Mechanical Design of HD2, a 15 T Nb$_3$Sn Dipole Magnet with a 35 mm Bore

After the fabrication and test of HD1, a 16 T Nb$_3$Sn dipole magnet based on flat racetrack coil configuration, the Superconducting Magnet Program at Lawrence Berkeley National Laboratory (LBNL) is developing the Nb$_3$Sn dipole HD2. With a dipole field above 15 T, a 35 mm clear bore, and nominal field harmonics within a fraction of one unit, HD2 represents a further step towards the application of block-type coils to high-field accelerator magnets. The design features tilted racetrack-type ends, to avoid obstructing the beam path, and a 4 mm thick stainless steel tube, to support the coil during the pre-loading operation. The mechanical structure, similar to the one used for HD1, is based on an external aluminum shell pre-tensioned with pressurized bladders. Axial rods and stainless steel plates provide longitudinal support to the coil ends during magnet excitation. A 3D finite element analysis has been performed to evaluate stresses and deformations from assembly to excitation, with particular emphasis on conductor displacements due to Lorentz forces. Numerical results are presented and discussed.