Magnetic Field Model Research Articles

Cosmic ray cutoff rigidity governing by solar wind and magnetosphere parameters during the 2017 Sep 6–9 solar-terrestrial event

For the 2017 Sep 6–9 geomagnetic disturbance, we calculated (within the Tsyganenko magnetospheric magnetic field model Ts01) the cosmic ray (CR) geomagnetic cutoff threshold rigidities. We also compared those values with the calculation results obtained from ground-based observations at the global network of neutron monitors (GNNM) through the spectrographic global survey (SGS). Shown is a satisfactory correlation between the geomagnetic cutoff threshold rigidity variations obtained based on the Ts01 model and those obtained from the GNNM ground-based observations. An intercorrelation of the CR geomagnetic threshold variations with the parameters for geomagnetic activity, for solar wind, and for the interplanetary magnetic field (IMF) was established to be different at different stages of the magnetospheric-geomagnetic disturbance. This is because such an intercorrelation is caused by the dynamics of current systems, whose intensifying and damping occur differently over different time intervals. During the storm main phase, the geomagnetic cutoff rigidity threshold variation is shown to be governed, mainly, by the Dst and by the solar wind velocity, as well as by the IMF southern component and by the electric field azimuth component.

Implications of Different Solar Photospheric Flux-transport Models for Global Coronal and Heliospheric Modeling

The concept of surface-flux transport (SFT) is commonly used in evolving models of the large-scale solar surface magnetic field. These photospheric models are used to determine the large-scale structure of the overlying coronal magnetic field, as well as to make predictions about the fields and flows that structure the solar wind. We compare predictions from two SFT models for the solar wind, open magnetic field footpoints, and the presence of coronal magnetic null points throughout various phases of a solar activity cycle, focusing on the months of April in even-numbered years between 2012 and 2020, inclusively. We find that there is a solar-cycle dependence to each of the metrics considered, but there is not a single phase of the cycle in which all the metrics indicate good agreement between the models. The metrics also reveal large, transient differences between the models when a new active region is rotating into the assimilation window. The evolution of the surface flux is governed by a combination of large-scale flows and comparatively small-scale motions associated with convection. Because the latter flows evolve rapidly, there are intervals during which their impact on the surface flux can only be characterized in a statistical sense, thus their impact is modeled by introducing a random evolution that reproduces the typical surface flux evolution. We find that the differences between the predicted properties are dominated by differences in the model assumptions and implementation, rather than the selection of a particular realization of the random evolution.

Revealing the Interior Structure of Icy Moons with a Bayesian Approach to Magnetic Induction Measurements

Some icy moons and small bodies in the solar system are believed to host subsurface liquid water oceans. The interaction of these saline, electrically conductive oceans with time-varying external magnetic fields generates induced magnetic fields. Magnetometry observations of these induced fields in turn enable the detection and characterization of these oceans. We present a framework for characterizing the interiors of icy moons using multifrequency induction and Bayesian inference applied to magnetometry measurements anticipated from the upcoming Europa Clipper mission. Using simulated data from the Europa Clipper Magnetometer, our approach can accurately retrieve a wide range of plausible internal structures for Europa. In particular, the ocean conductivity is recovered to within ±50% for all internal structure scenarios considered, and the ocean thickness can be retrieved to within ±25 km for five out of seven scenarios. Characterization of the ice shell thickness to ±50% is possible for six of seven scenarios. Our recovery of the ice shell thickness is highly contingent on accurate modeling of magnetic fields arising from the interaction of Europa with the ambient magnetospheric plasma, while the ocean thickness is more modestly affected and the ocean conductivity retrieval is largely unchanged. Furthermore, we find that the addition of a priori constraints (e.g., static gravity measurements) can yield improved ocean characterization compared to magnetometry alone, suggesting that multi-instrument techniques can play a key role in revealing the interiors of Europa and other ocean worlds.

