AC susceptibility of a long cylinder with a hard superconducting core and normal conducting shell

The complex ac susceptibility χ'-jχ'' is analytically derived for a long cylinder with a hard superconducting core and a normal conducting shell under a longitudinally applied ac magnetic field of amplitude Hm. The core obeys the critical-state model with a constant critical-current density Jc and the shell obeys Ohm's law with a constant conductivity σ. The low-frequency dependences of χ' and χ'' upon Hm/Hp (Hp being the full penetration field of the core) at various radius-filling fractions of the core are evaluated and their features are discussed