Magnetic Flux Trapping Research Articles

Large self-heating by trapped-flux reduction in Sn-Pb solders

Magnetic flux trapping in field-cooled (FC) Sn-Pb solders has been recently studied because of the observation of nonvolatile magneto-thermal switching (Arima H. et al., Commun. Mater., 5 (2024) 34) and anomalous magnetic field-temperature (H-T) phase diagrams (Murakami T. et al., AIP Adv., 13 (2023) 125008). In this paper, we investigate the origin of the anomalously low specific heat (C) in Sn10-Pb90 and Sn45-Pb55 solders after FC at H = 1500 Oe. We show that the FC solders exhibit self-heating possibly caused by the flux flow during the reduction of trapped fluxes when heating the sample during the C measurements. The T dependence of T rise clearly exhibits unexpectedly large values when the low-C states are observed. In addition, the cause of the transition-like behavior in C-T of FC solders is explained by local heating during H control and flux-jump phenomena.

Magnetic flux trapping in porous high-Tc superconductors

Porosity affects the properties of high-Tc superconductors and can improve their performance by enhancing oxygenation, cryocooling, etc. Among other factors, the presence of pores plays a significant role in the process of magnetic flux trapping. Relationships with the porosity manifest in the irreversibility field, the full penetration field, and the remnant magnetization of the samples. To account for the effect of porosity on the trapped magnetic flux into type-II superconductors, a simple toy model is suggested. Generally, as the porosity increases, the trapped flux and related parameters tend to diminish. However, in the case of microscopic samples, porosity can enhance magnetic flux trapping.

Anomalous field-temperature phase diagram of superconductivity in Sn–Pb solder

Sn–Pb solders are superconducting materials whose Sn and Pb are perfectly phase-separated. Recently, anomalous magnetic-flux trapping in a Sn45–Pb55 solder has been revealed, where the magnetic fluxes are selectively trapped in the Sn regions due to the supercurrents in the surrounding Pb regions. Here, we report on the observation of the anomalous critical field (Hc)-temperature (T) phase diagram of superconductivity in the Sn45–Pb55 solder. Although the Hc(T) for the Pb regions decreases with increasing field as in normal type-I superconductors and is consistent with the conventional trend with Hc(0) ∼ 800 Oe, the Hc(T) for the Sn regions exhibits anomalous behaviors. The most noticeable trend was observed in the field-cooled (under 1500 Oe) solder. The Hc-T phase diagram for the Sn regions largely varies when the applied external field is reversed, and Tc increases with increasing field amplitude when H < 0 Oe is applied. On the basis of the flux trapping and the observed anomalous Hc-T phase diagrams, we propose that the field-robust superconductivity in the Sn regions is related to the ferromagnetically aligned magnetic fluxes (or formation of vortices) in the Sn regions of the Sn45–Pb55 solder.

Numerical study on flux-jump occurrence in a cup-shaped MgB2 bulk for magnetic shielding applications

MgB2 is one of the most promising materials for superconducting bulk applications. However, thermomagnetic instabilities can arise in the material because of its low heat capacity and thermal conductivity as well as its high critical current density. Being able to predict these phenomena, can guide and optimize MgB2-based devices for magnetic flux shielding or trapping applications. In this work, the flux-jump occurrence in an MgB2 cup-shaped shield is numerically studied using the finite element method by means of the commercial software COMSOL 6.0 Multiphysics®. To this aim, we developed a 2D axial-symmetric model coupling the heat diffusion equation and the magnetic equations based on a magnetic vector-potential () formulation. The comparison of the computed shielding curves with the experimental ones evidenced a good agreement between the two sets of data at different temperatures and positions along the shield’s axis. The as-validated model was then exploited to investigate possible optimization routes via the improvement of both the thermal conductivity of the material and the thermal exchange between the device and the cooling stage.

Electromagnetic Response in an Expanding Quark–Gluon Plasma

The validity of conventional Ohm’s law is tested in the context of a rapidly evolving quark–gluon plasma produced in heavy-ion collisions. Here, we discuss the electromagnetic response using an analytical solution in kinetic theory. As conjectured previously, after switching on an electric field in a nonexpanding plasma, the time-dependent current is given by J(t)=(1−e−t/τ0)σ0E, where τ0 is the transport relaxation time and σ0 is the steady-state electrical conductivity. Such an incomplete electromagnetic response reduces the efficiency of the magnetic flux trapping in the quark–gluon plasma, and may prevent the observation of the chiral magnetic effect. Here, we extend the study to the case of a rapidly expanding plasma. We find that the decreasing temperature and the increasing transport relaxation time have opposite effects on the electromagnetic response. While the former suppresses the time-dependent conductivity, the latter enhances it.

