Magnetic Boundary Research Articles

Statistical modeling of soft magnetic composites’ permeability

Soft magnetic composites (SMC) also known as powder cores are widely used in many applications because of their linearity, controllable permeability and isotropy. Because of the distributed air gap, the permeability is governed by the inner demagnetizing fields. To model the permeability dependence on the filling fraction, essentially two approaches are used both based on spatial periodicity hypothesis: the non magnetic grain boundary model and the effective medium theory. Actually, the first one works only for dense materials and the second works at low concentration. Both need fitting of two parameters, the inner demagnetizing factor and the particle susceptibility, just because the periodicity hypothesis is never verified for magnetic filling factors larger than 20%. A breakaway model is proposed based on the computation of mathematical esperance of the statistical distribution of magnetic chains and the subsequent determination of demagnetizing coefficient of an ellipsoid of equivalent aspect ratio. The model is collated with permeability data from the literature for spherical or non-spherical particles based SMCs and shows a excellent agreement with only one or even without fitting parameter in the whole concentration range.

Performing Magnetic Boundary Modulation to Broaden the Operational Wind Speed Range of a Piezoelectric Cantilever-Type Wind Energy Harvester

Small piezoelectric wind-induced vibration energy harvesting systems have been widely studied to provide long-term sustainable green energy for a large number of wireless sensor network nodes. Piezoelectric materials are commonly utilized as transducers because of their ability to produce high output power density and their simple structure, but they are prone to material fracture under large deformation conditions. This paper proposes a magnetic boundary modulated stepped beam wind energy harvesting system. On the one hand, the design incorporates a composite stepped beam with both high- and low-stiffness components, allowing for efficient vibration and electrical energy output at low wind speeds. On the other hand, a magnetic boundary constraint mechanism is constructed to prevent the piezoelectric sheet from breaking due to excessive deformation. Experiments have confirmed that the effective operational wind speed range of the harvester with magnetic boundary constraints is doubled compared to that of the harvester without magnetic boundary constraints. Furthermore, by adjusting the magnetic pole spacing of the boundary, the harvesting system can generate sufficiently high output power under high-wind-speed conditions without damaging the piezoelectric sheet.

Evidence for magnetic boundary layer accretion in RU Lup

Context. It is well established that classical T Tauri stars accrete material from a circumstellar disk through magnetic fields. However, the physics regulating the processes in the inner (0.1 AU) disk is still not well understood. Aims. Our aim is to characterize the accretion process of the classical T Tauri Star RU Lup. Methods. Optical high-resolution spectroscopic observations with CHIRON and ESPRESSO were obtained simultaneously with photometric data from AAVSO and TESS. Results. We detected a periodic modulation in the narrow component of the He I 5876 line with a period that is compatible with the stellar rotation period, indicating the presence of a compact region on the stellar surface that we identified as the footprint of the accretion shock. We show that this region is responsible for the veiling spectrum, which is made up of a continuum component plus narrow line emission that fills in the photospheric lines. An analysis of the high-cadence TESS light curve reveals quasi-periodic oscillations on timescales shorter than the stellar rotation period, suggesting that the accretion disk in RU Lup extends inward of the corotation radius, with a truncation radius at ~2 R*. This is compatible with predictions from three-dimensional magnetohydrodynamic models of accretion through a magnetic boundary layer (MBL). In this scenario, the photometric variability of RU Lup is produced by a nonsta-tionary hot spot on the stellar surface that rotates with the Keplerian period at the truncation radius. We also qualitatively discuss how more complex hot spot shapes may generate the same variability pattern. The analysis of the broad components of selected emission lines reveals the existence of a non-axisymmetric, temperature-stratified flow around the star, in which the gas leaves the accretion disk at the truncation radius and accretes onto the star channeled by the magnetic field lines. The unusually rich metallic emission line spectrum of RU Lup might be characteristic of the MBL regime of accretion. Conclusions. Our extensive multiwavelength database of RU Lup reveals many similarities to predictions from the scenario of accretion through a magnetic boundary layer. Alternative explanations would require the existence of a hot spot with a complex shape, perhaps made of two brighter knots, or a warped structure in the inner disk.