The Initiation and Back-reaction of the X5.4 Flare on 2012 March 7

In this paper, we study the evolution of the X5.4 flare (SOL2012-03-07T00:02) in NOAA Active Region 11429, focusing on its initiation mechanisms and back-reaction effects. To help our study, three-dimensional (3D) coronal magnetic field models are extrapolated from the photospheric magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory under the assumptions of nonlinear force-free field (NLFFF) and non-force-free field (non-FFF). We investigate the 3D magnetic structure and MHD kink instability, torus instability, and double-arc instability (DAI), and find that this flare is most likely triggered by the tether-cutting reconnection and the subsequent DAI. For the back-reactions of the flare, both NLFFF and non-FFF models clearly show an increase in horizontal magnetic field (B h ) and a decrease in inclination angle (ϕ) of the magnetic field near the polarity inversion line, from the photosphere up to a certain height (5 Mm and 8 Mm for non-FFF and NLFFF, respectively). In addition, the non-FFF model shows an enhancement of the downward Lorentz force acting on the photosphere, and the location of the enhancement spatially coincides with the location of the flare onset. The observed back-reaction is likely a consequence of magnetic reconnection.

Reducing plasma shielding effect for improved nanosecond laser drilling of copper with applied direct current

Laser drilling of copper faces challenges due to its high reflectivity and high thermal conductivity of the laser beam. To enhance laser drilling efficiency and hole surface quality, the copper substrate was applied with a direct current (DC) during a 355 nm nanosecond laser drilling process. It was found that introduction of the DC current played a noticeable role in reducing the entrance hole diameter, increasing the depth of the blind hole, decreasing the taper angle, improving the inner surface finish, and enhancing the hole integrity with less amount of debris at the hole exit. Explanation of the processing mechanism is provided by investigation effects of key processing parameters and modeling of DC current-induced magnetic field on the laser-induced plasma. The applied DC current through the copper substrate during laser drilling generated an induced magnetic field and the Lorentz force of the induced magnetic field limited the expansion of the laser-induced plasma in the direction parallel to the laser beam, which weakened the shielding effect of the plasma and thus improved the processing efficiency and hole quality of the nanosecond laser drilling. The study results may open a new path for efficient and high quality laser machining of reflective, high thermal and electrical conductive materials.

Magnetic Inversion and Regional Tectonics of the Dabie Orogen

Physical property inversion techniques are the methods to reveal the internal structures of Earth’s lithosphere. In this study, we introduce an Occam-type inversion algorithm into a spherical coordinate system, and invert the magnetization based on the three-component magnetic anomalies. The synthetic model tests show that the inversion effects of the vertical components are relatively stable, while the anti-noise ability is strong. We apply the algorithm to a set of vertical component anomalies derived from the satellite magnetic field model and obtain Dabie orogen 3D magnetization distribution. Multiple magnetic sources are identified within the orogen and adjacent areas, and the related tectonic evolution processes are analyzed. The significant magnetization characteristics of the orogen can be associated with mantle upwelling caused by the Early Cretaceous lithospheric delamination, along with the partial melting of the mafic–ultramafic lower crust that had not participated in the delamination. The magnetic sources near the Mozitan–Xiaotian fault, and those located in the western Dabie area, are also restricted by Mesozoic and Jurassic–Cretaceous deep melt activities, respectively. The study provides evidence for the suture line position of the plate subduction in the deep lithosphere. Furthermore, the results display certain indications of mineralization activities in the middle–lower Yangtze Valley metallogenic belt.

Optimization of the Wire Diameter Based on the Analytical Model of the Mean Magnetic Field for a Magnetically Driven Actuator

A magnetic field induced by an electromagnetic coil is the key variable that determines the performance of a magnetically driven actuator. The applicability of the empirical models of the coil turns, static resistance, and inductance were discussed. Then, the model of the mean magnetic field induced by the coil was established analytically. Based on the proposed model, the sinusoidal response and square-wave response were calculated with the wire diameter as the decision variable. The amplitude and phase lag of the sinusoidal response, the time-domain response, steady-state value, and the response time of the square-wave response were discussed under different wire diameters. From the experimental and computational results, the model was verified as the relative errors were acceptably low in computing various responses and characteristic variables. Additionally, the optimization on the wire diameter was carried out for the optimal amplitude and response time. The proposed model will be helpful for the analytical analysis of the mean magnetic field, and the optimization result of the wire diameter under limited space can be employed to improve the performance of a magnetically driven actuator.

