Francesco Grilli1,Nicolo Riva2,Christian Lacroix3,Frederic Sirois3,Bertrand Dutoit4
Karlsruhe Institute of Technology1,Massachusetts Institute of Technology2,Polytechnique Montréal3,École Polytechnique Fédérale de Lausanne4
Francesco Grilli1,Nicolo Riva2,Christian Lacroix3,Frederic Sirois3,Bertrand Dutoit4
Karlsruhe Institute of Technology1,Massachusetts Institute of Technology2,Polytechnique Montréal3,École Polytechnique Fédérale de Lausanne4
In numerical models of high-temperature superconductor (HTS) applications, the electrical behavior of the superconductor material is often modeled as a material with a nonlinear resistivity, which is derived from a power-law E-J constitutive law. In that case, the critical current density J<sub>c</sub> is determined as the value corresponding to a threshold electrical field, usually set equal to 1 μV/cm for HTS. This approach has proved its reliability for simulating phenomena such as the AC losses caused by time-varying magnetic fields, created by transport currents, externally applied magnetic fields, or a combination of the two. The reason of such success is that, in those conditions, the currents flowing in the superconductor are very close to the critical current density J<sub>c</sub>. There are however situations where this condition is not met: on one side, when the current flowing in the superconductor exceeds its current-carrying capability – a typical case is represented by fault current limiters; on the other side, when the excitation is small or when relaxation phenomena are involved – for example in certain magnetization processes. In all these cases, the use of the power-law can become questionable and alternative E-J constitutive laws might be preferable.<br/>In this work, we present the result of electrical characterizations aiming at exploring the behavior of the superconductor material at electric fields considerably higher or lower than 1 μV/cm. For over-critical characterization, we use a fast pulsed current measurement system that allows injecting high currents in the superconducting sample on very short time scales. The E-J constitutive law of the HTS material is then extracted from the experimental data by means of an electro-thermal numerical model. For under-critical characterization, we measure the voltage-current characteristic with the usual four-point technique on long wire samples, by placing the voltage taps several meters apart. Both types of experiments are performed by placing the samples in liquid nitrogen at atmospheric pressure.<br/>We use the so-determined alternative E-J constitutive laws in finite-element simulations of HTS applications. We compare the results with those obtained by using the power-law and discuss the reasons behind the observed differences.