Alternating-Current-Induced Voltages in Superconducting Wires

A model introduced by Bean and extended by Kim is applied to predict voltages induced in a superconducting wire carrying low-frequency alternating current. A basic premise of Bean's model is that the magnitude of the local current density, $J$, is determined by the magnitude of the local magnetic induction, $B$. The function $J\left(B\right)\mathrm{}$ is assumed to have the form deduced by Kim from magnetization measurements, $J=\frac{\alpha }{(B+B_0)}$, with $\alpha$ and $B_0$ treated as adjustable constants. Relations for voltage as a function of current have been derived for ac and for ac plus superimposed dc. Predicted $V$-versus-$I$ curves are found to agree fairly well with oscilloscope tracings obtained for defect-saturated wires of Nb and various Nb alloys.