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 present the results of from DC magnetization and penetration depth measurements of cylindrical bulk large-grain (LG) and fine-grain (FG) niobium samples used for the fabrication of superconducting radio frequency (SRF) cavities. The surface treatment consisted of electropolishing and low temperature baking as they are typically applied to SRF cavities. The magnetization data were fitted using a modified critical state model. The critical current density Jc and pinning force Fp are calculated from the magnetization data and their temperature dependence and field dependence are presented. The…
Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity fo…
Long standing data from niobium thin film accelerating cavities will be revisited and analysed by a modified London model of RF superconductivity. Firstly, the applicability of this model is explored using data of the BCS surface resistance and its dependence on the RF magnetic field, temperature and mean free path. Secondly, the RF losses from trapped magnetic flux are analysed with regard to their dependence on these same parameters.
Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a columnar defect with the characteristic size of the cross-section much smaller than the coherence length. We present an extension of the electrostatic analogies method, which proved to be useful for calculations of the pinning force for large cavities, to the case of small defects. The pinning potential for an elliptic cavity is derived analytically. Also, we determine the depinning current for a circular defect.
The improvement of the performance of RF superconducting cavities has recently motivated a considerable research effort in order to elucidate the effect of trapped magnetic flux on the surface resistance $R_{s}$. In this paper we show that by introducing a non-linear pinning force in the Gittleman-Rosenblum equations for the RF power dissipation due to a trapped magnetic flux in a superconductor, we can empirically describe the linear dependence on the RF field amplitude $B_{rf0}$ of the additional surface resistance $R_{fl}$. We also show that the proportionality between the RF-field dependen…
As superconductors are cooled below their critical temperature, stray magnetic flux can become trapped in regions that remain normal. The presence of trapped flux facilitates dissipation of ac current in a superconductor, leading to losses in superconducting elements of microwave devices. In type II superconductors, dissipation is well-understood in terms of the dynamics of vortices hosting a single flux quantum. In contrast, the ac response of type I superconductors with trapped flux has not received much attention. Building on Andreev's early work [Sov. Phys. JETP 24, 1019 (1967)], here we s…
This paper reports the observation of hysteresis in the vortex pinning in a superconductor / ferromagnetic epitaxial nanocomposite consisting of fcc Gd particles incorporated in a Nb matrix. We show that this hysteretic pinning is associated with magnetic reversal losses in the Gd particles and is fundamentally different in origin to pinning interactions previously observed for ferromagnetic particles or other microstructural features.
Identifying the loss mechanisms of niobium film cavities enables an accurate determination of applications for future accelerator projects and points to research topics required to mitigate their limitations. Measurements on samples show that the electric field is a dominant loss mechanism for niobium films, acting through interface tunneling between localized states in surface oxides and delocalized states in the superconducting niobium.
The performance of superconducting radiofrequency (SRF) cavities used for particle accelerators depends on two characteristic material parameters: field of first flux entry $H_{entry}$ and pinning strength. The former sets the limit for the maximum achievable accelerating gradient, while the latter determines how efficiently flux can be expelled related to the maximum achievable quality factor. In this paper, a method based on muon spin rotation ($μ$SR) is developed to probe these parameters on samples. It combines measurements from two different spectrometers, one being specifically built for…
In order to study the vortex pinning determined by artificially introduced pinning centers in the small-vortex displacement regime, we measured the microwave surface impedance at 47.7 GHz in the mixed state of YBa$_{2}$Cu$_{3}$O$_{7-δ}$ thin films, where sub-micrometric BaZrO$_3$ particles have been incorporated. As a function of the BaZrO$_3$ content, we observe that the absolute losses slightly decrease up to a BaZrO$_3$ content of 5%, and then increase. We found that the magnetic-field-induced losses behave differently, in that they are not monotonic with increasing BaZrO$_3$ concentration:…
We investigate "hot" regions with anomalous high field dissipation in bulk niobium superconducting radio frequency cavities for particle accelerators by using low energy muon spin rotation (LE-$μ$SR) on corresponding cavity cutouts. We demonstrate that superconducting properties at the hot region are well described by the non-local Pippard/BCS model for niobium in the clean limit with a London penetration depth $λ_\mathrm{L} = 23 \pm 2$ nm. In contrast, a cutout sample from the 120$^\circ$C baked cavity shows a much larger $λ> 100$ nm and a depth dependent mean free path, likely due to gradien…
