Analysis of High-Temperature Superconducting Current Leads: Multiple Solutions, Thermal Runaway, and Protection

The multiple steady states of Ag/Bi2212-composite high- T c superconducting leads modeling current delivery to a superconducting magnet have been numerically calculated. The model is based on longitudinal conduction combined with convective heat dissipation from a helium gas stream along the conductor. Because of the nonlinearities introduced by the voltage–current relationship and the temperature-dependent material properties, up to three solutions have been identified within the range of parameters considered. Linear stability analysis reveals that two of them are stable, i.e., the superconducting and the normal branches, while the remaining one is unstable. The limit points separating the stable from the unstable steady states form the blow-up threshold, beyond which any further increase in the operating current results in a thermal runway. Interesting findings are that for low filling ratios no bounded solution exists when the length of the lead exceeds the lower limit point, while very high maximum temperatures may be encountered along the normal solution branch. The effect of various parameters such as the conduction–convection parameter, the applied current, and the reduction in coolant flow (LOFA) on the bifurcation structure and their stabilization effect on the blow-up threshold are also evaluated. Apart from the steady and unsteady operating modes, the multiplicity analysis is also used to identify the range of the design and operating variables where safe operation, with a sufficient margin from the onset of instabilities, may be established, thus facilitating the protection of the leads and the device connected to it.