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

For describing the E-J relation of high-Tc superconductors (HTS) in power applications, where the applied current I is generally limited by Ic, the critical state model, a piecewise linear generalization, or a simple power-law of the type E=Ec(J/Jc)^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 Ic, 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 Ic. 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 Ic; 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 1.3-2Ic$ (depending on the n-value), the usual power-law results in excessive AC loss estimation.