Symmetric Magnetic Field Research Articles

Control of Three-Dimensional Natural Convection of Graphene–Water Nanofluids Using Symmetrical Tree-Shaped Obstacle and External Magnetic Field

This numerical investigation explores the enhanced control of the 3D natural convection (NC) within a cubic cavity filled with graphene–water nanofluids, utilizing a bottom-center-located tree-shaped obstacle and a horizontal magnetic field (MF). The analysis includes the effects of the Rayleigh number (Ra), the solid volume fraction of graphene (φ), the Hartmann number (Ha), and the fins’ length (W). The results show complex flow patterns and thermal behavior within the cavity, indicating the interactive effects of nanofluid properties, the tree-shaped obstacle, and magnetic field effects. The MHD effects reduce the convection, while the addition of graphene improves the thermal conductivity of the fluid, which enhances the heat transfer observed with increasing Rayleigh numbers. The increase in the fins’ length on the heat transfer efficiency is found to be slightly negative, which is attributed to the complex interplay between the enhanced heat transfer surface area and fluid flow disruption. This study presents an original combination of non-destructive methods (magnetic field) and a destructive method (tree-shaped obstacle) for the control of the fluid flow and heat transfer characteristics in a 3D cavity filled with graphene–water nanofluids. In addition, it provides valuable information for optimizing heat transfer control strategies, with applications in electronic cooling, renewable energy systems, and advanced thermal management solutions. The application of a magnetic field was found to reduce the maximum velocity and total entropy generation by about 82% and 76%, respectively. The addition of graphene nanoparticles was found to reduce the maximum velocity by about 5.5% without the magnetic field and to increase it by 1.12% for Ha = 100. Varying the obstacles’ length from W = 0.2 to W = 0.8 led to a reduction in velocity by about 23.6%.

Twist periodic solutions of the electron beam focusing system with unshielded cathode

In this article, we consider the electron beam focusing system guided by an axially symmetric periodic magnetic field with unshielded cathode. Based on the third‐order approximation method and some quantitative methods, we establish two different sufficient conditions for the existence of twist periodic solutions of the system. Such twist periodic solutions are stable in the sense of Lyapunov. Some results in the literature are generalized and improved.

Energetic particle tracing in optimized quasi-symmetric stellarator equilibria

Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has been proven to enable the construction of magnetic configurations with good confinement properties while taking only a fraction of the usual computation time to generate optimized magnetic equilibria. However, not much is known about the overall features of fast-particle orbits computed in such analytical, yet simplified, equilibria when compared with those originating from accurate equilibrium solutions. This work aims to assess and demonstrate the potential of the near-axis expansion to provide accurate information on particle orbits and to compute loss fractions in moderate to high aspect ratios. The configurations used here are all scaled to fusion-relevant parameters and approximate quasi-symmetry to various degrees. This allows us to understand how deviations from quasi-symmetry affect particle orbits and what are their effects on the estimation of the loss fraction. Guiding-centre trajectories of fusion-born alpha particles are traced using gyronimo and SIMPLE codes under the NEAT framework, showing good numerical agreement. Discrepancies between near-axis and magnetohydrodynamic fields have minor effects on passing particles but significant effects on trapped particles, especially in quasi-helically symmetric magnetic fields. Effective expressions were found for estimating orbit widths and passing–trapped separatrix in quasi-symmetric near-axis fields. Loss fractions agree in the prompt losses regime but diverge afterwards.

