Three-dimensional Magnetic Field Research Articles

Growth of a filament channel by intermittent small-scale magnetic reconnection

Context. A filament channel (FC), a plasma volume where the magnetic field is primarily aligned with the polarity inversion line, is believed to be the pre-eruptive configuration of coronal mass ejections. Nevertheless, evidence for how the FC is formed is still elusive. Aims. In this paper, we present a detailed study of the build-up of a FC in order to understand its formation mechanism. Methods. The New Vacuum Solar Telescope (NVST) of the Yunnan Observatory and the Optical and Near-infrared Solar Eruption Tracer (ONSET) of Nanjing University, as well as the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), are used to study the growth process of the FC. Furthermore, we reconstruct the nonlinear force-free field (NLFFF) of the active region using the regularized Biot-Savart laws (RBSL) and the magnetofrictional method to reveal the three-dimensional (3D) magnetic field properties of the FC. Results. We find that partial filament materials are quickly transferred to longer magnetic field lines formed by small-scale magnetic reconnection, as evidenced by dot-like Hα and extreme ultraviolet (EUV) brightenings and subsequent bidirectional outflow jets, as well as untwisting motions. The Hα and EUV bursts appear repeatedly at the same location and are closely associated with flux cancelation, which occurs between two small-scale opposite polarities and is driven by shearing and converging motions. The 3D NLFFF model reveals that the reconnection takes place in a hyperbolic flux tube that is located above the flux-cancelation site and below the FC. Conclusions. The FC is gradually built up toward a twisted flux rope via a series of small-scale reconnection events that occur intermittently prior to the eruption.

Uniform Circular-Array-Based Borehole Pulsed Eddy-Current System for Asymmetry Defect Inspection in Downhole Casings

The inspection of wellbore casings has been extensively investigated owing to the increasing concern for safety in oil and gas production. However, efficient techniques for inspecting asymmetry defects have not been achieved. In this study, we developed a uniform circular array (UCA) to address the problem of borehole pulsed eddy current (PEC) techniques for asymmetry defect inspection in downhole casings. Based on the borehole PEC system model, the UCA developed with multiple independent probes was designed to achieve asymmetry defect inspection, and the three-dimensional magnetic field data of borehole depths, circumferential azimuths, and sampling times could be obtained. Furthermore, a multichannel data acquisition circuit, which guarantees downhole operation at 150 °C, was developed for the synthesized UCA. Using azimuth dimension information from the synthesized UCA at a certain borehole depth, we obtained an inspection approach for the width and penetration depth of asymmetry defects in the circumferential and radial directions, respectively. Simulations and field experiments were conducted, and the results demonstrate the effectiveness of the proposed method in inspecting asymmetry defects.

A three-dimensional magnetic field sensor based on a single spin–orbit-torque device via domain nucleation

Detecting a three-dimensional (3D) magnetic field by a compact and simple structure or device has always been a challenging work. The recent discovery of 3D magnetic field sensing through the single spin–orbit torque device consisting of the Ta/CoFeB/MgO heterostructure, based on the domain wall motion, offers a revolutionary way to tackle this problem. Here, we demonstrate a 3D magnetic field sensor based on the W/CoFeB/MgO heterostructure via domain nucleation dominated magnetization reversal. In such a heterostructure, the in-plane (IP) and out-of-plane (OOP) magnetic field components drive the grains reversal with different manners, enabling the distinguishment of the contributions from IP and OOP components. The linear modulations of anomalous Hall resistance by x, y, and z components of magnetic fields have been obtained, respectively, with the same linear range of −20 to +20 Oe for each component. Typically, a higher linearity is realized in this work compared with the previous domain wall motion based sensor, which is a critical characteristic for the magnetic field sensor.

