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A macroscopic model of nonlinear constitutive relations in superconductors

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3 Author(s)
Xia, J.J. ; Res. Lab. of Electron., MIT, Cambridge, MA, USA ; Kong, J.A. ; Shin, R.T.

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 ns(J) has a smooth variation near the macroscopic critical current density Jc. Agreement has been found between this n s(J,T) model and the temperature dependence of ns in the two-fluid model. The nonlinear conductivities σs(J) and σn(J) are obtained from the London's equation with the modified ns(J) function. Nonlinear resistance R(I), kinetic inductance Lk(I) and surface impedance Zs(I) in thin wire, slab, and strip geometries are calculated

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Microwave Theory and Techniques, IEEE Transactions on  (Volume:42 ,  Issue: 10 )