On the effect of strand damage on the operating margin of a Nb$_3$Sn Rutherford cable

Degradation of performance in superconducting magnets can be a major concern when a brittle material like Nb3Sn is employed. Indeed, degradation can significantly alter the transport properties of a cable if, e.g. an excessive stress is applied during coil and magnet manufacturing. In this paper, we study the limiting case of a strand in a Rutherford type cable that, at a given location, does not carry any current. We refer to such strand simplistically as the ‘broken strand’, regardless of the actual cause disrupting the current carrying capability. To this aim, a model was developed using the code THEA, to describe the electric and thermal properties of the Rutherford cable of the HL-LHC 11 T dipole magnet. First, we studied the current distribution in the cable, considering a uniform current in each strand at the boundaries, namely with single strands behaving as current generators, or zero-resistance joints, namely equipotential boundaries. We concluded that the two adjacent strands to the broken strand play the most significant role in the distribution of current out of the broken strand. A similar situation was found when a strand of the cable suddenly goes normal, i.e. it quenches. We then derived the characteristic times and lengths for the current redistribution in the case of an instantaneous strand breakage. We describe in detail the procedure to extract such quantities from the simulation results, and we demonstrate a good agreement between the numerically derived characteristic times and the analytical calculation from a previous theoretical work. The results of this study help to shed light on the repercussions of degradation in brittle materials such as Nb3Sn. This subject is indeed crucial for the next generation of accelerator coils and magnets for high-energy physics projects.