Parametric Analysis of Forces and Stresses in Superconducting Quadrupole Sector Windings

We first present a review of the existing analytical equations for electromagnetic forces and stress in a sector coil quadrupole, evaluating their extent of application in function of the coil geometrical layout. We analyze the distribution of stress provided on the coil retaining structure as well as on the coil mid plane, this one related to the degradation of critical current in the superconductor. We focuse on the maximum compressive stress dependence on the magnetic gradient at short sample conditions, considering two possible low temperature superconductors: Nb-Ti and Nb$_{3}$Sn. In the last part the effect of an iron yoke on the magnetic field and forces is presented, proposing a correction of the critical current density expression when an infinite permeable iron yoke is used.