The Critical State in Type-II Superconductors with Cross-Flow Effects

Abstract

A theoretical framework is presented, which allows to explain many experimental facts related to pinning and cross-flow effects between flux tubes in type-II superconductors. It is shown that critical state principles, in the manner introduced by C. P. Bean for parallel vortex lattices, may be used to describe the observed behavior. We formulate a least action principle, giving place to a variational interpretation of the critical state. The coarse-grained electrodynamic response of the superconductor is solved by minimizing the magnetic field changes, for a current density vector constrained to belong to some bounded set Δ. It is shown that the selection of Δ determines the specific critical state model in use. Meaningful choices of Δ are discussed in view of the related physical mechanisms.