Accuracy of kinetic equilibrium reconstruction of NSTX and NSTX-U plasmas and its impact on the transport and stability analysis

Abstract An accurate magnetohydrodynamic (MHD) equilibrium reconstruction is an essential starting point for stability and transport plasma analysis. This work describes an approach for obtaining kinetic equilibrium reconstructions using the OMFIT framework, which has been applied for the first time to spherical tokamak data from NSTX and NSTX-U. The EFIT equilibrium solver is integrated with experimental data analysis procedures and subsequent TRANSP transport simulations to enhance the accuracy of the reconstruction, in particular at the edge region, by adding constraints on the total pressure and current density profiles, based on the transport code solution. The accuracy of the equilibrium depends on the uncertainty and number of constraints, as well as the choice of basis functions to represent the pressure and current density profiles. An improved fidelity of the equilibrium reconstruction is demonstrated by reducing the variability of the magnetic axis and boundary locations from several centimeters for reconstructions based on magnetic and experimental pressure constraints to only several millimeters for kinetic reconstructions based on transport code constraints, when different representations for basis functions were tested. Variability of the safety factor on-axis was reduced ten times in the same sensitivity study. The accuracy of the equilibrium reconstruction and subsequent mapping of experimental kinetic profile data have a significant impact on TGLF and linear CGYRO turbulence simulations, which predict different spectra of unstable modes and turbulent fluxes for cases with different numbers of constraints in the equilibrium reconstruction. Conversely, the stability analysis performed with the GATO code shows plasmas stable to n = 1 MHD modes in both equilibria using magnetic and experimental pressure constraints as well as the transport code constrained equilibrium. However, a scan of parameters away from these conditions shows considerable deviation in the threshold of unstable modes between these reconstructions. Therefore, for reliable plasma analysis and use in turbulence and stability calculations, a high fidelity equilibrium reconstruction with accurate kinetic constraints based on transport code solutions is necessary.

Hydrodynamic stability of magnetic boundary layer flow of viscoelastic Walters' liquid B embedded in a porous medium

The present study investigates the linear stability of stagnation boundary layer flow of viscoelastic Walters' liquid B in the presence of magnetic field and porous medium by solving modified Orr–Sommerfeld equation numerically using the Chebyshev collocation method. The model is characterized mainly by the elasticity number (E), the magnetic number (Q), and the permeability parameter (K) in addition to the Reynolds number(Re). The Prandtl boundary layer equations derived for the present model are converted through appropriate similarity transformations, to an ordinary differential equation whose solution describes the velocity, which has oscillatory behavior. The solution of generalized eigenvalue problem governing the stability of the boundary layer has an interesting eigenspectrum. The spectra for different values of E, K, and Q are shown to be a continuation of Newtonian eigenspectrum with the instability belongs to viscoelastic wall mode for certain range of parameters. It is shown that the role of elasticity number is to destabilize the viscoelastic boundary layer flow, whereas both magnetic field and porous medium have the stabilizing effect on the flow. These interesting features are further confirmed by performing the energy budget analysis on the perturbed quantities. Region of negative production due to the Reynolds stress as well as production due to viscous dissipation and viscoelastic contributions in the positive region, and there is reduction in the growth rate of kinetic energy that causes stability. Other physical mechanisms related to flow stability are discussed in detail.

Evaluating the Electromagnetic Field Problem Generated by the Power Transmission Line Using High Order Compact Method

This paper compares a finite difference method-based computational scheme for evaluating electromagnetic field problems in power transmission lines in cases of on surface and in Ground. The scheme uses Maxwell's partial differential equations to represent electric and magnetic field components and approximate boundary conditions. The High Order Compact Method (HOC) is applied to estimate the electric field (Ez )in ground and compares it with the standard central difference scheme. The HOC produces more accurate results than the traditional central approximation at 99.7% for the electric field Ez. It also calculates both of Electric and magnetic intensity to evaluate the effect of Electric and magnetic intensities in ground and on surface respect to distance.

