Analytical estimates of stress in accelerator dipoles based on sector coils

• Ezio Todesco (CERN)

Room: ZOOM In a dipole based on sector coils, the stress induced by electromagnetic forces in the winding has a radial stress component towards the structure and azimuthal stress compressing the coil towards the midplane. In this seminar, we express the azimuthal 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 way of expression puts in evidence the independent parameters, and the role of iron in reducing stress for a given field. As known in the literature since Wilson, midplane stress induced by higher fields can be reduced using lower current densities and wider coils. On the other hand, radial stress scales with the magnetic pressure; here we give for the first time an analytical estimate of the scaling factor, in its dependence on the coil geometry, finding that the radial stress can be significantly larger than the magnetic pressure. The used geometrical model is a wedgeless sector coil, which 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 and hints on the different magnet designs.