Abstract
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.
Highlights
Upon cool down below critical temperature in the presence of an external magnetic field, magnetic flux quanta—so-called vortices—can exist in thermodynamic equilibrium in the mixed state of type-II superconductors [1,2].Below the lower critical field, vortices are not stable in the superconductor; because of the occurrence of defects in real materials, vortices get pinned and survive even in the Meissner state
The linear dependence has been shown to be well described by adding a cubic term to a parabolic pinning potential in the vortex equation of motion [38]. This approach is limited, since it is built around the single-vortex dynamics, while in the material there are several vortices contributing to the overall dissipation, each one interacting with its surroundings
The microwave-field-amplitude dependence has two regimes: (i) hysteretic losses at low amplitudes, where the dependence is linear; and (ii) viscous losses at higher amplitudes, where the surface resistance saturates to a constant value
Summary
Upon cool down below critical temperature in the presence of an external magnetic field, magnetic flux quanta—so-called vortices—can exist in thermodynamic equilibrium in the mixed state of type-II superconductors [1,2]. Intensive studies of the trapped-flux surface resistance at low and moderate accelerating gradients as a function of the electron mean free path (l) have discovered a bell-like trend as a function of l [6,34], which is described well by the interplay of pinning- and fluxflow-limited dissipation [35,36,37] These studies have reported an almost linear dependence of the vortex dissipation with the microwave field amplitude in the resonator up to moderate values. The linear dependence has been shown to be well described by adding a cubic term to a parabolic pinning potential in the vortex equation of motion [38] This approach is limited, since it is built around the single-vortex dynamics, while in the material there are several vortices contributing to the overall dissipation, each one interacting with its surroundings. The simulation scheme presented here allows us to gather insights into the dynamics of vortex oscillations in random pinning potentials such as vortex jumps and microwave depinning, which are not captured by previous models but are key to correct interpretation of the experimental data
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