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 Im. The core obeys the critical-state model with a constant critical-current density Jc and the shell obeys the Maxwell equations and the Ohm law with a constant permeability μ0 and conductivity σ. The dependence of the normalized ac loss per cycle per unit length upon Im/Ic (Ic 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.