Collective pinning of imperfect vortex lattices by material line defects   in extreme type-II superconductors
  The critical current density shown by a superconductor at the extreme type-II limit is predicted to follow an inverse square-root power law with external magnetic field if the vortex lattice is weakly pinned by material line defects. It acquires an additional inverse dependence with thickness along the line direction once pinning of the interstitial vortex lines by material point defects is included. Moderate quantitative agreement with the critical current density shown by second-generation wires of high-temperature superconductors in kG magnetic fields is achieved at liquid-nitrogen temperature. 
J.P. Rodriguez and M.P. Maley