Flux Trapping Research Articles

On the trapped magnetic moment in type-II superconductors

Abstract Measurements of the trapped (remanent) magnetic moment, $M_{trap}\left(H\right)$, when a small magnetic field $H$ is turned off after cooling below the superconducting transition temperature, $T_c$, or ramping a magnetic field up and down after cooling in a zero magnetic field, offer substantial advantages in difficult cases of small samples and large field-dependent backgrounds, which is relevant for hydrogen-based ultra-high-$T_{c}$ superconductors (UHTS). Until recently, there was no need for a separate paper on the trapped magnetic flux for well-known critical-state models due to the simplicity of the physics involved. However, recent publications showed the need for such an analysis. This note summarizes the expectations for the Bean model with constant critical current density and the Kim model with field-dependent critical currents. It is shown that if the trapped moment is fitted to the power law, $M_{trap}\propto H^{\alpha}$, the fixed exponent $\alpha=2$ is exact for the Bean model, while Kim models show a wide interval of possible values, $2\leq\alpha\leq4$. Furthermore, accounting for reversible magnetization expands the range of possible exponents to $1\leq\alpha\leq4$. In addition, demagnetizing factors are essential and make the trapped moment orientation dependent even in isotropic materials.

As a concrete application, it is shown that flux trapping experiments performed on H$_{3}$S UHTS compounds can be well described using this generalized approach, lending further support to the type-II superconducting nature of H$_{3}$S under ultra-high pressure.

A new experiment to enable rapid systematic investigations of flux trapping dynamics for superconducting radio-frequency cavity applications.

Many modern accelerators rely on superconducting radio-frequency (SRF) cavities to accelerate particles. When these cavities are cooled to the superconducting state, a fraction of the ambient magnetic field (e.g., Earth's magnetic field) may be trapped in the superconductor. This trapped flux can significantly increase the power dissipation of the SRF cavities. It is, therefore, crucial to understand the underlying mechanism of how magnetic flux is trapped and what treatments and operating conditions can reduce the flux-trapping efficiency. A new experiment was designed that enables a systemic investigation of flux trapping. It allows for independent control of cooldown conditions, which might have an influence on flux trapping: temperature gradient across the superconductor during cooldown, cooldown rate, and ambient magnetic field. For exhaustive studies, the setup was designed for quick thermal cycling, permitting up to 300 superconducting transitions in one day. In this paper, the setup and operation is described in detail and an estimation of the measurement errors is given. Exemplary data are presented to illustrate the efficacy of the system.

Enhanced plasma performance in C-2W advanced beam-driven field-reversed configuration experiments

TAE Technologies’ fifth-generation fusion device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in field-reversed configuration (FRC) plasma performance. C-2W produces record breaking, macroscopically stable, high-temperature advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady state, which is primarily limited by neutral-beam (NB) pulse duration. The NB power supply system has recently been upgraded to extend the pulse length from 30 ms to 40 ms, which allows for a longer plasma lifetime and thus better characterization and further enhancement of FRC performance. An active plasma control system is routinely used in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnet coils, edge-biasing electrodes, gas injection and tunable-energy NBs. Google’s machine learning framework for experimental optimization has also been routinely used to enhance plasma performance. Dedicated plasma optimization experimental campaigns, particularly focused on the external magnetic field profile and NB injection (NBI) optimizations, have produced a superior FRC plasma performance; for instance, achieving a total plasma energy of ∼13 kJ, a trapped poloidal magnetic flux of ∼16 mWb (based on the rigid-rotor model) and plasma sustainment in steady state up to ∼40 ms. Furthermore, under some operating conditions, the electron temperature of FRC plasmas at a quiescent phase has successfully reached up to ∼1 keV at the peak inside the FRC separatrix for the first time. The overall FRC performance is well correlated with the NB and edge-biasing systems, where higher total plasma energy is obtained with higher NBI power and applied voltage on biasing electrodes. C-2W operations have now reached a mature level where the machine can produce hot, stable, long-lived, and repeatable plasmas in a well-controlled manner.

