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

The complex ac susceptibility chi' - jchi" 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 H-m. The core obeys the critical-state model with a constant critical-current density J(c) and the shell obeys Ohm's law with a constant conductivity a. The low-frequency dependences of chi' and chi" upon H-m /H-p (H-p being the full penetration field of the core) at various radius-filling fractions of the core are evaluated and their features are discussed.