Time-varying External Magnetic Field Research Articles

Depinning of domain walls in a notched ferromagnetic nanostrip: role of inertial and nonlinear damping effects

Abstract In this work, we investigate theoretically the static and kinetic depinning field of a domain wall in a notched magnetic nanostrip under the generalized framework of the Landau–Lifshitz-Gilbert equation, which combines inertial and nonlinear viscous-dry friction damping effects. We assume a head-to-head transverse domain wall configuration and analyzed its motion subject to a time-varying external magnetic field. To deduce the equation ruling the spatio-temporal evoution of the magnetic domain wall, we adopt the Schryer and Walker trial function approach. The results show that static and kinetic depinning fields increase as the dry friction dissipation increases. Moreover, viscous dissipation exhibits a weak dependence on the kinetic depinning field and saturated domain wall velocity, while inertial damping due to the relaxation time of angular momentum significantly impacts the kinetic depinning field, depinning time, and breakdown velocity. Our numerical results are in good qualitative agreement with the recent observations reported in the literature.

Landau–Zener–Stückelberg–Majorana-like dynamics induced by tunneling of spin qubit states in a multiband two-state magnetic quantum wire

We investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.

Numerical modelling of HTS tapes under arbitrary external field and transport current via integral method: review and application to electrical machines *

Superconductors in practical use can be subjected to spatially non-uniform and time-varying external magnetic field as well as carrying a transport current, for example, in an electrical machine. This paper verifies that the integral method can be used in situations in which the external field is spatially non-uniform, by providing both theoretical reasoning and simulation results. Variations in the integral method are reviewed, such as how to impose transport current. Further, the integral method is applied to calculate ac loss in superconducting tapes in an air-cored electrical machine in a two-stage process: the external field is calculated in a COMSOL model without superconducting tapes, and exported into the integral method model that consists of the tapes only. The time taken by the integral method is a small fraction of the time taken by the full machine model in COMSOL, which uses the T-A formulation. There are good agreements between the full COMSOL model and two-stage method incorporating the integral method.

Comment on “Transverse vibration analysis of single-layered graphene sheet under magneto-thermal environment based on non-local plate theory [J. Appl. Phys. 116(16), 164303 (2014)]” and “Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems [J. Appl. Phys. 111(11), 113511 (2012)

The impact of a time-varying external magnetic field on carbon nanotubes has been studied using Maxwell’s equations in the mentioned articles. However, the Maxwell’s equations are erroneously presented in the papers. The incorrect Maxwell’s equations, their derivatives, and the Lorentz force equations have all been examined in this work. In this article, we have endeavored to ensure that the equations are formatted correctly and have made an effort to do so. We have made an effort to intuitively correct the equations’ errors. We did not comment on the other portions of the mentioned articles; instead, we restricted ourselves to the examination of the impact of Maxwell’s equations and Lorentz force equations.

Nonlinear dynamics and bifurcations of a planar undulating magnetic microswimmer.

Swimming microorganisms such as flagellated bacteria and sperm cells have fascinating locomotion capabilities. Inspired by their natural motion, there is an ongoing effort to develop artificial robotic nanoswimmers for potential in-body biomedical applications. A leading method for actuation of nanoswimmers is by applying a time-varying external magnetic field. Such systems have rich and nonlinear dynamics that call for simple fundamental models. A previous work studied forward motion of a simple two-link model with a passive elastic joint, assuming small-amplitude planar oscillations of the magnetic field about a constant direction. In this work, we found that there exists a faster, backward motion of the swimmer with very rich dynamics. By relaxing the small-amplitude assumption, we analyze the multiplicity of periodic solutions, as well as their bifurcations, symmetry breaking, and stability transitions. We have also found that the net displacement and/or mean swimming speed are maximized for optimal choices of various parameters. Asymptotic calculations are performed for the bifurcation condition and the swimmer's mean speed. The results may enable significantly improving the design aspects of magnetically actuated robotic microswimmers.

