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Colliders use final focus systems to reduce the transverse beam sizes at the interaction point in order to increase collision event rates. The maximum focal strength (gradient) of the quadrupoles, and the maximum beam size in them, together limit the beam size reduction that is possible. The goal of a final focus system design is to find the best compromise between quadrupole aperture and quadrupole gradient, for the magnet technology that is used. This paper develops a design method thatdoi:10.1103/physrevstab.11.031001 fatcat:ulr34fzirrgkdldsk5owtfyzpe