Design of Nb$_3$Sn coils for LARP long magnets.

The LHC Accelerator Research Program (LARP) has a primary goal to develop, assemble, and test full size Nb$_3$Sn quadrupole magnet models for a luminosity upgrade of the Large Hadron Collider (LHC). A major milestone in this development is to assemble and test, by the end of 2009, two 4 m-long quadrupole cold masses, which will be the first Nb$_3$Sn accelerator magnet models approaching the length of real accelerator magnets. The design is based on the LARP Technological Quadrupoles (TQ), under development at FNAL and LBNL, with gradient higher than 200 T/m and aperture of 90 mm. The mechanical design will be chosen between two designs presently explored for the TQs: traditional collars and Al-shell based design (preloaded by bladders and keys). The fabrication of the first long quadrupole model is expected to start in the last quarter of 2007. Meanwhile the fabrication of 4 m-long racetrack coils started this year at BNL. These coils will be tested in an Al-shell based supporting structure developed at LBNL. Several challenges have to be addressed for the successful fabrication of long Nb$_3$Sn coils. This paper presents these challenges with comments and solutions adopted or under study for these magnets. The coil design of these magnets, including conductor and insulation features, and quench protection studies are also presented.