In this work we investigate superconducting properties of niobium samples via application of the muon spin rotation/relaxation (muSR) technique. We employ for the first time the muSR technique to study samples that are cutout from large and small grain 1.5 GHz radio frequency (RF) single cell niobium cavities. The RF test of these cavities was accompanied by full temperature mapping to characterize the RF losses in each of the samples. Results of the muSR measurements show that standard cavity surface treatments like mild baking and buffered chemical polishing (BCP) performed on the studied sa…
New results of the investigations critical current problems in the high temperature oxide superconductors are presented, basing on an analysis of the flux pinning on nano-sized centers. New model of the interaction pancake vortices with the nano-sized centers is proposed, while comparison of obtained results with others pinning forces approaches presented. The energy balance approach is applied, which leads to the appearance of the potential barrier determining the pancake vortices movement in the flux creep process. Various initial positions of the captured vortex have been analyzed, while va…
The damping of the oscillations of a small permanent magnet (spherical shape, radius 0.1 mm) levitating between two parallel YBCO surfaces is measured as a function of oscillation amplitude and temperature. The losses in the samples (epitaxial thin films, bulk granular and bulk melt-textured) are analyzed in terms of oscillating shielding currents flowing through trapped flux lines whose motion gives rise to electric fields. We find dissipation to originate from different mechanisms of flux dynamics. At small amplitudes there is a linear regime described by a surface resistance varying from 10…
Measurements of the first-flux-penetration field in surface-treated and coated Nb: Distinguishing between surface pinning and an interface energy barrier
Three-dimensional microwave cavities have recently been combined with superconducting qubits in the circuit quantum electrodynamics (cQED) architecture. These cavities should have less sensitivity to dielectric and conductor losses at surfaces and interfaces, which currently limit the performance of planar resonators. We expect that significantly (>10^3) higher quality factors and longer lifetimes should be achievable for 3D structures. Motivated by this principle, we have reached internal quality factors greater than 0.5x10^9 and intrinsic lifetimes of 0.01 seconds for multiple aluminum super…
We study mechanisms of vortex nucleation in Nb$_3$Sn Superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy (STEM) image and energy dispersive spectroscopy (EDS) of some Nb$_3$Sn cavities show Sn segregation at grain boundaries in Nb$_3$Sn with Sn concentration as high as $\sim$35 at.\% and widths $\sim$3 nm in chemical composition. Using ab initio calculations, we estimate the effect excess tin has on the local superconducting properties of the material. We model Sn segregation as a lowering of t…
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum electrodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to a reduction of the device performance due to energy dissipating Abrikosov vortices. We experimentally investigate the vortex induced energy losses in such Nb resonators with different spatial distributions of micropatterned pinning sites (antidots) by transmission spectroscopy measurements at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex induced losses and th…
Abrikosov fluxonics, a domain of science and engineering at the interface of superconductivity research and nanotechnology, is concerned with the study of properties and dynamics of Abrikosov vortices in nanopatterned superconductors, with particular focus on their confinement, manipulation, and exploitation for emerging functionalities. Vortex pinning, guided vortex motion, and the ratchet effect are three main fluxonic ``tools'' which allow for the dynamical (pinned or moving), the directional (angle-dependent), and the orientational (current polarity-sensitive) control over the fluxons, res…
We present the design of a reflective stop-band filter based on quasi-lumped elements that can be utilized to introduce large dc and low-frequency voltage biases into a low-loss superconducting coplanar waveguide (CPW) cavity. Transmission measurements of the filter are seen to be in good agreement with simulations and demonstrate insertion losses greater than $20\,{\rm dB}$ in the range of ${\rm 3\,to\,10\,GHz}$. Moreover, transmission measurements of the CPW's fundamental mode demonstrate that loaded quality factors exceeding $10^5$ can be achieved with this design for dc voltages as large a…
Oscillatory dynamics and quasi-static Campbell regime of the vortex lattice (VL) in twinned YBa2Cu3O7 single crystals has been explored at low fields near the peak effect (PE) region by linear and non-linear ac susceptibility measurements. We show evidence that the PE is a dynamic anomaly observed in the non-linear response, and is absent in the Labusch constant derived from the linear Campbell regime. Static properties play a major role however, and we identify two H(T) lines defining the onset and the end of the effect. At H1(T) a sudden increase in the curvature of the pinning potential wel…
This letter describes a very simple electromechanical oscillator, consisting of a strong-pinning Nb-Ti superconductor loop subjected to static magnetic fields. A detailed calculation of the losses occurring during its low-frequency oscillations is carried out. The conclusion is that the quality factor for such oscillator might reach the 10^10-10^11 range, something comparable only to the best optical microcavities. Such device might permit the measurement of variations in static forces with the same precision a superconducting quantum interference device (SQUID) measures variations of magnetic…
