Abstract
In the present study the radio-frequency complex response of trapped vortices in superconductors is calculated and compared to experimental data previously published. The motion equation for a magnetic flux line is solved assuming a bi-dimensional and mean-free-path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the unprecedented bell-shaped trend as a function of the mean-free-path observed in our previous experimental work. We demonstrate that such bell-shaped trend of the surface resistance as a function of the mean-free-path may be described as the interplay of the two limiting regimes of the surface resistance, for low and large mean-free-path values: pinning and flux-flow regimes respectively. Since the possibility of defining the pinning potential at different locations from the surface and with different strengths, we discuss how the surface resistance is affected by different configurations of pinning sites. By tackling the frequency dependence of the surface resistance, we also demonstrate that the separation between pinning- and flux-flow-dominated regimes cannot be determined only by the depinning frequency. The dissipation regime can be tuned either by acting on the frequency or on the mean-free-path value.
Highlights
When the superconductive transition is performed in the presence of an external magnetic field, magnetic flux can be trapped in the superconducting materials as energetically stable flux quanta in the mixed state of type-II superconductors, or as magnetic flux pinned at defects in the Meissner state of type-I and type-II superconductors
Because of a too crude approximation assumed in the calculation of the surface resistance and the adoption of a mono-dimensional pinning potential, our previous approach suggested that the dynamic contribution to the vortex dissipation generates largely overestimated values of surface resistance
Our model can in principle explain why between one and two orders of magnitude lower values of vortex-related surface resistance are observed in Nb on Cu SRF cavities [38], compared to our experimental results
Summary
When the superconductive transition is performed in the presence of an external magnetic field, magnetic flux can be trapped in the superconducting materials as energetically stable flux quanta in the mixed state of type-II superconductors, or as magnetic flux pinned at defects in the Meissner state of type-I and type-II superconductors. The second approach assumes the flux line as a monodimensional object that possess a certain tension [3] When this description is assumed the pinning force is disregarded [16, 17] and the vortex response is calculated in absence of pinning. If both vortex line tension and pinning force are considered, the analytic form of the latter must possess the dependence on the distance from the rf surface, complicating substantially the problem. Because of a too crude approximation assumed in the calculation of the surface resistance and the adoption of a mono-dimensional pinning potential, our previous approach suggested that the dynamic contribution to the vortex dissipation generates largely overestimated values of surface resistance. We do demonstrate that the transition between pinning and flux-flow regimes may be obtained by crossing the depinning frequency [11], and by tuning the mean-free-path value of the superconducting material
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