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

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

Numerical Studies of Dynamic Characteristics of a Stack-Type HTS Maglev System Based on H-Formulation

High temperature superconducting (HTS) magnetic levitation (maglev) is a promising technology for future high-speed transit systems. Superconducting magnetic bearings are made of a permanent magnet guideway and HTS bulks (bulk-type) or stacks of 2G HTS tapes (stack-type). If the dynamic behavior of bulk-type HTS maglev systems has been well reported, there is little literature about the dynamics of stack-type HTS maglev system. To fill the gap, we built here an electromagnetic-mechanical model of a stack-type bearing. We used a segregated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> -formulation finite element model to account for the nonlinear resistivity. The multi-layer structure of the HTS tape is either homogenized or modeled in detail. We studied the bearing dynamic response when subjected to different time-varying external magnetic fields mimicking the guideway irregularity and the vehicle speed. The results show that the induced current in the copper layer negatively impacts the stability. By extension, since it cannot account for the copper layer, the homogenized model is not suitable for such analysis. This work contributes to finding viable measures for improving the stability of stack-type HTS maglev systems.

Two-dimensional ferromagnetic systems with finite driving

We study the effect of finite driving by the time-varying external magnetic field in the two-dimensional disordered ferromagnetic systems portrayed on the case of nonequlibrium athermal random field Ising model. The response of studied systems is rate-dependent exhibiting scaling and data collapsing above the dynamical critical point in the full range of driving rates provided that the system parameters satisfy both the finite-size and here introduced rate-dependent scaling conditions. These findings are based on extensive numerical simulations of large systems reliably demonstrating the observed behavior and could be relevant for real thin systems driven at finite rates.

Real-time magnetometry with coherent population trapping in a nitrogen-vacancy center

We demonstrate real-time magnetometry by detecting fluorescence from a nitrogen-vacancy center in the setting of coherent population trapping and by estimating the magnetic field from the time series of the observed photon counts, which are correlated with the underlying field variation. The proof-of-principle experiment uses an external time-varying magnetic field that follows an Ornstein-Uhlenbeck (OU) process. A conventional estimator based on the use of average photon counts per relevant time interval is susceptible to photon number shot noise and performs poorly at relatively low average photon counts. In comparison, by taking into consideration the statistical properties of the OU process, a Bayesian inference-based estimator can effectively update dynamical information of the field in real time with the detection of just a single photon.

Kinetic Ising model under sinusoidal oscillating external magnetic field: hysteresis and dynamic phase transition

Kinetic Ising ferromagnet, a bistable system, is studied in two dimensions on large systems under a time-varying sinusoidal external magnetic field of a fixed period P and different amplitudes $$h_0$$ . Far below the critical temperature $$T_c$$ of ferro to paramagnet transition of the equilibrium zero-field Ising model, another critical temperature $$\theta _c$$ is found to exist below which the system is in dynamic ordered phase (DOP) and above which the system is in dynamic disordered phase (DDP). Two important aspects of a bistable system under external time varying field, hysteresis and dynamic phase transition (DPT) are studied performing extensive numerical simulations. The hysteresis loops are asymmetric in DOP whereas they are symmetric in DDP. The hysteresis loop properties are estimated, developing a new methodology which provides information on loop orientation $$\alpha $$ and its aspect ratio $$\varPhi $$ over the usual properties such as area A and dynamic correlation C. The DPT occurs at a temperature $$\theta _c$$ ( $$\ll T_c$$ ) at which the mean metastable lifetime $$\langle \tau \rangle $$ becomes comparable to the half period $$P_{1/2}$$ of the applied filed. Though the smaller systems at higher field amplitudes are found to be in the stochastic resonance regime, the larger systems at all field amplitudes are found to display a continuous transition. The DPT is characterized by the critical exponents of 2d equilibrium Ising model. Discontinuous transition due to stochastic resonance at high field regime seems to be a finite size effect for the DPT under a sinusoidal oscillating field.

