Flux jumps and training in superconducting composites

The critical state stability in a composite superconductor under an external stress, causing plastic strain yield, is considered. The obtained criterion of the stability against thermomagnetic-mechanical perturbations allows the explanation of the training phenomenon as a process of consequent strain hardening of the superconductor. The training of superconducting materials is a well known phenomenon in superconducting magnetic systems. Recently the existence of training has been observed in short superconducting samples under significant mechanical stress (resulting from either external or ponderomotive forces) (Anashkin et a1 1975, 1977, Schmidt 1976, Schmidt and Pasztor 1977). The results obtained in this work confirmed the connection between the training phenomenon and the mechanical properties of superconducting materials. In the present paper we found the stability criteria of the current, magnetic field and mechanical stress distributions in the critical state in the composite superconductor, the stress being supposed to cause the plastic yield of the material. The thermomagneticmechanical instability (i.e. both flux jump and serrated yielding development) was investigated in the linear approximation for small perturbations. The plastic strain rate nonuniformity affecting the critical state stability of multifilamentary superconductors was also treated. Being interested in the critical state stability in the whole sample, we shall regard the composite superconductor as a uniform anisotropic superconducting medium. The physical properties of such a medium are defined by superconducting filaments and normal conducting matrix characteristics, averaged over the cross-section of the composite (see Mints and Rakhmanov 1977 and references therein). This approach is evidently valid provided that the scale of perturbations of interest is large compared to the characteristic dimensions of the composite superconductor structure and that the rise time of the perturbation is larger than the relaxation times of the individual elements of the medium. After averaging we obtain the equations for the temperature ( T ) perturbation 0 = TTO (TO is the initial temperature) and the electric field E in the linear 6 and E approximation: d = K V 2 6 + j o E + u(?;/?T)B (1) curl curl E= -(47r/c2)(?j/?#) (2) and the connection between the current density and the electric field