Wave transformations near a coronal magnetic null point

Context. Null points are often invoked in studies of quasi-periodic coronal jets and in connection with periodic signals preceding actual reconnection events. Although the periodicity of these events spans a wide range of periods, most show a 2- to 5-min periodicity compatible with the global p-modes. Aims We investigate whether magnetohydrodynamics (MHD) waves, in particular, acoustic p-modes, can cause strong current accumulation at the null points. This can in turn drive localized periodic heating in the solar corona. Methods. To do this, we began with a three-dimensional numerical setup incorporating a gravitationally stratified solar atmosphere and an axially symmetric magnetic field including a coronal magnetic null point. To excite waves, we employed wave drivers mimicking global p-modes. Using our recently developed wave-mode decomposition technique, we investigated the process of mode conversion, mode transmission, and wave reflection at various important layers of the solar atmosphere, such as the Alfvén acoustic equipartition layer and transition region. We examined the energy flux distribution in various MHD modes or in acoustic and magnetic components, as the waves propagate and interact with a magnetic field of null topology. We also examined current accumulation in the surroundings of the null point. Results. We found that most of the vertical velocity is transmitted through the Alfvén acoustic equipartition layer and maintains an acoustic nature, while a small fraction generates fast waves via the mode conversion process. The fast waves undergo almost total reflection in the transition region due to sharp gradients in density and Alfvén speed. There are only weak signatures of Alfvén wave generation near the transition region through the fast-to-Alfvén mode conversion. Because the slow waves propagate with the local sound speed, they are not much affected by the density gradients in the transition region and undergo secondary mode conversion and transmission at the Alfvén-acoustic equipartition layer surrounding the null point. This leads to fast-wave focusing at the null point. These fast waves have associated perturbations in current density and show oscillatory signatures that are compatible with the second harmonic of the driving frequency. This might result in resistive heating and in an enhanced intensity in the presence of finite resistivity. Conclusions. We conclude that MHD waves are a potential source for oscillatory current dissipation around the magnetic null point. We conjecture that in addition to oscillatory magnetic reconnection, global p-modes could lead to the formation of various quasi-periodic energetic events.

Higher-order magnetic skyrmions in nonuniform magnetic fields

For a two-dimensional Hubbard model with spin-orbit Rashba coupling in external magnetic field the structure of effective spin interactions is studied in the regime of strong electron correlations and at half-filling. It is shown that in the third order of perturbation theory, the scalar and vector chiral spin-spin interactions of the same order arise. The emergence of the latter is due to orbital effects of magnetic field. It is shown that for nonuniform fields, scalar chiral interaction can lead to stabilization of axially symmetric skyrmion states with arbitrary topological charges. Taking into account the hierarchy of effective spin interactions, an analytical theory on the optimal sizes of such states, the higher-order magnetic skyrmions, is developed for axially symmetric magnetic fields of the form $h(r)\ensuremath{\sim}{r}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\in}\mathbb{R}$.

Simulation study on 300mm monocrystalline silicon celerity single crystal

Since entering the 21st century, the survival and development of mankind are faced with great challenges and great opportunities. With the decrease of petroleum, coal, natural gas and other resources, a large number of harmful products generated in the combustion process of fossil fuels have caused incalculable adverse effects on human living environment. Thermal stress in crystals is one of the key factors affecting the properties of solar level monocrystalline silicon. In this paper, the relationship between the heat loss mode and the stress in crystal is studied. If carbon is introduced into the crystal growth process, it will promote the formation of oxygen precipitation and SiC precipitated phase, resulting in increased stress in the crystal, thus affecting the quality of monocrystalline silicon. The distribution of carbon impurities in the melt is closely related to the convection behavior of the melt. The carbon atoms in the atmosphere diffused into the melt mainly through the free surface area near the crucible wall. By adjusting the structural parameters of symmetric magnetic field and asymmetric magnetic field, the convection intensity in the carbon atom doped region can be suppressed, the thickness of carbon atom diffusion layer can be increased, and the oxygen content and distribution uniformity in the crystal can be controlled by magnetic pull technology to improve the crystal quality.