A Voltage Monitoring Approach for Faster Reducing Flux Trapping in Josephson Junction Arrays

A Voltage Monitoring Approach for Faster Reducing Flux Trapping in Josephson Junction Arrays

The effect of the non-uniform critical current density on the magnetoelastic behavior of bulk superconductors: Case of a long cylindrical superconductor

In this paper, the effect of non-uniform critical current density on bulk superconductors is studied, the case of a long cylindrical superconductor with transport current is chose to discussed. The critical current density is distributed non-uniformly along the radius of the cylinder. Based on the Bean critical state model, the distributions of trapped magnetic flux and shielding current in the cylinder are investigated. Combined with the plane strain approach, the analytical expressions of magnetic flux pinning force and stress are obtained. The magnetostriction of the cylinder is also discussed. Results show that the non-uniform critical current density changes the distribution law of the shielding current and trapped magnetic flux in the cylinder. The increase of non-uniform parameters n leads to an obvious increase in the flux pinning force. Thus, a larger extreme value of the pinning stress is obtained, a bigger structure deformation is produced inside the superconducting cylinder. All those conclusions will provide a helpful guide for engineering application.

Improving the performance of the photosynthetic apparatus of Citrus sinensis with the use of chitosan-selenium nanocomposite (CS + Se NPs) under salinity stress

BackgroundAbiotic stress, such as salinity, affects the photosynthetic apparatus of plants. It is reported that the use of selenium nanoparticles (Se NPs), and biochemical compounds such as chitosan (CS) increase the tolerance of plants to stress conditions. Therefore, this study aimed to elucidate the potential of Se NPs, CS, and their composite (CS + Se NPs) in improving the photosynthetic apparatus of C. sinensis under salt stress in greenhouse conditions. The grafted seedlings of C. sinensis cv. Valencia after adapting to the greenhouse condition, were imposed with 0, 50, and 100 mM NaCl. After two weeks, the plants were foliar sprayed with distilled water (control), CS (0.1% w/v), Se NPs (20 mg L− 1), and CS + Se NPs (10 and 20 mg L− 1). Three months after treatment, the levels of photosynthetic pigments, leaf gas exchange, and chlorophyll fluorescence in the treated plants were evaluated.ResultsUnder salinity stress, total chlorophyll, carotenoid, and SPAD values decreased by 31%, 48%, and 28% respectively, and Fv/Fm also decreased compared to the control, while the ratio of absorption flux (ABS), dissipated energy flux (DI0) and maximal trapping rate of PSII (TR0) to RC (a measure of PSII apparent antenna size) were increased. Under moderate (50 mM NaCl) and intense (100 mM NaCl) salinity stress, the application of CS + Se NPs significantly increased the levels of photosynthetic pigments and the Fv/Fm value compared to plants treated with distilled water.ConclusionsIt may be inferred that foliar treatment with CS + Se NPs can sustain the photosynthetic ability of C. sinensis under salinity stress and minimize its deleterious effects on photosynthesis.

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.

Flux Trapping Implementation in High-Temperature Superconducting Magnets for Superconducting Electric Machines

Flux Trapping Implementation in High-Temperature Superconducting Magnets for Superconducting Electric Machines

Comparative calculations of trapped field and trapped magnetic flux with different multi-pulse magnetization methods for a bulk high-temperature superconductor

Bulk high-temperature superconductors (HTSs) can trap high magnetic field and are potentially useful for a variety of applications as pseudo-permanent magnets. The pulsed field magnetization (PFM) for bulk HTSs is cost effective and flexible in application compared with quasi-static field cooling and zero field cooling techniques. Many PFM methods have been proposed in many studies to achieve the excellent magnetization performances such as high trapped field and large trapped magnetic flux. In order to clarify the magnetization characteristics of bulk HTSs using different typical PFM methods, we comparatively analyze several typical PFM methods using a simulation model based on the H-formulation combining the thermal conductivity equation. The electromagnetic and thermal behaviors during the magnetization of a bulk HTS with different PFM methods are numerically achieved using the solenoid-type coil to magnetize the bulk. The calculations show that multi-pulse magnetization methods can effectively enhance the trapped field and trapped magnetic flux of the bulk, and different multi-pulse magnetization methods have different efficiencies enhancing these performances. Among all considered PFM methods in the study, the combination method of modified multi-pulse technique with step-wise cooling and iteratively magnetizing pulsed-field method with reducing amplitude has the largest improvement for the trapped magnetic field and the trapped flux simultaneously.