Detecting Weak Physical Signal from Noise: A Machine-Learning Approach with Applications to Magnetic-Anomaly-Guided Navigation

Detecting a weak physical signal immersed in overwhelming noises entails separating the two, a task for which machine learning is naturally suited. In principle, such a signal is generated by a nonlinear dynamical system of intrinsically high dimension for which a mathematical model is not available, rendering unsuitable traditional linear or nonlinear state-estimation methods that require an accurate system model (e.g., extended Kalman filters). We exploit the architectures of reservoir computing and feed-forward neural networks (FNNs) with time-delayed inputs to solve the weak-signal-detection problem. As a prototypical example, we apply the machine-learning schemes to Earth's magnetic anomaly field-based navigation. In particular, the time series are collected from the interior of the cockpit of a flying aircraft during different maneuvering phases, where the overwhelmingly strong noise background is the result of other components of Earth's magnetic field and the fields generated by the electronic devices in the cockpit. We demonstrate that, when combined with the traditional Tolles-Lawson model for Earth's magnetic field, the articulated machine-learning schemes are effective for accurately detecting the weak anomaly field from the noisy time series. The schemes can be applied to detecting weak signals in other domains of science and engineering.

Mantle-driven north–south dichotomy in geomagnetic polar minima

The geomagnetic field on the core-mantle boundary (CMB) is characterized by weak or even reversed field in the polar regions and intense flux patches at the edges of the intersection of the inner-core tangent cylinder (TC) with the CMB. This high-latitude field morphology is in agreement with thermal wind theory inside the TC in which polar upwellings disperse magnetic field lines. Furthermore, inferences from the geomagnetic secular variation hint to the presence of a westward jet at high latitudes of the northern hemisphere, also in agreement with the TC dynamical theory, but not in the southern hemisphere. Here we study polar minima in an ensemble of geomagnetic field models that span the historical era and in a set of numerical dynamo simulations with a heterogeneous outer boundary heat flux inferred from a tomographic model of lowermost mantle seismic anomalies. We quantified the polar minima using a previously-proposed expression as well as a new measure which may better capture this phenomenon. We found that throughout the historical era the geomagnetic field is characterized by stronger polar minima and more reversed flux inside the northern TC than inside the southern TC. Likewise, almost all dynamo models exhibit on average stronger polar minima in the northern hemisphere. This north/south dichotomy is explained in terms of the pattern of lowermost mantle seismic anomalies, in particular the southern centers of the two Large Low Shear-wave Velocity Provinces below Africa and the Pacific. We also investigated polar minima in planets where magnetic field models at the top of the dynamo region are available. We speculate that the absence of polar minima in Mercury’s field is likely due to the thick stratified layer at the top of its core, while the strong polar minima in Jupiter’s field might have a different dynamical origin than the geomagnetic polar minima.

Modeling of Uneven Air Gap Magnetic Field for Disc Planetary Permanent Magnet Machine With Segmented Gap Halbach Array

A new analytical magnetic circuit hybrid model (AMCHM) is proposed to predict uneven air gap magnetic field for disc planetary permanent magnet machine (DP-PM machine) with segmented gap Halbach array. The 3-D model is transformed into 2-D model by using radial sectors-of-rings division method and coordinate transformation. The 2-D magnetic field model is obtained by analytical method, and the magnetic equivalent circuit (MEC) model is used to consider the leakage flux loops with and without magnetic coupling. Finally, the analytical models of uneven air gap magnetic field and torque are obtained. The results obtained from proposed model are in good agreement with those of 3-D finite element method (FEM), which verifies the validity of AMCHM. Compared with 3-D FEM model, the AMCHM is convenient for the analysis and optimization of structure parameters, and it improves the calculation efficiency. The research results can be utilized for the research on structural optimization and power analysis.

