Exact solution of the London equation for current carrying inhomogeneous cylindrical superconductors

We have solved exactly the London equation for the magnetic field and current density distribution inside an inhomogeous cylindrical superconductor bearing an overall subcritical assigned current I. The inhomogeneity consists in a sudden jump in the London penetration depth. The presence of two such jumps (with obvious generalization to n jumps) serves as a model to a cylindrical superconductor in which different size regions, with different penetration depths follow one another. We illustrate how the flowing current is distorted by the presence of these interfaces.