A macroscopic model of nonlinear constitutive relations in superconductors

A macroscopic model is proposed for nonlinear electromagnetic phenomena in superconductors. Nonlinear constitutive relations are derived by modifying the linear London's equations. The superelectron number density as a function of applied macroscopic current density, n/sub s/(J), is derived from a distribution of electron velocities at a certain temperature T. At temperature T/spl ne/0 K, the function n/sub s/(J) has a smooth variation near the macroscopic critical current density J/sub c/. Agreement has been found between this n/sub s/(J,T) model and the temperature dependence of n/sub s/ in the two-fluid model. The nonlinear conductivities /spl sigma//sub s/(J) and /spl sigma//sub n/(J) are obtained from the London's equation with the modified n/sub s/(J) function. Nonlinear resistance R(I), kinetic inductance L/sub k/(I) and surface impedance Z/sub s/(I) in thin wire, slab, and strip geometries are calculated.>