Influence mechanism of magnetic field direction on magnetic drag of reentry vehicle and better magnetic field direction

The magnetic field condition has a great influence on the magnetic control drag of reentry vehicle, so it is an important research topic to select appropriate magnetic field condition to control the drag force of vehicle. This paper analyzes the magnetic control drag by solving the hypersonic magnetohydrodynamic equations and combining the magnetic field working conditions, studies the influence of the axisymmetric magnetic field direction on the drag, supplements the mechanism of Lorentz force, pressure and conductivity on the axisymmetric magnetic control drag, and compares the drag value and drag composition ratio under different magnetic field directions. The problem is solved numerically for a particular model of a dipole magnetic field. Under different dipole magnetic fields, the magnitude and distribution shape of Lorentz force are different. There are several dividing lines where the Lorentz force is 0, and the Lorentz force directions on both sides are opposite, and this line divides the Lorentz force field into multiple parts. In addition, it is found that the change of the angle between the axis of the aircraft and the direction of the magnetic field will cause the change of the aircraft resistance, which will reduce or increase it.

New 2-D Quasi-Analytical Computation of Eddy Currents in Axisymmetrical Problems: Application to Tubular Linear Induction Motor

In this article, an exact 2-D analytical magnetic field modeling in time harmonic mode of axisymetrical problems is proposed. It is applied for a tubular linear induction motor (TLIM) at locked rotor operation to calculate the magnetic field, eddy currents distributions, and thrust force. The proposed electromagnetic modeling combines the truncated region eigenfunction expansion method (TREEM) with the separation of variables technique to solve Maxwell’s equations in terms of the magnetic vector potential. The developed analytical model allows considering the finite length in the axial direction of both inductor and conductive parts of the investigated structure at the same time and also solves the nonlinear equation to compute the complex eigenvalues. The analytical results are in very good agreement with those obtained using a 2-D finite element method (FEM).

Treasure Maps for Detections of Extreme Energy Cosmic Rays

The origin of ultra-high-energy cosmic rays is a 60 yr old mystery. We show that with more events at the highest energies (above 150 EeV) it may be possible to limit the character of the sources and learn about the intervening magnetic fields. Individual sources become more prominent, relative to the background, as the horizon diminishes. An event-by-event, composition-dependent observatory would allow a “tomography” of the sources as different mass and energy groups probe different GZK horizons. A major goal here is to provide a methodology to distinguish between steady and transient or highly variable sources. Using recent Galactic magnetic field models, we calculate “treasure” sky maps to identify the most promising directions for detecting Extreme Energy Cosmic Rays doublets, events that are close in arrival time and direction. On this basis, we predict the incidence of doublets as a function of the nature of the source host galaxy. Based on the asymmetry in the distribution of time delays, we show that observation of doublets might distinguish source models. In particular, the Telescope Array hotspot could exhibit temporal variability as it is in a “magnetic window” of small time delays. These considerations could improve the use of data with existing facilities and the planning of future ones such as Global Cosmic Ray Observatory (GCOS).

On the determination and interpretation of the lithospheric induced magnetisation

We present a new technique for reducing the uncertainties inherent in the interpretation of lithospheric magnetic field observations over the Earth. This technique, without involving iterations, provides an improved estimate of the depth-integrated magnetic susceptibility of the crust as compared to previous approaches. Departing from the normal practice of using observations at specific locations, we model directly Gauss coefficients of the lithospheric magnetic field and use an a-priori initial lithospheric thickness model to circumvent magnetic annihilators (i.e. magnetisation distributions that cannot be determined from magnetic data since they have no impact on the lithospheric magnetic field). Of the several initial magnetic layer models tested, we prefer the model where magnetic thickness is based on the Moho or the regional estimate of the Curie depth when it is shallower than the Moho because it is physically reasonable and produces the fewest artefacts. The method is applied to a recent high-degree lithospheric magnetic field model called LCS-1 derived from CHAMP and Swarm magnetic satellite data. The technique is appropriate for regions where induced magnetisation dominates over remanent magnetisation. We show that high degrees of the final depth-integrated magnetic susceptibility variation are dependent only on the corresponding high degrees of the LCS-1 magnetic field model. Thus, the depth-integrated magnetic susceptibility variation is an important quantity derived in the study which enables readily qualitative interpretation of regional geology.

