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.
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.
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. We
compare 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 and a dependence of the local critical current density
Jc
on the local magnetic field. For the simulation of YBCO conductors, a new ‘shell-region’
model is utilized. This overcomes the geometry and mesh problems typical of
superconductors with very high geometric aspect ratio. Different AC working conditions are
simulated: self-field, applied external field, and combined transport current and external
field of varying orientation. We outline 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 well known than those of BSCCO conductors.
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