A Method for Minimizing the Magnetic Cross Talk in Twin-Aperture $\cos \theta$ Superconducting Dipoles

We present an analytic method to minimize the magnetic cross-talk in twin-aperture cos θ dipoles. In the singleaperture cos θ layout, the coil design can be performed with an analytic approach, based on a sector coil approximation. This method allows a fast evaluation of the field harmonics and an almost exhaustive scan on the positions and dimensions of the sectors, for coil layouts made of a different number of sectors. This increases the probabilities to find the coil shape which best fits the specifications. In a twin-aperture arrangement, the magnetic cross-talk can be not negligible and, to the aim of an analytic minimization of the unwanted multipoles, an extension of the single-aperture sector model is required. This is the case of the recombination dipole D2 for the High Luminosity Large Hadron Collider (HL-LHC) and of the 16-T bending dipole for the Future Circular Collider (FCC). This analytical method has been used to find alternative coil designs for both dipoles.