Design of ERMC and RMM, the Base of the $Nb_3Sn$ 16 T Magnet Development at CERN

High-field superconducting accelerator magnets are a key technology of the future circular collider. In order to master the technical challenges and achieve the performance targets, CERN has launched a technology development program. The first step of the program is to explore the $Nb_3Sn$ performance limits at 18 T field level and high stress, simplifying to the maximum the coil geometry. The first magnet to be built, the enhanced racetrack model coil (ERMC), aims at a mid-plane field of 16 T with 10% margin on the load line at 4.2 K. The ERMC is composed of two flat racetrack coils with no bore. To further develop the block-coil geometry, a second magnet, the racetrack model magnet (RMM), will be composed of two ERMC coils and a middle coil with a 50-mm closed cavity, addressing the issue of the design of an inner support to compensate for the preload forces. The RMM aims at a central field of 16 T in a 50-mm cavity, with 10% margin at 4.2 K. The next step is to develop a more compact and cost-effective design using two cable sizes, and therefore two different current densities. The coils will be assembled in a shell-based support structure using bladders and keys, which allows a precise control of the stress with minimal spring back and conductor overstress. This paper describes the magnetic and mechanical design of the ERMC and the RMM.