ВПЛИВ ЧИСЛА ФАЗ ОБМОТКИ ОБЕРТАННЯ НА СТРУКТУРУ ТА ВЛАСТИВОСТІ ЕЛЕКТРИЧНОЇ МАШИНИ З ТРИСТУПЕНЕВИМ РОТОРОМ

The structure of an electric machine with a rotor, which has three degrees of freedom of rotation (EMTR) and consists of external and internal magnetic circuits, is considered. Between them, in the air gap of a spherical configuration, there is an m-phase rotation winding and a control winding. The excitation of the magnetic field in the EMTR is carried out by means of permanent magnets located on the external magnetic circuit. The scope of application of EMTP in systems of stabilization, observation, tracking, where the rotor performs the function of a gyro-stabilizing element, is outlined. Taking into account the structure of the considered EMTR, the absence of eddy currents in the design and the suitability of the mathematical model of the static magnetic field are substantiated. The calculation of the torque of the EMTR with two- and three-phase rotational windings at different angles of rotor’s inclination relative to the stator axis has been performed. It is shown that the rotation torque of the three-phase winding is 20% higher than that of the two-phase winding. A signifi-cant influence of the control winding on the torque of the three-phase winding and approximately the same influence of the two- and three-phase rotation windings on the processional torque with a significant value of the rotor inclination angle are noted. References 7, figures 8, tables 1.

Study on the surface integrity in ultrasonic vibration and magnetic field complex assisted low speed WEDM under different magnetic field coupling

In this paper, a complex process of ultrasonic vibration (USV) and magnetic field (MF) complex assisted WEDM-LS is proposed, which provides a new method to solve the problems of low machining efficiency and poor machining surface integrity of traditional WEDM-LS. The self-generated MF of wire electrode is taken as the medium, and the influence mechanism of USV and additional MF on the intensity of self-generated MF is explored. Firstly, combined with the Galvanomagnetic effect and Biot-Safar Law, the mathematical models of self-generated MF under USV assisted WEDM-LS and USV-MF assisted WEDM-LS were deduced respectively. And then the MF coupling law between inter electrode was revealed; Secondly, the distribution of self-generated MF of wire electrode under different working conditions was simulated and analyzed. The results showed that compared with traditional WEDM-LS, the self-generated magnetic density under USV assisted WEDM-LS and USV-MF assisted WEDM-LS was increased by 12.1 % and 17.5 % respectively. As a result, the volume of single discharge crater was increased by 12.3 %; Finally, Taguchi orthogonal method was used to complete the USV-MF assisted WEDM-LS orthogonal experiment and the MF coupling verification experiment. The results showed that the Ra was reduced by 23.8 % and the MRR was increased by 25.1 % compared with the traditional working condition. The number of microcracks and micropores on the workpiece surface was significantly reduced, and the degree of workpiece surface burn was effectively reduced, which showed that the surface integrity of the workpiece had been greatly improved. The verification experiment results showed that compared with the opposite coupling of the self-generated MF and the additional MF, when the self-generated MF and the additional MF were coupled in the same direction, the Ra of the workpiece surface was reduced by 18.21 % and the feed speed was increased by 16.68 %. In addition, the removed particles were more evenly adsorbed on the surface of the wire electrode, which increased the normal discharge probability, indicating that the inter electrode MF coupling was the main effect model of ultrasonic vibration and MF recombination.

