using experimental measurements made on ReBaCuO coated conductors. A new dynamical thermal calibration of the model is proposed using finite element method calculations. Inhomegeneity effects with different possible faults (e.g. three phase and single phase short-circuit) are presented.

Conceptual Design of a 24 kV, 1 kA Resistive Superconducting Fault Current Limiter

M. Noe; A. Hobl; P. Tixador; L. Martini; B. Dutoit 

In recent years many large scale demonstrators and prototypes of superconducting fault current limiters have been successfully developed and tested. Within the European Project ECCOFLOW (www.eccoflow.org), it is the first time that a resistive-type superconducting fault current limiter is developed for two different locations and that a permanent installation is foreseen. The limiter has a rating of 20 kV and 1 kA and will be tested in a busbar and transformer feeder application. The paper summarizes the conceptual design of this innovative limiter and reports in detail about the development of the superconducting limiting elements, their integration into a cryostat and the design of the whole limiter including cooling and grid integration. As a main result it can be summarized that the ECCOFLOW limiter fulfills all requirements according to the two different specifications. Approximately 3 km of 12 mm wide YBCO tape will be used to realize a three phase system.

Impact of Inhomogeneities in HTS Coated Conductors for Resistive FCLs

D. Colangelo; S. Memiaghe; C. Lacroix; F. Sirois; B. Dutoit 

Several issues remain to be addressed for the commercial development of ResistiveFault Current Limiters based on superconducting technologies (RFCL). In particular, the inhomogeneity of high temperature superconducting coated conductors (HTS-CC) combined with the diffculty to predict RFCLs behaviour when interfaced with the existing electrical grid represents an important bottleneck that limits their competitiveness on the electrical market. In order to study the influence of the local inhomogeneity of the HTS tape on the global effective performance of an RFCL, a modular equivalent circuit model has been developed using SimPowerSystemsTM. The model implements an inhomogeneity distribution based on statistical data and takes into account the thermal conduction between different zones of the HTS-CC. It has been calibrated with experimental measurements and finite element simulations. The model can be used to study various scenarios common to power systems, such as transformer in-rush currents, motor starts, etc.

Evaluation of the Applicability of Phenomenological HTS Models for Numerical Analysis of Quenches in Coated Conductors: Simulations vs. Experiments

F. Roy; B. Dutoit; F. Sirois 

The electrical resistivity of coated conductors is strongly related to the inter-dependent set of parameters (J, H, T), respectively current density, magnetic field and temperature. On the one hand, it is difficult to isolate the contribution of each of these parameters on the resistivity measured experimentally. On the other hand, numerical methods, which may allow this separation, require a good knowledge of the fundamental laws governing the superconducting transition which are, up to now, derived from curve fitting with experimental data. In this paper, we investigate the influence of phenomenological formulas on the outputs of a recently developed finite element model. The outputs are compared against experimental voltage curves, which have been obtained under pulsed transport currents between 80 and 160 A and external magnetic fluxes of 0 to 350 mT. The comparisons indicate that the numerical models may reproduce well the measurements, using the right set of phenomenological laws parameters. Nevertheless, the solution may still be inaccurate at low field values and high current amplitudes, where the curvature of the simulated E-J curves is more pronounced, indicating that further refinement is required in order to obtain models valid over a wider range of parameters.

Characterization of the electrical resistance of high temperature superconductor coated conductors at high currents using ultra-fast regulated current pulses

F. Sirois; J. Coulombe; F. Roy; B. Dutoit 

This paper focuses on the experimental determination of the electrical resistance (R) of commercial high temperature superconductor (HTS) coated conductors (CCs) at currents well above the critical current. The major novelty of this work rests on the unique experimental capability of applying constant current pulses in the sample (up to 1000 A) for durations as short as 15 mu s, which allows very precise control of the amount of energy dissipated in the sample (the Joule effect), as well as the resulting temperature rise. By varying the applied current and the duration of the pulses, we show that we can achieve a relatively accurate characterization of R(I, T) simply from the measured dynamical V-I characteristics of the CCs. The resistance model obtained in this way is very important, as R(I, T) is the most fundamental design parameter in many practical HTS applications, especially in fault current limiters.

