Expression with self-consistent magnetic units for calculation of critical current density using the Bean's Model

TL;DR

This paper introduces a universal equation for calculating the critical current density Jc,mag in superconductors using Bean's model, ensuring consistent units and eliminating common errors in the literature.

Contribution

A single, general equation is proposed for Jc,mag calculation that simplifies unit conversions and corrects previous discrepancies in the literature.

Findings

Different equations can lead to results at least one order of magnitude apart.

The proposed equation is dimensionally consistent and unit-independent.

Using the new equation reduces calculation errors and ambiguities.

Abstract

This study analyzes the calculation of the critical current density Jc,mag by means of Bean's critical state model, using the equation formulated by Gyorgy et al. and other similar equations derived from it reported in the literature. While estimations of Jc,mag using Bean's model are widely performed, improper use of different equations with different magnetic units and pre-factors leads to confusion and to significant errors in the reported values of Jc,mag. In this work, a SINGLE general equation is proposed for the calculation of Jc,mag for a rectangular parallelepiped sample in perpendicular field using Bean's critical state model, underlying how the simple conversion of magnetic units can lead to a Jc,mag in the desired units, without the need to introduce any other correction or use other specific equations depending on the units of Jc,mag. In this equation, the numerical pre-factor is dimensionless, independent of the unit system used. A comparison between the expression reported in the literature is done, showing how they can lead to different results depending on the used units, and that these results can be at least one order of magnitude different from the correct results obtained with the general equation proposed in this work. This resolves all ambiguities and aligns with the correct dimensional analysis, eliminates discrepancies in the calculated Jc,mag, and will avoid further propagation of errors in the literature.