Climatology of the open–closed boundary using ULF wave observations from South Pole, McMurdo, and distributed Antarctic AGOs

It has been shown that a proxy determination of the magnetospheric open–closed magnetic field line boundary (OCB) location can be made by examining the ultra-low-frequency (ULF) wave power in magnetometer data, with particular interest in the Pc5 ULF waves with periods of 3–10 min. In this study, we present a climatology of such Pc5 ULF waves using ground-based magnetometer data from the South Pole Station (SPA), McMurdo (MCM) station, and the Automatic Geophysical Observatories (AGOs) located across the Antarctic continent, to infer OCB behavior and variability during geomagnetically quiet times (i.e., Ap < 30 nT). For each season [i.e., austral fall (20 February 2017–20 April 2017), austral winter (20 May 2017–20 July 2017), austral spring (20 August 2017–20 October 2017), and austral summer (20 November 2017–20 January 2018)], north–south (i.e., H-component) magnetic field line residual power–spectral density (PSD) measurements taken during geomagnetically quiet periods within a 60-day window centered at the austral solstice/equinox are averaged in 10-min temporal bins to form the climatology at each station. These residual PSDs thus enable the analysis of Pc5 activity (and lower period “long-band” oscillations) and, thus, OCB location/variability as a function of season and magnetic latitude. The dawn and dusk transitions across the OCB are analyzed, with a discussion of dawn and dusk variability during nominally quiet geomagnetic periods. In addition, latitudinal dependencies of the OCB and peak Pc5 periods at each station are discussed, along with the empirical Tsyganenko model comparisons to our site measurements.

Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions

We study the small-time global approximate controllability for incompressible magnetohydrodynamic (MHD) flows in smoothly bounded two- or three-dimensional domains. The controls act on arbitrary nonempty open portions of each connected boundary component, while linearly coupled Navier slip-with-friction conditions are imposed along the uncontrolled parts of the boundary. Some choices for the friction coefficients give rise to interacting velocity and magnetic field boundary layers. We obtain sufficient dissipation properties of these layers by a detailed analysis of the corresponding asymptotic expansions. For certain friction coefficients, or if the obtained controls are not compatible with the induction equation, an additional pressure-like term appears. We show that such a term does not exist for problems defined in planar simply-connected domains and various choices of Navier slip-with-friction boundary conditions.

RFX-mod2 diagnostic capability enhancements for the exploration of multi-magnetic-configurations

The RFX-mod2 device, the upgraded version of the previous RFX-mod with a modified magnetic boundary, is presently under realization and will start to be operated in 2025. Significant upgrades of the diagnostic capabilities have been proposed and are under development. These include a largely increased number of in-vessel magnetic and electrostatic sensors, a new fast reciprocating manipulator for the exploration of the edge plasma in a wide range of experimental conditions, the improved Thomson scattering and soft x-ray diagnostics system for a detailed determination of the behavior of the electron temperature profile, new dedicated systems for the space and time resolved analysis of x-ray spectra and neutron rate, a reflectometric diagnostic for real-time determination of plasma position, two diagnostics devoted to the imaging of light impurities and influxes behavior along with arrays of halo current sensors. These diagnostic upgrades will be accompanied by a significant effort to improve the control of the electron density and of the impurity influxes by means of proper treatment of plasma facing components with in-vessel fixed electrodes distributed over the first wall. The described advancements will allow a deeper understanding of physics phenomena in the wide variety of magnetic configurations, including the tokamak, the reversed-field pinch and the Ultra-low q, which can be produced in RFX-mod2 thanks to its flexibility and unique MHD control capabilities.

Effects of the 2007 Martian Global Dust Storm on Boundary Positions in the Induced Magnetosphere

