Magnetic Energy Distribution Research Articles

Noncollinear spin texture-driven torque in deterministic spin–orbit torque-induced magnetization switching

To reveal the role of chirality on field-free spin–orbit torque (SOT) induced magnetization switching, we propose an existence of z-torque through the formation of noncollinear spin texture during SOT-induced magnetization switching in a laterally two-level perpendicular magnetic anisotropy (PMA) system. For the investigation of torque, we simulate magnetization dynamics in the two-level PMA system with SOT, which generates the noncollinear spin texture. From the spatial distribution of magnetic energy, we reveal the additional z-directional torque contribution in the noncollinear spin texture, which is unexpected in the conventional SOT-induced magnetization switching in collinear spin texture. The z-directional torque originates from the interaction between the chirality of the noncollinear spin texture and the interfacial Dzyaloshinskii-Moriya interaction of the system. Furthermore, the experimental observation of the asymmetric magnetization switching to the direction of the current flow in the two-level PMA system supports our theoretical expectation.

Pickup Ion Modulation on Plateau-like Turbulence in the Martian Magnetosheath

The distribution of magnetic energy across scales, represented by the turbulence spectrum, provides insights into magnetic field dynamics in astrophysical and space plasma. While the Earth’s magnetosheath exhibits a conventional two-slope spectrum, the Martian magnetosheath often displays a prominent plateau-like spectrum. However, the underlying physical mechanism remains unresolved. Based on MAVEN observations, we present appealing evidence of pickup ions (PUIs) modulating the plateau-like spectrum through proton cyclotron waves (PCWs). PCWs, driven by unstable pickup H+ ion distributions, significantly influence the formation of plateau-like spectra. Both case and statistical studies suggest that the spectral evolution is affected by the relative abundance of pickup O+ ions. A substantial presence of pickup O+ ions can suppress PCWs driven by pickup H+ ions, resulting in a decline in the slope of the plateau spectrum. Particle-in-cell simulations confirm the role of PUI-modulated PCWs in the plateau-range energy injection. Our results provide new insight into the impact of PUIs on magnetic turbulence evolution and associated energy transfer processes in space and astrophysical plasma.

From convective stellar dynamo simulations to Zeeman-Doppler images

Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the ‘real’ value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in terms of the angular degree ℓ. Secondly, the axisymmetry is overestimated. The poloidality versus toroidality is better recovered. The reconstruction works better for a stronger field and faster rotation velocity. Still, the ZDI method works surprisingly well even for a weaker field and slow rotation provided the data have a high signal-to-noise ratio and good rotation phase coverage.

Magnetic Lateral Ladder for Unidirectional Transport of Microrobots: Design Principles and Potential Applications of Cells-on-Chip.

Functionalized microrobots, which are directionally manipulated in a controlled and precise manner for specific tasks, face challenges. However, magnetic field-based controls constrain all microrobots to move in a coordinated manner, limiting their functions and independent behaviors. This article presents a design principle for achieving unidirectional microrobot transport using an asymmetric magnetic texture in the shape of a lateral ladder, which the authors call the "railway track." An asymmetric magnetic energy distribution along the axis allows for the continuous movement of microrobots in a fixed direction regardless of the direction of the magnetic field rotation. The authors demonstratedprecise control and simple utilization of this method. Specifically, by placing magnetic textures with different directionalities, an integrated cell/particle collectorcan collect microrobots distributed in a large area and move them along a complex trajectory to a predetermined location. The authors can leverage the versatile capabilities offered by this texture concept, including hierarchical isolation, switchable collection, programmable pairing, selective drug-response test, and local fluid mixing for target objects. The results demonstrate the importance of microrobot directionality in achieving complex individual control. This novel concept represents significant advancement over conventional magnetic field-based control technology and paves the way for further research in biofunctionalized microrobotics.

