Thermal stability characteristics of high temperature superconducting composites

The thermal stability characteristics of the high-T_c superconducting composites like multifilamentary current-carrying elements of superconducting magnets are discussed in the framework of the macroscopic continuum approximation. The performed analysis was based on the zero- and one-dimensional static and transient thermo-electric models. Various types of the voltage-current characteristic of a superconductor are considered. The thermal runaway conditions of the superconducting composite are investigated under the conditions cooled by cryocoolers with various operating temperatures, liquid helium or hydrogen coolants. The linear and nonlinear temperature dependences of the critical current were used. As a result, the evolution peculiarities of the stable and unstable thermal and electric modes as a function of sweep rate, volume fraction of the superconductor in a composite, and its cross section are formulated for the partially and fully penetrated states under the different cooling conditions. It was shown that permissible stable values of the current and electric field might be both lower and higher than those determined by use of the standard critical current criterion. The reasons leading to these regimes are discussed. Consequently, the unavoidable temperature rise of the superconducting composite before its transition to the normal state takes place. The latter depends on a broad shape of the voltage-current characteristic of the high-Tc superconductor and the current sharing between a superconducting core and a matrix. In the limiting case, a stable value of the temperature of a composite may equal the critical temperature of a superconductor. For these operating modes, the criterion of the complete thermal stability condition is written when the charging current will flow stably only in a matrix. It is also validated that there exists the thermal degradation mechanism of the currentcarrying capacity of a superconducting composite. According to this mechanism, the quench currents do not increase proportionally to the increase of the critical current of a composite. The performed analysis reveals also the connection between different criteria used to determine the thermal runaway conditions. In the framework of the nonlinear temperature dependence of the critical current, it is shown that the operating regimes may have manyvalued stable and unstable branches appearing in accordance with the nontrivial variation of the differential resistivity of a composite. These states exist, first of all, due to the temperature change of the quantity ∂J_c/∂T and are accompanied by the jump-like current-sharing mechanism. The thermal runaway parameters are numerically derived as a function of operating temperature accounting for the additional stable branches of the voltage-current characteristics. The formation peculiarities of these phenomena are discussed.