The Stored-Energy Ceiling of Superconducting Magnets, Recounted: Critical Current, Hoop Stress and Quench Protection in NbTi, Nb3Sn and REBCO Solenoids

The energy density stored in a magnetic field, B^2/2mu0, is also the magnetic pressure on the windings, so the stored-energy ceiling of a superconducting magnet is set by conductor limits, not the field formula. A single iteration (field -> critical current density from published 4.2 K parametrisations -> required winding thickness -> structure fraction needed to keep hoop stress within allowable limits) gives self-consistent maximum fields for a 50 mm bore solenoid of 9.5 T for NbTi (36 MJ/m3), 19.5 T for Nb3Sn (151 MJ/m3) and 33.0 T for REBCO (433 MJ/m3). The binding term differs per conductor: critical-current fall-off for NbTi, stress arriving jointly with current density (and governing design because its exceedance is irreversible) for Nb3Sn, and quench protection for REBCO, whose protection margin for a conventionally insulated winding is about 0.024 at its ceiling while its current-density margin is still 1.27. Computed ceilings are compared with the LHC dipoles, the ITER coils, the NHMFL 32 T all-superconducting magnet and the 28.2 T commercial NMR magnet. All numbers are produced by the accompanying script from the stated conductor data.