Three-dimensional Magnetic Field Research Articles

Investigating the Efficacy of Topologically Derived Time Series for Flare Forecasting. I. Data Set Preparation

Abstract The accurate forecasting of solar flares is considered a key goal within the solar physics and space weather communities. There is significant potential for flare prediction to be improved by incorporating topological fluxes of magnetogram data sets, without the need to invoke three-dimensional magnetic field extrapolations. Topological quantities such as magnetic helicity and magnetic winding have shown significant potential toward this aim, and provide spatiotemporal information about the complexity of active region magnetic fields. This study develops time series that are derived from the spatial fluxes of helicity and winding that show significant potential for solar flare prediction. It is demonstrated that time-series signals, which correlate with flare onset times, also exhibit clear spatial correlations with eruptive activity, establishing a potential causal relationship. A significant database of helicity and winding fluxes and associated time series across 144 active regions is generated using Space-Weather HMI Active Region Patches data processed with the Active Region Topology (or ARTop) code that forms the basis of the time-series and spatial investigations conducted here. We find that a number of time series in this data set often exhibit extremal signals that occur 1–8 hr before a flare. This publicly available living data set will allow users to incorporate these data into their own flare prediction algorithms.

Planar scanning probe microscopy enables vector magnetic field imaging at the nanoscale

Abstract Planar scanning probe microscopy is a recently emerging alternative approach to tip-based scanning probe imaging. It can scan an extended planar sensor, such as a polished bulk diamond doped with magnetic-field-sensitive nitrogen-vacancy (NV) centers, in nanometer-scale proximity of a planar sample. So far, this technique has been limited to optical near-field microscopy and has required nanofabrication of the sample of interest. Here we extend this technique to magnetometry using NV centers and present a modification that removes the need for sample-side nanofabrication. We harness this new ability to perform a hitherto infeasible measurement - direct imaging of the three-dimensional vector magnetic field of magnetic vortices in a thin film magnetic heterostructure, based on repeated scanning with NV centers with different orientations within the same scanning probe. Our result opens the door to quantum sensing using multiple qubits within the same scanning probe, a prerequisite for the use of entanglement-enhanced and massively parallel schemes.

Analysis of the air gap magnetic field in cylindrical magnetic couplings based on mathematical and finite element approach

The air gap magnetic field of a magnetic coupling plays a crucial role in the examination of its static torque and eddy current losses. Precise characterization of the air gap magnetic field is essential for ensuring the accuracy of performance assessments of the magnetic coupling. This study focuses on the cylindrical magnetic coupling as the subject of investigation, employing mathematical analysis and finite element methods to evaluate and quantify the magnetic field properties. The study establishes a mathematical model of the magnetic field of a magnetic coupling based on electromagnetic field principles and the superposition theorem. An analytical formula for the magnetic flux density distribution of the air-gap magnetic field is derived. Subsequently, a three-dimensional magnetic field finite element model is created using the finite element method to numerically calculate the air gap magnetic field and validate the analytical formula. The research also explores the periodic distribution characteristics of the magnetic field in the air gap, analyzing axial differences in magnetic flux density value and direction distribution influenced by end effects.

Experimental study on the time-dependent spatial distribution of the three-dimensional magnetic field in an inductive pulsed plasma thruster

Inductive pulsed plasma thrust generates thrust by ionizing and accelerating plasma through pulsed inductive electromagnetic field. The spatial distribution of the magnetic field within the discharge region influences both the Lorentz force exerted on plasma and the electromagnetic coupling between plasma and circuit. An experimental prototype of inductive pulsed plasma thruster with high repeatability and a three-dimensional transient magnetic field measurement system with low integration error are established. Time-dependent spatial distribution of the magnetic field in the plasma is obtained by scanning measurement employing repeated pulse discharges. Combined with the results of high-speed photographing and electrical parameter measurements, the relationship between the evolution of plasma structure and the magnetic field penetration is discussed.

