  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.
