The Superconducting Magnetic Energy Storage Quench-Protection Bound: The Adiabatic Hotspot Integral, the Voltage-Limited Protectable Energy, and the Cost of a Failed Dump for NbTi and REBCO Conductors

When a superconducting magnetic energy storage coil quenches, its stored energy must be extracted before it concentrates as heat at the initial normal zone. This paper derives the protection bound in three forms: the adiabatic quench integral F(T_hot) connecting the current-density history to the maximum hotspot temperature; the resulting largest permissible dump time constant after a stated detection delay; and the voltage-limited maximum protectable stored energy E_max = (1/2) I_op V_max tau_max. Evaluating the material integral from published cryogenic properties gives F(300 K) = 6.82e16 (A/m2)^2 s for NbTi/Cu from 4.5 K and 4.48e16 for REBCO tape from 20 K. At 200 A/mm2, with detection delays of 0.10 s and 0.50 s, the maximum dump time constants at a 300 K hotspot limit are 3.21 s (NbTi) and 1.24 s (REBCO), capping the protectable energy at 10 kA and 5 kV at 80.2 MJ and 31.0 MJ; at 150 K the caps are 48.9 MJ and 9.4 MJ. A 100 MJ store at the same operating point is not protectable in either conductor. If the dump fails, the hotspot reaches the melting point of copper in 3.24 s (NbTi) and 2.19 s (REBCO), although the same energy spread uniformly would warm the conductor only to 55 K and 96 K. All numbers are produced by the deposited compute.py; the calculations are simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, at the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.