Simulation of Magnetic Anisotropy Energy Surfaces for Cubic Crystals Using MATLAB in Remote Material Physics Lectures

The physical characteristics of a crystal can be viewed from the distribution of magnetic energy contained in it so that a simulation is needed which helps in visualizing the magnetic energy of the crystals. This study aims to present a simple solution for constructing a simulation of the physical properties of cubic crystals using MATLAB software. MATLAB can also be used to help organize physics lectures remotely. This is because MATLAB can be operated by anyone, anytime, and anywhere without being connected to the internet network to help visualize the material magnetization concept in the form of 2- and 3-dimensional graphics. The simulation aims to visualize the magnetic anisotropy energy surface for cubic crystals. This simulation can visualize the magnetic anisotropy energy surface of 3 types of cubic crystals, namely simple cubic, body-centered cubic, and face-centered cubic. In this simulation, the difference between the 3 types of crystals is the anisotropy energy constant. The mathematical equations in the magnetic anisotropy energy surface for cubic crystals are quite complicated. This simulation can help students in exploring mathematical equations and studying the magnetic anisotropy energy surface for cubic crystals more. Students can also develop mathematical representation skills and creative visual representations of the magnetic anisotropy energy surface for cubic crystals.
 HIGHLIGHTS
 
 The uniaxial anisotropy energy equation is closely related to helping to realize the behavior of materials
 Visualization of magnetic anisotropy energy surfaces in a crystal is influenced by the shape of the crystal and the value of its anisotropy constant
 Physics lectures during the Covid-19 pandemic require a variety of lectures that utilize the computational program-based physics equation simulation media
 Magnetic anisotropy energy surfaces on a crystal can be visualized through the help of computational programs to support physics lectures during the Covid-19 pandemic
 MATLAB can be used to visualize magnetic anisotropy energy surfaces because it can be operated by anyone, anytime, and anywhere without being connected to the internet network
 
 GRAPHICAL ABSTRACT

Universality of the Turbulent Magnetic Field in Hypermassive Neutron Stars Produced by Binary Mergers

Abstract The detection of a binary neutron star (BNS) merger in 2017 through both gravitational waves and electromagnetic emission opened a new era of multimessenger astronomy. The understanding of the magnetic field amplification triggered by the Kelvin–Helmholtz instability during the merger is still a numerically unresolved problem because of the relevant small scales involved. One of the uncertainties comes from the simplifications usually assumed in the initial magnetic topology of merging neutron stars. We perform high-resolution, convergent large-eddy simulations of BNS mergers, following the newly formed remnant for up to 30 ms. Here we specifically focus on the comparison between simulations with different initial magnetic configurations, going beyond the widespread-used aligned dipole confined within each star. The results obtained show that the initial topology is quickly forgotten, in a timescale of a few milliseconds after the merger. Moreover, at the end of the simulations, the average intensity (B ∼ 1016 G) and the spectral distribution of magnetic energy over spatial scales barely depend on the initial configuration. This is expected due to the small-scale efficient dynamo involved, and thus it holds as long as (i) the initial large-scale magnetic field is not unrealistically high (as often imposed in mergers studies), and (ii) the turbulent instability is numerically (at least partially) resolved, so that the amplified magnetic energy is distributed across a wide range of scales and becomes orders of magnitude larger than the initial one.

Analysis of Large Deflections of Prominence–CME Events during the Rising Phase of Solar Cycle 24

Motivated by the need to improve the ability to forecast whether a certain coronal mass ejection (CME) is to impact Earth, and by the insufficiency of statistical studies that analyze the whole erupting system with the focus on the governing conditions under CME deflections, we performed a careful analysis of 13 events along a one-year time interval showing large deflections from their source region. We used telescopes imaging the solar corona at different heights and wavelengths on board the Project for Onboard Autonomy 2 (PROBA2), Solar Dynamics Observatory (SDO), Solar TErrestrial RElations Observatory (STEREO), Solar and Heliospheric Observatory (SOHO) spacecraft and from National Solar Observatory (NSO). By taking advantage of the quadrature position of these spacecraft from October 2010 until September 2011, we inspected the 3D trajectory of CMEs and their associated prominences with respect to their solar sources by means of a tie-pointing tool and a forward model. Considering the coronal magnetic fields as computed from a potential field source surface model, we investigate the roles of magnetic energy distribution and kinematic features in the non-radial propagation of both structures. The magnetic environment present during the eruption is found to be crucial in determining the trajectory of CMEs, in agreement with previous reports.

Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields

By using both a phase field approach and a modified level set approach, two multiphase numerical models are proposed and compared in this paper to investigate the ferrodroplet deformation and merging process in a non-magnetic viscous medium under the influence of uniform magnetic fields. The finite element method is utilized for the spatial discretization of both numerical models. The numerical results show excellent agreement with the analytical solutions in the simple axisymmetric setting. The effects of different magnetic bond numbers and magnetic susceptibility on the deformation of ferrodroplets are systematically investigated. The coalescence process, in which two small ferrodroplets merge into a single larger droplet under uniform magnetic fields, is also studied by using both the phase field approach and the modified level set approach. Moreover the attraction phenomenon between two ferrodroplets, which was previously discovered in numerical experiments, is observed in our numerical tests. By comparing with analytical solutions, our study demonstrates that the diffuse interface (phase field) approach performs better than the modified level set approach when there is large topological deformation of the ferrodroplet. Several other important aspects, including the evolution of the flow field, the magnetic energy distribution, the spurious flows near the interfaces, and conservation of mass in both approaches, are studied as well.

The Relationship Between Root Locus and Transient Field Components of AC Machines

The dynamic analysis of induction motors is supported by well-known theories: the two-axes transformation, and the space vector theory. Yet some inconsistencies with the theory of dynamic systems exist. The machine eigenvalues suggest the existence of two damped oscillators, physically not understandable. The respective eigenfrequencies change with the angular velocity of the reference frame. This contradicts the understanding that eigenfrequencies are inherent system properties. Physically, the dynamics depend on the continuous distribution of magnetic energy and its spatial displacement during transient processes. Information on the system dynamics is lost when dividing the continuum of magnetic energy into discrete portions. Complex state variables associate the dynamics to the propagation in space of distributed magnetic fields. The dynamic analysis reveals the existence single-complex eigenvalues. These define a novel class of system identifiers. They are characterized by having only one imaginary part instead of a conjugate complex pair. The use of complex state variables conveys insight and physical understanding of the dynamic processes within the machine. The approach constitutes an extension to the theory of dynamic systems.

Multi-spacecraft Observations of the Rotation and Nonradial Motion of a CME Flux Rope Causing an Intense Geomagnetic Storm

Abstract We present an investigation of the rotation and nonradial motion of a coronal mass ejection (CME) from AR 12468 on 2015 December 16 using observations from SDO, SOHO, STEREO A, and Wind. The EUV and HMI observations of the source region show that the associated magnetic flux rope (MFR) axis pointed to the east before the eruption. We use a nonlinear force-free field (NLFFF) extrapolation to determine the configuration of the coronal magnetic field and calculate the magnetic energy density distributions at different heights. The distribution of the magnetic energy density shows a strong gradient toward the northeast. The propagation direction of the CME from a Graduated Cylindrical Shell (GCS) modeling deviates from the radial direction of the source region by about 45° in longitude and about 30° in latitude, which is consistent with the gradient of the magnetic energy distribution around the AR. The MFR axis determined by the GCS modeling points southward, which has rotated counterclockwise by about 95° compared with the orientation of the MFR in the low corona. The MFR reconstructed by a Grad–Shafranov (GS) method at 1 au has almost the same orientation as the MFR from the GCS modeling, which indicates that the MFR rotation occurred in the low corona. It is the rotation of the MFR that caused the intense geomagnetic storm with the minimum D st of −155 nT. These results suggest that the coronal magnetic field surrounding the MFR plays a crucial role in the MFR rotation and propagation direction.

