Analysis of non-uniform current distribution effects in multistage cable-in-conduit conductors

Abstract

An analysis procedure has been developed for non-uniform current effects in superconducting cables that contain many individual strands in limited electrical contact with each other. The procedure uses an approximation to the electrical diffusion equation to produce a lumped circuit model of the cable and a simplified zero dimensional heat balance equation to provide overall predictions of the cable stability to external disturbances. It is fast enough to be applied to the multistage cables (>1000 individual strands) that are required for large high field magnets. A model for the initial current distribution in such cables assumes that in steady state or slow ramp-up conditions the current in individual strands is limited to the critical value by the strand resistance. The distribution of current carrying strands is determined by the resistance distribution at the terminations, the cable transverse conductivity and variations in inductive coupling between individual strands. This model is applied to consider the effect of these parameters on the stability to short thermal disturbances. The particular case of the ITER Nb 3Sn CS model coil 13T, 40 kA cable-in-conduit conductor is analysed and it is shown that above a certain current level the cables can sometimes show a sharp drop in stability, qualitatively consistent with results observed on short sample tests. This stability drop is much more severe than that characterised by the conventional `well-cooled to ill-cooled' transition and represents the limit of steady state or slow ramp-up operation. The stability cut-off current is shown to be a function of the copper fraction in the cable, the uniformity of the current carrying strand distribution and the cable transverse conductance distribution. NbTi conductors with a similar configuration show the same behaviour.