We report temperature and magnetic-field dependence of flux pinning force in bulk MgB 2 with variable grain size. The samples are prepared by advanced methods, allowing minimizing effects of porosity, impurities, and inclusions of secondary phases. The effects of grain connectivity, flux-creep phenomena, and grain size on critical current density and flux pinning curves are analyzed. We have compared the field dependence of the pinning force for a range of samples with the predictions of theoretical models accounting for the effect of the grain size. There is qualitative agreement between grain-boundary pinning mechanism proposed by Hampshire and Jones ͓J. Phys. C 21, 419 ͑1987͔͒ and the experimentally observed grain-size dependence of pinning force in bulk MgB 2 .

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We report the grain size dependence of critical current and grain boundary pinning in bulk MgB2. By combining polarized optical microscopy and electron backscatter diffraction, we obtain evidence of special grain boundaries with a high density of dislocations that are able to provide high critical current in MgB2 polycrystals. We argue that reduction of grain size to the nanoscale level is sufficient to provide the critical current densities required for large-scale applications at the boiling temperature of liquid hydrogen.

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.

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