I-V characteristics and current instability in a high-temperature superconductor with a nonuniform temperature distribution over the cross section

The effect of a nonuniform temperature distribution in the cross section of a high-temperature superconductor on the formation of its I-V characteristic and the conditions for conservation of a stable distribution of the input current are analyzed. The equations permitting us to determine the boundary values of the electric field and current above which current instability can be developed with allowance for the dimensional effect are derived. It is shown that the input current quench determining the maximal permissible value of the input current decreases if thermal inhomogeneity of electrodynamic states is taken into account in theoretical analysis of its stability conditions. It is found that the limiting admissible values of the electric field and current are nonlinear functions of the thermal resistance of the superconductor, its critical parameters, and external heat-exchange conditions. Therefore, intense cooling of the superconductor does not result in an increase in the current corresponding to the emergence of instability in proportion to the increase in its cross-sectional area or critical current density.