Sub- and overcritical stable states of composite high-Tc superconductors with different E(J) dependences and their unavoidable overheating

Abstract

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.

Multi-Stable Static Resistive States of High-$T_{\rm c}$ Superconductors With Temperature-Decreasing Power Exponent of Their Voltage-Current Characteristic

“…In this case, the electric field increases monotonically and stably up to the boundary values known as the quench electric field separating the stable mode from unstable one. In the static approximation, the quench electric field and the corresponding values of the quench current or the allowable temperature rise of a superconductor are determined from the condition [12] or equivalent condition [8]- [10]. Accordingly, the mono-stable resistive states are unstable if the applied current exceeds the quench current defined by this manner.…”

“…As a result, the resistive states of high-superconductors exist in a wide current range. As it was proved experimentally and theoretically [3]- [10], they can be stable at higher currents and overheating than the corresponding values following from the fixed electric field criterion, for example, . These resistive states significantly expand the range of the permissible stable operating mode of high-superconducting materials.…”

“…These resistive states significantly expand the range of the permissible stable operating mode of high-superconducting materials. To describe their existence, the voltage-current characteristics with a constant value of the power law exponent are usually used [5]- [10]. At the same time, the -value decreases with the temperature or the induction of an external magnetic field (Fig.…”

Stable and unstable thermo -current states of high temperature superconductors

“…According to the initial parameters used, these boundary points exist in the over-critical electric field region. (The conditions describing the existence of the stable over-critical static states are formulated in [9]). However, the condition / E J ∂ ∂ → ∞ is not observed in the unsteady thermo-current states as the transient voltage-current characteristic of a high-T c superconductor has only positive values.…”

Development of Wind-and-React Bi-2212 Accelerator Magnet Technology

“…This lowering is usually attributed to thermal de-pinning of vortices. A practical implication is that, for example at a magnetic field of 10 T, the effective temperature margin is reduced to about 20 K, as can be seen from transport measurements [10]. A reduced effective temperature margin in the presence of a magnetic field means that, pending accurate analysis of the thermodynamics of such systems, normal zone development might be more favorable than expected on the basis of measurements without an externally applied magnetic field.…”