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Register a new userVortex Dynamics and Dissipation Under High-amplitude Microwave Drive
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In this paper, we describe the vortex dynamics under high-amplitude microwave drive and its effect on the surface resistance of superconductors. The vortex surface resistance is calculated with a Montecarlo approach, where the vortex motion equation is solved for a collection of vortex flux lines each oscillating within a random pinning landscape. This approach is capable of providing a detailed description of the microscopic vortex dynamics and in turn important insights into the microwave field amplitude dependence of the vortex surface resistance. The numerical simulations are compared against experimental data of vortex surface resistance at high microwave amplitude measured by means of bulk niobium superconducting-radio frequency cavities operating at 1.3 GHz. The good qualitative agreement of simulations and experiments suggests that the non-linear dependence of the trapped flux surface resistance with the microwave field amplitude is generated by progressive microwave depinning and vortex jumps.
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We use a model of vortex dynamics and collective weak pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency NbCu, doped-Nb and Nb$_3$Sn cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a function of the amplitude of the radio-frequency field. Our calculations also predict and describe the crossover from hysteretic-dominated to viscous-dominated regimes of dissipation. We propose simple formulas describing power losses and crossover behavior, which can be used to guide the tuning of material parameters to optimize cavity performance.
We report numerical simulations of a trapped elastic vortex driven by a strong ac magnetic field $H(t)=Hsinomega t$ parallel to the surface of a superconducting film. The surface resistance and the power dissipated by an oscillating vortex perpendicular to the film surface were calculated as functions of $H$ and $omega$ for different spatial distributions, densities, and strengths of pinning centers, including bulk pinning, surface pinning, and cluster pinning. Our simulations were performed for both the Bardeen-Stephen viscous vortex drag and the Larkin-Ovchinnikov (LO) drag coefficient $eta(v)$ decreasing with the vortex velocity $v$. The local residual surface resistance $R_i(H)$ calculated for different statistical realizations of the pinning potential exhibits strong mesoscopic fluctuations caused by local depinning jumps of a vortex segment as $H$ increases, but the global surface resistance $bar{R}_i(H)$ obtained by averaging $R_i(H)$ over different pin configurations increases smoothly with the field amplitude at small $H$ and levels off at higher fields. For strong pinning, the LO decrease of $eta(v)$ with $v$ can result in a nonmonotonic field dependence of $R_i(H)$ which decreases with $H$ at higher fields, but cause a runaway instability of the vortex in a thick film for weak pinning. It is shown that overheating of a single moving vortex can produce the LO-like velocity dependence of $eta(v)$, but can mask the decrease of the surface resistance with $H$ at a higher density of trapped vortices.
In this work we study by ac susceptibility measurements the evolution of the solid vortex lattice mobility under oscillating forces. Previous work had already shown that in YBCO single crystals, below the melting transition, a temporarily symmetric magnetic ac field (e.g. sinusoidal, square, triangular) can heal the vortex lattice (VL) and increase its mobility, but a temporarily asymmetric one (e.g. sawtooth) of the same amplitude can tear the lattice into a more pinned disordered state. In this work we present evidence that the mobility of the VL is reduced for large vortex displacements, in agreement with predictions of recent simulations. We show that with large symmetric oscillating fields both an initially ordered or an initially disordered VL configuration evolve towards a less mobile lattice, supporting the scenario of plastic flow.
We study effects of pinning on the dynamics of a vortex lattice in a type II superconductor in the strong-pinning situation and determine the force--velocity (or current--voltage) characteristic combining analytical and numerical methods. Our analysis deals with a small density $n_p$ of defects that act with a large force $f_p$ on the vortices, thereby inducing bistable configurations that are a characteristic feature of strong pinning theory. We determine the velocity-dependent average pinning-force density $langle F_p(v)rangle$ and find that it changes on the velocity scale $v_p sim f_p/eta a_0^3$, where $eta$ is the viscosity of vortex motion and $a_0$ the distance between vortices. In the small pin-density limit, this velocity is much larger than the typical flow velocity $v_c sim F_c/eta$ of the free vortex system at drives near the critical force-density $F_c = langle F_p(v=0)rangle propto n_p f_p$. As a result, we find a generic excess-force characteristic, a nearly linear force--velocity characteristic shifted by the critical force-density $F_c$; the linear flux-flow regime is approached only at large drives. Our analysis provides a derivation of Coulombs law of dry friction for the case of strong vortex pinning.
We report numerical simulations of large-amplitude oscillations of a trapped vortex line under a strong ac magnetic field $H(t)=Hsinomega t$ parallel to the surface. The power dissipated by an oscillating vortex segment driven by the surface ac Meissner currents was calculated by taking into account the nonlinear vortex line tension, vortex mass and a nonlinear Larkin-Ovchinnikov (LO) viscous drag coefficient $eta(v)$. We show that the LO decrease of $eta(v)$ with the vortex velocity $v$ can radically change the field dependence of the surface resistance $R_i(H)$ caused by trapped vortices. At low frequencies $R_i(H) $ exhibits a conventional increases with $H$, but as $omega$ increases, the surface resistance becomes a nonmonotonic function of $H$ which decreases with $H$ at higher fields. The effects of frequency, pin spacing and the mean free path $l_i $ on the field dependence of $R_{i}(H) $ were calculated. It is shown that, as the surface gets dirtier and $l_i$ decreases, the anomalous drop of $ R_{i}(H) $ with $H$ shifts to lower fields which can be much smaller than the lower critical magnetic field. Our numerical simulations also show that the LO decrease of $eta(v)$ with $v$ can cause a vortex bending instability at high field amplitudes and frequencies, giving rise to the formation of dynamic kinks along the vortex. Measurements of $R_i(H)$ caused by sparse vortices trapped perpendicular to the surface can offer opportunities to investigate an extreme nonlinear dynamics of vortices driven by strong current densities up to the depairing limit at low temperatures. The behavior of $R_i(H)$ which can be tuned by varying the rf frequency or concentration of nonmagnetic impurities is not masked by strong heating effects characteristic of dc or pulse transport measurements.
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