MAGNETO-THERMOELASTIC PROBLEM WITH EDDY CURRENT LOSS OF A THERMOSENSITIVE CONDUCTIVE PLATE

In this paper a two dimensional magneto-thermoelastic problem of a thermosensitive finite conducting plate with eddy current loss is considered. It is assumed that the plate is influenced by a time-varying external magnetic field and that the heating is caused by Joule heat. The fundamental equations for magnetic field, heat conduction and elastic fields are formulated. Temperature dependent material properties and heat source as eddy current loss is considered in the heat conduction equation. Kirchhoff's variable transformation is employed to convert nonlinear to linear heat conduction equation. Integral transform technique is used to solve the magnetic field and temperature distribution. The stresses in a plane state are determined by using Airy's stress function. The numerical analysis is carried out and the results are graphically displayed.

A feasible neuron for estimating the magnetic field effect

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

Thermodynamics of interacting magnetic nanoparticles

We apply the concepts of stochastic thermodynamics combined with transition-state theory to develop a framework for evaluating local heat distributions across the assemblies of interacting magnetic nanoparticles (MPs) subject to time-varying external magnetic fields. We show that additivity of entropy production in the particle state-space allows separating the entropy contributions and evaluating the heat produced by the individual MPs despite interactions. Using MP chains as a model system for convenience, without losing generality, we show that the presence of dipolar interactions leads to significant heat distributions across the chains. Our study also suggests that the typically used hysteresis loops cannot be used as a measure of energy dissipation at the local particle level within MP clusters, aggregates, or assemblies, and explicit evaluation of entropy production based on appropriate theory, such as developed here, becomes necessary.

3D Path-Following Using MRAC on a Millimeter-Scale Spiral-Type Magnetic Robot

This letter focuses on the 3D path-following of a spiral-type helical magnetic swimmer in a water-filled workspace. The swimmer has a diameter of 2.5 mm, a length of 6 mm, and is controlled by an external time-varying magnetic field. A method to compensate undesired magnetic gradient forces is proposed and tested. Five swimmer designs with different thread pitch values were experimentally analyzed. All were controlled by the same model reference adaptive controller (MRAC). Compared to a conventional hand-tuned PI controller, their 3D path-following performance is significantly improved by using MRAC. At an average speed of ${\text{50}}\,\text{mm}$ /s, the path-following mean error of the MRAC is 3.8 $ \;\pm\; $ 1.8 mm, less than one body length of the swimmer. The versatility of this new controller is demonstrated by analyzing path-following through obstacles on a helical trajectory and forward & backward motion.

Non-monotonic response of a sheared magnetic liquid crystal to a continuously increasing external field.

Utilizing molecular dynamics simulations, we report a nonmonotonic dependence of the shear stress on the strength of a continuously increasing (i.e., time-varying) external magnetic field (H) in a liquid-crystalline mixture of magnetic and nonmagnetic anisotropic particles. We relate the origin of this nonmonotonicity of the transient dynamics to the competing effects of particle alignment along the shear-induced direction, on the one hand, and the magnetic field direction, on the other hand. To isolate the role of these competing effects, we consider a two-component mixture composed of particles with effectively identical steric interactions, where the orientations of a small fraction, i.e., the magnetic ones, are coupled to the external magnetic field. By increasing H from zero, the orientations of the magnetic particles show a Fréederickz-like transition and eventually start deviating from the shear-induced orientation, leading to an increase in shear stress. Upon further increase of H, a demixing of the magnetic particles from the nonmagnetic ones occurs, which leads to a drop in shear stress, hence creating a nonmonotonic response to H. Unlike the equilibrium demixing phenomena reported in previous studies, the demixing observed here is neither due to size-polydispersity nor due to a wall-induced nematic transition. Based on a simplified Onsager analysis, we rather argue that it occurs solely due to packing entropy of particles with different shear- or magnetic-field-induced orientations.

Detection of slowly rotating n = 1 mode with signal compensation for an externally perturbed field in the KSTAR tokamak

A mode identification method for slowly rotating (or non-rotating) n (toroidal mode number) = 1 plasma instabilities has been newly established with the signal compensation method used for an external time-varying magnetic field. The mode identification method is based on the Fourier decomposition scheme and processes the signal of the magnetic probes (MPs) on the passive stabilizer in the Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak. To exclude the non-plasma magnetic perturbation by the external current coils and their secondary eddy currents on the passive stabilizer that may not be easily characterized, the ARX-SISO (autoregressive with exogenous terms-single input single output) method has been introduced in the signal compensation process. Preliminary off-line analysis presented herein confirms that this method can adequately detect the time evolution of the mode-locking, along with a slowly rotating state, even in the presence of external magnetic perturbations.

