Francesco Grilli

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 Analysis of the coupling effect between superconducting filaments of different aspect ratio

Using 3D finite element method (FEM) modelling, the present work investigates the coupling effect between two finite superconductors through a resistive matrix. This effect, related to the finite length of the conductors, is typically three-dimensional and cannot be analysed by the widely utilized 2D models. Superconductors are modelled with the nonlinear power-law E = Ec(J/Jc)n, which has been implemented in the FEM software. The main focus is to demonstrate the feasibility of such calculations and to establish the correlation between the coupling effect and the aspect ratio of the conductor cross-section, in order to extend the existing theory, which is only precise for superconductors of infinite slabs, fully penetrated by the magnetic field. The effect of other parameters such as the conductor length and the gap between the superconducting filaments is also considered. The latter is a parameter which does not feature in the approximate theories.

Prediction of resistive and hysteretic losses in a multi-layer high-Tc superconducting cable

In this work, a model of a multi-layer high-Tc superconducting (HTS) cable that computes the current distribution across layers as well as the AC loss is presented. Analyzed is the case of a four-layer cable, but the developed method can be applied to a cable with an arbitrary number of layers. The cable is modelled by an equivalent circuit consisting of the following elements: nonlinear resitances, linear self and mutual inductances, as well as nonlinear, hysteretic inductances. The first take into account the typical current-voltage relation for superconductors, the second introduce coupling among the layers and depend on the geometrical parameters of the cable, the third describe the hysteretic behaviour of superconductors. In the presented analysis, the geometrical dimensions of the cable are fixed, except for the pitch length and the winding orientation of the layers. These free parameters are varied in order to partition the current across the layers such that the AC loss in the superconductor is minimized. The presented model allows to evaluate rapidly the current distribution across the different layers and to compute the corresponding AC loss. The rapidity of the computation allows calculating the losses for many different configurations within a reasonable time. The model has so firstly been used for finding the pitch lengths giving an optimal current distribution across the layers and for computing the corresponding AC loss. Secondly, the model has been refined taking into account the effects of the magnetic self-field, which, especially at high currents, can sensibly reduce the transport capacity of the cable, in particular in the outer layers.

Numerical modelling of Bi-2223 multifilamentary tapes with position-dependent Jc

Different measurement techniques have demonstrated that due to better alignment during the manufacturing process, the central filaments in multifilamentary Bi-2223 tapes have higher critical current density than the outer filaments. A numerical model of non-twisted tapes has been used in Finite-Element-Method simulations. The model incorporates non-uniform lateral Jc distribution in accordance with direct Ic measurements, made along the width of a Bi-2223 tape. Two types of simulations are performed on 7 and 19-filamentary tapes with applied transport current – one with constant Jc in all filaments, and another with a Jc(x) dependence. The current distribution and AC loss in each filament are numerically calculated and compared. It is demonstrated that the current density distribution and power dissipation vary considerably in the different filaments, which is due to the position of the filament with respect to the edge of the tape and the different Jc values along the width.

Modelling of coupling between superconductors of finite length using an integral formulation

An integral formulation based on the stream function of sheet currents is applied to finite length superconductors to model the coupling through a normal matrix. This formulation is an extension of Brandts 2D formulation for modelling a 3D problem. Thin discs and infinite slabs were studied and the critical was obtained as a function of applied field. While an excellent agreement for fully penetrated infinite slabs was found with existing theories, original results are presented for partially penetrated slabs as well as for thin discs in a wide range of applied fields.

3D modeling of coupling between superconducting filaments via resistive matrix in AC magnetic field

The ac loss of superconducting composite depends strongly on coupling between superconducting filaments via the resistive matrix. The established technique for loss reduction using twisted filaments relies on the decoupling of the filaments below a critical coupling field Bc, which increases with the reduction of the twist pitch and the matrix conductivity. Although the concept of Bc may be clearly demonstrated using two infinite slabs of finite length, further details on its correlation with the filament/conductor geometry are not yet available. The main obstacle is due to the fact that any accurate analysis of such a problem must be carried out in 3d. In this paper, we describe the initial results from 3d modeling using Cedrats Flux3D, for which a superconductor module for handling power-law E-J characteristics was developed. Using a simple model of two rectangular superconductors connected through a normal metal, we demonstrate the feasibility for quantitative modeling of their coupling behavior over a wide range of field sweep rates for different conductor geometries. Typical examples were given for cases not addressed by the existing approximate theory, as well as for the evolution of field profile for varying field sweep rate.