LHC instertion upgrade combining $Nb_{3}Sn and Nb-Ti magnets

Superconducting magnet technology based on Nb-Ti cable cooled at 1.9 K has provided the present generation of LHC magnets. Magnetic fields above 10 T that will be required in future accelerators, including the upgrade of the LHC, call for the use of brittle conductors, such as Nb$_{3}$Sn or Nb3Al. However, these conductors are proving difficult to use, and while the development of acceleratortype magnets (dipoles and quadrupoles) is advancing, it is likely to be some time before we will be confident enough to replace sections of the LHC (for example the magnets of the inner triplets) using the new technology. It is shown that Nb-Ti superconducting magnets operating at 1.9 K could provide a viable intermediate step for the upgrade of the LHC insertions, taking advantage of the established technology, and including improvements that could be reasonably applied to a small-scale magnet production. Moreover, by incorporating one (or two) relatively short Nb$_{3}$Sn quadrupoles in each triplet, the optical and heat load performance could be tailored to approach that of triplets made entirely from Nb$_{3}$Sn magnets and allow us to consider an early upgrade with larger aperture magnets but having only limited reliance on Nb$_{3}$Sn technology.