Complex Magnetic Field Research Articles

Finding magnetic north: an extraordinary magnetic field detection in Polaris and first results of a magnetic survey of classical Cepheids

ABSTRACT Classical Cepheids are essential objects in the study of stellar evolution and cosmology; however, we know little about their magnetic properties. We report the detection of Stokes V features interpreted as Zeeman signatures in four classical Cepheids using high-resolution spectropolarimetric observations obtained with ESPaDOnS at the Canada–France–Hawaii Telescope. Eight observations of η Aql were acquired in 2017 covering its 7.2 d pulsation period, and single observations of Polaris, ζ Gem, δ Cep, and RT Aur were obtained in 2020 as part of our ongoing systematic survey. We use mean circular polarization Stokes V profiles generated using the least-squares deconvolution procedure to diagnose Zeeman signatures and measure mean longitudinal field strengths 〈Bz〉. We detect magnetic signatures across all pulsation phases of η Aql (−0.89 ± 0.47 G$\, \lt \langle B_{z}\rangle \lt 1.27\pm 0.40$ G), as well as in the single observations of Polaris (0.59 ± 0.16 G), ζ Gem (0.41 ± 0.16 G), and δ Cep (0.43 ± 0.19 G). The Stokes V profile of Polaris is detected at extremely high signal-to-noise ratio and implies a complex magnetic field topology. It stands in stark contrast to all other detected Stokes V profiles, which show unusual approximately unipolar positive circular polarization lobes analogous to those observed in some Am stars.

Angular dependence of coherent radio emission from magnetars with multipolar magnetic fields

ABSTRACT The recent detection of a fast radio burst (FRB) from a Galactic magnetar secured the fact that neutron stars (NSs) with superstrong magnetic fields are capable of producing these extremely bright coherent radio bursts. One of the leading mechanisms to explain the origin of such coherent radio emission is the curvature radiation process within the dipolar magnetic field structure. It has, however, already been demonstrated that magnetars likely have a more complex magnetic field topology. Here, we critically investigate curvature radio emission in the presence of inclined dipolar and quadrupolar (‘quadrudipolar’) magnetic fields and show that such field structures differ in their angular characteristics from a purely dipolar case. We analytically show that the shape of open field lines can be modified significantly depending on both the ratio of quadrupole to dipole field strength and their inclination angle at the NS surface. This creates multiple points along each magnetic field line that coincide with the observer’s line of sight, and may explain the complex spectral and temporal structure of the observed FRBs. We also find that in quadrudipole, the radio beam can take a wider angular range and the beamwidth can be wider than that in pure dipole. This may explain why the pulse width of the transient radio pulsation from magnetars is as large as that of ordinary radio pulsars.

Photometric signatures of corotating magnetospheres of hot stars governed by higher-order magnetic multipoles

Context. The light curves of magnetic, chemically peculiar stars typically show periodic variability due to surface spots that in most cases can be modeled by low-order harmonic expansion. However, high-precision satellite photometry reveals tiny complex features in the light curves of some of these stars that are difficult to explain as caused by a surface phenomenon under reasonable assumptions. These features might originate from light extinction in corotating magnetospheric clouds supported by a complex magnetic field dominated by higher-order multipoles. Aims. We aim to understand the photometric signatures of corotating magnetospheres that are governed by higher-order multipoles. Methods. We determined the location of magnetospheric clouds from the minima of the effective potential along the magnetic field lines for different orders of multipoles and their combination. From the derived magnetospheric density distribution, we calculated light curves accounting for absorption and subsequent emission of light. Results. For axisymmetric multipoles, the rigidly rotating magnetosphere model is able to explain the observed tiny features in the light curves only when the higher-order multipoles dominate the magnetic field not only at the stellar surface, but even at the Kepler radius. However, even a relatively weak nonaxisymmetric component leads to warping of equilibrium surfaces. This introduces structures that can explain the tiny features observed in the light curves of chemically peculiar stars. The light emission contributes to the light variability only if a significant fraction of light is absorbed in the magnetosphere.

