Multiplicities and thermal runaway of current leads for superconducting magnets

The multiple solutions of conduction and vapor cooled copper leads modeling current delivery to a superconducting magnet have been numerically calculated. Both ideal convection and convection with a finite heat transfer coefficient for an imposed coolant mass flow rate have been considered. Because of the nonlinearities introduced by the temperature dependent material properties, two solutions exist, one stable and one unstable regardless of the cooling method. The limit points separating the stable form the unstable steady states form the blow-up threshold beyond which, any further increase in the operating current results in a thermal runway. An interesting finding is that the multiplicity persists even when the cold end temperature is raised above the liquid nitrogen temperature. The effect of various parameters such as the residual resistivity ratio, the overcurrent and the variable conductor cross section on the bifurcation structure and their stabilization effect on the blow-up threshold is also evaluated.