Investigating the flux pinning dependence on grain orientation in YBa2Cu3O7−δ using neutron tomography

In this study, we report the first case of non-destructive characterization of the dependence of the flux trapping mechanism on the grain properties of a bulk type II superconductor using a combination of polarized neutron tomography and diffraction contrast tomography. The high temperature superconductor, YBa2Cu3O7−δ, has been used in this study due to its viable commercial growth processes typically resulting in the production of polycrystalline specimens. The diffraction tomography revealed the pseudo-single crystal nature of the sample i.e. a polycrystalline sample with 47 composite grains having a maximum grain misorientation angle of 1.86°. Polarized neutron tomography was used for characterization of the flux trapped in the material after field cooling to 90.5 K in a field of 0.5 mT and switching off the field. A combination of the results from these two non-destructive characterization techniques indicate a correlation between the anisotropy of the trapped flux with the orientation of the grains in the material in addition to a preference for the flux trapping in the grain boundaries.

Temporal Pattern and Profile of a Coastal‐Deep Sea Conveyor at a Marginal Deep Oligotrophic Sea

AbstractSediment trap data set and 234Th profiles (deep water excesses and deficits) reveal that particulate organic carbon (POC) export at the highly oligotrophic Levantine Sea is dominated by lateral transport from the nearby margin. These intermediate nepheloid layers (INL) operate at multi‐depth, with the silt‐to‐clay size particulate matter (PM) fraction transported at water depths of about 100–500 m, while finer fraction arrives also at deeper depths. The shallow NIL is triggered by winter storms, manipulated by coastal flash floods and shelf resuspension and assisted by cross‐shore currents, which allow the arrival of PM at a distance of 50 km within about 10 days. The deeper INL could be related to sediments initially driven to depth by density currents. Our data show that inter‐annual differences in sediment trap fluxes were related to changes in both the intensity of coastal floods and current velocity. The frequent observation of deep‐water 234Th excesses during a (relatively) low export winter (2018) is related to lessened cleansing of the water column, that is, reduced removal of fine‐grained PM by sinking coarser‐grained material. These observations highlight the importance of winter storm intensity in the POC budget of marginal seas like the Levantine Basin (LB) even in areas with limited river discharge. This further suggests that the anticipated increase in extreme weather events due to the on‐going climate change should have an impact on this coastal‐deep sea conveyor and on POC export in the LB.

Effects of Stray Magnetic Field on Transition-Edge Sensors in Gamma-Ray Microcalorimeters

Superconducting transition-edge sensors (TESs) used in X-ray and γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-ray microcalorimeters suffer degraded performance if cooled in a magnetic field B sufficient to trap flux in the sensors. We report measurements of γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-ray TESs before and after implementing measures to reduce stray B fields from sources inside and outside the cryostat. These measurements showed a correlation between anomalous features in TES current–voltage (IV) curves and degraded energy resolution. After reducing internal sources of stray B field and improving shielding against external sources, both IV curves and energy resolution improved. Finally, we placed magnetized screws with remnant fields ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document} 10 μT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \ extrm{T}$$\\end{document} near similar γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-ray TESs in a different type of detector package and observed the same effects.

Further analysis of flux trapping experiments on hydrides under high pressure

It has been claimed that measurements of trapped magnetic flux in hydrides under pressure provide evidence for superconductivity in these materials (Minkov et al., 2022; Minkov et al., 2023). In recent work we have questioned that claim (Hirsch and Marsiglio, 2022). Here we point out that recent experiments (Bud’ko et al., 2023) provide further evidence supporting our questioning of that claim. We also present calculations for a thin disk and compare these with those previously calculated for a long cylinder. The results are qualitatively similar, and therefore reinforce our previous conclusions. We also address recent criticism of our paper Ref. (Hirsch and Marsiglio, 2022) by Bud’ko (2024) and by Talantsev et al. (2023).

On creep of trapped flux near [formula omitted] in MgB2 and CaKFe4As4

We present flux creep data taken at different temperatures on single crystals of known, ambient pressure, superconductors, CaKFe4As4 and MgB2, taken using the protocol that is common for trapped flux measurements. Using our results, we show that the time dependence of the magnetic moment in H3S is remarkably similar to the magnetization relaxation rates observed in established superconductors at ambient pressure, where in the latter cases this can be unambiguously assigned to flux creep.

