Quasi-static Field Research Articles

An advanced numerical technique for a quasi-static electromagnetic field simulation based on the finite-difference time-domain method

In this paper, an advanced numerical technique is proposed for a low-frequency electromagnetic field simulation. The finite difference time domain (FDTD) method is one of the best methods for analyzing electromagnetic field problems, which require high levels of precision, such as a heterogeneous whole-body voxel human model. However, directly using the standard FDTD method in the quasi-static frequency band requires an extra-large number of iterations. We overcome this drawback using the hybrid of surface equivalence theorem and quasi-static FDTD (QS-FDTD) method. The surface equivalence theorem is used to consider arbitrary shape of source and the QS-FDTD is applied to obtain electromagnetic response quickly in the low-frequency region. The results of the proposed method are in good agreement with those from a commercial electromagnetic simulator. The proposed method is valid where the quasi-static approximation is satisfied.

Dynamic Green's functions for multiple circular inclusions with imperfect interfaces using the collocation multipole method

This paper presents a semi-analytical approach to solve anti-plane dynamic Green's functions for an elastic infinitely extended isotropic solid (matrix) containing multiple circular inclusions with imperfect interfaces. A linear spring model with vanishing thickness is employed to character the imperfect interface. The multipole expansions of anti-plane displacement of the matrix and inclusion, induced by a time-harmonic anti-plane line force located in the matrix or in the inclusion, are expanded by using Hankel and Bessel functions, respectively. The imperfect interface condition is satisfied by uniformly collocating points along the interface of each inclusion. For the imperfect interface condition, the normal derivative of the anti-plane displacement with respect to a non-local polar coordinate system is developed without any truncation error for multiply-connected domain problems. For the case of one circular inclusion, the proposed quasi-static stress field matches well with the analytical static solution. The proposed quasi-static stress fields containing two and three circular inclusions are critically compared with those calculated by static analysis using the finite element method. Finally, extensive studies are presented to investigate the effects of the frequency of excitation, imperfect interface and separation between inclusions on the dynamic Green's functions.

Effects of plasma density on laser-generated energetic electron generation and transport in a plasma channel

We use two-dimensional particle-in-cell simulations to investigate how the plasma density n0 of the channel target affects energetic-electron generation and transportation. The simulations show that the optimum plasma-density regime is 10 ≤ n0 ≤ 25 for the present simulation parameters, which results in a peak energy flux and coupling efficiency from laser to electrons. In this case, the laser beam propagates stably in the channel, which has the advantage of increasing the acceleration length and more effectively generating high-energy electrons. Furthermore, the high-current electron beam and the density modulation induce strong azimuthal magnetic fields and double-layer radial electric fields around the inner surface of the channel, which consistently guide and collimate the hot-electron bunch so that it propagates over rather long times and distances. Upon further increasing the plasma density n0, the hot electrons are scattered out of the channel by the damped laser pulse and the reduced quasistatic interface electromagnetic fields, reducing the long-time transport. The use of a proper plasma-density channel stably guides the relativistically intense laser pulse and greatly improves the properties of the electron beam.

Study of Three-dimensional Magnetic Structure and the Successive Eruptive Nature of Active Region 12371

Abstract We study the magnetic structure of a successively erupting sigmoid in active region 12371 by modeling the quasi-static coronal field evolution with nonlinear force-free field (NLFFF) equilibria. Helioseismic and Magnetic Imager/Solar Dynamic Observatory vector magnetograms are used as input to the NLFFF model. In all eruption events, the modeled structure resembles the observed pre-eruptive coronal sigmoid and the NLFFF core field is a combination of double inverse-J-shaped and inverse-S field lines with dips touching the photosphere. Such field lines are formed by the flux cancellation reconnection of opposite-J field lines at bald-patch locations, which in turn implies the formation of a weakly twisted flux-rope (FR) from large-scale sheared arcade field lines. Later on, this FR undergoes coronal tether-cutting reconnection until a coronal mass ejection is triggered. The modeled structure captured these major features of sigmoid-to-arcade-to-sigmoid transformation, which is reoccuring under continuous photospheric flux motions. Calculations of the field line twist reveal a fractional increase followed by a decrease of the number of pixels having a range of twist. This traces the buildup process of a twisted core field by slow photospheric motions and the relaxation after eruption, respectively. Our study infers that the large eruptivity of this AR is due to a steep decrease of the background coronal field meeting the torus instability criteria at a low height (≈40 Mm) in contrast to noneruptive ARs.

3D Visible-Light Invisibility Cloak.

The concept of an invisibility cloak is a fixture of science fiction, fantasy, and the collective imagination. However, a real device that can hide an object from sight in visible light from absolutely any viewpoint would be extremely challenging to build. The main obstacle to creating such a cloak is the coupling of the electromagnetic components of light, which would necessitate the use of complex materials with specific permittivity and permeability tensors. Previous cloaking solutions have involved circumventing this obstacle by functioning either in static (or quasistatic) fields where these electromagnetic components are uncoupled or in diffusive light scattering media where complex materials are not required. In this paper, concealing a large‐scale spherical object from human sight from three orthogonal directions is reported. This result is achieved by developing a 3D homogeneous polyhedral transformation and a spatially invariant refractive index discretization that considerably reduce the coupling of the electromagnetic components of visible light. This approach allows for a major simplification in the design of 3D invisibility cloaks, which can now be created at a large scale using homogeneous and isotropic materials.

