The Dynamics of the Bean Critical State

TL;DR

This paper introduces a one-dimensional model demonstrating that flux line dynamics in superconductors follow avalanche behavior, leading to a self-organized critical state characterized by power-law distributions and a parabolic flux density.

Contribution

It presents a novel simple model showing that flux entry in superconductors exhibits avalanche dynamics and self-organized criticality.

Findings

Flux line movements follow a power-law distribution with exponent -1.

Flux density profile is parabolic.

Flux dynamics are dominated by avalanches.

Abstract

A simple one dimensional model to simulate the establishment of the Bean critical state is introduced. It is shown that the dynamics of the flux lines as they enter the superconductor are dominated by `avalanches'. The distribution of distances moved by vortices in the avalanches obeys a power law with an exponent of -1. This suggests that the Bean state is a self-organised critical state. The density of flux lines is parabolic.