Modelling the E– J relation of high- Tc superconductors in an arbitrary current range

• Published in: Physica. C, Superconductivity Superconductivity, 2004-01, Vol.401 (1), p.231-235
• Main Authors: Duron, Joseph, Grilli, Francesco, Dutoit, Bertrand, Stavrev, Svetlomir
• Format: Article
• Language: English
• Subjects: AC losses; HTS materials; Numerical modelling; V– I relation
• ISSN: 0921-4534; 1873-2143
• DOI: 10.1016/j.physc.2003.09.044

For describing the E– J relation of high- T c superconductors (HTS) in power applications, where the applied current I is generally limited by I c, the critical state model, a piecewise linear generalization, or a simple power-law of the type E= E c( J/ J c) n are most often used. The power-law cannot be used for modelling the E– J relation with I≫ I c due to the unbound exponential increase of the electric field for currents above I c, while in reality the non-linear HTS resistivity is limited by its normal state value. This paper presents a modified E– J model for describing the V– I characteristic of HTS tapes with applied currents largely exceeding I c. This model is based on the power-law in combination with a parallel metallic branch and has a limited resistivity––the HTS one in the normal state. It can be used for black-box modelling of superconductors in a unlimited current range, as well as for numerical modelling of superconducting devices, which can be operated at currents far exceeding I c; for example fault-current limiters or cables with over-critical current excursions. The model has been tested in a simple numerical implementation and the modified power-law has been implemented in finite element method simulations. It is shown that for bulk material with currents above 1.3–2 I c (depending on the n-value), the usual power-law results in excessive AC loss estimation.