A New Three-Dimensional Empirical Reconstruction Model Using a Stochastic Optimization Method

Motivated by MMS mission observations near magnetic reconnection sites, we have developed a new empirical reconstruction (ER) model of the three-dimensional (3D) magnetic field and the associated plasma currents. Our approach combines both the measurements from a constellation of satellites and a set of physics-based equations as physical constraints to build spatially smooth distributions. This ER model directly minimizes the loss function that characterizes the model-measurement differences and the model departures from linear or nonlinear physical constraints using an efficient stochastic optimization method by which the effects of random measurement errors can be effectively included. Depending on the availability of the measured parameters and the adopted physical constraints on the reconstructed fields, the ER model could be either slightly over-determined or under-determined, yielding nearly identical reconstructed fields when solved by the stochastic optimization method. As a result, the ER model remains valid and operational even if the input measurements are incomplete. Two sets of new indices associated respectively with the model-measurement differences and the model departures are introduced to objectively measure the accuracy and quality of the reconstructed fields. While applying the reconstruction model to observations of an electron diffusion region (EDR) observed by NASA’s Magnetospheric Multiscale (MMS) mission, we examine the relative contributions of the errors in the plasma current density arising from random measurement errors and linear approximations made in application of the curlometer technique. It was found that the errors in the plasma current density calculated directly from the measured magnetic fields using a linear approximation were mostly contributed from the nonlinear configuration of the 3D magnetic fields.

An Electric-field-driven Global Coronal Magnetohydrodynamics Simulation Model Using Helioseismic and Magnetic Imager Vector-magnetic-field Synoptic Map Data

We present the simulation methodology and results of our new data-driven global coronal magnetohydrodynamics (MHD) simulation model. In this model, the solar-surface electric field is first calculated such that the curl will satisfy both the induction equation and the given temporal variations of the solar-surface magnetic field. We use the synoptic maps of the Helioseismic and Magnetic Imager three-component vector-magnetic-field data to specify the solar-surface magnetic-field vector for a period from Carrington Rotations (CRs) 2106 to 2110. A set of whole-Sun three-component electric-field maps are obtained for each CR transition interval of about 27.3 days. Using the inverted electric field as the driving variable, our new global coronal MHD model, with the angular resolution of π/64, can trace the evolution of the three-dimensional coronal magnetic field that matches the specified time-dependent solar-surface magnetic-field maps and simultaneously satisfies the divergence-free condition. A set of additional boundary treatments are introduced to control the contribution of the horizontal components of the magnetic field at the weak-field regions. The strength of the solar-surface magnetic field is limited to 20 Gauss for the sake of computational stability in this study. With these numerical treatments, the nonpotential coronal features, such as twisted loop structures, and their eruptive outward motions are obtained. This present model, capable of introducing three-component solar-surface magnetic-field observation data to coronal MHD simulations, is our first step toward a better model framework for the solar corona and hence solar wind.

Eruptivity Criteria for Two-Dimensional Magnetic Flux Ropes in the Solar Corona

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index.

A new dimension for magnetosensitive e-skins: active matrix integrated micro-origami sensor arrays

Magnetic sensors are widely used in our daily life for assessing the position and orientation of objects. Recently, the magnetic sensing modality has been introduced to electronic skins (e-skins), enabling remote perception of moving objects. However, the integration density of magnetic sensors is limited and the vector properties of the magnetic field cannot be fully explored since the sensors can only perceive field components in one or two dimensions. Here, we report an approach to fabricate high-density integrated active matrix magnetic sensor with three-dimensional (3D) magnetic vector field sensing capability. The 3D magnetic sensor is composed of an array of self-assembled micro-origami cubic architectures with biased anisotropic magnetoresistance (AMR) sensors manufactured in a wafer-scale process. Integrating the 3D magnetic sensors into an e-skin with embedded magnetic hairs enables real-time multidirectional tactile perception. We demonstrate a versatile approach for the fabrication of active matrix integrated 3D sensor arrays using micro-origami and pave the way for new electronic devices relying on the autonomous rearrangement of functional elements in space.

