A Method for Coil Design of Superconducting Quadrupoles Based on Sector Coils and Fourier Series

In this paper we present a novel method to optimize quadrupole coil cross-sections based on the cos2q-type. We first approximate real coil blocks made of cables with concentric sectors powered with a constant current density to make use of analytical expressions of the magnetic field based on the Fourier series development. This allows a rapid evaluation of the field harmonics which permits an almost exhaustive scan on sectors position and dimensions for coil layouts made of up to five sectors. The coil layouts having a larger short-sample gradient can be further explored, approximating them with blocks of Rutherford cables. This second step requires a second fine tuning of the cross-section around the previously found optimum. The method has been used to design a proposed coil cross-section for the new inner triplet quadrupole for the LHC