The role of magnetic fields in the structure and interaction of supershells

Context. Large-scale shocks formed by clustered feedback of young OB stars are considered an important source of mechanical energy for the interstellar medium (ISM) and a trigger of molecular cloud formation. Their interaction sites are locations where kinetic energy and magnetic fields are redistributed between ISM phases. Aims. In this work we address two questions, both involving the role of galactic magnetic fields in the dynamics of supershells and their interactions. On the one hand, we study the effect of the magnetic field on the expansion and fragmentation of supershells and, on the other hand, we look for the signatures of supershell collisions on dense structures and on the kinetic and magnetic energy distribution of the ISM. Methods. We performed a series of high-resolution, three-dimensional simulations of colliding supershells. The shocks are created by time-dependent feedback and evolve in a diffuse turbulent environment that is either unmagnetized or has different initial magnetic field configurations. Results. In the hydrodynamical situation, the expansion law of the superbubbles is consistent with the radius-time relation R ∝ t3/5 that is theoretically predicted for wind-blown bubbles. The supershells fragment over their entire surface into small dense clumps that carry more than half of the total kinetic energy in the volume. However, this is not the case when a magnetic field is introduced, either in the direction of the collision or perpendicular to the collision. In both situations, the shell surfaces are more stable to dynamical instabilities. When the magnetic field opposes the collision, the expansion law of the supershells also becomes significantly flatter than in the hydrodynamical case. Although a two-phase medium arises in all cases, in the magnetohydrodynamical (MHD) simulations the cold phase is limited to lower densities and the cold clumps are located further away from the shocks with respect to the hydrodynamical simulations. Conclusions. For the parameters we explored, self-gravity has no effect on either the superbubble expansion or the shock fragmentation. In contrast, a magnetic field, whether mostly parallel or mostly perpendicular to the collision axis, causes a deceleration of the shocks, deforms them significantly, and largely suppresses the formation of the dense gas on their surface. The result is a multi-phase medium in which the cold clumps are not spatially correlated with the supershells.

Solar and stellar coronae and winds

AbstractSolar-like stars influence their environments through their coronal emis- sion and winds. These processes are linked through the physics of the stellar magnetic field, whose strength and geometry has now been explored for a large number of stars through spectropolarimetric observations. We have now detected trends with mass and rotation rate in the distribution of magnetic energies in different geometries and on also different length scales. This has implications both for the dynamo processes that generate the fields and also for the dynamics and evolution of the coronae and winds. Modelling of the surface driving processes on stars of various masses and rotation rates has revealed tantalising clues about the dynamics of stellar coronae and their ejecta. These new observations have also prompted a resurgence in the modelling of stellar winds, which is now uncovering the range of different interplanetary conditions that exoplanets might experience as they evolve.

Magnetic Energy Harvesting and Concentration at a Distance by Transformation Optics

Based on transformation optics, we introduce a magnetic shell with which one can harvest magnetic energy and distribute it as desired in space with unprecedented efficiency at an arbitrary scale. It allows a very large concentration of magnetic energy in a free space region, which can be used for increasing the sensitivity of magnetic sensors, and the transfer of magnetic energy from a source to a given distant point separated by empty space, with possible applications in wireless transmission of energy.

MHD numerical simulations of colliding winds in massive binary systems - I. Thermal versus non-thermal radio emission

In the past few decades detailed observations of radio and X-rays emission from massive binary systems revealed a whole new physics present in such systems. Both thermal and non-thermal components of this emission indicate that most of the radiation at these bands originates in shocks. OB and WR stars present supersonic and massive winds that, when colliding, emit largely due to the free-free radiation. The non-thermal radio and X-ray emissions are due to synchrotron and inverse compton processes, respectively. In this case, magnetic fields are expected to play an important role on the emission distribution. In the past few years the modeling of the free-free and synchrotron emissions from massive binary systems have been based on purely hydrodynamical simulations, and ad hoc assumptions regarding the distribution of magnetic energy and the field geometry. In this work we provide the first full MHD numerical simulations of wind-wind collision in massive binary systems. We study the free-free emission characterizing its dependence on the stellar and orbital parameters. We also study self-consistently the evolution of the magnetic field at the shock region, obtaining also the synchrotron energy distribution integrated along different lines of sight. We show that the magnetic field in the shocks is larger than that obtained when the proportionality between $B$ and the plasma density is assumed. Also, we show that the role of the synchrotron emission relative to the total radio emission has been underestimated.

Magnetic energy distribution in the four‐dimensional frequency and wave vector domain in the solar wind

We present a measurement of the energy distribution in the four‐dimensional (4‐D) frequency and wave vector domain of magnetic field fluctuations in the solar wind. The measurement makes use of the wave telescope technique that has been developed particularly for multispacecraft data analysis. We review briefly the theoretical background and then present a numerical test using synthetic data; the technique is then applied to magnetic field data obtained while the Cluster spacecraft was in the solar wind. The energy distribution is determined in the flow rest frame in the frequency range below 0.2 rad/s and the wave number range below 0.0015 rad/km, corrected for the Doppler shift. We find the following properties in the energy distribution in the rest frame: (1) a double anisotropy in the wave vector domain associated with the mean magnetic field and the flow directions, (2) a symmetric distribution with respect to the sign of wave vector, and (3) no evidence for a linear dispersion relation in the frequency and wave number domain. Since the flow direction in the analyzed time interval is close to the normal direction to the bow shock, the anisotropy may well be associated with the bow shock. These results suggest that the solar wind is in a state of well‐developed strong turbulence and justifies the theoretical picture of quasi‐two‐dimensional turbulence that obtains in the presence of a (relatively) strong DC magnetic field. However, the fluctuations are not axisymmetric around the mean field and the energy distribution is extended in the perpendicular direction to the flow or shock normal. Anisotropy associated with the boundary is reminiscent of previously reported magnetosheath turbulence. This study opens a way to investigate solar wind turbulence in the full 4‐D frequency and wave vector space.