Development of three-dimensional magnetic field detection device based on FPGA

Abstract Aiming at the acquisition and real-time processing of three-dimensional magnetic field in space, this paper proposes a magnetic field detection device. It uses 64 three-dimensional magnetic field sensors to consist an 8x8 array measuring the magnetic field within the array range. It uses FPGA as the main control chip to simultaneously acquire the data collected by these three-dimensional magnetic sensors, and implements bilinear interpolation algorithm in FPGA to preprocess the magnetic image. Then it is transmitted to the computer through the Ethernet. The direction and magnetic field intensity of the magnetic vector are calculated by vector synthesis formula, and the data are further processed and plotted by MATLAB, which shows the measured space magnetic field vector information intuitively. The results of the experiment show that the device can obtain the three-dimensional magnetic field information of the space.

Characterization of Crack Geometry Parameters Based on Three-dimensional Transient Magnetic Field of Rectangular Pulsed Eddy Current

Eddy current testing plays an important role in assessing the surface quality of metal structures. Based on pulsed eddy current (PEC) testing, a new magnetic field characterization technique for surface cracks is proposed in this paper. The three-dimensional transient magnetic field is studied, revealing its distribution characteristics and transient response in the presence of cracks. The results show that the transient magnetic field contains valuable information. Specifically, the distributions of the magnetic field components Bx and Bz at the initial time are effective in evaluating crack length and depth. The time response of Bx provides characteristic information about defect length, emphasizing the importance of selecting the appropriate detection location. Additionally, the peak position and response amplitude of Bz can characterize crack depth. The effects of the pulse rising time and coil liftoff on the transient magnetic field are also studied. The study shows that the pulse rising time should be as short as possible, and the characteristics of rectangular PEC help mitigate the effects of liftoff. The rich features extracted from the transient magnetic field provide a new means to evaluate crack geometry, improving testing capabilities and detection accuracy.

Probing Three-dimensional Magnetic Fields. III. Synchrotron Emission and Machine Learning

Synchrotron observation serves as a tool for studying magnetic fields in the interstellar medium and intracluster medium, yet its ability to unveil three-dimensional (3D) magnetic fields, meaning probing the field’s plane-of-the-sky (POS) orientation, inclination angle relative to the line of sight, and magnetization from one observational data, remains largely underexplored. Inspired by the latest insights into anisotropic magnetohydrodynamic (MHD) turbulence, we found that synchrotron emission’s intensity structures inherently reflect this anisotropy, providing crucial information to aid in 3D magnetic field studies: (i) the structure’s elongation gives the magnetic field’s POS orientation and (ii) the structure’s anisotropy degree and topology reveal the inclination angle and magnetization. Capitalizing on this foundation, we integrate a machine learning approach—convolutional neural network (CNN)—to extract this latent information, thereby facilitating the exploration of 3D magnetic fields. The model is trained on synthetic synchrotron emission maps, derived from 3D MHD turbulence simulations encompassing a range of sub-Alfvénic to super-Alfvénic conditions. We show that the CNN is physically interpretable and the CNN is capable of obtaining the POS orientation, inclination angle, and magnetization. Additionally, we test the CNN against the noise effect and the missing low-spatial frequency. We show that this CNN-based approach maintains a high degree of robustness even when only high-spatial frequencies are maintained. This renders the method particularly suitable for application to interferometric data lacking single-dish measurements. We applied this trained CNN to the synchrotron observations of a diffuse region. The CNN-predicted POS magnetic field orientation shows a statistical agreement with that derived from synchrotron polarization.