Assessment of photosynthetic capacity of two blackberry cultivars subjected to salt stress by the JIP fluorescence test

BACKGROUND: Salt stress has recently emerged as one of the most significant abiotic stresses with negative impact on crop production. Photosynthesis is a vital biochemical process in plants, very sensitive to environmental constraints, including salt stress. OBJECTIVE: The aim of this study was to evaluate the impact of salt stress on photosystem II in the leaves of blackberry cultivars (Rubus fructicosus L.). METHODS: Two blackberry cultivars (Thornfree and Boysen) were exposed to salt stress (20, 40, and 60 mM NaCl) for 28 days in in vitro culture. The photosynthetic activity was evaluated by probing chlorophyll a fluorescence (JIP test) and photosynthetic pigments. RESULTS: The maximum quantum yield of PSII (Fv/Fm), performance indexes (PIABS and PItotal), and photosynthetic driving force (DFABS) were greatly affected by salt stress in the leaves of Boysen cultivar. Lower photosynthetic efficiency was confirmed by the increased values of absorption flux per RC (ABS/RC), trapping flux per PSII RC (TR0/RC), dissipation flux per RC (DI0/RC), decreased values of chlorophyll and carotenoid contents, disruption in the interaction between the light-harvesting complex and the core proteins of PSII, as well as disruption of the oxygen-evolving complex. CONCLUSIONS: The provided informations suggest that the photosynthetic apparatus of Thornfree cultivar was found to be more tolerant to salt stress compared to Boysen.

Effects of Cu2O nanoparticles on the kinetic characteristics of rapid chlorophyll fluorescence induction and related genes in wheat seedlings.

Metal nanoparticles could be accumulated in soils, which threatens the ecological stability of crops. Investigating the effects of cuprous oxide nanoparticles (Cu2O-NPs) on photosystem Ⅱ (PSⅡ) of wheat seedling leaves holds considerable importance in comprehending the implications of Cu2O-NPs on crop photosynthesis. Following the hydroponic method, we investigated the effects of 0, 10, 50, 100, and 200 mg·L-1 Cu2O-NPs on chlorophyll fluorescence induction kinetics and photosynthetic-related genes in wheat seedlings of "Zhoumai 18". The results showed that, with the increases of Cu2O-NPs concentrations, chlorophyll contents in wheat leaves decreased, and the standardization of the OJIP curve showed a clearly K-phase (ΔK＞0). Cu2O-NPs stress increased the parameters of active PSⅡ reaction centers, including the absorption flux per active RC (ABS/RC), the trapping flux per active RC (TRo/RC), the electron transport flux per active RC (ETo/RC), and the dissipation flux per active RC (DIo/RC). Cu2O-NPs stress decreased the parameters of PSⅡ energy distribution ratio including the maximum quantum yield of PSⅡ (φPo), the quantum yield of electron transport from QA (φEo), and the probability that a trapped exciton moved an electron further than QA (Ψo), while increased the quantum ratio for heat dissipation (φDo). Moreover, there was a decrease in photosynthetic quantum yield Y(Ⅱ), photochemical quenching coefficient (qP), net photosynthetic rate (Pn), stomatal conductance (gs), intercellular CO2 concentration (Ci), and transpiration rate (Tr) of leaves with the increases of Cu2O-NPs concentration. Under Cu2O-NPs stress, the expression levels of genes which included PSⅡ genes (PsbD, PsbP, Lhcb1), Rubisco large subunit genes (RbcL), cytochrome b6/f complex genes (PetD, Rieske), and ATP synthase genes (AtpA, AtpB, AtpE, AtpI) were downregulated. These results indicated that Cu2O-NPs stress altered the activity and structure of PSⅡ in wheat seedlings, affected the activity of PSⅡ reaction centers, performance parameters of PSⅡ donor and acceptor sides. PSⅡ related genes were downregulated and exhibited significant concentration effects.

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.

Imaging the Meissner effect in hydride superconductors using quantum sensors.

