Florida electro-mechanical cable model of Nb₃Sn CICCs for high-field magnet design

Performance degradation of Nb₃Sn cable-in-conduit-conductors (CICCs) is a critical issue in large-scale magnet design such as in the International Thermonuclear Experimental Reactor (ITER) and the series-connected hybrid (SCH) magnets currently under development at the National High Magnetic Field Laboratory (NHMFL). The critical current Ic of Nb₃Sn conductors is strongly affected by thermal pre-strain in strand filaments in a CICC from differential thermal contraction between strands and conduit during cooling down after heat treatment. Mitchell and Nijhuis recently introduced strand bending under locally accumulated Lorentz force for the interpretation of observed transverse load degradation, defined as the Ic reduction due to strand bending and contact stress at strand crossing with respect to the expected Ic from strand data at the thermal compressive strain. In this paper, a new numerical model of CICC performance has been developed based upon earlier work by Mitchell and Nijhuis. The new model, called the Florida electro-mechanical cable model (FEMCAM), combines the thermal bending effects during cooling down and the electromagnetic bending effects during magnet operation, as well as effects due to strand filament fracture. We present the FEMCAM formulation and benchmark the results against about 40 conductor tests of first-cycle performance and 20 tests that include cyclic loading. We also consider the effects of different jacketing materials on CICC performance. We conclude that FEMCAM can be a helpful tool for the design of Nb₃Sn-based CICCs and that both thermal bending and transverse bending play important roles in the performance of Nb₃Sn CICCs.