Thermal runaway criterion as a basis for the protection of high-temperature superconductor magnets

High-temperature superconductor (HTS) based high-field magnet systems are essential for particle accelerators and fusion energy applications. Quench protection of such magnets is difficult owing to a slow quench propagation velocity in HTS. While in conventional NbTi and Nb3Sn-based magnets, a normal zone expands typically quickly, and the stored energy is dissipated across a large volume of the windings, a normal zone in an HTS magnet propagates slowly and, thus, can heat up quickly to high temperatures destroying the conductor. At the same time, growing experimental evidence suggests that HTS conductors can operate in a stable dissipative flux flow regime for a substantial range of operational currents before entering an irreversible thermal runaway. Therefore, a new protection paradigm for HTS magnets has emerged, aiming to prevent quenching, using advanced diagnostics to detect the dissipative regime onset. In the present paper, we propose a simple criterion for the thermal runaway in HTS conductors and calculate allowable temperature margins within which an HTS magnet can be operated safely. Outside of those temperature margins, a common quench integral approach may be used to estimate the upper boundary of the time margin for activating the protection system. We verify the applicability of our approach by comparing the calculated runaway conditions for a Bi-2223 conductor with the experimentally measured values. The thermal and time margins can define the quench protection system's requirements for implementing the quench-avoiding protection paradigm.