Observation of quenching-induced magnetic flux trapping using a magnetic field and temperature mapping system

Highly efficient superconducting radio-frequency cavities exhibit low heat loss and are used as components in accelerators and superconducting devices due to their high $Q$-values. The precise location of magnetic flux trapping in cavities is necessary to identify its effects on the performance of superconducting cavities. In this study, we report a new combined mapping system to measure the temperature and magnetic field on the equator. The proposed system comprehensively maps local magnetic field changes as magnetic flux trapping due to quenching. Our experimental results show that magnetic flux trapping due to quenching increases the local surface resistance of superconducting cavities at 2 K. Thus, the proposed system elucidates the relationship between local flux trapping due to quenching and surface resistance in superconducting cavities and highlights the effect of quenching on the surface resistance. This system can aid in the development of superconducting cavities with higher $Q$ values.

Jump quantum phase transitions in a vortex sistem and the dinamiccomplex magnetic permeability of high-temperature binaryYBa-=SUB=-2-=/SUB=-Cu-=SUB=-3-=/SUB=-O-=SUB=-7-x-=/SUB=- superconductors

A nonlocal high-frequency method for measuring the dynamic complex magneticpermeability with enhanced spatial resolution is developed to simultaneouslydetermine the bulk and local character of stepwise penetration of a magneticflux through twin boundaries (TBs) into a YBa2Cu3O7-x HTSC sample during itsstepwise decomposition into twins. By the values of fields corresponding tothe regions of steps, the thermodynamic first critical magnetic fields aredetermined: the penetration of a flux into a sample --- a Josephson medium;the development of a critical state in the Josephson medium; the penetrationof a flux into twins; and the values of the critical fields of phasetransitions in the vortex system of the HTSC sample, such as the meltingfields of a vortex crystal, the formation of a superconducting glass statein the sample, and the transition to the vortex glass and Bragg glassstates. Keywords: high-frequency inductance, bulk and local dynamic complexmagnetic permeability, magnetic flux trapping, effective demagnetizationfactor, twins (monodomains, crystallites, sub- and nanocrystallites), twinboundaries.\

Jump quantum phase transitions in a vortex sistem and the dinamic complex magnetic permeability of high-temperature binary YBa-=SUB=-2-=/SUB=-Cu-=SUB=-3-=/SUB=-O-=SUB=-7-x-=/SUB=- superconductors

A nonlocal high-frequency method for measuring the dynamic complex magnetic permeability with enhanced spatial resolution is developed to simultaneously determine the bulk and local character of stepwise penetration of a magnetic flux through twin boundaries (TBs) into a YBa2Cu3O7-x HTSC sample during its stepwise decomposition into twins. By the values of fields corresponding to the regions of steps, the thermodynamic first critical magnetic fields are determined: the penetration of a flux into a sample --- a Josephson medium; the development of a critical state in the Josephson medium; the penetration of a flux into twins; and the values of the critical fields of phase transitions in the vortex system of the HTSC sample, such as the melting fields of a vortex crystal, the formation of a superconducting glass state in the sample, and the transition to the vortex glass and Bragg glass states. Keywords: high-frequency inductance, bulk and local dynamic complex magnetic permeability, magnetic flux trapping, effective demagnetization factor, twins (monodomains, crystallites, sub- and nanocrystallites), twin boundaries.

Magnetic field sensors for detection of trapped flux in superconducting radio frequency cavities.

Superconducting radio frequency (SRF) cavities are fundamental building blocks of modern particle accelerators. They operate at liquid helium temperatures (2-4 K) to achieve very high quality factors (1010-1011). Trapping of magnetic flux within the superconductor is a significant contribution to the residual RF losses, which limit the achievable quality factor. Suitable diagnostic tools are in high demand to understand the mechanisms of flux trapping in technical superconductors, and the fundamental components of such diagnostic tools are magnetic field sensors. We have studied the performance of commercially available Hall probes, anisotropic magnetoresistive sensors, and flux-gate magnetometers with respect to their sensitivity and capability to detect localized, low magnetic flux amplitudes, of the order of a few tens of magnetic flux quantum at liquid helium temperatures. Although Hall probes have the lowest magnetic field sensitivity (∼96 nV/μT at 2K), their physical dimensions are such that they have the ability to detect the lowest number of trapped vortices among the three types of sensors. Hall probes and anisotropic magnetoresistive sensors have been selected to be used in a setup to map regions of trapped flux on the surface of a single-cell SRF cavity.

