Note on the cryostatic stability of superconducting composites

A careful discussion is given of the ''equal area condition'' developed by Maddock et al. In order to make the essential points as clear as possible, analytical solutions are derived under simplifying assumptions (simple model for heat transfer by nucleate and film boiling liquid helium; constant heat conduction and specific heat) instead of using more realistic but less controllable computer calculations. A quantitative definition of the concept of a long wire is given. Numerical examples for the Maddock transition characterized by the equal area condition are given for a long superconducting composite with linear cooling and for a liquid helium-cooled resistance wire of finite length. In addition, cases are shown where instead of applying the equal area stability condition, time-dependent solutions should be considered