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 →J_∥·→E_∥. where →J_∥ and →E_∥ 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∥ or a critical angle gradient kc, 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.