High-throughput precise particle transport at single-particle resolution in a three-dimensional magnetic field for highly sensitive bio-detection

Precise manipulation of microparticles have fundamental applications in the fields of lab-on-a-chip and biomedical engineering. Here, for the first time, we propose a fully operational microfluidic chip equipped with thin magnetic films composed of straight tracks and bends which precisely transports numerous single-particles in the size range of ~ 2.8–20 µm simultaneously, to certain points, synced with the general external three-axial magnetic field. The uniqueness of this design arises from the introduced vertical bias field that provides a repulsion force between the particles and prevents unwanted particle cluster formation, which is a challenge in devices operating in two-dimensional fields. Furthermore, the chip operates as an accurate sensor and detects low levels of proteins and DNA fragments, being captured by the ligand-functionalized magnetic beads, while lowering the background noise by excluding the unwanted bead pairs seen in the previous works. The image-processing detection method in this work allows detection at the single-pair resolution, increasing the sensitivity. The proposed device offers high-throughput particle transport and ultra-sensitive bio-detection in a highly parallel manner at single-particle resolution. It can also operate as a robust single-cell analysis platform for manipulating magnetized single-cells and assembling them in large arrays, with important applications in biology.

Toroidal modeling of runaway electron loss due to 3D fields in ITER

Mitigation of runaway electrons (REs) by three-dimensional (3D) magnetic field perturbations is numerically investigated for the ITER 15 MA baseline D–T scenario, utilizing the MARS-F code (Liu et al Phys. Plasmas 7 3681) with a drift orbit test particle tracing module. Considered are two types of 3D fields: the n = 3 (n is the toroidal mode number) resonant magnetic perturbation (RMP) utilized for the purpose of controlling the edge localized modes in ITER, and perturbations generated by the n = 1 magneto-hydrodynamic (MHD) instabilities in a post-disruption plasma. The RMP field, applied to a pre-disruption plasma, is found to be moderately effective in mitigating the RE seeds in ITER when vacuum field model is assumed. Up to ∼40% loss fraction is possible at 90 kA-turn coil current. The mitigation efficiency is however substantially reduced, down to less than 5%, when the plasma response is taken into account. This is due to strong screening of the resonant magnetic field components by the plasma response resulting in much less field line stochasticity. On the other hand, the MARS-F modeling, based on the DINA-simulated post-disruption equilibria, shows that the n = 1 resistive kink instabilities develop in these plasmas, as the edge safety factor q a evolves and drops below integer numbers. RE mitigation by these MHD instabilities is sensitive to the eigenmode structure. The best mitigation is achieved as q a drops below 3, when a global kink instability occurs that encompasses both internal and external components. This global instability is found to be capable of mitigating over 80% MeV-level passing RE orbits at a field perturbation |δB|/B 0 that is comparable to that observed in DIII-D experiments, and full mitigation if the perturbation amplitude is doubled. The ‘wetted’ area on the ITER limiting surface, due to MHD instability induced RE loss, generally increases with the perturbation amplitude (together with increasing loss fraction). At the highest perturbation level assumed in this study, the wetted area reaches ∼60% of the total limiting surface area. The lost RE orbits mainly strike the outer divertor region of the limiting surface, with some fraction also hitting a wide area along the inboard side of the surface.

Loss of energetic particles due to resistive wall mode instability in ITER

Effects of an unstable n = 1 (n is the toroidal mode number) resistive wall mode (RWM) on the energetic particle (EP) confinement and loss are numerically investigated, for an ITER steady state scenario with 10 MA plasma current and 5.3 T toroidal field. The eigenfunction of the RWM is computed, with the associated three-dimensional magnetic field perturbation superposed with the 2D equilibrium field for tracing the EP drift orbits. Considered are mono-energetic EPs at 0.5 MeV and 1 MeV for deuterium ions, and 3.5 MeV for fusion-born alphas, with a range of distribution in the particle pitch angle. Modeling finds that less than 20% of EPs can be lost to the limiting surface in ITER assuming a source distribution uniform in minor radius, due to an unstable RWM that produces 100 Gauss poloidal field perturbation at the outboard mid-plane just inside the (effective) resistive wall surface. On top of the initial prompt drift orbit loss for counter-current EPs, the RWM induced particle loss occurs on a one second time scale, which is comparable to the RWM growth time in ITER. The ‘wetted’ area, due to the lost EPs striking the limiting surface, is generally found to be large due to the RWM. This is a favorable prediction for ITER. The loss distribution in the poloidal angle is more uniform for co-current EPs. Counter-current EPs experience outward orbit drift when launched from the low-field side, and tend to more often hit the bottom region of the limiting surface.

