A MACROSCOPIC MODEL OF NONLINEAR CONSTITUTIVE RELATIONS IN SUPERCONDUCTORS

A macroscopic model is proposed for nonlinear electromagnetic phenomen a in superconductors. Nonlinear constitutive relations are derived by modifying the linear London's equations. The superelectron number dens ity as a function of applied macroscopic current density, n(s)(J), is derived from a distribution of electron velocities at a certain temper ature T. At temperature T not equal 0 K, the function n(s)(J) has a sm ooth variation near the macroscopic critical current density J(c). Agr eement has been found between this n(s)(J,T) model and the temperature dependence of n(s) in the two-fluid model. The nonlinear conductiviti es sigma(s)(J) and sigma(n)(J) are obtained from the London's equation with the modified n(s)(J) function. Nonlinear resistance R(I), kineti c inductance L(k)(I) and surface impedance Z(s)(I) in thin wire, slab, and strip geometries are calculated.