Modeling and Characterization of Coated Conductors Applied to the Design of Superconducting Fault Current Limiters

Comparison Between the Behavior of HTS Thin Film Grown on Sapphire and Coated Conductors for Fault Current Limiter Applications

L. Antognazza; M. Therasse; M. Decroux; F. Roy; B. Dutoit et al. 

The major drawback for the commercialization of fault current limiter (FCL) made of YBCO on sapphire is their expensive price. In the recent years, coated conductors (CC) have been extensively developed and, due to their lower prices, have been recently tested for current limitation application. One weakness of these CC is the very low electric fields they can sustain, typically below 1 V/cm as compared to 20-40 V/cm observed in YBCO films grown on sapphire. The limitation of this electric field in CC comes certainly from the very low propagation velocities of the dissipative state, a property which might be correlated with the poor thermal behavior of the architecture of these materials. Both the thermal conductivities of the Hastelloy substrate and of the conducting bilayer (superconducting DyBCO and Ag conducting layer) influence the thermal behavior of the CC and therefore have to be optimized to get the best performance. We have then investigated the thermal and electrical behavior and the propagation velocities in CC during constant current pulses above. The comparison with the results obtained on YBCO films grown on sapphire shows several differences. In CC, the flux flow resistivities are 2-3 orders of magnitude higher than in film grown on sapphire and quench propagation velocities are 2-3 orders of magnitude lower (of the order of cm/s). The propagation velocities in CC and in films on sapphire are analysed with a simple adiabatic model.

Assessment of the Computational Performances of the Semi-Analytical Method (SAM) for Computing 2-D Current distributions in Superconductors

F. Sirois; F. Roy; B. Dutoit 

The semi-analytical method (SAM) is a fast integral technique for solving small 2-D, time-transient electromagnetic problems in high temperature superconductors (HTS) with transport current and/or applied field. The method in itself is a generalization of the so-called “Brandt method”. In order to determine its optimal context of utilization, computation times were compared with those of the finite element method (FEM), for the case of a simple monocore superconducting tape. In order to perform an objective comparison, the same adaptive time step integration algorithm (DASPK) was used in both cases. This algorithm is built-in in the COMSOL Multiphysics ackage, which served as our benchmark for the FEM, whereas we had to implement it within a compiled version of the SAM based on a C proprietary code. To this end, we used the IDA solver (from the SUNDIALS package), available as a public C code. Comparisons were performed for different “n” values for the superconducting material, and for different mesh coarsness. As a result, the SAM proved to be 10 times faster than the FEM for problems involving 300 elements in the mesh (conducting regions only), and showed equal performances with the FEM with 850-900 elements. As the number of element further grows, the SAM looses its advantage over the FEM.

Numerical studies of the quench propagation in coated conductors for Fault Current Limiters

F. Roy; M. Therasse; B. Dutoit; F. Sirois; L. Antognazza et al. 

A fundamental understanding of the quench phenomenon is crucial in the future design and operation of HTS based Fault Current Limiters (FCLs). The key parameter that quantifies the quenching process in superconductors is the normal zone propagation (NZP) velocity, which is defined as the speed with at which the normal zone expands into the superconducting volume. Recent experimental measurements in YBCO tapes have shown that the NZP velocity in these materials is extremely slow in comparison with theoretical predictions. In the present paper, we compared experimental results with FEM models developed in our group recently. With our models, we have shown that the NZP of YBCO tapes depends strongly on the substrate properties.

Quench propagation in coated conductors for fault current limiters

F. Roy; S. Perez; M. Therasse; B. Dutoit; F. Sirois et al. 

A fundamental understanding of the quench phenomenon is crucial in the future design and operation of high temperature superconductors based fault current limiters. The key parameter that quantifies the quenching process in superconductors is the normal zone propagation (NZP) velocity, which is defined as the speed at which the normal zone expands into the superconducting volume. In the present paper, we used numerical models developed in our group recently to investigate the quench propagation in coated conductors. With our models, we have shown that the NZP in these tapes depends strongly on the substrate properties.

Magneto-thermal finite element modeling of 2nd generation HTS for FCL design purposes

F. Roy; B. Dutoit; F. Grilli; F. Sirois 

Coated conductors are very promising for the design of novel and e±cient Fault Current Limiter (FCL). However, before considering using them in a power grid, their thermal and electromagnetic behaviors in the presence of over-critical currents need to be investigated in details. In this context, we performed ¯nite element magneto-thermal modeling of coated conductors under over-critical current on several geometries. Accordingly, we have investigated the substrate electrical connectivity and thermal properties on the HTS-FCL behavior. All simulations were performed using in COMSOL Multiphysics, a commercial finite element package, which has a built-in coupling between the thermal and electrical equations, allowing us to compute both quantities simultaneously during the solving process. Our simulations allowed us to formulate thresholds for the current density usable in coated HTS as well as limitation capability of a device made of these new conductors.