τSPECT: a spin-flip loaded magnetic ultracold neutron trap for a determination of the neutron lifetime

The confinement of ultracold neutrons (UCNs) in three-dimensional magnetic field gradient or magneto-gravitational traps allows for a measurement of the free neutron lifetime τ n with superior control over loss channels related to UCNs interacting with material surfaces. The most precise measurement τ n has been achieved using a magneto-gravitational trap, in which UCN are prevented from escaping at the top of their trap by gravity. More compact horizontal confinement geometries with variable energy acceptance ranges can be obtained by using steep magnetic field gradients in all spatial directions, generated by combinations of either permanent or (variable) superconducting magnets. In this paper, we present the first successful implementation of a pulsed spin-flip based loading scheme to fill a three-dimensional magnetic trap with externally produced UCN. The measurements with the τSPECT experiment were performed at the pulsed UCN source of the research reactor TRIGA Mainz. The extracted neutron storage time constant of τ = 859(16) s is compatible with the most precise determinations of τ n . We report on detailed, but statistically limited, investigations of major systematic effects influencing the neutron storage time. The statistical limitations are mitigated by the relocation of the experiment to a stronger UCN source.

Toroidal distribution of heat load on castellated plasma facing components for lower divertor target in EAST

In tokamak devices, the performance of plasma facing components (PFCs) under high heat loads is a key challenge for achieving long-pulse and high-performance plasma operations. The lower divertor of EAST adopts an ITER-like cassette modules (CMs) structure. However, regular distribution of damage along the toroidal direction have been observed on the divertor target plates, which not only affects the lifespan of PFCs but also limits the long-pulse and high-performance plasma operations. Therefore, investigating the toroidal distribution of the heat load on the divertor target in EAST is crucial for understanding the mechanism of damage on the target plate surface. The toroidal characteristics of heat loads on CMs of the lower divertor in EAST was analyzed using a three-dimensional magnetic field line tracing program (PFCFlux). For the inner vertical target (IVT) and outer vertical target (OVT) within a single CM, the heat load varies monotonically along the toroidal direction. In contrast, the heat load distribution on the outer horizontal target (OHT) is uniform, except at the chamfers, which is directly correlated with the target’s geometric structure and the magnetic field configuration. The surface heat load distribution exhibits toroidal non-uniformity, with the heat deposition pattern being generally consistent and displaying periodic variations. The toroidally uneven heat load distribution is attributed to the change in the magnetic field’s tilt angle. Additionally, the peak heat load is observed at the chamfer positions between cassettes, and an analysis is conducted on the relationship between peak heat load and the size of the chamfer. Smaller tilt angles result in lower surface heat load. Furthermore, a comparative analysis of peak heat loads at the chamfer under different plasma current conditions reveals that higher plasma currents generally result in increased peak heat loads. This investigation into the toroidal heat load distribution on the divertor surface contributes to understanding of the damage mechanism of W PFC as the target plate and provides valuable data for divertor design of future fusion devices.

The Spatial Correlation between CN-line- and Dust-continuum-emitting Regions in High-mass Star-forming Clouds

Measuring the strength of a three-dimensional (3D) magnetic field vector is challenging as it is not easy to recognize whether its line-of-sight (LOS) and plane-of-sky (POS) components are obtained from the same region. CN (N = 1–0) emission has been used to get the LOS component of a magnetic field (B LOS) from its Zeeman splitting lines, while dust continuum emission has been used to get the POS component of a magnetic field (B POS). We use the CN (N = 1–0) data observed with the Taeduk Radio Astronomy Observatory 14 m telescope and the dust continuum data from the Herschel archive toward six high-mass star-forming regions in order to test whether CN line and dust continuum emission can trace a similar region and thus can be used for inferring 3D magnetic field strength. Our comparison between CN and H2 column densities for all targets indicates that CN line emission tends to be strong toward bright continuum regions. The positions of peak CN column densities are particularly well correlated with those of peak H2 column densities, at least over the H2 column density of 8.0 × 1022 cm−2 within one or two telescope beam sizes in all targets, implying that CN-line- and dust-continuum-emitting regions are likely spatially coincident. This enabled us to make the reliable measurement of the 3D magnetic field strengths of five targets by taking a vector sum of their B LOS and B POS, helping to decide the magnetical criticality of the targets as supercritical or transcritical.

Development of a compact bolometer camera concept for investigation of radiation asymmetries at Wendelstein 7-X.