Periodic deformation of semiflexible colloidal chains in eccentric time-varying magnetic fields

Elastic filaments driven out of equilibrium display complex phenomena that involve periodic changes in their shape. Here, the periodic deformation dynamics of semiflexible colloidal chains in an eccentric magnetic field are presented. This field changes both its magnitude and direction with time, leading to novel nonequilibrium chain structures. Deformation into S-, Z-, and 4-mode shapes arises via the propagation and growth of bending waves. Transitions between these morphologies are governed by an interplay among magnetic, viscous, and elastic forces. Furthermore, the periodic behavior leading to these structures is described by four distinct stages of motion that include rotation, arrest, bending, and stretching of the chain. These stages correspond to specific intervals of the eccentric field’s period. A scaling analysis that considers the relative ratio of viscous to magnetic torques via a critical frequency illustrates how to maximize the bending energy. These results provide new insights into controlling colloidal assemblies by applying complex magnetic fields.

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.

Two-Stage Solar Flare Forecasting Based on Convolutional Neural Networks

Solar flares are solar storm events driven by the magnetic field in the solar activity area. Solar flare, often associated with solar proton event or CME, has a negative impact on ratio communication, aviation, and aerospace. Therefore, its forecasting has attracted much attention from the academic community. Due to the limitation of the unbalanced distribution of the observation data, most techniques failed to effectively learn complex magnetic field characteristics, leading to poor forecasting performance. Through the statistical analysis of solar flare magnetic map data observed by SDO/HMI from 2010 to 2019, we find that unsupervised clustering algorithms have high accuracy in identifying the sunspot group in which the positive samples account for the majority. Furthermore, for these identified sunspot groups, the ensemble model that integrates the capability of boosting and convolutional neural network (CNN) achieves high-precision prediction of whether the solar flares will occur in the next 48 hours. Based on the above findings, a two-stage solar flare early warning system is established in this paper. The F1 score of our method is 0.5639, which shows that it is superior to the traditional methods such as logistic regression and support vector machine (SVM).

An Extension of the Vector-Play Model to the Case of Magneto-Elastic Loadings

The influence of mechanical stress on the magnetic hysteretic behavior is modeled through the association of a reversible simplified multiscale approach, and a macroscopic energy-based magnetic hysteresis model in a vector-play form. A phenomenological description of the dissipation parameters under mechanical stress is proposed. The non-monotonic effect of tensile stress on the magnetic permeability is modeled using a second-order development in the magneto-elastic energy. Material parameters for both reversible and irreversible behavior are identified from experimental characterization under mechanical stress performed on a DC04 electrical steel. The experimental tests include anhysteretic and hysteretic measurements. Modeling results of the anhysteretic magnetic permeability, the coercive field, and the remanent induction under several levels of peak magnetic field and uniaxial mechanical stress are satisfactorily compared with those obtained experimentally. The model is shown to reasonably predict the hysteresis losses under tensile and compressive stress, as well as the response of the material under a complex magnetic field waveform with harmonic content.

Investigating coronal wave energy estimates using synthetic non-thermal line widths

Aims. Estimates of coronal wave energy remain uncertain as a large fraction of the energy is likely hidden in the non-thermal line widths of emission lines. In order to estimate these wave energies, many previous studies have considered the root mean squared wave amplitudes to be a factor of $ \sqrt{2} $ greater than the non-thermal line widths. However, other studies have used different factors. To investigate this problem, we consider the relation between wave amplitudes and the non-thermal line widths within a variety of 3D magnetohydrodynamic (MHD) simulations. Methods. We consider the following 3D numerical models: Alfvén waves in a uniform magnetic field, transverse waves in a complex braided magnetic field, and two simulations of coronal heating in an arcade. We applied the forward modelling code FoMo to generate the synthetic emission data required to analyse the non-thermal line widths. Results. Determining a single value for the ratio between the non-thermal line widths and the root mean squared wave amplitudes is not possible across multiple simulations. It was found to depend on a variety of factors, including line-of-sight angles, velocity magnitudes, wave interference, and exposure time. Indeed, some of our models achieved the values claimed in recent articles while other more complex models deviated from these ratios. Conclusions. To estimate wave energies, an appropriate relation between the non-thermal line widths and root mean squared wave amplitudes is required. However, evaluating this ratio to be a singular value, or even providing a lower or upper bound on it, is not realistically possible given its sensitivity to various MHD models and factors. As the ratio between wave amplitudes and non-thermal line widths is not constant across our models, we suggest that this widely used method for estimating wave energy is not robust.

