Optimization of Nb$_{3}$Sn Rutherford Cables Geometry for the High Luminosity LHC

The quadrupole and dipole magnets for the LHC High Luminosity (HL-LHC) upgrade will be based on Nb$_{3}$Sn Rutherford cables that operate at 1.9 K and experience magnetic fields of up to about 12 T. An important step in the design of these magnets is the development of the high aspect ratio Nb$_{3}$Sn cables to achieve the nominal field with sufficient margin. The strong plastic deformation of unreacted $Nb_3Sn$ strands during the Rutherford cabling process may induce non negligible $I_c$ and RRR degradation. In this paper, the cabling degradation is investigated as a function of the cable geometry for both PIT and RRP conductors. Based on this analysis, new baseline geometries for both 11 T and QXF magnets of HL-LHC are proposed.