Theory of normal-zone propagation along a superconducting wire with allowance for thermal-relaxation processes

Abstract

For high velocity of a longitudinal propagation of a normal zone along a superconducting wire, one should take into account heat-flux relaxation processes. In such cases these waves are described by a hyperbolic heat-transfer equation, which involves not only the heat-source function but also its derivative. The relaxation effects lead to a limitation of possible values of the normal-zone velocities and to the nonuniqueness of wave solutions. Moreover, the relationships that determine the temperature field in a wire and the propagation speed of the normal zone are obtained. The transient boundary condition between the wire and substrate (e.g., helium bath) is deduced from a heat-flux relaxation theory.