P-Mode Oscillations in Highly Gravitationally Stratified Magnetic Solar Atmospheres

The aim of the study reported in this paper is to gain understanding of solar global oscillations and the propagation characteristics of p-mode oscillations in the highly gravitationally stratified magnetic solar atmosphere. The paper presents the results of 3D (3-dimensional) numerical magnetohydrodynamic (MHD) simulations of a model solar atmosphere with a uniform, vertical and cylindrically symmetric magnetic field. We use simulation drivers which result in oscillations mimicking the behaviour of p-mode oscillations. The paper reports the variation of the energy flux and oscillation frequency of the magnetosonic modes and examines their dependence on the magnetic field strength. We report results for the temporal analysis of observational data for the quiet Sun and for a region containing a small sunspot (solar pore). We compare the temporal analysis of results from observations of these ubiquitous intensity oscillations with numerical simulations of potential signatures of global oscillations of the solar atmosphere. We conclude that magnetic regions of the solar atmosphere are favourable regions for the propagation of a small leakage of energy by slow magnetosonic modes. The results also exhibit a variation in the frequency of the oscillations at different heights in the low-to-mid solar atmosphere and for different values of the magnetic field. The numerically obtained periodic behaviour and variation in frequency, even in this simplified model atmosphere, is consistent with the observational data. We find frequencies and frequency variations that are similar to measurements obtained from the intensity time series of images taken by the Solar Dynamics Observatory.

Effects of Gradient Magnetic Field on Electrical Tree Growth Characteristics in Silicone Rubber

In this article, the positive and inverse gradient symmetric magnetic field and the asymmetric magnetic field with different angles are constructed. The influence of the magnetic field distribution on the electrical tree characteristics is investigated. The experimental results show that both the positive and the inverse gradient magnetic fields can promote the deterioration of the electrical trees. Under the symmetrical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta 1.5$ </tex-math></inline-formula> T gradient magnetic field, the tree initiation probability increases from 55% to 100%, and the breakdown time decreases by 67.5%. Under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -1.5 T, the tree initiation probability increases from 55% to 75%, and the breakdown time declines by 57.5%. The morphology of the electrical trees is largely affected by the distribution of the magnetic field. The dispersion of the degradation channels increases with the enhancement of the magnetic field. Under the asymmetric magnetic field, the deterioration process is also accelerated, with the increase of the magnetic field. More importantly, the growth direction of the electric trees shifts to the side with the higher magnetic flux density. The magnetic field enhances the local electric field and promotes the occurrence of partial discharge by exerting a deflection force on the charges. Consequently, the growth rate and morphology of electrical trees are affected.

К аналитической теории магнитных скирмионов высокого порядка в неоднородном магнитном поле

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q| &gt; 1 due to orbital effects. We describe the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor - chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10 /MgO/Nb.

To an analytical theory of higher-order magnetic skyrmions in nonuniform magnetic fields

It is shown that axially symmetric inhomogeneous magnetic fields can lead to stabilization of higher-order magnetic skyrmions with topological charge |Q|&amp;gt;1 due to orbital effects. We developed the analytical theory on the energy, size, and domain wall width of the such skyrmions in a power-law inhomogeneous fields, with a parameters corresponding to strongly correlated electron systems. The results obtained may have applications in describing the formation of nontrivial magnetic structures in inhomogeneous fields of superconducting vortices in heterostructures superconductor --- chiral magnet of the type [Ir1Fe0.5Co0.5Pt1]10/MgO/Nb. Keywords: magnetic skyrmions, nonuniform magnetic fields.

Investigation of the magnetron balancing effect on the ionized flux fraction and deposition rate of sputtered titanium species for the high-power impulse magnetron sputtering pulses of different lengths

