Critical state in type-II superconductors of arbitrary shape

TL;DR

This paper develops a method to determine the critical state in arbitrarily shaped type-II superconductors, revealing a smooth, diffusive current distribution change in contrast to traditional abrupt transitions.

Contribution

It introduces a novel approach to find the critical state in superconductors of any shape, extending beyond symmetric cases.

Findings

Current distribution in nonsymmetric samples propagates smoothly.

Contrasts with abrupt changes in traditional Bean critical state.

Provides a framework for arbitrary-shaped superconductor analysis.

Abstract

The well-known Bean critical state equations in general are not sufficient to describe the critical state of type-II superconductors when the sample shape is not symmetric. We show how one can find the critical state in superconductors of arbitrary shape. Analyzing a simple example of nonsymmetry, we demonstrate that in the general case, a perturbation of the current distribution in the critical state propagates into the sample smoothly in a diffusive way. This is in contrast to the usual Bean critical state where the current distribution changes abruptly at a narrow front.