Flux-line-cutting losses in type-II superconductors

Energy dissipation associated with flux-line cutting (intersection and cross-joining of adjacent nonparallel vortices) is considered theoretically. The flux-line-cutting contribution to the dissipation per unit volume, arising from mutual annihilation of transverse magnetic flux, is identified as ${\overrightarrow{\mathrm{J}}}_{\parallel }·{\overrightarrow{\mathrm{E}}}_{\parallel }$. where ${\overrightarrow{\mathrm{J}}}_{\parallel }$ and ${\overrightarrow{\mathrm{E}}}_{\parallel }$ are the components of the current density and the electric field parallel to the magnetic induction. The dynamical behavior of the magnetic structure at the flux-line-cutting threshold is shown to be governed by a special critical-state model similar to that proposed by previous authors. The resulting flux-line-cutting critical-state model, characterized in planar geometry by a parallel critical current density $J_{c\parallel }$ or a critical angle gradient $k_c$, is used to calculate predicted hysteretic ac flux-line-cutting losses in type-II superconductors in which the flux pinning is weak. The relation of the theory to previous experiments is discussed.