Vortex-penetration field at a groove with a depth smaller than the   penetration depth
  Analytical formula to evaluate the vortex-penetration field at a groove with a depth smaller than penetration depth is derived, which can be applied to surfaces of cavities or test pieces made from extreme type II superconductors such as nitrogen-doped Nb or alternative materials like Nb3Sn or NbN. 
Takayuki Kubo
physics.acc-ph cond-mat.supr-con