Testing the Linearity of Vector Fields in Cold and Dense Space Plasmas

Linearization of the vector field, as a common multispacecraft data analysis technique, has been widely used in (1) reconstruction of three-dimensional magnetic and velocity fields, (2) predictions of the possible topologies of linear fields, especially for the magnetic null-point classification, and (3) other data analysis techniques, such as the curlometer technique. However, the length scale of validity of the linear approximation in space plasmas is still an open question. In this study, we utilize the frozen-in condition as the criterion to estimate the accuracy of the linear method. We derive the linearization error theoretically, and find that the frozen-in condition cannot be satisfied everywhere in the linearly reconstructed fields as long as the fields have nonzero spatial gradients. This indicates that the use of the linear method must be treated with caution. We further investigate the length scale of validity of the linear method in space plasmas by utilizing the Magnetospheric Multiscale Mission data. Through two case studies and statistical analysis, we demonstrate that the linear approximation is acceptable at a length scale of, on average, 1.1 ion inertial lengths in the solar wind/magnetosheath, while in the magnetosphere the linear method exhibits great uncertainties. This study provides the theoretical basis for the application of the linear method in space plasmas.

Orion A’s complete 3D magnetic field morphology

Magnetic fields permeate the interstellar medium and are important in the star formation process. Determining the three-dimensional (3D) magnetic fields of molecular clouds will allow us to better understand their role in the evolution of these clouds and the formation of stars. We fully reconstruct the approximate 3D magnetic field morphology of the Orion A molecular cloud (on scales of a few to ∼100 pc) using Galactic magnetic field models, as well as available line-of-sight and plane-of-sky magnetic field observations. While previous studies identified the 3D magnetic field morphology of the Orion A cloud as an arc shape, in this study we provide the orientation of this arc-shaped field and its plane-of-sky direction for the first time. We find that this 3D field is a tilted, semi-convex (from our point of view) structure and mostly points in the direction of decreasing latitude and longitude on the plane of the sky from our vantage point. The previously identified bubbles and events in this region were key in shaping this arc-shaped magnetic field morphology.

Magnet system design for the new 18 GHz ECR ion source at GSI

In order to increase intensities and charge states of available ion species, a new room-temperature ECR Ion Source (ECRIS) operating at 18 GHz is currently under development at GSI. The new ECRIS is based on a Heavy Ion Ion Source Injector (HIISI), developed at the Department of Physics, University of Jyvüskyla (JYFL), and features three normal conducting coils and a permanent magnet hexapole for plasma confinement. The latter has to be installed inside a refrigerated hexapole chamber, allowing to achieve the required radial confining field and avoiding demagnetization of permanent magnets. Computer simulations are carried out with Opera software package for two Halbach hexapole arrangements and the resulting three-dimensional magnetic fields are compared. The demagnetization of permanent magnets due to the superposition of fields generated by the coils and the hexapole is also simulated for both arrangements.

Quantitative evaluation of defects based on the characteristics of the induced eddy current field

A quantitative evaluation method for determining the shape, length and depth of surface defects is proposed for the purpose of non-destructive testing (NDT) and evaluation of metal materials. The COMSOL Multiphysics finite element software is used to calculate and analyse the eddy current magnetic field and the influence of the geometric parameters of defects on the spatial three-dimensional magnetic field distributions are studied. The results show that the shape of the surface defect can be judged from the measurement result of the x-Bx curve. The quantitative analysis of the crack length is realised according to the corresponding position of the peak (trough) of surface magnetic field Bz . The depth of the crack can be inversely calculated by the quantitative relationship between the trough depth of Bx (or the peak value of Bz) and the crack depth. Therefore, this method provides convenient and contactless detection technology in which the characteristic quantities corresponding to the defect parameters are independent from each other to improve the accuracy of defect evaluation.