The study is focused on the impact of different magnetic field configurations of a high-power impulse magnetron sputtering (HiPIMS) in a nonreactive mode on the film precursors. Ionized flux fraction and total flux deposited onto the substrate were measured with the magnetic quartz crystal microbalance probe placed in front of the target racetrack. Particularly, we investigated the degree of magnetron balancing and the geometry of the magnetic field above the Ti target surface (4 in. diameter), as crucial factors influencing the thin film deposition, for different HiPIMS pulse lengths. Three unbalanced (II type) magnetron configurations have been chosen for this study: two symmetric geometries—with a regular magnetic field (B parallel to the target about 80 and 35 mT) and one asymmetric (highly unbalanced) magnetron configuration with an intermediate magnetic field (B parallel to the target about 48 mT). The HiPIMS was operated keeping constant the peak current at 43 A for C0-E0 and C10-E0 B-field configurations and a lower value, 33 A, when operating in C10-E10 configuration. In addition to the peak current, the pulse frequency was kept constant at 100 Hz but the pulse length (power on-time, Ton) was varied from 50 up to 100 μs. Obviously, the pulse power and the average power continuously increase with the length of the pulse. The results reveal a significant difference in the trends of the deposition rate and ionized flux fraction reaching the substrate with respect to the degree of balancing of the magnetron. It was found that the ionized fraction of metal arriving at the substrate reaches its maximum for the pulse length between Ton ≈ 70–80 μs in both symmetric cases, with strong and weak magnetic fields. The ionized fraction of Ti atoms in the asymmetric configuration increased in all measured range with the pulse length and the growth rate has a smooth increase.

Graphene Dirac fermions in symmetric electric and magnetic fields: the case of an electric square well

In this paper, a simple method is proposed to get analytical solutions (or with the help of a few numerical calculations) of the Dirac-Weyl equation for low energy electrons in graphene in the presence of certain electric and magnetic fields. In order to decouple the Dirac-Weyl equation we have assumed a displacement symmetry of the system along a direction and some conditions on the magnetic and electric fields. The resulting equations have the natural form to apply the technique of supersymmetric quantum mechanics. The example of an electric well with square profile is worked out in detail to illustrate some of the most interesting features of this procedure.

Numerical Simulation for Magnetohydrodynamic Flow and Solidification in an Ultra-wide Slab Continuous Caster with Electromagnetic Stirring Roller

Electromagnetic stirring with segment roller in the secondary cooling zone is a very important metallurgical technology for the continuous casting of the ultra-wide slab. Thus, numerical simulation is applied to investigate magnetohydrodynamic flow and solidification in the continuous caster with strand electromagnetic stirring. Numerical results showed that, the predicted values agree well with the experimental data. If the electromagnetic stirring roller with the symmetric split structure forms the symmetric magnetic field, there are the symmetric electromagnetic force, the symmetric flow field and the symmetric solidified shell. If the single electromagnetic stirring roller with the symmetric split structure forms the symmetric electromagnetic force, the flow field is like a butterfly. If the two electromagnetic stirring rollers forms the symmetric electromagnetic force, the flow field is like two butterflies. The effect of strand electromagnetic stirring on the fluid flow in the mold can not be ignored in the case of SSR (Same direction for upper rollers, Same direction for lower roller, Reverse direction for relation between upper/lower rollers), and it can be ignored in the case of NAS (No upper rollers, Away direction for lower roller, Single roller for relation between upper/lower rollers) and CAR (Close direction for upper rollers, Away direction for lower roller, Reverse direction for relation between upper/lower rollers).

Asymmetric excitations of toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum in hybrid graphene-dielectric metasurface

We study asymmetric excitations of toroidal dipole resonance and magnetic dipole quasi-bound state in the continuum (BIC) in hybrid graphene-dielectric metasurface consisting of a nanoring and a Y-shaped nanobar. Through reducing or increasing inner radius of nanoring, the quasi-BIC dominated by magnetic dipole moment can be excited and effectively modulated via adjusting the Fermi energy and layer numbers of the graphene. The proposed metasurface can not only produce a symmetric localized magnetic field distribution but also create two asymmetric localized magnetic field distributions in near-infrared wavelength, providing a new way of indirectly manipulating the localized magnetic field enhancement. Our results can be of practical interest for a variety of applications including optical modulator, filter, switches and light trapping.

