About Current-Carrying Capacity of Superconductors with Smoothed Current–Voltage Characteristic

The physical characteristics of stable formation of the limiting permissible thermo-electrodynamic states of superconductors with various types of nonlinearity in their current–voltage characteristics (CVC) are discussed. The analysis was based on describing the CVC using a model that assumes its continuous increase with varying degrees of smoothing (different intensities of increase at a fixed value of the critical current). A power-law equation was used to describe it. The results were compared with those from numerical experiments simulating thermo-electrodynamic states of superconductors with a zero-voltage subcritical region and an idealized CVC (nonsmoothed CVC), described by a piecewise continuous equation derived from the viscous flux-flow model. It is shown that an increase in the smoothing of the CVC of a superconductor, under otherwise equal conditions (at a fixed value of critical current density and cooling conditions), is accompanied by a decrease in its current-carrying capacity. Its degradation is caused by a corresponding increase in heat losses, which inevitably exist owing to the continuous increase in the CVC of the superconductor throughout the current injection process. As a consequence, the values of the limiting permissible currents stably flowing through the superconductor with a nonsmoothed CVC, under otherwise equal conditions, are higher than the corresponding values calculated for superconductors with a smoothed CVC. This feature is observed despite the different nature of current filling the cross section of the superconductor. It is proven that, for the correct determination of the current-carrying capacity of superconductors, the permissible values of temperature and electric field intensity preceding the onset of current instability cannot be predefined. They depend on the degree of smoothing of the CVC, the current injection rate, the transverse size of the superconductor, and the conditions of cooling. As a consequence, there is a nontrivial relationship between the maximum allowable losses and the maximum stable value of injected current. These features must be taken into account when experimentally measuring the CVCs of superconductors and their current-carrying capacity.