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 _s(J), is derived from a distribution of electron velocities at a certain temperature T. At temperature T≠0 K, the function n_s(J) has a smooth variation near the macroscopic critical current density J_c. Agreement has been found between this n _s(J,T) model and the temperature dependence of n_s in the two-fluid model. The nonlinear conductivities σ_s(J) and σ_n(J) are obtained from the London´s equation with the modified n_s(J) function. Nonlinear resistance R(I), kinetic inductance L_k(I) and surface impedance Z_s(I) in thin wire, slab, and strip geometries are calculated