A New Symbolic Time Series Analysis Method Based on Time-to-Space Mapping, through a Symmetric Magnetic Field, Quantized by Prime Numbers

This work presents a new analysis method for two-symbol symbolic time series based on the time-to-space mapping achieved through a device of current carrying circular rings. An algorithm based on the theory of prime numbers is proposed for the approximate estimation of the stratified magnetic field produced by the aforementioned device. The main property of the specific algorithm is that it quantizes the stratified magnetic field. If a two-symbol symbolic time series is used to determine the flow directions of the rings’ currents, a time-to-space mapping of the dynamics of the system producing the time series is observed. A unique “fingerprint” of the symbolic dynamics is shaped by the spatial allocation of the values of the six-valued symmetric quantized magnetic field produced by the device. This allows for the quantitative evaluation of the original system’s dynamics by analyzing the resultant quantized magnetic field values space allocation, in a spectrum ranging from the lack of dynamics (randomness) to the presence of dynamics at all scales (criticality). Two examples of application–corresponding to the extremes of the dynamics spectrum, specifically, for symbolic time series resulting from (a) a random numbers generator and (b) the spin alternation of 2D-Ising in its critical state, verify the reliable time-to-space mapping of the involved symbolic dynamics. Moreover, an application to the symbolic sequence produced by the DNA of the GAPDH (Glyceraldehyde-3-Phosphate Dehydrogenase) human gene is presented as a real-world, intermediate dynamics case. The proposed symbolic time series analysis method presents the advantage that can take into account information related to both symbols, which is particularly useful in analyzing two-symbol time series of relatively short length where the probabilities of occurrence of the two symbols are not equal. By inferring the universality class of an artificial-neural-network-based hybrid spin model through the value of the critical exponent δ, it is shown that for such time series, the proposed method provides a unique way to expose the real dynamics of the underlying complex system, in contrast to the analysis of waiting times in the time domain that leads to an ambiguous quantitative result.

A 4.4-GHz 193.2-dB FoM 8-Shaped-Inductor Based LC-VCO Using Orthogonal-Coupled Triple-Coil Transformer

A 4.2-to-4.6 GHz 8-shaped-inductor based LC-VCO with an orthogonal-coupled triple-coil transformer is presented in this brief. The orthogonal-coupled triple-coil transformer is designed to reduce magnetic coupling and improve phase noise. The mutual inductance between the 8-shaped inductor and the tail-filtering inductor is negligible due to the symmetrical and reversal magnetic field generated by the two loops of the 8-shaped inductor, which avoids the additional chip area occupation of the bulky tail-filtering inductor. In addition, an 8-shaped transformer with thin line width is proposed to bias the varactor instead of using resistors, which avoids the resistor thermal noise contribution. The VCO is implemented in a 180 nm CMOS process, which consumes 7.4 mA current from a 1 V power supply. By adopting the 8-shaped inductor with noise filtering and noise-free biasing technique from the orthogonal-coupled triple-coil transformer, the measured phase noise achieves −149.3 dBc/Hz at 10 MHz offset away from a 4.3 GHz carrier and the resulting figure-of-merit (FoM) is −193.2 dB. To the best knowledge of the authors, this brief presents the VCO with the best FoM among published 8-shaped-inductor based LC-VCOs.

Investigating the Asymmetry of Magnetic Field Profiles of “Simple” Magnetic Ejecta through an Expansion-modified Flux Rope Model

Magnetic clouds (MCs) are most often fitted with flux rope models that are static and have symmetric magnetic field profiles. However, spacecraft measurements near 1 au show that MCs usually expand when propagating away from the Sun and that their magnetic field profiles are asymmetric. Both effects are expected to be related, since expansion has been shown to result in a shift of the peak of the magnetic field toward the front of the MC. In this study, we investigate the effects of expansion on the asymmetry of the total magnetic field strength profile of MCs. We restrict our study to the simplest events, i.e., those that are crossed close to the nose of the MC. From a list of 25 such “simple” events, we compare the fitting results of a specific expanding Lundquist model with those of a classical force-free circular cross-sectional static Lundquist model. We quantify the goodness of the fits by the χ 2 of the total magnetic field and identify three types of MCs: (i) those with little expansion, which are well fitted by both models; (ii) those with moderate expansion, which are well fitted by the expanding model, but not by the static model; and (iii) those with expansion, whose asymmetry of the magnetic field cannot be explained. We find that the assumption of self-similar expansion cannot explain the measured asymmetry in the magnetic field profiles of some of these magnetic ejecta (MEs). We discuss our results in terms of our understanding of the magnetic fields of the MEs and their evolution from the Sun to Earth.

