On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

Abstract

In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained.

Electrothermal Instabilities in Barium Titanate Based Ceramics

“…An important conclusion that can drawn from Figure 6 is that the abrupt change in the resistivity (PTC effect) is responsible for the multiplicity below approximately the temperature of maximum resistivity while the NTC effect leads to a thermal runaway since the heat generation rate exceeds the heat that can be dissipated by natural convection and radiation. A similar thermal runaway phenomenon is observed in metallic conductors and high temperature superconductors as a result of the non-linear relationship between the temperature and the electric resistivity [21,37].…”

“…The numerical bifurcation analysis reveals that the PTC effect gives rise to several multiplicites above the Curie point, whereas the NTC effect is responsible for the temperature blowup (thermal runaway) which unless detected and prevented will lead to the destruction of the device. This result is further supported from a similar behavior that is encountered in other bistable systems such as superconductors [20] and boiling wires [21].…”

“…The linear stability of a certain steady state s j , ( ) s z Θ to small perturbations is determined by substituting the below expansions into Eqs. (16,21) ( , ) ( ) ( , )…”

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

“…Although the multiplicity and the solution structure for copper current leads is different since only two solutions exist, the thermal runaway phenomenon is common to both composite and metallic conductors, as for example it is shown in [26]. Thermal runaway due to Joule heating is also observed when the composite or the metallic wire is immersed in a boiling liquid pool [47], although the solution structure in this case is far more complicated because of the nonlinear and nonmonotonic boiling curve. Hot spot curves have been also calculated by Wesche and Fuchs [30] in their Figure 6, simulating a complete loss of coolant for composite HTS leads (Bi-2212 bulk material and Bi-2223/Ag tapes).…”

“…Furthermore, the inherent difficulties in the protection of HTS magnets from abrupt thermal runaways have been underscored by Maeda and Yanagisawa [53]. Hence, thermal runaway is a common problem for the components of the superconducting magnet, including the coil and both the HTS and the metallic parts of the current lead [47]. Therefore, the line connecting the limit points is also the threshold for thermal runaway (blow-up threshold) and should be taken into consideration when designing protective apparatus for the superconducting composite.…”