Magnetic Field Expulsion from an Infinite Cylindrical Superconductor
  The solutions of the London equations for the magnetic field expulsion from superconductors are presented in this paper for the cylindrical symmetry. The result is analyzed in detail and represented numerically for the case of a uniform external magnetic field in the transverse plane. In particular, several contour plots of the magnetic energy density are depicted for the regions inside and around the superconducting area for a wide range of penetration lengths, showing how the expulsion and penetration of the magnetic field evolve with the ratio between the penetration length and the cylinder radius. 
Miguel C. N. Fiolhais and Hanno Ess\'en
cond-mat.supr-con