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A hypothesis shall be confirmed: Non-convergence of a series of numerical solutions, to simulate transient temperature under increasing losses in a superconductor, might tightly be correlated with the superconducting to normal conducting phase transition. Consider as an analogue a standard, mathematical power series expansion: While the exact limit cannot be captured within the series, there is no doubt about its existence. A series of numerical solutions in stability analysis is considered a parallel to the mathematical series convergence problem: Likewise, there is no doubt that a limit of the numerical solution series exists (the phase transition) but it cannot be reached within the series. The concept is applied to multi-filamentary BSCCO 2223 and coated, thin film YBaCuO 123 superconductors and to NbTi superconductor filaments. Support is provided by a microscopic stability model and from comparison of order parameters. Simulation of current transport near phase transitions may become severely in error if length of load steps is in conflict with time needed for its completion. [ABSTRACT FROM AUTHOR]

This paper addresses the applicability of the "additive approximation" of total thermal conductivity in heat transfer and in superconductor stability calculations. If cases (a), (b) and (c) denote total (conductive plus radiative), or only conductive or only radiative heat flux, respectively, each flux q ̇ calculated with Fourier's conduction law using the corresponding thermal conductivity (λa, λb, λc), the additive approximation would be confirmed if the heat flux difference Δ q ̇ = q ̇ a - q ̇ b - q ̇ c , at any position of an investigated object, and at any time, converges to zero. This is not trivial because of the strong, non-linear temperature dependence of the radiation component. Heat transfer calculations including radiative transfer are presented in this paper, first for simple, homogeneous, thin film test samples and later for a multi-filamentary BSCCO 2223 superconductor. The simulated heat sources either result from a sudden increase of conductor boundary temperature or from flux flow and Ohmic resistances in the superconductor under a disturbance (like transport current exceeding critcal current density). The conductors, though very thin, are non-transparent to mid-IR radiation. Validity of the additive approximation is critical for superconductor stability against quench. Based on the applied numerical scheme, a hypothesis is suggested concerning correlation of the results of the simulation (the "numerical space") with the experimental situation (the "physical reality"): Non-convergence of the numerical scheme might tightly be correlated with occurrence of a quench in the simulated superconductor. [ABSTRACT FROM AUTHOR]

Standard stability calculations for superconductors following the traditional Stekly, adiabatic or dynamic stability models apply purely solid thermal conduction mechanism and derive predictions under (quasi-) stationary and adiabatic conditions. In the present paper, also thermal radiative heat transfer in the superconducting solid and pool boiling to a coolant is taken into account. The analysis applies a combined Monte Carlo/Finite Element model to calculate transient fields of temperature, critical current densities and stability functions under single, isolated disturbances that could interrupt zero loss current transport and lead to a quench. The Monte Carlo/Finite element method is applied to a 1G filament, high temperature superconductor. Results obtained for maximum, zero loss current transport in the filament are different up to 30% from solutions achieved with standard, solely solid conduction heat transfer. Release of mechanical strain energy or of impinging particle radiation are taken as examples for single, isolated point-like disturbances. Deviations may be larger if other kinds of disturbances have to be considered. [ABSTRACT FROM AUTHOR]

Stability functions are an important analytical/numerical tool for appropriate design of conductor geometry and dimensions to prevent conductor losses under a transport current. While standard stability calculations following the Stekly, adiabatic, or dynamic stability models apply purely solid thermal conduction mechanism and derive results under (quasi) stationary conditions, the present paper investigates if, and to which extent, also radiation heat transfer, in addition to solid conduction, can exert impacts on conductor stability. Further, the full transient conductor temperature evolution after a disturbance is calculated. The analysis applies an interplay between Monte Carlo radiative transfer calculations, to describe absorption of heat pulses and their distribution in the conductor, and a rigorous finite element method to calculate the resulting temperature field and stability functions. The results show that radiative heat transfer cannot be neglected in particular if periodic disturbances have to be considered that can arise, e.g., in a flux flow fault current limiter. [ABSTRACT FROM AUTHOR]