The Phase Space Density Evolution of Radiation Belt Electrons under the Action of Solar Wind Dynamic Pressure

Earth’s radiation belt and ring current are donut-shaped regions of energetic and relativistic particles, trapped by the geomagnetic field. The strengthened solar wind dynamic pressure (Pdyn) can alter the structure of the geomagnetic field, which can bring about the dynamic variation of radiation belt and ring current. In the study, we firstly utilize group test particle simulations to investigate the phase space density (PSD) under the varying geomagnetic field modeled by the International Geomagnetic Reference Field (IGRF) and T96 magnetic field models from 19 December 2015 to 20 December 2015. Combining the observation of the Van Allen Probe, we find that the PSD of outer radiation belt electrons evolves towards different states under different levels of Pdyn. In the first stage, the Pdyn (~7.94 nPa) results in the obvious rise of electron anisotropy. In the second stage, there is a significant reduction in PSD for energetic electrons at all energy levels and pitch angles under the action of intense Pdyn (~22 nPa), which suggests that the magnetopause shadowing and outward radial diffusion play important roles in the second process. The result of the study can help us further understand the dynamic evolution of the radiation belt and ring current during a period of geomagnetic disturbance.

Generation, measurement, and modeling of strong magnetic fields generated by laser-driven micro coils

Generation, measurement, and modeling of strong magnetic fields generated by laser-driven micro coils

Coupled numerical modelling and experimental analysis of domestic induction heating systems

Continuous demands on resources of energy heighten the need for better and smarter use of available resources. Induction heating (IH) is a technology that is proved to be more efficient in many industrial applications compared to direct resistive heating. Also, IH can be used in domestic devices, as it provides clean and contactless regime of heating. In this paper, a fully coupled numerical approach of a domestic IH system for water boiling is presented. The approach couples the modelling of magnetic field generated in the system with both heat transfer and fluid flow phenomena. The nonlinear and temperature-dependent characteristics of materials are accounted for in the coupled numerical approach. The numerical approach is validated by experimental measurements that are implemented for four case studies. In addition, a detailed parametric study is presented to investigate the effects of different design parameters. The results provide a picture of the nonlinear, complex, transient buoyancy-driven fluid motion. It is found that the heating efficiency is highly affected by different design parameters such as susceptor material, thickness, and offset distance from the bowl base. These effects are highly nonlinear due to the inclusion of nonlinear magnetic and thermal characteristics. The results also highlight the importance of the investigation of IH systems as integrated systems, in contrast to most of existing similar studies. By this holistic approach, different thermal processes and effects of different design parameters are involved, and consequently the heating efficiency can be clearly assessed.

Simulation of the Solar Energetic Particle Event on 2020 May 29 Observed by Parker Solar Probe

This paper presents a stochastic three-dimensional focused transport simulation of solar energetic particles (SEPs) produced by a data-driven coronal mass ejection (CME) shock propagating through a data-driven model of coronal and heliospheric magnetic fields. The injection of SEPs at the CME shock is treated using diffusive shock acceleration of post-shock suprathermal solar wind ions. A time-backward stochastic simulation is employed to solve the transport equation to obtain the SEP time–intensity profile at any location, energy, and pitch angle. The model is applied to a SEP event on 2020 May 29, observed by STEREO-A close to ∼1 au and by Parker Solar Probe (PSP) when it was about 0.33 au away from the Sun. The SEP event was associated with a very slow CME with a plane-of-sky speed of 337 km s−1 at a height below 6 R S as reported in the SOHO/LASCO CME catalog. We compute the time profiles of particle flux at PSP and STEREO-A locations, and estimate both the spectral index of the proton energy spectrum for energies between ∼2 and 16 MeV and the equivalent path length of the magnetic field lines experienced by the first arriving SEPs. We find that the simulation results are well correlated with observations. The SEP event could be explained by the acceleration of particles by a weak CME shock in the low solar corona that is not magnetically connected to the observers.