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The current-carrying capacity of the Ag/Bi 2 Sr 2 CaCu 2 O 8 multifilament conductor is studied in detail as a function of the heat transfer coefficient, resistivity of the matrix, and volume fraction of the superconductor. The thermal runaway parameters corresponding to the irreversible superconducting-to-normal transition are derived analytically under the aspect of possible finite temperature rise of the composite conductor before thermal runaway. The static analytical model determines the thermal runaway parameters. The power law describes the voltage-current characteristic of a superconductor with a linear temperature dependence of the critical current (linear approximation). The performed analysis reveals that the allowable magnitude of the current and electric field before the thermal runaway may be higher than those determined by the criterion E c = 10 −6 V cm −1 in many practical cases. The condition of the stable state for the over-critical current is formulated and the peculiarities of such operation regimes are discussed. It is shown that the essential stationary overheating of the superconductor may occur before the thermal runaway. The minimum value of the current at which the thermal runaway starts is found if the volume fraction of superconductor in the composite is changed.

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To understand the underlying physical trends of the current instability in a composite high-Tc superconductor, the limiting margin of its current-carrying capacity is derived in dc magnetic fields in the framework of the macroscopic continuum approximation. A static zero-dimensional model was used to formulate the peculiarities of the nonisothermal electric field distribution in a composite in the fully penetrated current states. The power and exponential equations describing the E(J) dependences of a superconductor are used. The boundary of the allowable stable values of the electric field, current, and temperature are investigated using qualitative and quantitative models. Permissible stable values of the electric field and current, which might be lower (subcritical states) or higher (overcritical states) than those determined by the critical voltage criterion, are discussed. It is stated that the subcritical quenching electric states are more probable in the operating regimes, which are observed in the high magnetic field. The overcritical stable quantities of the electric field exist, for example, if the superconducting composite has a relatively small volume fraction of the superconductor in a composite. In the meantime, the stable current modes may be both subcritical and overcritical when the permissible value of the electric field is overcritical. As a consequence of these features, an unavoidable increase in temperature of the composite superconductor occurs before its transition to the normal state. The latter depends on a broad shape of the E(J) dependence of high-Tc superconductor and the current sharing between the superconducting core and the matrix. In the limiting case, a stable value of the composite temperature may equal the critical temperature of the superconductor. For such operating states, the criterion of the complete thermal stability condition is written taking into consideration the nonlinear character of the E(J) dependence. Simultaneously, an allowable change in temperature of the superconducting composite leads to the thermal degradation of its current-carrying capacity. It depends on the critical current density of the superconductor at bath temperature, amount of a superconductor, and cross section of a composite under fixed cooling conditions. In particular, it is shown that the currents corresponding to the instability onset do not increase proportionally with relevant increase of the superconductor’s amount. The estimates presented have general character and may be used to verify the operating states of low-Tc superconducting composite.