Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

We consider the nonlinear dynamics of a single vortex in a superconductor in a strong rf magnetic field B₀0.2em0exsin0.2em0exωt. Using the London theory, we calculate the dissipated power Q(B₀,ω) and the transient time scales of vortex motion. For the linear Bardeen-Stephen viscous drag force, vortex velocities reach unphysically high values during vortex penetration through the oscillating surface barrier. It is shown that penetration of a single vortex through the ac surface barrier always involves penetration of an antivortex and the subsequent annihilation of the vortex-antivortex pairs. Using the nonlinear Larkin-Ovchinnikov (LO) viscous drag force at higher vortex velocities $v(t)$ results in a jumpwise vortex penetration through the surface barrier and a significant increase of the dissipated power. We calculate the effect of dissipation on the nonlinear vortex viscosity η(v) and the rf vortex dynamics and show that it can also result in the LO-type behavior, instabilities, and thermal localization of penetrating vortex channels. We propose a thermal feedback model of η(v), which not only results in the LO dependence of η(v) for a steady-state motion, but also takes into account retardation of the temperature field around a rapidly accelerating vortex and a long-range interaction with the surface. We also address the effect of pinning on the nonlinear rf vortex dynamics and the effect of trapped magnetic flux on the surface resistance Rₛ calculated as a function of rf frequency and field. It is shown that trapped flux can result in a temperature-independent residual resistance Rᵢ at low T and a hysteretic low-field dependence of Rᵢ(B₀), which can decrease as B₀ is increased, reaching a minimum at B₀ much smaller than the thermodynamic critical field Bc. We propose that cycling of the rf field can reduce Rᵢ due to rf annealing of the magnetic flux which is pumped out by the rf field from a thin surface layer of the order of the London penetration depth.