{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T23:22:20Z","timestamp":1791933740113,"version":"4.3.4"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000921","name":"EU COST Actions","doi-asserted-by":"publisher","award":["CA19108 Hi- SCALE"],"award-info":[{"award-number":["CA19108 Hi- SCALE"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"EU COST Actions","doi-asserted-by":"publisher","award":["CA20116 OPERA"],"award-info":[{"award-number":["CA20116 OPERA"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"EU COST Actions","doi-asserted-by":"publisher","award":["CA21144 SUPERQUMAP"],"award-info":[{"award-number":["CA21144 SUPERQUMAP"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"EU COST Actions","doi-asserted-by":"publisher","award":["P2022KWFBH"],"award-info":[{"award-number":["P2022KWFBH"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"EU COST Actions","doi-asserted-by":"publisher","award":["N00014-21-1-2534"],"award-info":[{"award-number":["N00014-21-1-2534"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"name":"PRIN 2022 PNRR Project QUESTIONs","award":["CA19108 Hi- SCALE"],"award-info":[{"award-number":["CA19108 Hi- SCALE"]}]},{"name":"PRIN 2022 PNRR Project QUESTIONs","award":["CA20116 OPERA"],"award-info":[{"award-number":["CA20116 OPERA"]}]},{"name":"PRIN 2022 PNRR Project QUESTIONs","award":["CA21144 SUPERQUMAP"],"award-info":[{"award-number":["CA21144 SUPERQUMAP"]}]},{"name":"PRIN 2022 PNRR Project QUESTIONs","award":["P2022KWFBH"],"award-info":[{"award-number":["P2022KWFBH"]}]},{"name":"PRIN 2022 PNRR Project QUESTIONs","award":["N00014-21-1-2534"],"award-info":[{"award-number":["N00014-21-1-2534"]}]},{"DOI":"10.13039\/100000006","name":"ONR","doi-asserted-by":"publisher","award":["CA19108 Hi- SCALE"],"award-info":[{"award-number":["CA19108 Hi- SCALE"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"ONR","doi-asserted-by":"publisher","award":["CA20116 OPERA"],"award-info":[{"award-number":["CA20116 OPERA"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"ONR","doi-asserted-by":"publisher","award":["CA21144 SUPERQUMAP"],"award-info":[{"award-number":["CA21144 SUPERQUMAP"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"ONR","doi-asserted-by":"publisher","award":["P2022KWFBH"],"award-info":[{"award-number":["P2022KWFBH"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"ONR","doi-asserted-by":"publisher","award":["N00014-21-1-2534"],"award-info":[{"award-number":["N00014-21-1-2534"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>This study analyzes the calculation of the critical current density Jc,mag by means of Bean\u2019s 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\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/ma18020269","type":"journal-article","created":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T09:54:27Z","timestamp":1736416467000},"page":"269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Equation for Calculation of Critical Current Density Using the Bean\u2019s Model with Self-Consistent Magnetic Units to Prevent Unit Conversion Errors"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4534-3301","authenticated-orcid":false,"given":"Massimiliano","family":"Polichetti","sequence":"first","affiliation":[{"name":"Laboratory \u201cLAMBDA\u201d for Analysis of Materials Behaviour in DC and AC Fields, Department of Physics \u201cE.R. Caianiello\u201d, University of Salerno and CNR-SPIN Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, SA, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1372-357X","authenticated-orcid":false,"given":"Armando","family":"Galluzzi","sequence":"additional","affiliation":[{"name":"Laboratory \u201cLAMBDA\u201d for Analysis of Materials Behaviour in DC and AC Fields, Department of Physics \u201cE.R. Caianiello\u201d, University of Salerno and CNR-SPIN Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, SA, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rohit","family":"Kumar","sequence":"additional","affiliation":[{"name":"Laboratory for Heteroepitaxial Growth of Functional Materials & Devices, Department of Chemical & Biological Engineering, State University of New York (SUNY) at Buffalo, Buffalo, NY 14260, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amit","family":"Goyal","sequence":"additional","affiliation":[{"name":"Laboratory for Heteroepitaxial Growth of Functional Materials & Devices, Department of Chemical & Biological Engineering, State University of New York (SUNY) at Buffalo, Buffalo, NY 14260, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1126\/science.abq4137","article-title":"The Prospects of High-Temperature Superconductors","volume":"380","author":"Molodyk","year":"2023","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TASC.2017.2671680","article-title":"High-Temperature Superconductivity: A Roadmap for Electric Power Sector Applications, 2015\u20132030","volume":"27","author":"Marchionini","year":"2017","journal-title":"IEEE Trans. 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