Coupled nonlinear electrodynamics of type-II superconductors in the mixed state

A theory of the nonlinear electrodynamics of isotropic high-κ type-II superconductors containing an array of vortices is presented. The theory generalizes a self-consistent approach to vortex dynamics wherein the effects of nonlocality, vortex inertia, pinning, flux flow, and flux creep are treated in a unified fashion. We derive and solve a single vector partial differential equation describing the nonlinear response of a type-II superconductor at frequencies well below the gap frequency. The generation of nth-order harmonics due to bilinear field nonlinearity is discussed.