Flux Expulsion Research Articles

Effect of defects on flux expulsion of pure niobium superconducting radio frequency cavities via spatial temperature gradient

Since flux vortices are easily pinned by defects in superconducting radio frequency (SRF) cavities, trapped magnetic flux increases the surface resistance of the SRF cavity. It has been experimentally demonstrated that trapped magnetic flux can be expelled by cooling down a superconducting cavity under a large spatial temperature gradient. In this paper, we use the time-dependent Ginzburg–Landau (TDGL) theory to theoretically investigate the effect of defects on the flux expulsion ability of pure niobium superconducting cavities with an applied spatial temperature gradient. It is shown that the residual flux vortex density displays a notable stepwise decreasing trend with increasing temperature gradient at smaller residual fields, while it shows a stepwise rising with increasing defect size. Both larger defect number and size make vortices difficult to be expelled. Moreover, long cooling time is beneficial for vortices to be expelled, and the cooling time has nearly no significant effect on flux expulsion under conditions of large cooling times. The results in this paper provide some theoretical guidelines for improving the performance of superconducting cavities in practical situations.

Asymmetric Dipole Trends in Geodynamo Models and the Paleomagnetic Field

AbstractTemporal trends in the paleomagnetic dipole moment exhibit the property of positive skewness. On average, positive trends are larger and occur less frequently than negative trends over timescales of several tens of kyr. We explore the origin of this property using numerical geodynamo models. A suite of models reveals that skewness arises for a restricted set of boundary conditions. Models driven by heat flow at the top and bottom boundaries exhibit very little skewness, whereas models driven solely by heat flow on the lower boundary produce significant positive skewness. Further increases in skewness occur in the presence of thermal stratification at the top of the core. The level of skewness in the geodynamo models is correlated with estimates of upwelling near the core‐mantle boundary. Sustained upwelling is expected to increase magnetic‐flux expulsion, contributing to higher levels of skewness. Similar behavior is recovered from stochastic models in which the dipole is generated by a random series of cyclonic convection events. Skewness in the stochastic models is quantitatively similar to estimates from the geodynamo models when the average recurrence time of the convection events is 100 years. Extending the stochastic models to the paleomagnetic field implies a longer recurrence time of 1,000 years or more. We interpret this recurrence time in terms of the timing of flux‐expulsion events rather than individual convective events. Abrupt increases in the dipole moment from flux expulsion can produce skewed trends on timescales of tens of kyr.

Achieving optimal magnetic flux expulsion of a Nb3Sn superconducting radio-frequency cavity via spatial temperature gradient

The trapped magnetic flux leads to residual resistance, thereby reducing the quality factor of the superconducting cavity and affecting its power consumption. It has been experimentally shown that the trapped magnetic flux of the superconducting radio-frequency cavity can be expelled during cooldown under a spatial temperature gradient. In the present paper, we simulate the magnetic flux expulsion behavior during the cooling process of a Nb3Sn superconducting cavity using time-dependent Ginzburg-Landau (TDGL) theory. In order to achieve optimal magnetic flux expulsion, the effect of grain size, grain boundary strength |ψ|GB, and cooling time on flux expulsion ratio ε for different temperature gradients are studied theoretically. The results show that ε first increases rapidly and then varies slightly to a steady value with increasing temperature gradient, which is in good agreement with the experimental results. In general, for larger |ψ|GB, ε decreases with increasing grain size. While for smaller |ψ|GB, ε first increases to the maximum then decreases with increasing grain size. Moreover, It is found that a larger cooling time is more beneficial for the expulsion of the flux vortices from the sample. The results of this paper The vortex dynamics behavior can give an insight into the mechanism of magnetic flux expulsion, which can provide a theoretical basis for further enhancing the performance of superconducting cavities.

Evaluation of predictive correlation between flux expulsion and grain growth for superconducting radio frequency cavities

Abstract A series of experiments were carried out in an effort to develop a simple method for predicting the magnetic flux expulsion behavior of high purity niobium used to fabricate superconducting radio frequency (SRF) cavities. Using conventional metallographic characterizations in conjunction with high spatial resolution electron backscattered diffraction-orientation imaging microscopy, we find that the flux expulsion behavior of 1.3 GHz single cell SRF Nb cavities is significantly associated with the grain growth of the Nb material during heat treatment. Most of the Nb grains rapidly grew during 900 °C heat treatment, and were likely full-recrystallized with 1000 °C HT. When compared to the magnetic flux expulsion ratio (B sc/B nc) at ΔT = 5 K, the flux expulsion efficiency of the cavities increases with the increase of grain size. Most interestingly, 900 °C HT shows a roughly linear trend that suggests that this criterion could be used to predict the appropriate heat treatment temperature for sufficient flux expulsion behavior in SRF-grade Nb. This result can be used to see if flux expulsion can be predicted by examining the materials coming from Nb vendors, prior to cavity fabrication.

