A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.

Abstract-EuCARD-2 is a project supported by FP7-European Commission that includes, inter alia, a work-package (WP10) called "Future Magnets". This project is part of the long term development that CERN is launching to explore magnet technology at 16 T to 20 T dipole operating field, within the scope of a study on Future Circular Colliders. The EuCARD2 collaboration is closely liaising with similar programs for high field accelerator magnets in the USA and Japan. The main focus of EuCARD2 WP10 is the development of a 10 kA-class superconducting, high current density cable suitable for accelerator magnets, The cable will be used to wind a stand-alone magnet 500 mm long and with an aperture of 40 mm. This magnet should yield 5 T, when stand-alone, and will enable to reach a 15 to 18 T dipole field by placing it in a large bore background dipole of 12-15 T. REBCO based Roebel cables is the baseline. Various magnet configurations with HTS tapes are under investigation and also use of Bi-2212 round wire based cables is considered. The paper presents the structure of the collaboration and describes the main choices made in the first year of the program, which has a breadth of five to six years of which four are covered by the FP7 frame.

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-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.

In the quest for high-current high-temperature superconducting (HTS) cables suitable for application to high-field magnets, the Roebel cable made from (RE)-Ba 2 Cu 3 O 7−δ (RE for rare earth: Y, Sm, Gd, Dy or a mixture of them) coated conductors is identified as meeting the requirements for high-current capability, compactness, transposition and good mechanical properties. In accelerator high-field magnets, Roebel cables will be operated in liquid helium at 4.2 K or lower temperatures. Previous papers have reported on the electrical characterization of Roebel cables at 77 K, but measurements at 4.2 K have not been published yet. This paper summarizes the results of the critical current measurements performed at CERN on (RE)-Ba 2 Cu 3 O 7−δ Roebel cables at 4.2 K and in external fields of up to 9.6 T.

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Bulk-textured YBa 2 Cu 3 O 7−x single domains could be used for current-limiting applications by cutting and assembling long meanders, which would be submitted to network electric fields before using a breaker to interrupt a fault current. For that purpose, large YBaCuO single domains up to 93 mm in diameter can be isothermally grown by using a standard melt texturing growth (MTG) process with a SmBaCuO seed. The essential parameters that have to be controlled in order to reach this size are the temperature growth window, the substrate reactivity and the temperature homogeneity in the sample. Standard 45 mm diameter single domains show excellent superconducting properties, such as J c above 10 5 A cm −2 and a homogeneous superconducting-to-normal transition at 91.8 K for 20 cm long conductors cut in these pellets. These measurements demonstrate the long -range homogeneity of single domains regarding T c and J c . Nevertheless the high J c values lead to a too large a dissipation in the normal state at T = 77 K. Different methods to reduce the critical current density are described in order to fulfill the conditions for a safe recovery of the material after undergoing a magnetothermal transition.