Coronal magnetic field evolution over cycle 24

Context. The photospheric magnetic field vector is continuously derived from measurements, while reconstruction of the three-dimensional (3D) coronal magnetic field requires modelling with photospheric measurements as a boundary condition. For decades, the cycle variation of the magnetic field in the photosphere has been investigated. Until now, there has been no study of the evolution of the coronal magnetic flux in the corona or of the evolution of solar cycle magnetic free energy. Aims. The aim of this paper is to analyze the temporal variation of the magnetic field and free magnetic energy in the solar corona for solar cycle 24 and the behavior of the magnetic field in the two hemispheres. We want to investigate whether or not we can obtain better estimates of the magnetic field at Earth using the nonlinear force-free field extrapolation method. Methods. To model the magnetic field over cycle 24 we apply the nonlinear force-free field (NLFFF) optimization method to the entire set of the synoptic vector magnetic maps derived from observations made using the Heliospheric and Magnetic Imager (HMI) on board Solar Dynamic Observatory (SDO). Results. From our results, we find that during solar cycle 24, the maximum of the Sun’s dynamics is different than the sunspot number (SSN) maximum peak. The major contribution to the total unsigned flux is provided by the flux coming from the magnetic field structures other than sunspots (MSOS) within latitudes of −30° and +30°. The magnetic flux variation during solar cycle 24 shows a different evolution in the corona than in the photosphere. We find a correlation value of 0.8 between the derived magnetic energy from our model and the flare energy index derived from observations. On average, cycle 24 had a higher number of sunspots in the northern hemisphere (NH) but stronger flux in the southern hemisphere (SH) which could more effectively reach the higher layers of the atmosphere. The coupling between the hemispheres increases with height. The strongest asymmetries in the unsigned magnetic flux are between the two SSN peaks.

Anomalous magnetic interference of cross-type Josephson junctions exposed to oblique magnetic fields

Gauge-invariant phase difference and critical currents of cross-type Josephson junctions with thin and narrow superconducting strips exposed to three-dimensional magnetic fields are theoretically investigated. When a sandwich-type Josephson junction in the xy plane is exposed to parallel magnetic fields H x and H y , the phase difference linearly depends on the spatial coordinates, x and y, and the critical currents exhibit the standard Fraunhofer-type magnetic interference. The perpendicular field H z , on the other hand, nonlinearly modulates the distribution of the phase difference and the critical currents as the functions of the oblique field exhibit anomalous magnetic interference. We obtain simple analytical expressions for critical currents of small cross-type junctions by neglecting the effects of self-field and trapped vortices. The resulting dc critical currents show anomalous and diverse interference patterns depending on the parallel and perpendicular magnetic fields.

An Analytical Method for Calculating the Cogging Torque of a Consequent Pole Hybrid Excitation Synchronous Machine Based on Spatial 3D Field Simplification

Consequent pole hybrid excitation synchronous (CPHES) machines have the advantage of symmetrical bidirectional magnetomotive force increments. Compared with a traditional hybrid excitation motor (HEM), a CPHES machine improves the disadvantage of asymmetry in the adjustment range when magnetization and demagnetization occur. The calculation and analysis of the cogging torque of the CPHES machine are complex due to the complicated structure. This paper proposes an analytical method for calculating the cogging torque of a CPHES machine. This analytical method converts the complex three-dimensional magnetic field problem into a two-dimensional magnetic circuit problem and, through the accumulation method, can quickly and accurately calculate the cogging torque of the CPHES machine. In contrast with the finite element method, the calculation results basically follow each other, but the analytical method is more efficient and omits complicated meshing. This is of great significance to the preliminary electromagnetic design and performance optimization of a CPHES machine.

