Current sharing effect on the current instability and allowable temperature rise of composite high-T_C superconductors

To understand the basic mechanisms of the thermal runaway phenomenon, the limiting margin of the current instability, which may spontaneously occur in composite high-T_C superconductors like multifilament Bi-based wire or tape, is derived under DC magnetic field. The current sharing and allowable temperature rise effects were considered. A static zero-dimensional model was utilized to describe the basic formulae dealing with the peculiarities of the non-isothermal change of superconducting composite voltage-current characteristic. The boundary of allowable stable values of the temperature, electric field and current are derived analytically. It was shown that permissible values of the current and electric field might be higher than those determined by use of the standard critical current criterion. In consequence of this feature, the noticeable allowable temperature rise of the composite superconductor before its transition to the normal state may be seen. The criterion for complete thermal stability condition is written describing the state when temperature of the composite equals critical temperature of a superconductor and the transport current flows stably only in matrix. The performed analysis also proves the existence of value of the volume fraction of a superconductor in composite at which its current-carrying capacity has minimum. These peculiarities are due to the stable current redistribution between superconductor and stabilizing matrix. Therefore, the current sharing not only leads to the matrix/ superconductor ratio effect on the stable operating characteristics of the composite high-T_C superconductors but also becomes important in the adequate description of quench process in the high-T_C superconducting magnets.