Equation for Calculation of Critical Current Density Using the Bean’s Model with Self-Consistent Magnetic Units to Prevent Unit Conversion Errors

This study analyzes the calculation of the critical current density <i>J_c,mag</i> 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 <i>J_c,mag</i> 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 <i>J_c,mag</i>. In this work, a SINGLE general equation is proposed for the calculation of <i>J_c,mag</i> 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 <i>J_c,mag</i> in the desired units, without the need to introduce any other correction or use other specific equations depending on the units of <i>J_c,mag</i>. 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 <i>J_c,mag</i>, and will avoid further propagation of errors in the literature.