Design of HD2: A 14-Tesla Nb$_3$Sn dipole with a 35-mm bore

The Nb$_3$Sn dipole HD1, recently fabricated and tested at LBNL, pushes the limits of accelerator magnet technology into the 16 T field range, and opens the way to a new generation of HEP colliders. HD1 is based on a flat racetrack coil configuration and has a 10 mm bore. These features are consistent with the HD1 goals: exploring the Nb/sub 3/Sn conductor performance limits at the maximum fields and under high stress. However, in order to further develop the block-coil geometry for future high-field accelerators, the bore size has to be increased to 30-50 mm. With respect to HD1, the main R&D; challenges are: (a) design of the coil ends, to allow a magnetically efficient cross-section without obstructing the beam path; (b) design of the bore, to support the coil against the pre-load force; (c) correction of the geometric field errors. HD2 represents a first step in addressing these issues, with a central dipole field above 15 T, a 35 mm bore, and nominal field harmonics within a fraction of one unit. This paper describes the HD2 magnet design concept and its main features, as well as further steps required to develop a cost-effective block-coil design for future high-field, accelerator-quality dipoles.