The Bean model of the critical state in a magnetically shielded   superconductor filament
  We study the magnetization of a cylindrical type-II superconductor filament covered by a coaxial soft-magnet sheath and exposed to an applied transverse magnetic field. Examining penetration of magnetic flux into the superconductor core of the filament on the basis of the Bean model of the critical state, we find that the presence of a non-hysteretic magnetic sheath can strongly enhance the field of full penetration of magnetic flux. The average magnetization of the superconductor/magnet heterostructure under consideration and hysteresis AC losses in the core of the filament are calculated as well. 
S.V. Yampolskii, Yu.A. Genenko, H. Rauh, A.V. Snezhko