Svetlomir Stavrev

Comparison of numerical methods for modeling of superconductors

Different finite-element method (FEM) formulations have been developed in order to model the electromagnetic behavior of type-II superconductors. This paper presents a comparison between simulations with A-V formulation models implemented in two FEM software packages (FLUX2D and FLUX3D) and a numerical method based on analytical model for superconductors in applied magnetic field. These models can be used for superconductors with complex geometry and power-law current-voltage characteristics. Simulated is a 37-filamentary tape with applied transport current in self-field and alternating current (ac) magnetic field parallel to the wide side of the tape. A good agreement is found between the ac-loss and current distributions obtained with the different models.

Finite element method simulation of AC loss in HTS tapes with B-dependent E-J power law

The nonlinear behavior of high temperature superconductors (HTS) is often modeled by an E-J power law in order to describe their electromagnetic properties. This paper presents AC loss calculations in HTS tapes, performed by means of FEM commercial software using the A-V method. The implemented nonlinear model of the HTS tapes takes into account the B-dependence of the critical current density J/sub c/ and the power index n. The expressions for J/sub c/(B) and n(B) are obtained from electrical measurements of a Bi-2223 tape under applied DC magnetic field. Numerical simulations of HTS tapes under different experimental conditions have been performed, i.e. the application of a transport current and/or AC external perpendicular magnetic field at 59 Hz. A comparative analysis of AC loss is then presented where J/sub c/ and n are maintained either constant or B-dependent. The combined J/sub c/(B) and n(B) formulation leads to a better understanding of HTS electromagnetic behavior, especially when a perpendicular magnetic field is applied.

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

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.

Bi(2223) Ag sheathed tape Ic and exponent n characterization and modelling under DC applied magnetic field

We use a dual channel digital lock-in to perform electrical measurement of AC losses at power frequencies. A DC magnetic field between 2 and 400 mT is applied with a varying angle from parallel to perpendicular to the tape surface, thus having a complete view of the loss behavior under DC applied field. Furthermore, the same experimental layout is used to acquire time series of current and voltage across the sample. Using a triangular input current, we measure and average the voltage, which then is fitted to a power law (I/I/sub c/)/sup 11/. The measurements are repeated for the mentioned magnetic field and angle domain to give the dependencies of I/sub c/ and n with magnetic field and angle. For device modeling purposes, we can then express a phenomenological law giving I/sub c/ and n as a function of the applied magnetic fields intensity and direction.

Geometry considerations for use of Bi-2223/Ag tapes and wires with different models of J/sub c/(B)

In typical power applications, Bi-2223 conductors carrying AC current will be subjected to external magnetic fields whose orientation and conductors geometry are of major significance for the AC loss magnitude. This paper investigates the influence of the geometry and aspect ratio of nontwisted Bi-2223 conductors in reducing the AC loss for such applications. A numerical model of high-T/sub c/ materials has been used in finite-element-method (FEM) simulations. The model incorporates power-law E-J characteristics with J/sub c/ and n defined by both parallel and perpendicular local magnetic field components. It allows computations of field and current distributions with transport current and/or applied field of any orientation. Monofilamentary tapes of rectangular and elliptical geometry with anisotropic J/sub c/(B), as well as square and round wires with isotropic J/sub c/(B) have been used for simulations under various operating conditions. A comparison between AC losses, magnetic field, and current distributions in the tapes and wires is presented.

Frequency dependence of AC loss in Bi(2223)Ag-sheathed tapes

The a.c. self-field loss in Bi(2223)Ag sheathed tapes with different number of filaments has been measured between 59 and 2500 Hz by means of a dual lock-in amplifier. Due to the wide frequency range of the measurements we have been able to dissociate quantitatively the different self-field loss contributions: hysteretic, eddy current and resistive loss (near Ic). This is an important advantage compared to single frequency measurements where such loss dissociation is only qualitative. The hysteresis losses of the different tapes fall between Norris’ predictions for elliptical and strip cross section. The relative weight of eddy current loss is found to be inversely proportional to the current ratio – the higher i, the less is their contribution. Frequency independent resistive loss due to flux creep is observed for high currents at low frequencies; this loss becomes quickly negligible with the increasing frequency.

Numerical modelling and AC losses of multifilamentary Bi-2223/Ag conductors with various geometry and filament arrangement

This paper presents results from numerical modelling of non-twisted multifilamentary Bi-2223/Ag conductors with various geometry and filament arrangement. New anisotropic models of Jc(B) and n(B) have been employed in finite element method simulations under different operating conditions – with applied AC transport current, in external parallel and perpendicular AC magnetic field, and with combined current and field of varying orientation. AC losses, as well as current and magnetic flux densities in square and round Bi-2223/Ag wires with different filament arrangement have been calculated and compared to those of a 7-filamentary tape. The notion of effective Ic(B) in transport current applications is introduced and discussed. It is demonstrated that the shape factor of the conductors and the orientation of the local magnetic field with respect to the individual filaments are of primary importance for the AC loss magnitude in different applications. Outlined are the advantages of using conductors with specific filament configuration for a given application.

Effect of the geometry of HTS on AC loss by using finite element method simulation with B-dependent E-J power law

Mono and multifilamentary HTS tapes exhibit nonnegligible AC loss in self-field and considerably higher losses in the presence of external magnetic field. The effect of the conductors geometry on the AC loss has been investigated in this paper. The nonlinear electromagnetic properties of the superconducting material are expressed with a B-dependent E-J power law and are implemented in finite element method commercial software. The critical current density and the power index n dependence on B are obtained from DC measurements of a real Bi-2223 tape. AC loss comparison between monofilamentary conductors of rectangular, elliptical, square and round geometry has been performed in self-field and applied external perpendicular magnetic field. The areas of the cross-section and the superconducting-core-to-Ag ratio have been kept constant in the simulations. To complement the AC loss analysis, the distribution of the current density and the magnetic field of the different geometries are presented.

3-D finite element Simulations of strip lines in a YBCO/Au fault current limiter

Geometrical aspects of the design of fault current limiters (FCL) have a great impact on their performances. Recently, the University of Geneva have made certain optimizations by splitting the FCL into many small dissipative lengths in order to achieve a distributed transition along the device. For this paper, we have performed new 3D finite element method (FEM) simulations for studying the behavior of strip lines of a YBCO/Au FCL in an AC nominal use (sinusoidal current at industrial frequency) up to 3 I/sub c/. The very large aspect ratio of the device needs a particular attention to the modeling and meshing process. The numerical results show that presence of sharp corners can influence the performance of the device. Due to the high value of the electric field in these areas, the local losses are much higher than in the case of smooth corners, and this may lead to burning and cracking the wafer. Irreversible damage experiments have confirmed these locations. In this paper we proposed new geometries, taking into account the length of the connecting path and the corners optimization in order to decrease the risk of very high localized losses in the meander.

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

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.