Stability of DC transport in HTS conductor with local critical current reduction

A common feature of commercially available conductors based on high-temperature superconducting compounds is the fluctuation of critical current along the length. Fortunately, the practice adopted by manufacturers nowadays is to supply the detailed Ic(x) data with the conductor. Compared to knowing just the average of critical current, this should also allow a much better prediction of the conductor performance. Statistical methods are suitable for this purpose in the case when the fluctuations are regular at the low end of critical current distribution. However, a different approach is necessary at the presence of 'weak spots' that drop out of any statistics. Because of the strong nonlinearity of the current-voltage curve, such a location could transform into a 'hot spot' at transporting direct current (DC), with an abrupt increase of temperature endangering the conductor operation. We present a set of analytical formulas including the prediction of the maximum DC that could be carried sustainably before the thermal runaway appears. It is necessary to know the cooling conditions as well as the properties of the conductor constituents and their architecture. A formula for the voltage appearing on a weak spot, and its dependence on the DC, is also proposed. For this purpose the result of previous theoretical work has been slightly modified after comparing it with numerical iterative computations and finite element modeling. We demonstrate that the derived model allows a powerful analysis of experimental data comprising an estimation of the weak spot parameters i.e. its critical current and the length of the defect zone.