Stability refers to the ability of a device employing superconductors to remain in its superconducting state after part of the superconductor transitions back to its normal conducting state due to a disturbance. While the concept can apply to many superconducting devices—transmission lines, generators, motors, etc.—it is most commonly considered in the context of superconducting magnets.
Consider a superconducting magnet in which a portion of the superconductor has become normally conducting. This situation may come about due to any of a number of events that could cause local heating, including motion of the conductor within the magnetic field, mechanical shock or the impact of a particle beam.
The part of the superconductor that becomes normally conducting as a result is called the normal zone. This normal zone may propagate through the magnet, causing the rest of the magnet to become normally conducting (i.e. quench), or the normal zone may shrink over time allowing the entire magnet to return to its superconducting state (i.e. recover).A superconducting magnet is said to be stable if it recovers from a given size normal zone. The stability of a superconducting magnet depends on the conductor, magnet and cooling system design. Engineers have dedicated significant amounts of research to determining the stability of superconductors and superconducting magnets. In effect, a magnet is stable if the heat removed by the cooling system is larger than that generated by the normal zone.
Practical superconducting wires and cables contain a good normal conductor, such as copper or aluminum, in parallel with the superconductor. The primary role of the normal conductor, known as a stabilizer, is to provide a path for the current in the event of a normal zone in the superconductor. Superconducting materials typically have poor electrical conductivity when in the normal state. When a normal zone is formed, current moves out of the superconductor and into the now lower resistance path of the stabilizer. This process, known as current sharing, reduces the amount of resistive heating in the normal zone and may allow the normal zone to shrink and the magnet to remain stable. The amount, type and distribution of the stabilizer are key factors in determining a magnet’s stability.
There are various types of stability. A fully cryostable magnet is the most conservative example, where the magnet remains superconducting for any size normal zone, provided the cooling system still functions. Engineers obtain full cryostability by using large amounts of stabilizer and/or extremely efficient cooling.
Figure 1 shows an example of a fully cryostable design, the conductor for the BaBar detector solenoid magnet operated at SLAC National Accelerator Laboratory. Note that the small amount of superconductor in the center is surrounded by a large amount of high purity aluminum stabilizer. The disadvantage of fully cryostable magnets is that the design generally requires bulky conductors that take up space, adding cost and increasing cooldown time. Full cryostability is generally reserved for magnets that you never want to quench, for example large particle detector magnets that store sizable amounts of energy.
Most superconducting magnets have a limited stability in which they are stable for certain size disturbances but unstable if a big enough disturbance occurs. Cable-in-conduit conductors tend to have very large (though not necessarily full) stability due to both efficient cooling by the forced flow of helium and also to the large amounts of helium surrounding the conductor. The specific heat of the helium is much higher than that of the superconductor at cryogenic temperatures and thus can absorb significant heat without a large temperature increase.
Good overviews on stability may be found in M.N. Wilson, Superconducting Magnets, Oxford, 1983; Y. Iwasa, Case Studies in Superconducting Magnets, Springer, 2009; P. Lee (ed.), Engineering Superconductivity, Wiley, 2001; and A. Devred et al., “Superconducting Magnet Technology,” in Handbook of Cryogenic Engineering, J.G. Weisend II (ed.), Taylor and Francis, 1998.
A specific example of the determination of stability in a cable-in-conduit conductor is presented in S. Nicollet et al., “Stability Analysis of ITER Poloidal Field Coils Conductors,” Cryogenics, Vol. 49, Issue 12, 2009. An example of stability in high temperature superconductors is found in J.P. Voccio et al., “Solid Cryogen Stabilized Cable-in-Conduit Superconducting Cables,” Advances in Cryogenic Engineering, IOP Conference Series: Materials Science & Engineering, Vol. 101, 2015.