Practical criteria for the thermal stability of a unidimensional superconductor

The criterion of "equal area" [4, 5] is known as a necessary and sufficient condition in order that a unidimensional superconductor of infinite length, submitted to fixed current density and magnetic field, could not evolve towards a resistive state after an accidental local overheating ; this criterion relates only to the normalized source term of heating (competition between the heat power generated by joule effect and the one which is absorbed by the cryogenic bath). We give here an optimal criterion, valid for any length (case of an uncooled region situated between two well cooled ones) ; it allows the engineers to play upon a non dimensional grouping of parameters (characterizing the intensity of the source term), related to the conductor, in order to extend the field of its superconducting properties. We give also some intermediate complementary criteria which are only sufficient but much more easy to check