Graded High Field$rm Nb_3rm Sn$Dipole Magnets

Dipole magnets with fields beyond 16T will require superconducting coils that are at least 40 mm thick, an applied pres-stress around 150 MPa and a protection scheme for stored energy in the range of 1-2 MJ/m. The coil size will have a direct impact on the overall magnet cost and the stored energy will raise new questions on protection. To reduce coil size and minimize risk, the coil may have to be graded. Grading is achieved by splitting the coil into several layers with current densities that match the short sample field in each layer. Grading, especially at high fields, can be effective; however it will also significantly raise the stress. In this paper we report on the results of a study on the coil size and field relation to that of the stress and stored energy. We then extend the results to graded coils and attempt to address high stress issues and ways to reduce it