macroscopic region ⍀ ʚ R 3 , in the presence of an applied uniform magnetic field, H a . For H a below some critical
We present a method to compute the magnetic moment of a bulk, finite-size, three-dimensional, anisotropic superconductor. Our nu-value, superconductors are in the so called Meissner regime merically implemented perturbative procedure is based on a solu- [2], where the magnetic flux is expelled from the bulk of tion of the nonlinear Maxwell-London electrodynamic equations, the sample. Their behavior is similar to that of material where we include the nonlinear relation between current and gauge which is both an ideal conductor and an ideal diamagnet.
invariant velocity. The method exploits the small ratio of the finite
The applied magnetic field generates a resistance-free curpenetration depths to the sample size. We show how to treat the rent which produces a magnetic field that opposes H a .
open boundary conditions over an infinite domain and the continuity requirement at the interface. We demonstrate how our method As a consequence, everywhere except very close to the substantially reduces the computational work required, and discuss interface (within a few penetration depths), the magnetic its implementation to an oblate spheroid. The numerical solution field vanishes: this is known as the Meissner effect. Except is obtained from a finite-difference method. We briefly discuss the for the most trivial geometries such as infinite slabs or relevance of this work to similar problems in other fields. ᮊ 1997 isotropic spheres, the relevant boundary value problem Academic Press becomes then numerically very awkward: basically one is faced with solving the appropriate electrodynamic equations in the entire space, not just in ⍀, while the most the physical information one obtains in experiments comes in fact from the penetration of the fields inside the sample, ponent, m Ќ , perpendicular to the field H a even when this is applied along a direction of symmetry of the sample. characterized by penetration depths which, although small, cannot be neglected.
This occurs when the applied field lies in the a Ϫ b crystallographic plane [7] (the z-axis is taken to be along the c Consider a superconductor that occupies a bounded, 337