DOUBLE LAYERED COMPRESSIBLE MASKS

AbstractDouble-masking may be used to reduce the transmission of a virus. If additionally the masks are compressible, with different permeabilities and behaviour under compression, then it may be possible to design a mask that allows for easy breathing under normal breathing conditions, but is relatively impermeable under coughing or sneezing conditions. Such a mask could be both comfortable to wear and effective. We obtain analytical solutions for the steady-state flow-through behaviour of such a double mask under flow-out conditions. The results show that the reduction in permeability required to produce a relatively impermeable mask under high flux expulsion (sneezing) conditions could be achieved using either a single filter compressible mask or two filters with different poroelastic parameters. The parameters can be more easily adjusted using a double mask. For both single- and double-mask cases, there is an abrupt cut off, whereby through-flux levels reduce from a maximum value to zero as pressure drop levels increase beyond a critical value. Additionally, in the double-mask case, there exists a second steady-state solution for particular parameter ranges. This second solution is unlikely to occur under normal circumstances.

Effect of Successive Heat Treatment on the Performance of Superconducting Radio Frequency Niobium Cavities

One of the primary sources of radio frequency residual losses leading to lower quality factor is trapped residual magnetic field during the cooldown of superconducting radio frequency cavities. It has been reported that non-uniform recrystallization of niobium cavities after the post fabrication heat treatment leads to higher flux trapping during the cooldown, and hence the lower quality factor. Here, we fabricated two 1.3 GHz single cell cavities from high purity fine grain niobium and processed with successive heat treatments in the range 800-1000 °C to measure the flux expulsion and flux trapping sensitivity. The result indicates that although flux expulsion improves with increased heat treatments, there is a noticeable difference between the flux trapping sensitivity depending on the cavity. Evaluation of microstructure maybe crucial to understand the impact of flux trapping sensitivity on cavity performance.

Localized Origin at the Core‐Mantle Boundary of the 1969 Geomagnetic Impulse

Localized Origin at the Core‐Mantle Boundary of the 1969 Geomagnetic Impulse

Trapped K‐feldspar phenocrysts as a signature of melt migration pathways within active high‐strain zones

AbstractMelt migration through high‐strain zones in the crust fundamentally influences their rheological behaviour and is important for the transfer of fluids to upper crustal regions. The inference of former melt‐present deformation, based on field observations, may be hampered if the high‐strain zone experience a low time‐integrated melt flux or high melt volume expulsion during deformation. In these cases, typical macro‐scale field evidence of former melt presence limits interpretations. In this contribution, we investigate igneous field evidence ranging from obvious to cryptic in the Gough Dam shear zone (central Australia), a 2‐ to 4‐km‐wide high‐strain zone shown to have acted as a significant melt pathway during the Alice Springs Orogeny. Within bands of the high‐strain zone, granitic lenses are easily discernible in the field and are inferred to have formed during melt present deformation. Related coarse K‐feldspar is observed in biotite‐rich (>75 vol%) schist (glimmerite) as either isolated grains, forming trails (sub)parallel to the main foliation, or in aggregates with subordinate quartz. Detailed characterization of the granitic lenses shows that pockets of phenocrysts may be entrained in the shear zone. If melt expulsion and melt‐rock interaction is severe, isolated K‐feldspar grains in glimmerite may form. These grains exhibit (i) partially preserved crystal faces; (ii) a lack of internal grain deformation; (iii) reaction textures preferentially formed along the main crystallographic axes showing dissolution of K‐feldspar and precipitation of dominantly biotite; (iv) low‐strain domains between multiple K‐feldspar grains being inferred to enclose crystallized melt pockets, with some apparently isolated grains showing connectivity in three dimensions; and (v) a weak quartz and K‐feldspar crystallographic preferred orientation. These observations suggest an igneous phenocrystic origin for the isolated K‐feldspar grains hosted in glimmerite, which is consistent with the observed REE concentration patterns with positive Eu anomaly. We propose that the K‐feldspar phenocrysts are early‐formed crystals that were entrained into the glimmerite rocks as reactive melt migrated through the actively deformatting high‐strain zone. Previously entrained K‐feldspar phenocrysts were trapped during the collapse of the melt pathway when melt flux‐related fluid pressure waned while confining pressure and tectonic stress were still significant. The active deformation facilitated expulsion or loss of the melt phase but retainment and trapping of phenocrysts. Hence, the presence of isolated or ‘trains’ of K‐feldspar phenocrysts is a cryptic signature of syndeformational melt transfer. If melt transfer occurs in an open chemical system, phenocrysts will be entrained within the reaction product of melt‐rock interaction. We suggest that these so‐called trapped phenocrysts are a viable indicator of former syntectonic melt passage through rocks.

