AC transport losses calculation in a Bi-2223 current lead using thermal coupling with an analytical formula

When a superconductor is fed with an alternating current, the temperature rise created by the losses tends to reduce the current carrying capacity. If the amplitude of the current exceeds the value of the critical current, then the losses become particularly high and the thermal heating considerable. In this paper, a numerical and an analytical model which allow to estimate AC transport losses are presented. These models, which use the expression of I_c(T) and n(T), are available for any applied current (below and above I_c). The results are compared and the validity of the analytical model is considered. Then, the analytical formula allows to easily obtain the thermoelectric balance point of the system, when the losses and the temperature do not vary any more. Moreover, a maximum value of the current transport, beyond which the balance point does not exist, is detected. Indeed, when this maximum value is exceeded, the system is not stable and, say, superconducting current leads may quench.