Pressure-induced critical current reduction in impregnated Nb₃Sn Rutherford cables for use in future accelerator magnets

The measured critical current reduction in Nb3Sn Rutherford cables under magnet-relevant transverse pressure levels is analyzed in terms of the strain state of the filaments inside their strands. Several straightforward mechanical 2D FE models of the cables' cross-section are used to translate the stress that is applied to the surface of the impregnated cables into a strain distribution on its strands. The resulting critical current reduction of the cable is then estimated from the average deviatoric strain in the strands' filamentary zone, using the well-established strain scaling relations obtained for isolated strands. This allows to identify the main factors that influence the pressure response of impregnated Nb3Sn accelerator cables. The analysis is presented for state-of-the-art cable samples that were measured at the University of Twente and shows how especially stiff and incompressible resins reduces the deviatoric strain in the filamentary zone of the cable strands, but also how relatively small alignment errors can lead to stress concentrations that reduce the critical current density significantly.