Transverse-pressure susceptibility of high-$J_c$ RRP and PIT types of Nb$_3$Sn Rutherford cables for accelerator magnets

In the frame of the High-Luminosity Large Hadron Collider construction and Future Circular Collider development program, the magnetic field in the accelerator dipole magnets is being enhanced to 11 T, and 15 T to 16 T level, respectively. Advanced Nb3Sn superconductors with a non-copper critical current density exceeding 2500 A mm$^{−2}$ at 4.2 K and 12 T, are being developed using the Restacked-Rod-Process (RRP) and Powder-In-Tube (PIT) wire technologies. However, since Nb$_3$Sn is extremely brittle, it is a significant challenge to construct the high-field dipole magnets with such very strain-susceptible superconductor. The high-level of stress acting on the wide face of the Rutherford cables in the coils of 120 MPa to 200 MPa generated by the Lorenz’ force, causes initially a reversible reduction and eventually at some stress level followed by permanent degradation of the critical current when strain goes to high. This study sets out to examine the critical current and upper critical field performance of state-of-the-art RRP and PIT Nb$_3$Sn Rutherford cables in terms of transverse pressure. The variation of the critical current and upper critical field due to the thermal- and mechanical load-cycling was investigated as well. For reference, the critical current of witness wires characterized on standard ITER type barrels were also measured. The results indicate that the RRP type of Nb$_3$Sn Rutherford cables, when fully impregnated with epoxy resin, are able to withstand a transverse stress of 170 MPa to 250 MPa without noticeable irreversible critical current reduction. For the transverse pressure limit for present PIT type of Nb3Sn Rutherford cables somewhat lower values are found at the level of 50 MPa to 120 MPa. Therefore, given the present cables, the high-field dipole magnet construction can be realized using the RRP Nb$_3$Sn Rutherford cables, while for PIT type cables more cable development is requested to enhance the onset of irreversible degradation. The reversible critical current reduction in RRP type of cables of 10% at 150 MPa to 250 MPa needs to be taken into account when predicting magnet performance. Finally, extreme care needs to be taken into account for Nb$_3$Sn coil fabrication, since the experimental results show significant critical current reduction due to stress concentrations already at 0.2° misalignment angles between the pressure applying surface and the surface of the impregnated cable.