Best practices for a proper evaluation and conversion of physical property equations in superconductors: the examples of WHH formulation, Bean model and other cases of interest

Abstract

In recent years there have been growing concerns about the proper evaluation of physical properties of superconductors, in particular for quantities extracted from magnetic characterizations. Errors can and often do occur due to the following issues: i) several measurement instruments still use Gaussian & cgs-emu units instead of the preferable International System (SI) units; ii) there are decades of valuable publications where, however, equations were expressed in Gaussian & cgs-emu or other unit systems or where constants were normalized to unity, which requires proper understanding and unit conversion in order to correctly evaluate the measured physical quantities; iii) the conversion between unit systems sometimes appears challenging and may not be properly performed. In this paper we will describe how to properly convert physical quantities relevant for the evaluation of magnetic and other properties focusing on the still most used unit systems, SI and Gaussian & cgs-emu. We will provide examples of how to properly verify and understand the physical formulae. We will include examples for the correct method to determine the critical current density Jc of a superconductor from the measurement of its magnetic hysteresis loop through the Bean model, and the correct conversion to SI of the equations for Hc2(T) according to the Werthamer-Helfand-Hohenberg (WHH) formulation. The goals of this paper are to make the readers aware of the unit conversion issue, to provide useful hands-on tools for proper conversion and to strongly encourage future exclusive use of the SI units and formulae.