Equation for Calculation of Critical Current Density Using the Bean's Model with Self-Consistent Magnetic Units to...

Area of Science:

• Condensed Matter Physics
• Materials Science
• Superconductivity

Background:

• Bean's critical state model is widely used for estimating critical current density (J).
• Existing equations for J calculation often lead to confusion and errors due to inconsistent magnetic units and pre-factors.
• Discrepancies in reported J values can be significant, sometimes differing by an order of magnitude.

Purpose of the Study:

• To propose a single, general equation for calculating critical current density (J) in rectangular samples using Bean's model.
• To clarify the impact of magnetic units and pre-factors on J calculations.
• To resolve ambiguities and prevent errors in reporting critical current density.

Main Methods:

• Analysis of existing equations for critical current density (J) based on Bean's model.
• Formulation of a single, dimensionless general equation for J calculation.
• Comparison of the proposed general equation with literature-reported expressions using different unit systems.

Main Results:

• A single, dimensionless general equation for calculating critical current density (J) is proposed.
• The proposed equation simplifies J calculation by allowing unit conversion without altering the core formula.
• Calculations using the general equation yield accurate J values, contrasting with potentially erroneous results from other methods.

Conclusions:

• The proposed general equation eliminates ambiguities in critical current density (J) calculations.
• Accurate J determination is crucial for advancing superconductivity research and applications.
• This work ensures correct dimensional analysis and prevents propagation of errors in the field.