Mars's magnetosphere is a sensitive system, varying due to external and internal factors, such as solar wind conditions and crustal magnetic fields. A signature of this influence can be seen in the position of two boundaries; the bow shock and the induced magnetospheric boundary (IMB). The bow shock moves closer to Mars during times of high solar activity, and both the bow shock and IMB bulge away from Mars over crustal magnetic fields in the southern hemisphere. This study investigates whether large-scale atmospheric events at Mars have any signature in these two magnetic boundaries, by investigating the 2007 storm. The 2007 global storm lasted for several months and increased atmospheric temperatures and densities of both water vapor and carbon dioxide in the atmosphere, leading to an increase in atmospheric escape. Using Mars Express, we identified boundary locations before, during, and after the event, and compared these to modeled boundary locations and areographical locations on Mars. We find that, while it is unclear whether the bow shock position is impacted by the storm, the IMB location does change significantly, despite the orbital bias introduced by Mars Express. The terminator distance for the IMB peaks at longitudes 0°–40° and 310°–360°, leaving a depression around 180° longitude, where the boundary usually extends to higher altitudes due to the crustal magnetic fields. We suggest this may be due to the confinement of ionospheric plasma over crustal fields preventing mixing with the dust, creating a dip in ionospheric pressure here.

Comparison of Solar Wind Interaction with Mars and Earth: Energy Transfer

Using a global magnetohydrodynamics numerical simulation, this work compares the interaction of the solar wind with Mars and Earth from the perspective of energy transfer under north–south interplanetary magnetic fields (IMFs). Mars lacks a global dipole magnetic field like Earth’s and instead has a small-scale crustal magnetic field near highlands in the southern hemisphere. Unlike Earth’s magnetopause reconnection (at the subsolar point or tail under a southward IMF, or behind the cusp under a northward IMF), the reconnection of the Martian magnetic pileup boundary (MPB) occurs near solar zenith angle (SZA) ≈ 45° (SZA ≈ 30° and 60°) for a southward (northward) IMF, resulting in asymmetric energy transfer between the northern and southern hemispheres. The Martian outflow of mechanical energy appears near SZA ≈ 45° (SZA ≈ 30° and 60°) under a southward (northward) IMF, accompanied by an inflow due to the process of “solar wind pickup.” For energy transfer across the MPB, whether the IMF is northward or southward, the input of electromagnetic energy is twice as large as the input of mechanical energy, which is similar to Earth’s magnetopause for a southward IMF, but opposite to it for a northward IMF. The energy transfer rate of the MPB is slightly higher in a northward IMF than in a southward one, whereas the energy transfer rate of Earth’s magnetopause is far higher in a southward IMF than in a northward one.

Magnetic field analysis and modeling of gradient coils based on ferromagnetic coupling inside magnetically shielded cylinder

To accurately analyze the magnetic field of gradient coils inside a magnetically shielded cylinder (MSC) and enhance the precision of remanence compensation, analytical models for calculating the magnetic field of the gradient coils are proposed. First, the coupling between the high-permeability MSC and the coils is accurately analyzed based on Green’ s function method, magnetic field boundary conditions and image method. Secondly, the current density of four commonly used gradient coils is analyzed, and analytical models for the magnetic fields of these four types of gradient coils are established. Finally, the validity of the analytical models is proved through finite element simulations and experimental tests. The experimental results indicate that within the range of x,z∈−80,80mm (± 0.5R), the analytical values have good consistency with experimental values, and the maximum relative error between the two is only 0.91%. The analytical models will be beneficial to the research on the coil optimization design inside the MSC.

Inequalities à la Pólya for the Aharonov–Bohm eigenvalues of the disk

We prove an analogue of Pólya’s conjecture for the eigenvalues of the magnetic Schrödinger operator with Aharonov–Bohm potential on the disk for Dirichlet and magnetic Neumann boundary conditions. This answers a question posed by R. L. Frank and A. M. Hansson.

Effect of phase exchange kinetics on Taylor dispersion of chemically reactive solutes in an oscillatory magnetohydrodynamics flow between two parallel plates