Stability of axially symmetric magnetic fields in stars

Abstract The magnetic fields observed in Ap stars, white dwarfs, and neutron stars are known to be stable for long times. However, the physical conditions inside the stellar interiors that allow these states are still a matter of research. It has been formally demonstrated that both purely toroidal and purely poloidal magnetic fields develop instabilities at some point in the star. On the other hand, numerical simulations have proved the stability of roughly axisymmetric magnetic field configurations inside stably stratified stars. These configurations consist of mutually stabilizing toroidal and poloidal components in a twisted torus shape. Previous studies have proposed rough upper and lower bounds on the ratio of the magnetic energy in the toroidal and poloidal components of the magnetic field. With the purpose of mapping out the parameter space under which such configurations remain stable, we used the Pencil Code to perform 3D magnetohydrodynamic simulations of the evolution of the magnetic field in non-rotating, non-degenerate stars in which viscosity is the only dissipation mechanism, both for stars with a uniform (barotropic) and radially increasing (stably stratified) specific entropy. Furthermore, we considered different conditions regarding the degree of stable stratification and the magnetic energy in each component, roughly confirming the previously suggested stability boundaries for the magnetic field.

Radial spin echo small-angle neutron scattering method: concept and performance.

A novel spin echo small-angle neutron scattering (SESANS) concept based on a rotationally symmetric magnetic field geometry is introduced. The proposed method is similar to the conventional linear SESANS technique but uses longitudinal precession fields and field gradients in a radial direction, as typically found in neutron spin echo (NSE) spectrometers. Radial SESANS could thus be implemented as an add-on to NSE setups. The neutron trajectory through the instrument is encoded with the help of radial gradients generated by radial shifters, which are coils placed in the beam area similar to Fresnel coils. The present work introduces the setup of the instrument and explores its performance and the relationship between the encoded momentum transfer and the precession angle. The results indicate that radial SESANS is only sensitive to scattering along the radial direction and thus measures the projected correlation function along this direction as a function of the spin echo length, defined similarly to linear SESANS. For an evaluation of the performance of the setup, the case of scattering from solid spheres is considered and the results calculated for the radial and linear SESANS cases are compared. Also discussed is the implementation of the radial magnetic field geometry in spin echo modulated small-angle neutron scattering.

Effects of unsymmetrical magnetic field on discharge characteristics of Hall thruster with large height-radius ratio

The large height-radius ratio design of the Hall thruster increases the difference of radial distributions of magnetic field and plasma parameters in the channel, so that the optimal discharge effect of the thruster cannot be guaranteed under the symmetrical magnetic field configuration relative to the channel centerline. In this work, the effects of the unsymmetrical magnetic field on discharge characteristics of Hall thruster with large height-radius ratio were studied through experiments and PIC simulations. The results show that the thruster can realize stable discharge in a wide power range under unsymmetrical magnetic fields. Also, the unsymmetrical magnetic field plays a positive role in improving the discharge performance and prolonging the service life of the thruster. The inward-inclined magnetic field can effectively improve the discharge performance of the thruster, and the discharge efficiency can be increased by 1.5% under the rated working condition compared with the symmetrical magnetic field. The advantage in performance is mainly attributed to the improvement of ionization efficiency of propellant. The outward-inclined magnetic field is more conducive to prolong the service life of the thruster, and the peak value of ion power deposition on the inner wall can be reduced by 40% under the rated working condition due to the outward inclination of the ionization zone and the reduction of the radial electric field. However, under unsymmetrical magnetic field, the ionization zone deviates from the channel center, and the high ionization rate zone is more dispersed in distribution, thus leading to the increase in plume divergence angle. This study verifies that the unsymmetrical magnetic field has certain advantages under the structure of large height-radius ratio, which could be used as a guidance for the optimal design of Hall thruster with large height-radius ratio.