Evolution of Kelvin–Helmholtz Instability in the Fan-spine Topology

Abstract We use multiwavelength imaging observations from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory to study the evolution of the Kelvin–Helmholtz (K–H) instability in a fan-spine magnetic field configuration. This magnetic topology exists near an active region AR12297 and is rooted in a nearby sunspot. In this magnetic configuration, two layers of cool plasma flow in parallel and interact with each other inside an elongated spine. The slower plasma flow (5 km s−1) is the reflected stream along the spine’s field lines from the top, which interacts with the impulsive plasma upflows (114–144 km s−1) from below. This process generates a shear motion and subsequent evolution of the K–H instability. The amplitude and characteristic wavelength of the K–H unstable vortices increase, satisfying the criterion of the fastest-growing mode of this instability. We also describe how the velocity difference between two layers and the velocity of K–H unstable vortices are greater than the Alfvén speed in the second denser layer, which also satisfies the criterion of the growth of the K–H instability. In the presence of the magnetic field and sheared counterstreaming plasma as observed in the fan-spine topology, we estimate the parametric constant Λ ≥ 1, which confirms the dominance of velocity shear and the evolution of the linear phase of the K–H instability. This observation indicates that in the presence of complex magnetic field structuring and flows, the fan-spine configuration may evolve into rapid heating, while the connectivity changes due to the fragmentation via the K–H instability.

Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC + and comparing with simulation

ABSTRACT Optical and infrared polarization mapping and recent Planck observations of the filametary cloud L1495 in Taurus show that the large-scale magnetic field is approximately perpendicular to the long axis of the cloud. We use the HAWC + polarimeter on SOFIA to probe the complex magnetic field in the B211 part of the cloud. Our results reveal a dispersion of polarization angles of 36°, about five times that measured on a larger scale by Planck. Applying the Davis–Chandrasekhar–Fermi (DCF) method with velocity information obtained from Institut de Radioastronomie Millimétrique 30 m C18O(1-0) observations, we find two distinct sub-regions with magnetic field strengths differing by more than a factor 3. The quieter sub-region is magnetically critical and sub-Alfv$\acute{\rm e}$nic; the field is comparable to the average field measured in molecular clumps based on Zeeman observations. The more chaotic, super-Alfv$\acute{\rm e}$nic sub-region shows at least three velocity components, indicating interaction among multiple substructures. Its field is much less than the average Zeeman field in molecular clumps, suggesting that the DCF value of the field there may be an underestimate. Numerical simulation of filamentary cloud formation shows that filamentary substructures can strongly perturb the magnetic field. DCF and true field values in the simulation are compared. Pre-stellar cores are observed in B211 and are seen in our simulation. The appendices give a derivation of the standard DCF method that allows for a dispersion in polarization angles that is not small, present an alternate derivation of the structure function version of the DCF method, and treat fragmentation of filaments.

The magnetic fields and stellar winds of the mature late F-stars: β Virginis and θ Draconis

ABSTRACT Mapping the large-scale magnetic field in late F-type stars is important for understanding the nature of the stellar dynamo and the dynamics of thin outer convection zones. We use Zeeman Doppler Imaging to produce multi-epoch maps of the surface magnetic field for two mature late F-type stars: β Virginis (F9V) and θ Draconis (F8IV). We also provide a magnetohydrodynamic model for the stellar winds from the corona to the inner astrosphere, which exists in an environment at the hot end of habitability for exoplanets. Our results show that either simple or complex dynamo magnetic fields are present in mature late F-type stars, with shallow outer convection zones. The results of stellar wind modelling show the average space weather for β Vir at a distance of 1 au falls within the range of space weather conditions observed at Earth, while θ Dra produces a wind pressure an order of magnitude stronger than the Sun’s wind pressure.

Plasma flux and energy enhancement in BP-HiPIMS discharge via auxiliary anode and solenoidal coil

