Flux-line-cutting and flux-pinning losses in type-II superconductors in rotating magnetic fields

A general critical-state theory, including the effects of both flux-line cutting and flux pinning, is proposed for calculations of hysteresis in type-II superconductors in parallel applied magnetic fields that vary in both magnitude and direction. In this theory, if the magnitude of the electrical-current-density component perpendicular to the magnetic induction $\overrightarrow{\mathrm{B}}$ exceeds the corresponding critical value $J_{c\perp }$, depinning occurs, and an electric field component $E_{\perp }$ perpendicular to $\overrightarrow{\mathrm{B}}$ appears; if the magnitude of the current-density component parallel to $\overrightarrow{\mathrm{B}}$ exceeds the corresponding critical value $J_{c\parallel }$, flux-line cutting occurs, and an electric field component $E_{\parallel }$ parallel to $\overrightarrow{\mathrm{B}}$ appears. Model calculations are performed to solve for the electrodynamic response of a slab subjected to a parallel, constant magnetic field whose direction undergoes either continuous rotation or periodic oscillation. The relation of the theory to the pioneering experiments of LeBlanc and co-workers is discussed.