Power exhaust is one of the central challenges in magnetically confined fusion plasmas. Radiative detachment can be employed to reduce particle and heat fluxes to the divertor target, mitigating divertor damage and erosion. However, accomplishing this for a non-axisymmetric machine such as Wendelstein 7-X is a non-trivial task because of the complex role of transport and plasma-wall interaction in a three-dimensional magnetic field topology. We introduce a new bolometer camera design that can be easily installed in multiple toroidal locations and adapted to the required geometry, providing additional spatial coverage. This can be used to locally enhance tomographic capabilities or to resolve spatial variations of the plasma emissivity. By including these non-uniformities in the total radiated power estimate, global power balance measurements can be improved. We model each bolometer camera using ray tracing. We then analyze the forward-modeled detector response to several physically motivated synthetic emission phantoms with respect to its capability to quantify the local average emissivity. The results prove this concept as a promising asset for the investigation of poloidal and toroidal radiated power asymmetries in Wendelstein 7-X. The first CBC prototypes have undergone development and installation for the next experimental campaign.

A perturbative multi-mode model with finite parallel electric field for fast-ion-driven Alfvén eigenmodes

Abstract Alfvén eigenmodes are of great interest in any fusion device as they can be excited by fast ions in the plasma. If the modes grow to large amplitudes, they can cause transport and redistribution of the fast ions, thus limiting fusion performance. To save computational resources, the resonant kinetic interaction between the fast-particle species and the modes is often modelled by MHD-kinetic hybrid codes. Here, we present such a hybrid model which is applicable to three-dimensional magnetic fields, accounts for a finite parallel electric field and multiple MHD modes present at the same time. The model extends the one previously implemented in the CKA-EUTERPE code allowing for a better estimate of the damping due to the parallel electric field and nonlinear mode-mode interaction. The capabilities of our model are illustrated by applying the code to model nonlinear frequency chirping and fast-ion profile flattening.

Loss of energetic particles due to feedback control of resistive wall mode in HL-3

Effects of three-dimensional (3D) magnetic field perturbations due to feedback control of an unstable ( is toroidal mode number) resistive wall mode (RWM) on the energetic particle (EP) losses are systematically investigated for the HL-3 tokamak. The MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) code, facilitated by the test particle guiding center tracing module REORBIT, is utilized for the study. The RWM is found to generally produce no EP loss for co-current particles in HL-3. Assuming the same perturbation level at the sensor location for the close-loop system, feedback produces nearly the same loss of counter-current EPs compared to the open-loop case. Assuming however that the sensor signal is ten times smaller in the close-loop system than the open-loop counter part (reflecting the fact that the RWM is more stable with feedback), the counter-current EP loss is found significantly reduced in the former. Most of EP losses occur only for particles launched close to the plasma edge, while particles launched further away from the plasma boundary experience much less loss. The strike points of lost EPs on the HL-3 limiting surface become more scattered for particles launched closer to the plasma boundary. Taking into account the full gyro-orbit of particles while approaching the limiting surface, REORBIT finds slightly enhanced loss fraction.

Periodic Coronal Rain Driven by Self-consistent Heating Process in a Radiative Magnetohydrodynamic Simulation

The periodic coronal rain and in-phase radiative intensity pulsations have been observed in multiple wavelengths in recent years. However, due to the lack of three-dimensional coronal magnetic fields and thermodynamic data in observations, it remains challenging to quantify the coronal heating rate that drives the mass cycles. In this work, based on the MURaM code, we conduct a three-dimensional radiative magnetohydrodynamic simulation spanning from the convective zone to the corona, where the solar atmosphere is heated self-consistently through dissipation resulting from magnetoconvection. For the first time, we model the periodic coronal rain in an active region. With a high spatial resolution, the simulation well resembles the observational features across different extreme-ultraviolet wavelengths. These include the realistic interweaving coronal loops, periodic coronal rain, and periodic intensity pulsations, with two periods of 3.0 hr and 3.7 hr identified within one loop system. Moreover, the simulation allows for a detailed three-dimensional depiction of coronal rain on small scales, revealing adjacent shower-like rain clumps ∼500 km in width and showcasing their multithermal internal structures. We further reveal that these periodic variations essentially reflect the cyclic energy evolution of the coronal loop under thermal nonequilibrium state. Importantly, as the driver of the mass circulation, the self-consistent coronal heating rate is considerably complex in time and space, with hour-level variations in 1 order of magnitude, minute-level bursts, and varying asymmetry reaching ten times between footpoints. This provides an instructive template for the ad hoc heating function and further enhances our understanding of the coronal heating process.