Graphene as a Perfect Conductor

Here, we show that the graphene sheet, which is designed to behave a band insulator, can be turned into a perfect conductor, when the difference of the current from the two valleys gets coupled to an Abelian gauge field. The graphene sheet in such a case is found to display infinite DC conductivity, Debye screening and magnetic flux expulsion.

Magnetic flux expulsion in a superconducting wire

An electric current generates a magnetic field, and magnetic fields cannot exist in the interior of type I superconductors. As a consequence of these two facts, electric currents can only flow near the surface of a type I superconducting wire so that the self-field vanishes in the interior. Here we examine how an electric current flowing through the entire cross-section of a normal conducting wire becomes a surface current when it enters a superconducting portion of the wire. This geometry provides insight into the dynamics of magnetic flux expulsion that is not apparent in the Meissner effect involving expulsion of an externally applied magnetic field. It provides clear evidence that the motion of magnetic field lines in superconductors is intimately tied to the motion of charge carriers, as occurs in classical plasmas (Alfven's theorem) and as proposed in the theory of hole superconductivity [1], in contradiction with the conventional London-BCS theory of superconductivity.

Metamorphosis of discontinuity lines and rectification of magnetic flux avalanches in the presence of noncentrosymmetric pinning forces

Considering a noncentrosymmetric pinning texture composed of a square array of triangular holes, the magnetic flux penetration and expulsion are investigated experimentally and theoretically. A direct visualization of the magnetic landscape obtained using a magneto-optical technique on a Nb film is complemented by a multiscale numerical modeling. This combined approach allows the magnetic flux dynamics to be identified from the single flux quantum limit up to the macroscopic electromagnetic response. Within the theoretical framework provided by time-dependent Ginzburg-Landau simulations, an estimation of the in-plane current anisotropy is obtained and its dependence with the radius of the curvature of hole vertices is addressed. These simulations show that current crowding plays an important role in channeling the flux motion, favoring hole-to-hole flux hopping rather than promoting interstitial flux displacement in between the holes. The resulting anisotropy of the critical current density gives rise to a distinct pattern of discontinuity lines for increasing and decreasing applied magnetic fields, in sharp contrast to the invariable patterns reported for centrosymmetric pinning potentials. This observation is partially accounted for by the rectification effect, as demonstrated by finite-element modeling. At low temperatures, where magnetic field penetration is dominated by thermomagnetic instabilities, highly directional magnetic flux avalanches with a fingerlike shape are observed to propagate along the easy axis of the pinning potential. This morphology is reproduced by numerical simulations. Our findings demonstrate that anisotropic pinning landscapes and, in particular, ratchet potentials produce subtle modifications to the critical state field profile that are reflected in the distribution of discontinuity lines.

Anomalous anisotropy of the lower critical field and Meissner effect in UTe2

We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.

Direct evidence of microstructure dependence of magnetic flux trapping in niobium

Elemental type-II superconducting niobium is the material of choice for superconducting radiofrequency cavities used in modern particle accelerators, light sources, detectors, sensors, and quantum computing architecture. An essential challenge to increasing energy efficiency in rf applications is the power dissipation due to residual magnetic field that is trapped during the cool down process due to incomplete magnetic field expulsion. New SRF cavity processing recipes that use surface doping techniques have significantly increased their cryogenic efficiency. However, the performance of SRF Nb accelerators still shows vulnerability to a trapped magnetic field. In this manuscript, we report the observation of a direct link between flux trapping and incomplete flux expulsion with spatial variations in microstructure within the niobium. Fine-grain recrystallized microstructure with an average grain size of 10–50 µm leads to flux trapping even with a lack of dislocation structures in grain interiors. Larger grain sizes beyond 100–400 µm do not lead to preferential flux trapping, as observed directly by magneto-optical imaging. While local magnetic flux variations imaged by magneto-optics provide clarity on a microstructure level, bulk variations are also indicated by variations in pinning force curves with sequential heat treatment studies. The key results indicate that complete control of the niobium microstructure will help produce higher performance superconducting resonators with reduced rf losses1 related to the magnetic flux trapping.

