Electro-mechanical modelling of the iron force distribution with superconducting magnets

This paper shows the influence of the local magnetic forces on the mechanical analysis of a superconducting dipole magnet employing Nb3Sn technology. On high field magnets, the iron yoke has several functions: (1) magnetically, it increases the magnetic field in the bore and it has a shielding function; (2) mechanically, iron helps on the coil pre-load, transferring the mechanical forces provided by the external support structure. In many Nb3Sn magnets for particle accelerators, the cable is wound around an iron piece. As a consequence, the magnetic force on the iron can play an important role on the coil stress. The magnetic forces on the iron components can be computed using several different methods and the goal of this paper is to compare three expressions for the Maxwell stress tensor to compute local magnetic forces on iron considering a B-H curve. The influence of these forces on the mechanical behavior of the magnets is then analyzed, taking into account the uncertainties in determining their correct distribution. To achieve this goal, a numerical tool to perform Finite Element Analysis (FEA) was developed using vector potential formulation with first order nodal elements. The solution obtained from the magneto-static problem was used to calculate and compare the magnetic force distribution. The contributions from the Lorentz forces on coils are also taken into account in the mechanical analysis and are compared to the ones computed by using the Maxwell stress tensor on coils.