The interaction distance between flux lines and pinning centres

TLDR

Pinned flux lines exhibit a linear, reversible response to low‑amplitude ripple fields, contradicting the Bean model. Elastic flux motion explains this behavior, enabling calculation of lattice forces; unpinning starts at about 30 Å displacement, the full critical state at ~400 Å, and ac losses are lower than Bean model predictions, confirmed experimentally.

Abstract

A number of workers have reported that, at low amplitudes the response of pinned flux lines to a ripple field is linear and reversible, in contradiction to the Bean model. It is shown that this can be explained by the elastic movement of flux. The results allow the force exerted on the flux lines by the lattice to be calculated as a function of their displacement from equilibrium. It is found that unpinning first occurs for displacements of about 30 AA but that the full critical state is not built up until they have moved about 400 AA. One result is that the ac losses are less than would be calculated from the Bean model and this is confirmed by the experimental measurements.