Nonlinear response of superconductors to alternating fields and currents

Nonlinearities caused by vortex pinning and weak links in superconductors are considered. The effects of vortex pinning will be treated in both the parallel and perpendicular geometries using the critical state model. The results for the parallel geometry will be used to calculate the nonlinear surface impedance of a hard type-II superconductor. The results for the perpendicular geometry will be used to treat harmonic generation (HG) and intermodulation distortion (IM) in superconducting transmission lines and resonators. Nonlinearites due to weak links will be modelled using both the resistively shunted junction model (RSJ) for small junctions, and the damped sine-Gordon equation for long junctions. I will investigate HG in small junctions, and in long junctions with various geometries, and the unusual phenomenon of second HG due to Josephson fluxons in long junctions will be discussed