The study of kinetic sorptive effects on the transport phenomena of reactive solute has numerous real-world applications, including in the industrial and environmental sectors. These kinds of investigations become more realistic when an oscillatory pressure gradient with both the reversible and irreversible reactions at the channel walls is considered in a magnetohydrodynamics flow. In the past, Ng and Yip [J. Fluid Mech. 446, 321–345 (2001)] studied the effect of sorptive phase exchange at boundaries on the solute transport phenomena in an open-channel flow using Mei's multiple-scale homogenization technique. They considered fluid flows without magnetic field and boundary absorption. This work uses the above-mentioned method to investigate the phase exchange kinetics of Taylor dispersion phenomena in a two-dimensional magnetohydrodynamics fluid flowing through a parallel channel. The paper discusses how various parameters and dimensionless numbers, such as the Hartmann, oscillatory Reynolds, and Damkohler, affect the flow velocity, transport coefficient, multi-dimensional concentration distributions, and transverse variation rate. Due to the strong magnetic field, the flow velocity and Taylor dispersivity are adversely affected and conspicuously reduced. Additionally, for large Damkohler numbers, the total dispersion coefficient and the Taylor dispersion coefficient both decrease. However, the longitudinal concentration distribution rises with the Hartmann number and partition coefficient. It is worth noting that in the presence of unequal boundary absorption, there is no occurrence of transverse symmetry in solute concentration at any given time. Controlling various processes of tracer dispersion in environmental systems, especially water purification and the chemical industry, may benefit from these intriguing findings.

Acceleration of Pick‐Up Ions in the Martian Magnetosheath: A Tianwen‐1 Case Study

AbstractThis study delves into a Pick‐Up Ion (PUI) event captured by the Mars Ion and Neutral Particle Analyzer aboard Tianwen‐1, revealing a faster acceleration than expected within the Martian magnetosheath. This event suggests the presence of a convection electric field considerably stronger than that typically observed in the solar wind. Through Magnetohydrodynamic simulation, we identified two regions of intensified convection electric fields within the inner magnetosheath, prominently manifested at mid to high solar zenith angles (SZA = 40°–70°) in the X‐Z plane of the Mars Solar Electric field coordinates. Tianwen‐1 observed that the peak of the electric field strength, up to five times of that in the solar wind, is located at the upper edge or within the Magnetic Pileup Boundary. Further study by test particle simulations showed acceleration by the electric field effectively doubles the energy gain of PUIs, in comparison to scenarios absent of this extra acceleration. It is revealed that the presence of such electric field regions within the Martian magnetosheath is a prevailing feature, shaped by the solar wind's interaction with Mars and modulated by the planet's rotating crustal magnetic fields.

Boundary condition effects on runaway electron mitigation coil modeling for the SPARC and DIII-D tokamaks

Extended-MHD modeling of planned Runaway Electron Mitigation Coils (REMC) for SPARC and DIII-D is performed with the NIMROD code. A coil has been designed for each machine, with the two differing in shape and location, but both having n = 1 symmetry (with n the toroidal mode number). Compared to previous modeling efforts, three improvements are made to the simulations boundary conditions. First a resistive wall model is used in place of an ideal wall. Second, the ThinCurr code is used to compute the time-dependent 3D fields used as magnetic boundary conditions for the simulations. Third, the simulation boundary is moved from the first-wall location to the Vacuum Vessel (VV), which extends the boundary past the location of the internal REMC. To remove the 3D coil from the simulation domain, an equivalent set of 3D fields is calculated at the VV boundary that produce approximately the same field distribution at the last closed flux surface assuming vacuum between the two. Each of these three boundary condition improvements leads to an improvement in the predicted performance of the REMC for both machines. The resistive wall alone primarily effects the resonance of the coil with the plasma after the TQ, affecting the q-profile evolution in the SPARC modeling, and allowing the applied spectrum to be modified in response to the plasma in the DIII-D modeling. The movement of the simulation boundary has the most significant effect on the RE confinement overall, including in the early stages, particularly for a DIII-D inner wall limited equilibrium, where the RE loss fraction increases from 90% to > 99%, with SPARC RE losses also occurring much earlier when the boundary is placed at the VV.

BepiColombo observations of cold oxygen and carbon ions in the flank of the induced magnetosphere of Venus

On 10 August 2021, the Mercury-bound BepiColombo spacecraft performed its second fly-by of Venus and provided a short-lived observation of its induced magnetosphere. Here we report results recorded by the Mass Spectrum Analyzer on board Mio, which reveal the presence of cold O+ and C+ with an average total flux of ~4 ± 1 × 104 cm−2 s−1 at a distance of about six planetary radii in a region that has never been explored before. The ratio of escaping C+ to O+ is at most 0.31 ± 0.2, implying that, in addition to atomic O+ ions, CO group ions or water group ions may be a source of the observed O+. Simultaneous magnetometer observations suggest that these planetary ions were in the magnetosheath flank in the vicinity of the magnetic pileup boundary downstream. These results have important implications regarding the evolution of Venus’s atmosphere and, in particular, the evolution of water on the surface of the planet.