As an emerging and extraordinary plasma source, the bipolar-pulse high power impulse magnetron sputtering (BP-HiPIMS) has promising prospects and wide industrial applications. In this paper, an effort to optimize the plasma flux and energy in BP-HiPIMS via auxiliary anode and solenoidal coil was made. This novel plasma source contains two types of auxiliary anode voltage (direct current and pulse) and one type of solenoidal coil current (direct current) to synergistically enhance the plasma generation and diffusion by electric field and magnetic field together. Systematic evaluations of discharge characteristics demonstrate that applying auxiliary anode voltage and coil magnetic field effectively contribute to a reduction in delay time of target current onset and increase in peak amplitude of target current, which are beneficial for improving plasma generation and target sputtering. The complex plasma dynamics are diagnosed by Langmuir probe and optical emission spectroscopy, and simulated by particle-in-cell/Monte Carlo collision approach. These comprehensive investigations on plasma parameters demonstrate that the plasma density, emission intensity of the metal ions, substrate current density, and ionization fraction of sputtered target particles have been improved with the increase of coil current. The observations of the increase in excitation temperature T exc of Ar atoms, and more extended high-energy tails in electron energy distribution function curves imply that the plasma can be significantly heated by the auxiliary anode. Combining the simulation results and theoretical model proposed in the last sub-content, the diffusion and transport mechanism of charged-particles in complex electric and magnetic fields are discussed. From the theoretical analysis, the qualitative relation between the plasma density and coil current is well consistent with the measurements of electron density obtained by Langmuir probe. These evidences all support the idea that the plasma flux and energy can be enhanced in BP-HiPIMS discharge via auxiliary anode and solenoidal coil together.

Контроль дефектов в прошедшем через металл импульсном магнитном поле

Experimental dependences U (t) of electric voltage on time t, taken from an induction magnetic head (MG), moving relative to a magnetic carrier (MG) with records of the magnetic fields of defects of an aluminum object, are presented. Contact access to the surface of a metal object, above which there is a layer of air and solid dielectric in an arbitrary proportion and with a total thickness of more than 5 mm, is completely excluded. There is also no access to the rear side of the object, since it is a massive dielectric. The object with MN was exposed to a complex magnetic field pulse with a duration from 1 μs to 200 μs. The studies were carried out in a field that passed through the metal. Raster images of hidden holes with a diameter of 3 mm and 6 mm in layers of aluminum with a thickness of 0.67 mm of samples made up of layers of aluminum of different thickness and separated by layers of dielectric (air) were obtained. The thickness of the metal layers of the samples was 1.96 mm and 2.96 mm. The measurements were carried out in hard-to-reach places of the samples. The algorithm of the developed method was drawn up. The method allows to significantly increase the sensitivity and accuracy of the control of the parameters of defects and to carry out their control of areas of objects where control by other methods is impossible.

Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

Complex and chaotic magnetic fields and the nature of gravity

Complex and chaotic magnetic fields and the nature of gravity

Kink instability of triangular jets in the solar atmosphere

Context. It is known that hydrodynamic triangular jets (i.e. the jet with maximal velocity at its axis, which linearly decreases at both sides) are unstable to anti-symmetric kink perturbations. The inclusion of the magnetic field may lead to the stabilisation of the jets. Jets and complex magnetic fields are ubiquitous in the solar atmosphere, which suggests the possibility of the kink instability in certain cases. Aims. The aim of the paper is to study the kink instability of triangular jets sandwiched between magnetic tubes (or slabs) and its possible connection to observed properties of the jets in the solar atmosphere. Methods. A dispersion equation governing the kink perturbations is obtained through matching of analytical solutions at the jet boundaries. The equation is solved analytically and numerically for different parameters of jets and surrounding plasma. The analytical solution is accompanied by a numerical simulation of fully non-linear magnetohydrodynamic (MHD) equations for a particular situation of solar type II spicules. Results. Magnetohydrodynamic triangular jets are unstable to the dynamic kink instability depending on the Alfvén Mach number (the ratio of flow to Alfvén speeds) and the ratio of internal and external densities. When the jet has the same density as the surrounding plasma, only super-Alfvénic flows are unstable. However, denser jets are also unstable in a sub-Alfvénic regime. Jets with an angle to the ambient magnetic field have much lower thresholds of instability than field-aligned flows. Growth times of the kink instability are estimated to be 6−15 min for type I spicules and 5−60 s for type II spicules matching with their observed lifetimes. The numerical simulation of full non-linear equations shows that the transverse kink pulse locally destroys the jet in less than a minute in type II spicule conditions. Conclusions. Dynamic kink instability may lead to the full breakdown of MHD flows and consequently to an observed disappearance of spicules.