Archaeomagnetic results from Cambodia in Southeast Asia: Evidence for possible low-latitude flux expulsion

Extensive spatial and temporal distribution of high-quality data are essential for understanding regional and global behaviors of the geomagnetic field. We carried out chronological and archaeomagnetic studies at the Angkor-era iron-smelting site of Tonle Bak in Cambodia in Southeast Asia, an area with no data available to date. We recovered high-fidelity full-vector geomagnetic information from the 11th to 14th century for this region, which fill gaps in the global distribution of data and will significantly improve the global models. These results reveal a sharp directional change of the geomagnetic field between 1200 and 1300 CE, accompanied by an intensity dip between 1100 and 1300 CE. The fast geomagnetic variation recorded by our data provides evidence for the possible existence of low-latitude flux expulsion. Related discussions in this paper will inspire a new focus on detailed geomagnetic research in low-latitude areas around the equator, and exploration of related dynamic processes.

Static field homogeneity artifacts due to magnetic flux expulsion by HTS coils for high-resolution magnetic resonance imaging

High-Temperature Superconducting (HTS) radio frequency coils can greatly improve the sensitivity of Magnetic Resonance Imaging (MRI), with signal to noise ratios increased by up to 16 times. However, as homogeneity of the static field B0 is a major condition for MR acquisitions, their propensity to warp the magnetic field in their vicinity as a result of magnetic flux expulsion could cause severe image degradation. In this Letter, we report on the observation of artifacts generated by magnetic flux expulsion from a HTS coil. To that end, we acquired MR images of a water sample in the vicinity of a nonresonant HTS coil for different cooling conditions. These are zero field cooling and field cooling of the coil inside a clinical MRI bore magnet of 1.5 T, for a range of working temperatures of the HTS coil. After zero-field cooling, we observed significant artifacts in the MR images, increasing with lower temperature; images acquired after field cooling did not display these alterations. We propose a phenomenological model for the magnetic field disturbance induced by the HTS coil. This model reproduces, in good agreement with the experiments, the phase distortion observed in the MR images and allows one to extract the critical current density of the HTS coil, an important technological parameter of superconductors. Finally, we discuss the necessity of field cooling as a way to avoid these B0 inhomogeneity artifacts.

Coaxial multimode cavities for fundamental superconducting rf research in an unprecedented parameter space

Recent developments in superconducting radio-frequency (SRF) research have focused primarily on high frequency elliptical cavities for electron accelerators. Advances have been made in both reducing RF surface resistance and pushing the readily achievable accelerating gradient by using novel SRF cavity treatments including surface processing, custom heat treatments, and flux expulsion. Despite the global demand for SRF based hadron accelerators, the advancement of TEM mode cavities has lagged behind. To address this, two purpose-built research cavities, one quarter-wave and one half-wave resonator, have been designed and built to allow characterization of TEM-mode cavities with standard and novel surface treatments. The cavities are intended as the TEM mode equivalent to the 1.3GHz single cell cavity, which is the essential tool for high frequency cavity research. Given their coaxial structure, the cavities allow testing at the fundamental mode and higher harmonics, giving unique insight into the role of RF frequency on fundamental loss mechanisms from intrinsic and extrinsic sources. In this paper, the cavities and testing infrastructure are described and the first performance measurements of both cavities are presented.

Magnetic boundary layers in numerical dynamos with heterogeneous outer boundary heat flux

It has been proposed that magnetic flux expulsion due to outer core fluid upwellings may affect the geomagnetic secular variation on the core-mantle boundary (Bloxham, 1986). In this process intense horizontal field lines are concentrated below the outer boundary, introducing small radial length scales and consequently strong radial diffusion. Here we explore such magnetic boundary layers in numerical dynamo simulations with heterogeneous outer boundary heat flux inferred from a tomographic model of lower mantle seismic shear waves velocity anomalies. Our scheme associates magnetic boundary layers to peak horizontal magnetic fields at the top of the shell. In our models mean magnetic boundary layer thickness ranges ≈200 − 400 km and decreases with increasing magnetic Reynolds number. Extrapolation or interpolation to Earth's core conditions based on total core flow amplitude or its poloidal part gives mean magnetic boundary layer thickness of ≈220 and ≈260 − 330 km, respectively. We find magnetic boundary layers associated with the azimuthal field at the equatorial region, whereas magnetic boundary layers associated with the meridional field are found at mid latitudes. Negative outer boundary heat flux anomalies yield preferred locations of expulsion of azimuthal field below Africa and the Pacific, while positive outer boundary heat flux anomalies yield preferred locations of expulsion of meridional field below the Americas and East Asia. Furthermore, we find a tendency of the azimuthal field to low latitudes of the Northern Hemisphere. Our results suggest that the local diffusion time is on the order of several kyr and the local magnetic Reynolds number is on the order of ≈10, both much smaller than classical estimates.

