Time-Dependent Ginzburg-Landau Simulation of Critical Current Density Including z-axis Anisotropy

In this study, the three-dimensional time-dependent Ginzburg-Landau equations were numerically solved to visualize the motion of the flux lines in a superconductor under a transverse magnetic field. Pins were inserted into a superconducting rectangular parallelepiped, and the magnetic field dependence of the normalized critical current density J_c was calculated. Anisotropy y_Z of different magnitudes was introduced along the direction of the magnetic field (z-axis). Different pin shapes and orientations were also considered: columnar pins aligned parallel to the direction of either the magnetic field or the current flow, spherical pins, and a planar pin in the field-current plane. For the columnar pins aligned parallel to the field (along the flux lines), J_c showed almost no dependence on y_Z. Additionally, a peak in the J_{c -B c}urve for this pin geometry was observed at normalized magnetic field, B= 0.4 for all considered y_z. In contrast, J_c was dependent on y_Z for the columnar pins aligned parallel to the current flow (perpendicular to the flux lines) and the spherical pins. At low magnetic fields (B= 0.1), J_c increased with increasing y_Z in both these cases. In the case of the planar pin, J_c showed no dependence on y_Z. In conclusion, when a pin was inserted parallel to the normalized magnetic field B, J_c did not decrease even when the z-axis anisotropy y_Z was large.