Super-eddington emission from accreting, highly magnetized neutron stars with a multipolar magnetic field

ABSTRACT Pulsating ultraluminous X-ray sources (PULXs) are characterized by an extremely large luminosity (>1040 erg s−1). While there is a general consensus that they host an accreting, magnetized neutron star (NS), the problem of how to produce luminosities >100 times the Eddington limit, LE, of a solar mass object is still debated. A promising explanation relies on the reduction of the opacities in the presence of a strong magnetic field, which allows for the local flux to be much larger than the Eddington flux. However, avoiding the onset of the propeller effect may be a serious problem. Here, we reconsider the problem of column accretion on to a highly magnetized NS, extending previously published calculations by relaxing the assumption of a pure dipolar field and allowing for more complex magnetic field topologies. We find that the maximum luminosity is determined primarily by the magnetic field strength near the NS surface. We also investigate other factors determining the accretion column geometry and the emergent luminosity, such as the assumptions on the parameters governing the accretion flow at the disc–magnetosphere boundary. We conclude that a strongly magnetized NS with a dipole component of ∼1013 G, octupole component of ∼1014 G, and spin period ∼1 s can produce a luminosity of ∼1041 erg s−1 while avoiding the propeller regime. We apply our model to two PULXs, NGC 5907 ULX-1, and NGC 7793 P13, and discuss how their luminosity and spin period rate can be explained in terms of different configurations, either with or without multipolar magnetic components.

Eccentricity fault detection in brushless doubly fed induction machines

A new fault diagnosis method for detecting the rotor eccentricity faults including static, dynamic and mixed eccentricity is proposed for brushless doubly-fed induction machines (BDFIMs). BDFIMs are attractive alternatives for the conventional doubly-fed induction generator (DFIG) for offshore wind power generation; therefore, paying attention to their fault detection is essential. Existing fault detection methods for conventional induction machines cannot be directly applied to the BDFIM due to its special rotor structure and stator winding configurations as well as complex magnetic field patterns. This article proposes a novel fault detection method based on motor current signal analysis to determine stator current harmonics, induced by the nested-loop rotor slot harmonics (NRSHs), as fault indices. The analysis is performed under healthy conditions and with different types of rotor eccentricity. Finally, a sensitivity analysis is carried out to confirm the practicability of the proposed technique with various fault intensities and load conditions. Analytical winding function approach, finite element analysis and experimental tests on a prototype D180 BDFIM are used in this study to validate the proposed fault detection technique.

Development of an M6.4 Circular Solar Flare According to the Observations in the Нα Line

The development of the 3N/M6.4 flare on July 19, 2000, in the active region NOAA 9087 was studied based on the analysis of its images in the Нα line. Нα filtergrams obtained at the Meudon Observatory were used. The flare-active region NOAA 9087 had a complex multipolar magnetic field structure. The flare of 3N/M6.4 class began with the appearance of two bright kernels near a large spot. A few minutes later, flare kernels appeared in the central part of the active region, where a coronal source of hard X-ray radiation was identified. The flare lasted 2.5 h. Its energy was released sequentially in different places of the active region. The flare kernels were located along the polarity inversion line at the boundaries of the chromospheric cells. The flare ribbons had a circular shape. An assumption is made about the magnetic topology of the fan-spine type containing a null point. In this case, flare ribbons are the intersections of the fan quasi-separatrix layer with the lower atmosphere. The successive appearance of flare kernels may indicate a slipping magnetic reconnection in the flare. The Нα images in the main phase of the flare show reconnecting loops in the eastern part of the active region that are clearly visible in the ultraviolet wavelength range.

Automatic Shimming Method Using Compensation of Magnetic Susceptibilities and Adaptive Simplex for Low-Field NMR

During the past several decades, inexpensive compact nuclear magnetic resonance (NMR) instruments have been widely used for on-site detections of chemical identity and sample analyses in industrial applications. In general, via shim coils and control strategies, automatic search shimming methods are capable of improving the magnetic field uniformity so that optimized signals can be acquired and particularly suited for rapid detections in compact NMR instruments. However, because these methods inherently endure the inefficiency in multidimensional shims and the sensitivity of starting points, it is time-consuming to obtain acceptable results in a field infected with distortions and strays. Here, two remedies that improve the shimming speed for the search shimming method are proposed. First, analyzing and compensating for magnetic susceptibility effects, we relocate starting points closely to optima and reduce the complexity of global exploration. Second, modifying the simplex movement with adaptive scale factors and gradient-like centroid, we have improved the convergence of the simplex shimming algorithm in a multidimensional search space. Via theoretical analyses and lab experiments, we find that the proposed shimming method outperforms regular shimming methods in terms of handling complex magnetic fields and reducing shimming times and hope that our study can help further improve NMR shimming methods in the future.