Imprint of magnetic flux expulsion at the core–mantle boundary on geomagnetic field intensity variations

SUMMARY During the last decade, rapid or extreme geomagnetic field intensity variations associated with rates greater than the maximum currently observed have been inferred from archeomagnetic data in the Near-East and in Western Europe. The most extreme events, termed geomagnetic spikes, are defined as intensity peaks occurring over a short time (a few decades), and are characterized by high variation rates, up to several μT yr–1. Magnetic flux expulsion from the Earth’s outer core has been suggested as one possible explanation for these peaks but has not yet been examined in detail. In this study, we develop a 2-D kinematic model for magnetic flux expulsion whose key control parameter is the magnetic Reynolds number Rm, the ratio of magnetic diffusion time to advection time. This model enables the tracking of magnetic field lines which are distorted and folded by a fixed flow pattern. Two processes govern the magnetic evolution of the system. The first is the expulsion of magnetic flux from closed streamlines, whereby flux gradually concentrates near the boundaries of the domain, which leads to an increase of the magnetic energy of the system. If the upper boundary separates the conducting fluid from an insulating medium, a second process then takes place, that of diffusion through this interface, which we can quantify by monitoring the evolution of the vertical component of magnetic induction along this boundary. It is the conjunction of these two processes that defines our model of magnetic flux expulsion through the core–mantle boundary. We analyse several configurations with varying flow patterns and magnetic boundary conditions. We first focus on flux expulsion from a single eddy. Since this specific configuration has been widely studied, we use it to benchmark our implementation against analytic solutions and previously published numerical results. We next turn our attention to a configuration which involves two counter-rotating eddies producing an upwelling at the centre of the domain, and comprises an upper boundary with an insulating medium. We find that the characteristic rise time and maximum instantaneous variation rate of the vertical component of the magnetic field that escapes the domain scale like $\sim R_m^{0.15}$ and $\sim R_m^{0.45}$, respectively. Extrapolation of these scaling laws to the Earth’s régime is compared with various purported archeointensity highs reported in the Near-East and in Western Europe. According to our numerical experiments magnetic flux expulsion is unlikely to produce geomagnetic spikes, while intensity peaks of longer duration (one century and more) and smaller variation rates appear to be compatible with this process.

Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity

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 for different cooldown dynamics and surface treatments. The results show that lower purity material results in a higher fraction of trapped flux and that the trapped flux sensitivity parameter $S$ is significantly affected by surface treatments but without much change in the mean free path $l$. We discuss our results within an overview of published data on the dependencies of $S(l,f)$ on $l$ and frequency $f$ using theoretical models of rf losses of elastic vortex lines driven by weak rf currents in the cases of sparse strong pinning defects and collective pinning by many weak defects. Our analysis shows how multiscale pinning mechanisms in cavities can result in a maximum in $S(l)$ similar to that observed by the FNAL and Cornell groups and how pinning characteristics can be extracted from the experimental data. Here the main contribution to $S$ come from weak pinning regions at the cavity surface, where dissipative oscillations along trapped vortices perpendicular to the surface propagate into the bulk well beyond the layer of rf screening current. However, the analysis of $S$ as a function of only the mean free path is incomplete since cavity treatments change not only $l$ but pinning characteristics as well. The effect of cavity treatments on pinning is primarily responsible for the change of $S$ without much effect on $l$ observed in this work. It also manifests itself in different magnitudes and peak positions in $S(l)$, and scatter of the $S$-data coming from the measurements on different cavities which have undergone different treatments affecting both $l$ and pinning. Optimizations of flux pinning to reduce flux sensitivity at low rf fields is discussed.

Optimal Thermal Gradient for Flux Expulsion in 600°C Heat-treated CEBAF 12 GeV Upgrade Cavities

Optimal Thermal Gradient for Flux Expulsion in 600°C Heat-treated CEBAF 12 GeV Upgrade Cavities