Evaluation of two commercial finite element packages for calculating AC losses in 2-D high temperature superconducting strips

F. Sirois; D. Mouhamadou; F. Roy; F. Grilli; B. Dutoit 

This paper compares the speed and accuracy of two commercial packages based on the finite element method (FEM) for calculating the AC losses in high temperature superconductors (HTS). The softwares investigated in this paper were COMSOL Multiphysics and FLUX 3D (2D module). This choice was motivated by 1) the ability of the packages to model the nonlinear resistivity of HTS (mandatory condition), 2) the possibility to extend the analysis to 3-D in the future, and 3) the possibility to solve the associate thermal problem (with additional modules). Nevertheless, in this paper, the analysis was restricted to 2-D and no thermal coupling. To generate objective comparisons, the base case of a 2-D rectangular strip was considered under three important regimes, i.e. 1) transport current, 2) perpendicular applied field, and 3) both excitations simultaneously. In all cases, the superconductor was modelled with a classical E-J power-law characteristic. The results are summarized in a number of graphics showing the sensitivity of each package to 1) the number of elements in the mesh, 2) the n-value in the power-law characteristic, and 3) the aspect ratio of the strip.

Magneto-Thermal Modeling of Second-Generation HTS for Resistive Fault Current Limiter Design Purposes

F. Roy; B. Dutoit; F. Grilli; F. Sirois 

Coated conductors are very promising for the design of novel and efficient resistive Fault Current Limiters (FCLs). However, a detailed knowledge about their thermal and electromagnetic behaviors in the presence of over- critical currents is crucial for their improvement. In this context, we performed finite element magneto-thermal modeling of coated conductors under over-critical current on several geometries. Accordingly, we have investigated the influence of the physical properties of stabilizer and substrate on the thermal stability to improve the HTS-FCL design. All simulations were performed using COMSOL Multiphysics, a commercial finite element package, which has a built-in coupling between the thermal and electrical equations, allowing us to compute both quantities simultaneously during the solving process. Our results allow us to determine the current threshold to achieve thermal stability of HTS fault current limiters made with coated conductors.

2D Magneto-Thermal Modeling of Coated High-Temperature Superconductors

F. Roy; B. Dutoit; F. Sirois; F. Grilli 

Thin films are very promising for the design of novel and efficient Fault Current Limiter (FCL) made of high-temperature superconductors (HTS). However, their thermal and highly non-linear electromagnetic behavior in the presence of over-critical currents is crucial to their use in future electrical grid. In this paper, we propose a numerical approach to solve magneto-thermal models for geometries of high aspect ratio. The used electromagnetic formulation, inspired in good part from the work of Brambilla et al., were performed in 2D using COMSOL Multiphysics. Also, the thermal part of our model has been implemented to consider the thermal exchange with the nitrogen bath needed for HTS-FCL operation. Our simulations allow us to observe design limitations of FCL made of these new shaped conductors.

Computer Modeling of YBCO Fault Current Limiter Strips Lines in Over-Critical Regime With Temperature Dependent Parameters

J. Duron; B. Dutoit; F. Grilli; M. Decroux; L. Antognazza et al. 

We present the results of an advanced numerical model for fault current limiter (FCL) based on HTS thin films in which both thermal and electromagnetic aspects are taken into account. This model allows simulating the behavior of FCL in the over-critical current regime and we used it for studying strip lines of a YBCO/Au FCL on sapphire substrate. The electromagnetic and thermal equations have been implemented in finite-element method (FEM) software in order to obtain a model for investigating the comportment of the superconductor when the current exceeds $I_{c}$ . In particular, materials equations have been implemented in order to simulate the electrical behavior of superconducting devices with strong over-critical currents. We report results of simulations in voltage source mode where currents largely exceed $I_{c}$ . The global behavior of the FCL is compared with measurements, showing a good agreement. The use of FEM simulations offers the advantage to give access to local variables such as current density or temperature. Studies with this model can replace expensive experiments where very high current density might damage or destroy the FCL device.