By directly altering microscopic interactions, pressure provides a powerful tuning knob for the exploration of condensed phases and geophysical phenomena1. The megabar regime represents an interesting frontier, in which recent discoveries include high-temperature superconductors, as well as structural and valence phase transitions2-6. However, at such high pressures, many conventional measurement techniques fail. Here we demonstrate the ability to perform local magnetometry inside a diamond anvil cell with sub-micron spatial resolution at megabar pressures. Our approach uses a shallow layer of nitrogen-vacancy colour centres implanted directly within the anvil7-9; crucially, we choose a crystal cut compatible with the intrinsic symmetries of the nitrogen-vacancy centre to enable functionality at megabar pressures. We apply our technique to characterize a recently discovered hydride superconductor, CeH9 (ref. 10). By performing simultaneous magnetometry and electrical transport measurements, we observe the dual signatures of superconductivity: diamagnetism characteristic of the Meissner effect and a sharp drop of the resistance to near zero. By locally mapping both the diamagnetic response and flux trapping, we directly image the geometry of superconducting regions, showing marked inhomogeneities at the micron scale. Our work brings quantum sensing to the megabar frontier and enables the closed-loop optimization of superhydride materials synthesis.

Checking Key Assumptions of the Kennel‐Petschek Flux Limit With ELFIN CubeSats

AbstractIn planetary radiation belts, the Kennel‐Petschek flux limit is expected to set an upper limit on trapped electron fluxes at 80–600 keV in the presence of efficient electron loss through pitch‐angle diffusion by whistler‐mode chorus waves generated around the magnetic equator by the same 80–600 keV electron population. Comparisons with maximum measured fluxes have been relatively successful, but several key assumptions of the Kennel‐Petschek model have not been experimentally tested. The Kennel‐Petschek model notably assumes an exponential growth of chorus waves as the trapped electron flux increases, and a fixed maximum wave power gain of about 3. Here, we describe a method for inferring the near‐equatorial wave power gain using only measurements of trapped, precipitating, and backscattered electron fluxes at low altitude. Next, we make use of Electron Losses and Fields Investigation (ELFIN) CubeSats measurements of such electron fluxes during two moderate geomagnetic storms with sustained electron injections to infer the corresponding chorus wave power gains as a function of time, energy, and equatorial trapped electron flux. We show that wave power increases exponentially with trapped flux, with a wave power gain roughly proportional to the theoretical linear convective gain, and that the maximum inferred gain near the upper flux limit is roughly 10, with a factor of 2 uncertainty. Therefore, two key theoretical underpinnings of the Kennel‐Petschek model are borne out by the present results, although the strong inferred gains should correspond to higher flux limits than in traditional estimates.

Positive effect of co-addition of Dy2O3/Ag and Dy2O3/WO3 nanoparticles on the physical critical parameters and electrical transport properties of YBCO ceramic

In this study, YBa2Cu3O7−δ (YBCO) polycrystalline samples with co-addition of nanostructure materials (NSMs) of 0.1 wt% Dy2O3/Ag and 0.1 wt% Dy2O3/WO3 were synthesized via solid-state reaction sintering. Herein, the considered NSMs are of two shapes: nanoparticles (NPs) of dysprosium oxide and silver and nanowires of tungsten oxide. X-ray powder diffraction (XRD) and scanning electron microscopy (SEM) were used to examine the structure and morphology of samples. Resistivity versus temperature (ρ(T)), ac susceptibility (χ(T)), and dc magnetization (M(H)) measurements have been carried out on superconducting YBCO to deduce critical superconducting parameters like Bc1 and Jc. Using the Aslamazov-Larkin approach, the induced excess conductivity analysis was performed to complete values of critical lengths such as ξco, λo, critical magnetic fields (Bc1, Bc2), and critical current density Jc at 0 K. The combined addition of Dy2O3/Ag and Dy2O3/WO3 conserves the orthorhombic structure, the grain size of about some micrometers, and the volume fraction of superconductor grain (Vsg%). NSMs co-addition ameliorates the assembly of grains and their connectivity to empower the carriers' charge transportation between the grains. Dy-rich entities are inserted into the YBCO grains' surfaces. The critical superconducting parameters Bco, Bc1, Bc2, and Jc are high in co-added samples due to the decrease in intergrain resistivity and the better competence of trapping flux lines inside the samples. The combination of different types of NSMs inside YBCO constitutes a hopeful way to compromise between better grain coupling and higher flux pinning. AgNPs coupled with Dy2O3NPs act more efficiently than WO3NW coupled with Dy2O3NPs in YBCO compounds to make its properties better.