In this article we revisit a well-known effect in superconductors, which is the penetration of the magnetic field by regions of greater radius of curvature (Tinkham, 2008; De Gennes, 1966). This is exposed in the literature but without a quantitative solution. Here we solve this problem by two distinct numerical simulations. We calculate the superconducting current density using numerical simulations via the London theory in the Meissner state and numerical simulations using the time-dependent Ginzburg–Landau (TDGL) theory for the vortex state. In both simulations, the results obtained are in agreement, as could not be otherwise. We show that in the Meissner state the current density increases much faster in the region where the radius of curvature is larger, thus reaching the critical value first in this location, and therefore local breakdown of superconductivity occurs. In the vortex state, our simulations, using TDGL, show that the vortices penetrate through exactly the same location pointed out by the previous simulation. For this study we worked with a superconducting needle with an ellipsoidal mesoscopic cross section.

在本文中，我们重新审视超导体中众所周知的效应，即曲率半径较大的区域会穿透磁场（Tinkham，2008；De Gennes，1966）。这在文献中有所揭示，但没有定量的解决方案。在这里，我们通过两个不同的数值模拟来解决这个问题。我们通过迈斯纳态下的伦敦理论进行数值模拟，并使用涡旋态下的瞬态金兹堡-朗道 (TDGL) 理论进行数值模拟，计算超导电流密度。在这两次模拟中，获得的结果是一致的，否则不可能是一致的。我们发现，在迈斯纳态下，曲率半径较大的区域电流密度增加得更快，因此在该位置首先达到临界值，从而发生超导的局部击穿。在涡旋状态下，我们使用 TDGL 进行的模拟表明，涡旋穿透的位置与先前模拟指出的位置完全相同。在这项研究中，我们使用了具有椭圆形介观横截面的超导针。