Transport ac loss in a long cylinder with a hard superconducting core and normal conducting shell

The power loss is analytically derived for a long cylinder with a hard superconducting core and a normal conducting shell under an applied ac current of amplitude I-m. The core obeys the critical-state model with a constant critical-current density J(c) and the shell obeys the Maxwell equations and the Ohm law with a constant permeability mu(0) and conductivity sigma. The dependence of the normalized ac loss per cycle per unit length upon I-m/I-c (I-c being the critical current), the normalized frequency, and the radius-filling fraction of the core are studied. We provide a detailed discussion on the nature of the loss in the shell and the description of its low-frequency low-current limit and high-frequency limit.