Magnetic properties of finite superconducting cylinders. II. Nonuniform applied field and levitation force

We study the current penetration profiles inside a finite type-II superconducting cylinder when it is in the presence of an axially symmetric applied field created by a cylindrical and uniformly magnetized permanent magnet. The results are obtained using the general framework derived in the first paper of this series. The levitation force in such a system is calculated from the current distribution, for the cases of a constant critical current in the superconductor and an exponential dependence of the critical current upon the internal magnetic field. From the obtained results, we study in detail how the levitation force depends upon the system parameters. We conclude from the results that (i) the levitation force is optimized when the magnet and the superconductor have similar dimensions, (ii) an excess of length in the superconductor can yield no significant increase in the force, and (iii) demagnetizing effects can lead to an important enhancement of the levitation force, particularly in the case of thin films, for which the force per unit volume of material is the highest.