Impact of geometry on the magnetic flux trapping of superconducting accelerating cavities

Controlling trapped magnetic flux in superconducting radiofrequency (RF) cavities is of crucial importance in modern accelerator projects. In order to study flux trapping efficiency and sensitiv- ity of surface resistance, dedicated experiments have been carried out on different types of low-\b{eta} superconducting accelerating cavities. Even under almost full trapping conditions, we found that the measured magnetic sensitivities of these cavity geometries were significantly lower than the theoretical values predicted by commonly-used models based on local material properties. This must be resolved by taking account of geometrical effects of flux trapping and flux oscillation under RF surface current in such cavity shape. In this paper, we propose a new approach to convolute the influence of geometries. We point out a puzzling contradiction between sample measurements and recent cavity experiments, which leads to two different hypotheses to simulate oscillating flux trapped in the cavity surface. A critical reconsideration of flux oscillation by the RF Lorentz force, compared with temperature mapping studies in elliptical cavities, favoured the results of previous sample measurements, which suggested preferential flux trapping of normal component to the cavity inner surface. Based on this observation, we builded a new model to our experimental results and the discrepancy between old theory and data were resolved.

Study of Possible Frequency Dependence of Small AC Fields on Magnetic Flux Trapping in Niobium by Polarized Neutron Imaging

Reducing the size of ambient magnetic flux trapping during cooldown in superconducting radio-frequency niobium cavities is essential to reaching the lowest power dissipation as required for continuous wave application. Here, it is suggested that applying an alternating magnetic field superimposed to the external DC field can potentially reduce the size of trapped flux by supporting flux line movement. This hypothesis is tested for the first time systematically on a buffered chemically polished (BCP) niobium sample before and after high temperature annealing, a procedure which is known to reduce flux pinning. External low-frequency (Hz-range) magnetic fields were applied to the samples during their superconducting transition and the effect of varying their amplitude, frequency and offset was investigated. A few results can be highlighted: The influence of the frequency and magnitude of the AC fields on the flux trapping in the untreated Nb sample cannot be neglected. The trapped flux seems to be homogeneously distributed, unlike the flux trapping in, e.g., lead (Pb), which is a type I superconductor. After annealing, the Nb sample shows practically no dependency of flux trapping on external AC fields. The trapped magnetic flux was measured by polarized neutron imaging, and calculations of trapped fields show good agreement with experimental results.

Inductance of superconductor integrated circuit features with sizes down to 120 nm

Data are presented on the inductance of various features used in superconductor digital integrated circuits: microstrip and stripline inductors with linewidths down to 120 nm and different combinations of ground plane layers, effect of perforations of various sizes in the ground planes and their distance to the inductors on inductance, inductance of vias of various sizes between adjacent layers, inductance of composite vias between distant superconducting layers. Test circuits used for the measurements were fabricated in a new 150 nm node of a fully planarized process with eight niobium layers developed at MIT Lincoln Laboratory for superconductor electronics as well as in our standard SFQ5ee and SC1 fabrication processes with 250 nm minimum feature size. The new SC2 process utilizes 193 nm photolithography in combination with plasma etching and chemical mechanical planarization of interlayer dielectrics to define inductors with linewidth down to about 100 nm on critical layers. The standard processes use 248 nm photolithography. The measured data are compared with the results of inductance extraction using software packages InductEx and wxLC. Variations of circuit inductors caused by the fabrication processes are discussed. Magnetic flux trapping in ground plane moats and its coupling to nearby inductors are discussed for circuit cooling in a residual field of several configurations.

Influence of the thickness of the base Nb layer in a Josephson junction on magnetic flux trapping

We measured the two-dimensional magnetic field dependence of a Josephson current by applying external magnetic fields Hx and Hy parallel to the plane of a Nb/Al-AlOx/Nb Josephson junction from two directions. In addition, we measured the modulation characteristics of the Josephson current by applying a magnetic field Hz in the direction perpendicular to the plane of the junction. When the perpendicular magnetic field Hz was applied to the Josephson junction and removed, the main peak of the Fraunhofer pattern did not return to the origin of the (Hx, Hy) plane completely because the magnetic flux was trapped in the Nb superconducting film around the Josephson junction. In the present study, we investigated the influence of the thickness of the base Nb layer on magnetic flux trapping in a Josephson junction by fabricating Josephson junctions with base Nb layers of different thickness. We found that the magnetic flux became increasingly difficult to be trapped in the Nb superconducting thin film with increasing thickness of the Nb superconducting film.

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.

Reliable 4.8 T trapped magnetic fields in Gd–Ba–Cu–O bulk superconductors using pulsed field magnetization

A robust and reliable in-situ magnetization method is essential for exploiting the outstanding magnetic flux trapping ability of bulk superconductors in practical applications. We report a 4.8 T peak trapped magnetic field, B T, achieved at 30 K in a 36 mm diameter GdBa2Cu3O7-δ –Ag bulk superconductor using pulsed field magnetization (PFM). To realize this, we have developed a reliable two-step multi-pulse PFM process based on understanding and exploiting the avalanche-like flux jump phenomenon observed in these materials. The magnitude of the applied pulsed magnetic field (B a) necessary to trap 4.8 T was merely 5.29 T, corresponding to a remarkable magnetization efficiency (B T/B a) of 90%.

