Graded High Field Nb3Sn Dipole Magnets

Graded High Field Nb 3 Sn Dipole Magnets S. Caspi, P. Ferracin and S. Gourlay Abstract— 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. Index Terms—Grading, Superconducting magnets, Stress, Stored energy. II. D IPOLE MODEL A. Model Description To study the limits of superconducting dipole magnets, we formulated a simple but realistic model based on several assumptions: 1) the bore is round and the coil is a thick cylinder (Fig 1); 2) the engineering current density is equal to J e cos θ and the field is therefore a pure dipole; 3) the field magnitude in the bore and along the conductor inner surface is identical; 4) the short-sample current density in the superconductor J ss and the engineering current density J e-ss (obtained by averaging J ss over copper, insulation, and voids) are a function of field B and temperature T; 5) the coil is initially not graded (section II) followed by graded coils (section III); 6) there is no ferromagnetic material nearby. I. I NTRODUCTION W hen the LHC pushed NbTi conductor closer to its high- field limit, the 56 mm bore dipoles reach 9.7 T at 1.9 K, and a stored energy of 334 kJ/m (per bore) [1]. Replacing the cable in that magnet with identical size Nb 3 Sn conductor (31.3 mm of overall coil thickness) would raise the field to 15.3 T, the stored energy to 900 kJ/m, and the Lorentz stress from 88 MPa to 220 MPa. If we farther grade the coil (20.3 mm layer 1 and 11.0 mm layer 2) the central field will increase to 16.2 T, the Lorentz stress in layers 1 and 2 will increase to 202 MPa and 377 MPa respectively, and the stored energy will increase to 1.14 MJ/m. (we assume a Nb 3 Sn wire carrying 3000 A/mm 2 at 12 T, 4.2 K in the non-copper with a 50% reduced engineering current density). This comparison between NbTi and Nb 3 Sn conductors points out both the promise and the challenge for high field magnets. Accelerator magnets can not be treated as a “one-of- a-kind” magnet; their cost must be at a minimum and the reliability high. Pushing the limits on high field Nb 3 Sn magnets requires the best superconductor, a reasonably small size magnet, and a compact structure. In this paper we address the relations between field, coil size, bore diameter, stress and stored energy, and we then extend them to graded coils pointing out areas where we presently meet the challenge and areas that will require further RD fax: 001 510 486 5310; e-mail: s_caspi@lbl.gov). 2 B ss µ 0 J e − ss ( B ss , T ) where the coil thickness is expressed as a function of short- sample field and temperature only. We note and emphasize that the relation is independent of bore diameter.