A numerical study on MHD Maxwell fluid with nanoparticles over a stretching surface: Impacts of thermal radiation, convective boundary condition and induced magnetic field

The current study investigates the influence of induced magnetic field and convective boundary condition on the behavior of a magnetohydrodynamic (MHD) Maxwell fluid including nanoparticles flowing through a stretching sheet. Furthermore, the analysis considers the existence of radiation. Numerical solutions to the basic governing equations are achieved using the Runge–Kutta–Fehlberg technique. The impact of various physical parameters on concentration, velocity, and temperature profiles is deployed through graphs. The primary conclusions of this study are that increasing the Magnetic parameter decreases the Induced Magnetic field while increasing the Deborah parameter improves the velocity profile. Temperature distribution is growing due to increased estimates of the Radiation, Biot number, and Deborah number values. When the Lewis number values are raised, the concentration profiles get smaller but there is an opposite scenario deployed as the Thermophoresis parameter upsurges. The findings of this study are consistent with those that have been previously reported. The phenomenon of flow induced by a stretched surface finds several applications in various industrial and technological domains, including copper wire production, polymer extrusion, article manufacturing, and fiber synthesis. Induced magnetic fields are extremely prominent in many areas of science and technology, including electromagnetism, magnetic materials, and magnetic resonance imaging (MRI).

Numerical solutions for magneto-convective boundary layer slip flow from a nonlinear stretching sheet with wall transpiration and thermal radiation effects

A mathematical model is presented for magnetohydrodynamic viscous incompressible flow of an electrically conducting Newtonian polymeric fluid from a moving permeable horizontal stretching sheet with variable magnetic field, momentum and thermal slip boundary conditions. The emerging nonlinear ordinary differential boundary value problem is solved numerically by the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple symbolic software. The effects of the governing parameters on the dimensionless stream function, dimensionless flow velocity and the dimensionless temperature have been investigated, displayed graphically and discussed. It is found that greater momentum slip and magnetic field parameters reduce the dimensionless velocity. It is further observed that higher values of Prandtl number, thermal slip, and conductionradiation parameter (weaker radiation contribution) reduce the dimensionless temperature whilst stronger magnetic field increases the temperature due to the supplementary work expended in dragging the polymer against the action of the magnetic field which is dissipated as heat. Comparisons of numerical results with previous published results show an excellent agreement. The study finds applications in electro-conductive polymer (ECP) processing systems.

Martian bow shock and magnetic pileup boundary models based on machine learning

Traditional Martian bow shock and magnetic pileup (magnetopause) boundary models are based on the fitting of free parameters in a prescribed formula. The form of the formula, fitted data, and considered controlling parameters distinguish the individual models from each other. However, all these models have one thing in common: the shape of the boundary and the parametric dependence assumed are fixed by the prescribed formula. The fitted data set typically consists of individual identified boundary crossings. This approach can suffer from a significant bias, as the boundary crossings are more likely to be identified in regions where a spacecraft spends more time. In this study, we use an automated region classification of the data measured by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft to solar wind, magnetosheath, or magnetosphere. This is achieved by applying the Support Vector Machine method to individual spacecraft half-orbits (from periapsis to apoapsis or vice versa). Two different models of the locations of the bow shock and magnetic pileup boundaries are then constructed based on neural networks: i) a model trained using the classified data, and ii) a model trained using individual identified boundary crossings. As compared to formal empirical modeling efforts, the neural network models do not assume any prescribed shape/distance formula. Optimal model parameterization (considering the solar wind dynamic pressure, solar ionizing flux, crustal magnetic field magnitude, Alfvén Mach number, and interplanetary magnetic field magnitude) is discussed and the model performance evaluated.