Mechanism of the Generation of the Critical Current in High-Temperature Superconductors with Through Microdefects

The critical current of a model high-temperature superconductor (HTSC) with defects in the form of through holes (antidots) with characteristic sizes on the order of the magnetic-field penetration depth (or larger) is calculated. To this end, subprocesses equivalent to the magnetic-flux trapping by a hole and creation of a vortex near the hole edge are introduced into the model of a layered HTSC. It is shown that account for these subprocesses yields a physical mechanism, which makes it possible to describe correctly the nonmonotonic dependence of the critical current on the antidot characteristic size, which is similar to the experimental one. The calculations are carried out for a pure superconductor and a superconductor with nanoscale pinning centers. It is shown that the presence of nanoscale pinning centers along with antidots does not make qualitative changes in the relationship between the antidot radius and magnetic-flux pinning character and the critical-current behavior in an HTSC.

S-N border instability, magnetic flux trapping and cumulative effect during pulsed S-N switching of high quality YBaCuO thin films

Unexpected irreversible damage appeared in samples while investigating pulsed S-N switching in YBaCuO thin films. Examination of a scanning electron microscope image of a damaged film containing a defect revealed a step-like motion of the N-zone. Restoration of crack movement dynamics points to the formation of coherent jets. This would mean that cumulative convergence of unknown incompressible media took place. The known model of an edge barrier, when the S-N border, characterized by width λeff, bounds a semi elliptical N-zone at the film edges, was applied for clarification of the cumulative convergence. In that model, counteracting forces cause a wave-like unstable form of the barrier S-N border, and further current growth increases the amplitude of wave-like distortions of the border. Then, current reconnection separates bulges from the N-zone and induces the appearance of the circular currents with a trapped magnetic flux. Heat release at the places with trapped flux cause an expansion in these locations and coherent jets originate from touch points due to cumulative convergence. We substantiate that specific properties of the S-N border at λeff, such as high tensile strength, very high flexibility and also incompressibility, are responsible for the appearance of the cumulative effect. Thus, the N-zone propagation into S state begins by motion of the wave-like border. The non-damaging step-like N-zone propagation into the films without defects is clarified. It is concluded that both the critical current and the damage current are determined by the same barrier with the unstable S-N border, and, therefore, the irreversible damage of the films comes quickly after the current reaches the critical value.

Magnetic Flux Trapping and Flux Jumps in Pulsed Field Magnetizing Processes in REBCO and Mg-B Bulk Magnets

Pulsed-field magnetization technique (PFM) is expected as a cheap and an easy way for HTS bulk materials for utilizing as intense magnets. As the generation of heat due to magnetic flux motion in bulk magnets causes serious degradation of captured fields, it is important to investigate the flux motions during PFM in various field applications. The authors precisely measured the magnetic flux motion in the cryocooled MgB2 bulk magnets containing various amount of Ti. We classified the motions to “no flux flow (NFF)”, “fast flux flow (FFF)”, and “flux jump (FJ)” regions. The results showed that addition of Ti shifts the field invasion area to high field areas, and expands the NFF regions. The highest field-trapping appears at the upper end of the NFF region. Since the heat generation and its propagation should attribute to the dissipation of magnetic flux, FFF leads to FJ. Compared with MgB2, we referred to GdBCO as for the flux motion. A flux jump was observed at 30 K when the pulse field of 7 T was applied to the preactivated sample, showing its stability against FJ.

Strictly application-oriented REBCO bulk fabrication

The ability to produce large-grain REBCO (RE=Y, Rare Earth) bulk superconductors by melt texturing growth has been improved and refined significantly over the last 20 years. Magnetic bearings, transportation systems, and scientific instrumentation are becoming major innovations of HTS bulk materials. Large grain production is dominated by cold top-seeding melt growth (TSMG). For material optimizing we demonstrate strictly application-oriented fabrication close to the final geometry and thus reducing mechanical machining and assembling work. YBCO hollow cylinder design for journal bearings with radial c axes orientation are obtained by radial-seeding geometry (RSMG). YBCO ring tiles up 120 mm show a perfect cylinder geometry with in-wall a, b orientation and radial c axes. We report improved electric and mechanical bulk properties and demonstrate great production effectiveness. For achieving high field permanent magnets up to 10 T we compare YBCO bulk and ring geometry. Top/bottom double seeded melt growth (DSMG) grain samples provide better magnetic flux trapping capability and show more homogenous properties.

Possible role of grain-boundary and dislocation structure for the magnetic-flux trapping behavior of niobium: A first-principles study

Possible role of grain-boundary and dislocation structure for the magnetic-flux trapping behavior of niobium: A first-principles study