Thermal Design of an Nb$_{3}$Sn High Field Accelerator Magnet

Within the framework of the European project EuCARD, a Nb$_{3}$Sn high field accelerator magnet is under design to serve as a test bed for future high field magnets and to upgrade the vertical CERN cable test facility, Fresca. The Fresca 2 block coil type magnet will be operated at 1.9 K or 4.2 K and is designed to produce about 13 T. A 2D numerical thermal model was developed to determinate the temperature margin of the coil in working conditions and the appropriate cool-down scenario. The temperature margin, which is DTmarge=5.8 K at 1.9 K and DTmarge=3.5 K at 4.2 K, was investigated in steady state condition with the AC losses due to field ramp rate as input heat generation. Several cool-down scenarios were examined in order to minimize the temperature difference and therefore reducing the mechanical constraints within the structure. The paper presents the numerical model, the assumptions taken for the calculations and several results of the simulation for the cool-down and temperature distributions due to several cases of heat loads.