The stability of a one-dimensional composite superconductor subjected
to a thermal disturbance is studied by considering, in addition to the
amount of disturbance energy, the effect of the disturbance temperatu
re profile. An analysis is conducted for the stationary thermal condit
ion, and the result is compared with the transient solution in terms o
f characteristic functionals. It is shown that a map involving two cha
racteristic functionals can precisely characterize the recovery-quench
ing behaviour of the superconductor.