Analytical estimates of stress in superconducting dipole magnets for particle accelerators

Abstract For superconducting accelerator magnets based on an overall current density of the order of 500 A mm −2 , the electromagnetic forces induce a stress in the winding whose order of magnitude is 100 MPa. This poses special challenges for the mechanical structure, for the insulation, and for the strain induced in the superconductor. The state of stress in a sector coil has two features: an accumulation of the azimuthal component towards the magnet midplane, and an accumulation of radial components towards the structure. In this paper we express the midplane stress as the product of current density, field and aperture radius, plus a shape factor. This equation has been written in similar but not totally equivalent forms, and this form is not only more precise but is also putting in evidence the independent parameters. As known in the literature, for midplane stress higher fields can be mitigated by lower current densities. On the other hand, radial stress scales with the magnetic pressure; here we give a new analytical estimate of the scaling factor, in its dependence on the coil geometry. The used geometrical model is a wedgeless sector coil, that is a good approximation for ratios between coil width and aperture radius up to 2. We present a detailed comparison of the analytical estimates to the finite element results for several cases of coils, and we draw some conclusions on the different magnet designs.