Global fluid simulation of plasma turbulence in stellarators with the GBS code

The implementation of three-dimensional magnetic fields, such as the ones of stellarators, in the GBS code (Ricci et al 2012 Plasma Phys. Control. Fusion 54 124047; Giacomin et al 2022 J. Comput. Phys. 464 111294) is presented, and simulation results are discussed. The geometrical operators appearing in the drif-reduced Braginskii equations evolved by GBS are expanded considering the typical parameter ordering of stellarator configurations. It turns out that most of the operators have a similar structure as the one implemented in the tokamak axisymmetric version of the code. In particular, the perpendicular laplacian only acts on the poloidal plane, which avoids the need of a three-dimensional solver for the electrostatic potential. The simulation of an island divertor stellarator is then presented, showing the derivation of the magnetic equilibrium in detail and extending the results in (Coelho et al 2022 Nucl. Fusion 62 074004). Although the island magnetic field-lines divert the plasma towards the strike points of the walls, the islands do not seem to have a significant impact on the turbulence properties. The dominant mode, identified as interchange-driven, is field-aligned and breaks the stellarator toroidal symmetry. The radial and poloidal extensions of the mode are of the same order, in contrast to typical tokamak simulations. This has consequences on the poloidal dependence of turbulent transport.

An Advanced Hall Element Array-Based Device for High-Resolution Magnetic Field Mapping.

The precise mapping of magnetic fields emitted by various objects holds critical importance in the fabrication of industrial products. To meet this requirement, this study introduces an advanced magnetic detection device boasting high spatial resolution. The device's sensor, an array comprising 256 unpackaged gallium arsenide (GaAs) Hall elements arranged in a 16 × 16 matrix, spans an effective area of 19.2 mm × 19.2 mm. The design maintains a 1.2 mm separation between adjacent elements. For enhanced resolution, the probe scans the sample via a motorized rail system capable of executing specialized movement patterns. A support structure incorporated into the probe minimizes the measurement distance to below 0.5 mm, thereby amplifying the magnetic signal and mitigating errors from nonparallel probe-sample alignment. The accompanying interactive software utilizes cubic spline interpolation to transform magnetic readings into detailed two- and three-dimensional magnetic field distribution maps, signifying field strength and polarity through variations in color intensity and amplitude sign. The device's efficacy in accurately mapping surface magnetic field distributions of magnetic and magnetized materials was corroborated through tests on three distinct samples: a neodymium-iron-boron magnet, the circular magnetic array from a smartphone, and a magnetized 430 steel plate. These tests, focused on imaging quality and magnetic field characterization, underscore the device's proficiency in nondestructive magnetic field analysis.

Partial Acquisition of Spectral Projections Accelerates Four-dimensional Spectral-spatial EPR Imaging for Mouse Tumor Models: A Feasibility Study.