Thermally Assisted Transition in Thin Film Based FCL: A Way to Speed Up the Normal Transition Across the Wafer

L. Antognazza; M. Decroux; M. Therasse; M. Abplanalp; J. Duron et al. 

The adjunction of constrictions along the meander of a superconducting Fault Current Limiter (FCL) greatly improves its behavior thanks to a better distribution of the dissipative zones at the occurrence of a short circuit. This design works perfectly for symmetrical short circuit (i.e. short circuit at the maximum voltage). However for asymmetrical short circuits (at voltages close to 0), we are facing a problem due to the small number of the initially switched constrictions. To solve this problem, we test the possibility to speed up the transition into the normal state of the whole meander by heating it locally. This thermally assisted transition is realized by growing a gold layer on the backside of the substrate and by patterning it into a meander with its dissipative parts lying just underneath the constrictions of the FCL. This gold meander can be either connected in parallel with the superconducting meander or a capacitor bank can supply the current. In order to confirm the benefit of the thermally assisted transition we have carefully measured the behavior of the FCL during constant current and low voltage pulses as a function of the power injected into the gold line. We present results showing that the response of the FCL to the generated heat is very fast; typically less than 100 $mu{rm s}$. Furthermore the distribution of the dissipated power across the wafer, during asymmetrical AC short circuit, is clearly improved.

Finite-element analysis and comparison of the AC loss performance of BSCCO and YBCO conductors

S. Stavrev; F. Grilli; B. Dutoit; S. Ashworth 

The AC loss performance of two BSCCO and two YBCO conductors of different geometry, characterized by the same self-field critical current of 150 A, is analysed and compared quantitatively. The comparison is made using the finite-element method with a non-linear B-dependent E-J relation. A new shell-region model is utilised for the simulations of thin YBCO strips. Different AC working conditions are simulated: self-field, applied external field, and combined transport current and external perpendicular field application. Magnetic field and current density profiles are investigated in order to illustrate the reasons for the loss difference in the conductors. Depending on the application, the advantages of using BSCCO or YBCO conductors with specific geometry are outlined.

Finite-element modelling of superconductors in over-critical regime with temperature dependent resistivity

J. Duron; F. Grilli; L. Antognazza; M. Decroux; S. Stavrev et al. 

In this paper, we present a new numerical model, in which both the thermal and the electromagnetic aspects of the over-critical current regime of HTS materials are taken into account. The electromagnetic and thermal equations have been implemented in finite-element-method (FEM) software in order to obtain a novel, closer to reality model for investigating the behaviour of the superconductor when the current exceeds $I_{c}$. This model has been applied for studying the behaviour of strip lines of an YBCO/Au FCL with a sapphire substrate. Simulations with currents largely exceeding $I_{c}$ have been performed, showing that the total current limitation occurs only when the temperature dependence of the electrical parameters is taken into consideration. Such modelling can replace experiments with currents far exceeding $I_{c}$ which may damage or destroy the studied sample or HTS device.

Analysis of magnetic field and geometry effects in the design of HTS devices for AC power applications

F. Grilli; L. Martini; B. Dutoit; S. Stavrev; R. Brambilla 

The performance of HTS devices is strongly influenced by local values of the current/field distributions. In this paper, we investigate the influence of the magnetic field and of the geometrical configuration on the loss behaviour of a 200kVA FCL prototype, composed by Bi-2223/Ag tapes wound around a cylindrical support, as function of different operating ac currents. The investigation is done by means of FEM computations, with the use of an axisymmetric 2D A-V formulation for taking into account the cylindrical geometry. The electrical behaviour of the superconductor is described by means of a B-dependent E-J power-law relation, derived from experimental measurements with field of different orientation. Several geometrical configurations are analyzed and compared, in order to find the ones with lowest AC loss. The developed method can be applied for investigating devices other than FCL, such as superconducting transformers and magnets, where the local distribution of the magnetic field and the arrangement of the conductors play an important role. This work is supported partially by the Swiss project “MaNEP” and partially by the Italian project “Ricerca di Sistema”.

3D Finite Element Simulations of strip lines of a YBCO/Au Fault Current Limiter

J. Duron; F. Grilli; B. Dutoit; L. Antognazza; M. Decroux et al. 

Geometrical aspects of the design of fault current limiters (FCL) have a great impact on their performance. Recently, the University of Geneva have presented optimized geometries obtained by splitting the FCL into many small dissipative lengths in order to distribute the power along the device. We have performed 3D finite element method (FEM) simulations for studying the behavior of strip lines of a YBCO/Au FCL in AC nominal use (sinusoidal current at industrial frequency) up to 3 Ic. Particular attention has been paid to the mesh, due to the very large involved aspect ratios. The numerical results show a concentration of the electric field in the sharp corners. This results in very large power dissipation, which has been experimentally confirmed by wafer cracks during over-Ic tests. A new geometry, taking into account the length of the connecting path and the corner optimization, has been proposed. Finally, simulations coupling electromagnetic and thermal equations show the behavior of the device when a default occurs on the electrical network. This work is supported by the Swiss National Science Foundation through the National Center of Competence in Research “Materials with Novel Electronic Properties – MaNEP”