Statistical dynamo theory: Mode excitation

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .

Magnetic energy distribution in polycrystalline sputtered CoCr magnetic thin films

Magnetic thin films of Co 80 Cr 16 Ta 4 were sputtered onto identical CrMo seed-layers at –200 V bias and 3 different substrate temperatures (150, 200, and 250 °C). Energy-filtered transmission electron microscopy (EFTEM) was performed to analyze Cr levels at the grain boundaries as well as inside the grains. These quantitative Cr measurements were used to estimate the local values of magnetocrystalline anisotropy ( K u ) and, together with grain size distributions, calculate the product of K u and the grain volume ( K uV ), a quantity which is a measure of thermal stability. The results show that the coercivity as well as the fraction of stable grains increased with increasing substrate temperature. The increase in the fraction of stable grains is produced by the enhancement in the K u value due to Cr depletion of the grain interiors and the magnetic decoupling between the grains from Cr grain-boundary segregation.

Effect of High‐Degree Harmonics in IGRF Models on Secular Variation of the Geomagnetic Field

AbstractThe contributions to the main geomagnetic field from high‐degree harmonics of IGRF models are usually neglected, since the high‐degree Gauss coefficients are much less than low‐degree ones. However, the high‐degree harmonics have significant contribution to secular variations of the magnetic field. The effects of the unusual behaviors in high‐degree Gauss coefficients of IGRF 1945~1955 on the determination of the secular variation are studied by using the eighth generation of IGRF. By comparing the original with the revised IGRF models, the errors in the high‐degree coefficients are estimated and corrected. Since the magnitudes of high‐degree terms increase rapidly with increasing depth, these errors will distort greatly the magnetic field configuration and magnetic energy distribution in the deep interior. Significant effects are also expected in the calculation of the liquid flow pattern at the outer core surface and in the geomagnetic estimation of the core radius.

Distribution of magnetic energy in αΩ-dynamos, I: The method

Abstract In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density ε ≡ B 2/8π of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s−1, which is an order of magnitude larger than usually adopted in solar mean field models.

Kinematic dynamos associated with large scale fluid motions

Abstract A standard approach to the kinematic dynamo problem is that pioneered by Bullard and Gellman (1954), which utilizes the toroidal-poloidal separation and spherical harmonic expansion of the magnetic and velocity fields. In these studies, the velocity field is given as a combination of small number of toroidal and poloidal harmonics, with their radial dependences prescribed by some physical considerations. Starting from the original paper of Bullard and Gellman (1954), a number of authors repeated such analyses on different combination of velocity fields, including the most recent and comprehensive effort by Dudley and James (1989). In this paper, we re-examine the previous kinematic dynamo models, using the computer algebra approach initiated by Kono (1990). This method is particularly suited to this kind of research since different velocity fields can be treated by a single program. We used the distribution of magnetic energies in various harmonics to infer the convergence of the results. The numerical results obtained in this study for the models of Bullard and Gellman (1954), Lilley (1970), Gubbins (1973), Pekeris et al. (1973), Kumar and Roberts (1975), and Dudley and James (1989) are consistent with the previously reported results, in particular, with the extensive calculation of Dudley and James. In addition, we found that the combination of velocities used by Lilley can support the dynamo action if the radial dependence of the velocity is modified. We also examined the helicity distributions in these dynamo models, to see if there is any correlation between the helicity and the efficiency of dynamo action. A successful dynamo can result both from the cases in which the helicity distributions are symmetric or antisymmetric with respect to the equator. In both cases, it appears that the dynamo action is efficient if the volume integral of helicity over a hemisphere is large.