Title :
A macroscopic model of nonlinear constitutive relations in superconductors
Author :
Xia, Jake J. ; Kong, Jin A. ; Shin, Robert T.
Author_Institution :
Res. Lab. of Electron., MIT, Cambridge, MA, USA
fDate :
10/1/1994 12:00:00 AM
Abstract :
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
Keywords :
critical current density (superconductivity); electric impedance; inductance; microstrip lines; microwave integrated circuits; modelling; superconducting materials; applied macroscopic current density; electron velocities; kinetic inductance; linear London´s equations; macroscopic critical current density; macroscopic model; microstrips; microwave integrated circuits; ns(J,T) model; nonlinear conductivities; nonlinear constitutive relations; nonlinear electromagnetic phenomena; nonlinear resistance; slab geometries; smooth variation; strip geometries; superconductors; superelectron number density; surface impedance; temperature dependence; thin wire; two-fluid model; Conductivity; Critical current density; Current density; Electromagnetic modeling; Electrons; Nonlinear equations; Superconductivity; Surface resistance; Temperature dependence; Temperature distribution;
Journal_Title :
Microwave Theory and Techniques, IEEE Transactions on