Analytical solution of the induced currents in multilayer cylindrical conductors under external electromagnetic sources

We present a closed-form solution for the induced losses in round conductors consisting of several concentric layers. The geometry under study corresponds to an infinitely-long and isolated multilayer cylinder where layers can have different electromagnetic properties and the number of layers is not restricted. The multilayer conductor is under an external time-varying magnetic field which induces currents and, accordingly, generates Joule dissipation. Total induced losses are obtained by integrating the losses of each layer. Mathematical expressions of the current distribution in each layer are derived from the solution of Maxwell’s equations. These expressions consist of a combination of Bessel functions of different kinds and orders. The current distribution in a particular layer not only depends on the properties of the layer but also on the properties of the rest of layers. Consequently, matrix formalism is adopted for describing current distribution of layers. Matrix description is numerically solved and results are compared with finite element simulations for different arrangements and cases.

Mitigation of Demagnetization of Bulk Superconductors by Time-Varying External Magnetic Fields

Large single-grain high-temperature superconducting bulks have significant potential to replace permanent magnets in various engineering applications. However, based on our previous research, the trapped field in a bulk superconductor can be attenuated or even erased when a bulk is subjected to a time-varying external magnetic field. Therefore, it is important to develop a method to protect bulks from demagnetization by improving the thermal conduction of the bulk and/or reducing ac losses. Improvement in the thermal conduction of bulks involves modification of the material fabrication process, which may have a detrimental effect on its superconducting properties. Employing shielding materials around a bulk helps to decrease the ac losses, but also provides a durable way to maintain the original material properties. In this paper, two shielding cases are proposed and evaluated numerically: ring-shaped shielding with a copper coil and surface shielding with a ferromagnetic material. Based on the numerical modeling results, the ring-shaped coil works well for externally applied ac fields of larger magnitude and higher frequency. However, the ferromagnetic material was preferable for surface shielding for relatively lower fields. Finally, an optimal shield design is presented.

Development of an Analytical-Oriented Extensive Model for AC Coupling Losses in Multilayer Superconducting Composites

Previous analytical models of ac coupling losses in multifilamentary composites under a time-varying external magnetic field were developed for specific strand geometries. Therefore, no global expression of coupling losses was established for any circular geometry. The purpose of this paper is, thus, to present the general analytical strategy and the assumptions of the model developed at CEA. Furthermore, coupling losses are generally characterized by a global time constant nτ.In this paper, effective coefficients (analogous to time constants) are developed to reflect the coupling between the different layers. A global linear equation system linking the amplitudes of the electric field in each layer and their time variation and that of the external magnetic field is deduced, establishing a coupling matrix built with time constant coefficients. In addition to the physical interpretation of the quantities defined, the global equation is numerically solved. Local fields are quantified, as well as currents and ac coupling losses in different types of composites. A better physical understanding of the composite is tentatively achieved by the use of this analytical model.

Experimental Analysis on Initial Current Decay Characteristics of Persistent-Mode HTS Coil by External Alternating Magnetic Field

This paper deals with the current decay characteristics of a high-T c superconducting (HTS) coil operated in persistent current mode (PCM) under alternating magnetic field. In superconducting synchronous machine applications, such as linear synchronous motor (LSM), the superconducting coils are designed to operate in PCM to obtain steady-magnetic field with DC transport current. This superconducting coil operates on a direct current, but it can be exposed to alternating magnetic field due to the armature winding. When the field coils are subjected to an external time-varying magnetic field, it is possible to result in a current decay for those coils in PCM operation due to electrical AC loss. In this research, a current decay measurement system, which consists of field coil and armature coil, was fabricated to verify current decay characteristics of field coil in PCM operation against external alternating magnetic field. The current decay rate for the field coil was measured by using a hall sensor as a function of amplitude and frequency of armature coil.