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

TL;DR

This paper develops a theoretical framework for understanding the critical state in type-II superconductors, incorporating cross-flow effects and pinning phenomena, through a variational principle approach.

Contribution

It introduces a least action variational principle to describe the electrodynamics of type-II superconductors with flux tube interactions.

Findings

The model explains experimental pinning and cross-flow effects.

Critical state behavior is derived from minimizing magnetic field changes.

Selection of the bounded set Delta influences the specific critical state model.

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 (Delta). It is shown that the selection of Delta determines the specific critical state model in use. Meaningful choices of Delta are discussed in view of the related physical mechanisms.