Dynamic field mapping for obtaining the current distribution in high-temperature superconducting tapes

B. Dutoit; J. Duron; S. Stavrev; F. Grilli 

The magnetic field profile on the surface of Bi-2223/Ag tapes has been dynamically measured across the width of the samples. The experimental technique uses a Hall-probe array with 7 sensors connected to a multiple channel lock-in amplifier especially programmed for fast and synchronous data acquisition measurements. The speed of the system is high enough to measure real-time profiles with 7 probes and 50 Hz sine current through the sample. A numerical method to estimate the current distribution inside the tapes using the measured field profile data is proposed. The inverse problem has been solved using certain assumptions on the current distribution in the superconductor. Validation of the results has been done by comparison with finite element method simulations.

Comparison of the AC losses of BSCCO and YBCO conductors by means of numerical analysis

S. Stavrev; F. Grilli; B. Dutoit; S. Ashworth 

This paper presents a quantitative comparison of the AC loss performance of two BSCCO and two YBCO conductors, characterized by the same self-field critical current of 150 A. In particular, compared are a 37-filamentary BSCCO tape, a 16-filamentary BSCCO square wire, a standard YBCO tape, and a stack of four narrower YBCO tapes. The comparison is made using a numerical technique, based on the finite-element method, which employs a non-linear E-J relation with the dependence of the critical current density Jc on the local magnetic field. For the simulations of YBCO, a new shell-region model is utilised, which allows overcoming the geometry and mesh problems, typical for superconductors with very high aspect ratio. Different AC working conditions are simulated: self-field, applied external field, and combined transport current and external field of varying orientation. Outlined are the advantages of using BSCCO or YBCO conductors for the different applications. Various magnetic field and current density profiles are investigated in order to illustrate the reasons for the loss difference in the four conductors. Particular attention is drawn to the YBCO tape and the YBCO stack, whose AC loss characteristics are less studied than those of BSCCO conductors.

Parameterized hysteresis model for high-temperature superconductors

M. Sjöström; D. Djukic; B. Dutoit 

High-temperature superconductors (HTS) exhibit hysteresis, which is the main cause for losses in the subcritical domain. This behavior is well predicted by Bean’s critical-state model, which is a subset of the classical Preisach model. We present a parameterized Preisach model that describes the hysteresis of HTS specimens in self-field, where the parameters are identified from electrical lock-in (loss) measurements. That means the model can be used independent of geometry, number of filaments, and other physical measures as long as Bean’s model applies. An advantage of the model is that it can predict outputs (flux, voltage) and losses for arbitrary input currents once the HTS has been characterized from measurements. We have further derived exact models for the hysteretic losses in strip and elliptic geometry strips, where the energy losses were calculated by Norris.

Experimental study of the geometrical barrier in type-I superconducting strips

H. Castro; B. Dutoit; A. Jacquier; M. Baharami; L. Rinderer 

We study the energy barrier for flux entry of a geometric origin in type-I superconducting strips using magneto-optical observations of the flux structure. The magnetic field is applied perpendicularly to the broad surface and, optionally, a dc current is sent along the strip. As a direct manifestation of this barrier, the appearance of flux-free zones at the edges of the strip is observed. The width of these zones, the field for first-flux penetration, and the critical current originated due to the geometrical barrier are measured. The dependence of these parameters on the geometry of the sample, applied field, transport current, and temperature presented here is in good qualitative agreement with a recent theory by Benkraouda and Clem.

The geometrical edge barrier in type I superconductors

H. Castro; L. Rinderer; B. Dutoit 

The magneto-optical technique was used to study the edge barrier for flux entry in type I superconducting strips (In, Pb). The width of the flux-free zones appearing at the sample edges, due to the barrier, was measured at different applied fields and temperatures. Standard I–V measurements allowed us to study the critical current originated by the edge barrier in these pinning-free samples and its dependence on different parameters like magnetic field, temperature and sample’s size. Our results confirm the geometrical origin of this edge barrier and show its dependence on different relevant variables.

Use of europium selenide films for magneto-optical studies at low temperatures

B. Dutoit; L. Rinderer 

The resolution of the magneto-optical technique to observe directly the structure of the intermediate state in superconductors has been considerably improved by the replacement of EuS–EuF2 mixture by EuSe thin films with higher specific Faraday rotation. This allows a reduction of the magneto-optical film thickness, and consequently an enhancement of the optical and magnetic resolution. This greater rotation gives the possibility to work with the polarizers not completely crossed, and therefore to produce more luminous images. Theses images can directly be observed with a video camera so the rapidly changing structures can be recorded and flux tube velocities measured.