Azimuthal coil size and field quality in the main CERN Large Hadron Collider dipoles

Field quality in superconducting magnets strongly depends on the geometry of the coil. Fiberglass spacers (shims) placed between the coil and the collars have been used to optimize magnetic and mechanical performances of superconducting magnets in large accelerators. A change in the shim thickness affects both the geometry of the coil and its state of compression (prestress) under operational conditions. In this paper we develop a coupled magnetomechanical model of the main Large Hadron Collider dipole. This model allows us to evaluate the prestress dependence on the shim thickness and the map of deformations of the coil and the collars. Results of the model are compared to experimental measurements carried out in a dedicated experiment, where a magnet model has been reassembled 5 times with different shims. A good agreement is found between simulations and experimental data both on the mechanical behavior and on the field quality. We show that this approach allows us to improve this agreement with respect to models previously used in the literature. We finally evaluate the range of tunability that will be provided by shims during the production of the Large Hadron Collider main dipoles. (24 refs).