AC losses in superconductors with a power-law constitutive relation

The observed constitutive relation between the electrical field and current density in cuprates high temperature superconductors is a power-law of the current. This functional dependence is presumably related to the giant flux-creep domain. It is shown that this constitutive relation reflects the statistical spread of the pinning potential associated with creep motion of vortex bundles. The AC losses emanating from a power-law constitutive relation are calculated in an approach focused on the superconductor's electric field. For a slab geometry in the presence of a parallel AC magnetic field or transport current, the calculated AC-loss scaling laws are consistent with BSCCO data and the critical state model. Extensions of the approach are briefly discussed.