Our study aimed to accelerate the acquisition of four-dimensional (4D) spectral-spatial electron paramagnetic resonance (EPR) imaging for mouse tumor models. This advancement in EPR imaging should reduce the acquisition time of spectroscopic mapping while reducing quality degradation for mouse tumor models. EPR spectra under magnetic field gradients, called spectral projections, were partially measured. Additional spectral projections were later computationally synthesized from the measured spectral projections. Four-dimensional spectral-spatial images were reconstructed from the post-processed spectral projections using the algebraic reconstruction technique (ART) and assessed in terms of their image qualities. We applied this approach to a sample solution and a mouse Hs766T xenograft model of human-derived pancreatic ductal adenocarcinoma cells to demonstrate the feasibility of our concept. The nitroxyl radical imaging agent 2H,15N-DCP was exogenously infused into the mouse xenograft model. The computation code of 4D spectral-spatial imaging was tested with numerically generated spectral projections. In the linewidth mapping of the sample solution, we achieved a relative standard uncertainty (standard deviation/| mean |) of 0.76 μT/45.38 μT = 0.017 on the peak-to-peak first-derivative EPR linewidth. The qualities of the linewidth maps and the effect of computational synthesis of spectral projections were examined. Finally, we obtained the three-dimensional linewidth map of 2H,15N-DCP in a Hs766T tumor-bearing leg in vivo. We achieved a 46.7% reduction in the acquisition time of 4D spectral-spatial EPR imaging without significantly degrading the image quality. A combination of ART and partial acquisition in three-dimensional raster magnetic field gradient settings in orthogonal coordinates is a novel approach. Our approach to 4D spectral-spatial EPR imaging can be applied to any subject, especially for samples with less variation in one direction.

MODELLING AND SIMULATION OF AN MR BRAKE BASED ON TORQUE COMPENSATION

A new design for a repetitive compression magnetorheological (MR) brake has been introduced, aiming to enhance both the efficiency and safety of vehicle safety systems, thereby accelerating the commercial adoption of such brakes in the automotive industry. This innovative brake uses a hybrid operational mode, replacing the conventional rotary motion with a unique recessive structure to enhance the braking performance. In the non-braking state, the design maintains the fluidity of the MR fluid, while in the braking state, it leverages the brake disc's recessive movement. Additionally, the study incorporates a temperature compensation mechanism to mitigate potential performance variations due to temperature changes. A three-dimensional static magnetic field analysis confirmed the magnetic circuit design's effectiveness and the suitability of the selected parameters and materials. The simulation showed that the brake's average magnetic field intensity rose by 145.26% when increasing the current from 1A to 4A, achieving a maximum braking torque of 51.4 Nm.

Comparison of aggregation effect of axial and polar Magnetotactic bacteria for tumor therapy

Magnetotactic bacteria (MTB), possessing chains of iron oxide nanoparticles, are potential tools for controlled therapy due to their responsiveness to weak magnetic fields. This study aims to evaluate the targeting and aggregation capabilities of axial AMB-1 and polar MO-1 MTB for therapeutic applications. A three-dimensional focusing magnetic field (fMF)-producing device was designed and established with a gradient magnetic field of 0.08 mT/mm at the central region for the guidance of MTB in vitro and in vivo. Under a unidirectional magnetic field, polar Magneto-ovoid MO-1 formed a single line in the culture dish, whereas axial Magnetospirillum magneticum AMB-1 displayed a small portion aggregated on the centerline. With simultaneous X and Y magnetic field application, MO-1 cells aggregated at a point, while AMB-1 bacteria gathered incompletely. Further, magnetic resonance imaging of breast cancer-bearing nude mice injected subcutaneously with MTB peritumorally and navigated by a fMF revealed more substantial aggregation of MO-1 cells within the tumor than AMB-1 bacteria. Prussian blue staining corroborated the penetration of MO-1 cells into the tumor tissue. These findings suggest that polar MO-1 bacteria exhibit superior targeting and aggregation properties compared to axial AMB-1, indicating their potential suitability for targeted therapeutic applications.

Photonic spin Hall effect under the action of a full-angle three-dimensional magnetic field in space

In this paper, we have measured the magneto-optical spin Hall effect influenced by an arbitrary oriented magnetic field using CeDyAl thin films on Gd3Ga5O12 (GGG) substrates as reflective materials. Plots of the variation of the magneto-optic spin Hall effect (MOPSHE) with magnetic field strength, the hysteresis line, in three different unit-direction magnetic fields are simulated and experimentally measured. The comparison of the simulation results with the experiments allows the method of weak measurement to determine the MOPSHE under the influence of the magnetic field to be validated. MOPSHE under a three-dimensional magnetic field is measured and the measurement error is within 4 μm.