Stability of superconducting magnet systems subject to thermal disturbances

Abstract

The problem of the thermal stability of superconducting magnetic systems is considered. The general criteria of stability with respect to finite thermal disturbances are given in terms of Lyapunov functional theory. We formulate also a variational principle for the determination of the minimum critical energy causing a quench. Then the problem of stability of magnets under weak random thermal disturbances is considered. These disturbances correspond to sudden energy releases due to construction noise (epoxy cracks, fractures, microdeformations etc.). We apply the theory of stochastic processes to assess the permissible critical level of thermal noise. The theory appears formally to resemble noise-induced transitions. Criteria of stability for Gaussian and Poissonian thermal disturbances are obtained, and the permissible level of temperature fluctuations at a given current is determined. We consider the two extreme limits of distributed and point transient disturbances. The stability criteria depend on the effective spatial dimensionality of a problem and the statistics (Gaussian or Poissonian) of the disturbances. Finally, we discuss the problem of thermomechanical instability (serrated yielding of metals at low temperatures).