ЗНИЖЕННЯ РІВНЯ МАГНІТНОГО ПОЛЯ ПІДЗЕМНОЇ КАБЕЛЬНОЇ ЛІНІЇ НА ВІДПОВІДАЛЬНИХ ДІЛЯНКАХ ЗА ДОПОМОГОЮ КОМПОЗИЦІЙНИХ МАГНІТНИХ ЕКРАНІВ КІНЦЕВОЇ ДОВЖИНИ

In the article, the numerical calculation and analysis of three-dimensional magnetic field of underground power cable line with finite-length magnetic shields used to reduce the level of this field on the ground are carried out. Both fill-up soil and filling soil containing magnetic particles and then having effective magnetic properties (=1÷1000) are proposed to used as magnetic shields. The shielding efficiency is studied for underground 330 kV cable line depending on the dimensions and effective magnetic permeability () of the shields. As shown, the use of filling soil with magnetic properties gives a possibility to reduce the field on the ground five times. This type of shielding is more efficient as compared to magnetic fill-up soil. The computed results reveal the non-monotonic variation of magnetic field on the ground above the soil edge zones. The longitudinal size of these zones is in the order of the depth of the cables. References 16, figures 9.

Numerical evaluation of the ferrofluid behaviour under the influence of three-dimensional non-uniform magnetic field

Ferrofluids have always been the centre of interest for a broad range of applications where the flow manipulation is achieved using different types of magnetic fields. In the present work, a Finite Volume Method based numerical study is performed to investigate the ferrofluid behaviour in the laminar flow regime using the complete set of Ferrohydrodynamics equations. Four distinct single layer finite solenoids of different Ls/Ds (length to diameter ratio) are considered to replicate a 3D (three-dimensional) non-uniform magnetic field, and a twofold validation is also reported to authenticate the generated field distributions. Moreover, a magnetic field dependent viscosity model is used to take into account the variation of ferrofluid viscosity in the presence of a non-uniform magnetic field. To accommodate the varying particle size distribution of ferrofluid, an effective relaxation time constant is used that can accurately predict the magnetization using Debye relaxation mechanism. The obtained flow characteristics are then further discussed and compared along with the case of stationary ferrofluid for all solenoid configurations. New insights about the flow structures are provided using the λ2 criteria of vortex identification technique and the critical point theory analysis. It is observed that each solenoid arrangement have a distinct magnetic field distribution which leads to the occurrence of unique vortex structures and fluid deformations. Also, different flow trajectories are noticed within the fluid domain owing to the peculiar distribution of Kelvin force density. Results from the present work have direct implications in all ferrofluid based momentum transport devices and can be effectively used to further improve our understanding about their performances.

Tracing the large-scale magnetic field morphology in protoplanetary disks using molecular line polarization

Context. Magnetic fields are fundamental to the accretion dynamics of protoplanetary disks and they likely affect planet formation. Typical methods to study the magnetic field morphology observe the polarization of dust or spectral lines. However, it has recently become clear that dust-polarization in ALMA’s (Atacama Large (sub)Millimeter Array) spectral regime does not always faithfully trace the magnetic field structure of protoplanetary disks, which leaves spectral line polarization as a promising method for mapping the magnetic field morphologies of such sources. Aims. We aim to model the emergent polarization of different molecular lines in the ALMA wavelength regime that are excited in protoplanetary disks. We explore a variety of disk models and molecules to identify those properties that are conducive to the emergence of polarization in spectral lines and may therefore be viably used for magnetic field measurements in protoplanetary disks. Methods. We used POlarized Radiative Transfer Adapted to Lines in conjunction with the Line Emission Modeling Engine. Together, they allowed us to treat the polarized line radiative transfer of complex three-dimensional physical and magnetic field structures. Results. We present simulations of the emergence of spectral line polarization of different molecules and molecular transitions in the ALMA wavelength regime. We find that molecules that thermalize at high densities, such as HCN, are also the most susceptible to polarization. We find that such molecules are expected to be significantly polarized in protoplanetary disks, while molecules that thermalize at low densities, such as CO, are only significantly polarized in the outer disk regions. We present the simulated polarization maps at a range of inclinations and magnetic field morphologies, and we comment on the observational feasibility of ALMA linear polarization observations of protoplanetary disks. Conclusions. We conclude that those molecules with strong dipole moments and relatively low collision rates are most useful for magnetic field observations through line polarization measurements in high density regions such as protoplanetary disks.