General critical states in type-II superconductors

TL;DR

This paper develops a generalized variational framework for modeling magnetic flux dynamics in type-II superconductors, extending existing models to three dimensions and analyzing various flux states and their transitions.

Contribution

It introduces a variational approach to describe flux transport and cutting in 3D superconductors, enhancing numerical analysis and physical understanding.

Findings

Extended double critical state model to 3D configurations.

Derived a generalized flux cutting threshold in 3D.

Analyzed the interaction between shielding and transport in longitudinal problems.

Abstract

The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework, by using a variational theory supported by well established physical principles. The equivalence between the variational statement and more conventional treatments, based on the solution of the differential Maxwell equations together with appropriate conductivity laws is shown. Advantages of the variational method are emphasized, focusing on its numerical performance, that allows to explore new physical scenarios. In particular, we present the extension of the so-called double critical state model to three dimensional configurations in which only flux transport (T-states), cutting (C-states) or both mechanisms (CT-states) occur. The theory is applied to several problems. First, we show the features of the transition from T to CT states. Second, we give a generalized expression for the flux cutting threshold in 3-D and show its relevance in the slab geometry. In addition, several models that allow to treat flux depinning and cutting mechanisms are compared. Finally, the longitudinal transport problem (current is applied parallel to the external magnetic field) is analyzed both under T and CT conditions. The complex interaction between shielding and transport is solved.