Global Evolution of an Accretion Disk with a Net Vertical Field: Coronal Accretion, Flux Transport, and Disk Winds

Abstract We report results from global ideal MHD simulations that study thin accretion disks (with thermal scale height H/R = 0.1 and 0.05) threaded by net vertical magnetic fields. Our computations span three orders of magnitude in radius, extend all the way to the pole, and are evolved for more than 1000 innermost orbits. We find that (1) inward accretion occurs mostly in the upper magnetically dominated regions of the disk at z ∼ R, similar to predictions from some previous analytical work and the “coronal accretion” flows found in GRMHD simulations. (2) A quasi-static global field geometry is established in which flux transport by inflows at the surface is balanced by turbulent diffusion. The resulting field is strongly pinched inwards at the surface. A steady-state advection–diffusion model, with a turbulent magnetic Prandtl number of order unity, reproduces this geometry well. (3) Weak unsteady disk winds are launched beyond the disk corona with the Alfvén radius R A /R 0 ∼ 3. Although the surface inflow is filamentary and the wind is episodic, we show that the time-averaged properties are well-described by steady-wind theory. Even with strong fields, β 0 = 103 at the midplane initially, only 5% of the angular momentum transport is driven by the wind, and the wind mass flux from the inner decade of the radius is only ∼0.4% of the mass accretion rate. (4) Within the disk, most of the accretion is driven by the Rϕ stress from the MRI and global magnetic fields. Our simulations have many applications to astrophysical accretion systems.

New Type of Second-Order Tetrahedral Edge Elements by Reducing Edge Variables for Quasi-Static Field Analysis

Second-order tetrahedral edge elements afford much better accuracy in magnetic field analysis compared with first-order elements. However, they often entail higher computational cost due to the higher number of unknowns, many of them being redundant. The partial tree-gauging approach eliminates only a portion of the redundant edge variables, often reducing the overall computational cost. In this paper, we propose a new partial tree-gauging approach in second-order tetrahedral edge elements by unifying the two edges on the sides of elements into one, resulting in a new type of second-order tetrahedral edge element. Using the proposed elements in the analysis of two linear quasi-static magnetic field problems reveal the superiority of the edge unification over the conventional partial tree gauging in term of computational load.

Cauer Ladder Network Representation of Eddy-Current Fields for Model Order Reduction Using Finite-Element Method

A novel model order reduction method for efficient analysis of linear eddy-current problems is proposed in which the quasi-static electromagnetic fields are expressed by a weighted sum of a sequence of static electric- and magnetic-field modes. The modes are calculated sequentially by static electric and static magnetic computations using the conventional finite-element method, and the time-dependent weights are the voltages and currents of an equivalent Cauer ladder network of the problem. In this paper, the formulation of the method and a numerical test problem are presented, and the accuracy and enormous efficiency of the method are demonstrated by solving a 3-D nonlinear inductor model with a voltage excitation by a dc–dc converter, linearized around the dc current using frozen differential permeability.

A Full-Wave Integral Equation Method Including Accurate Wide-Frequency-Band Wire Models for WPT Coils

A full-wave surface integral equation method is used for modeling coils in a wide frequency range. This is of high importance in the analysis of resonant wireless power transfer links, for example. This paper presents a nonlocal generalization of the impedance boundary condition (BC) concept by incorporating a 2-D model (using the finite element method here) of the quasi-static electromagnetic field within the wire. This yields a numerical approximation of the nonlocal impedance BC on the wire surface that holds true at any frequency. The 2-D eddy-current model has to be evaluated only twice at one frequency, which makes the scheme computationally efficient. The method accurately predicts the ohmic loss as shown by the validations against alternative methods.

Diffractive Hyperbola of a Skin Layer

Based on an analysis of physics of the phase transition from the quasistatic state field to the running wave field of elementary electric and magnetic dipoles located in absorbing media, it is concluded that the skin layer is formed at the boundary of this phase transition. The possibility is considered of obtaining the diffractive hyperbola of the skin layer and its subsequent application for sensing of objects in strongly absorbing media.

Wideband Electromagnetic Model and Analysis of Shielded-Pair Through-Silicon Vias

The 3-D multistrata integration puts forward high requirements for signal integrity. The shielded-pair through-silicon vias (SPTSVs) proposed in this paper feature superior transmission properties and high jamming immunity suitable for differential-mode and common-mode transmission. Based on the quasi-static field theory, a wideband impedance model of SPTSVs considering the proximity effect, the line-to-line crosstalk, and the eddy current effect is derived. The parasitic parameters calculated by the impedance model are further given. The finite-element analysis shows that the proposed model highly agrees with the 3-D full-wave simulation and the analytical calculation. In addition, the characteristics of the impedance and the transmission coefficient are deeply analyzed with different design parameters. Finally, the impacts of the substrate effect and the metal–oxide–semiconductor effect on electrical characteristics of SPTSVs are revealed.

On Quasi-stationary Mean Field Games Models

We explore a mechanism of decision-making in mean field games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the players observe the evolution of the system and adapt to their new environment without anticipating. With a specific cost structures, these models give rise to coupled systems of partial differential equations of quasi-stationary nature. We provide sufficient conditions for the existence and uniqueness of classical solutions for these systems, and give a rigorous derivation of these systems from N-players stochastic differential games models. Finally, we show that the population can self-organize and converge exponentially fast to the ergodic mean field games equilibrium, if the initial distribution is sufficiently close to it and the Hamiltonian is quadratic.

Overcoming the Chu lower bound on antenna Q with highly dispersive lossy material

Beginning with a brief overview of the history of lower bounds on the quality factor Q of antennas and the fundamental relationships between the impedance, bandwidth, and Q of antennas, it is demonstrated by means of RLC circuit models of electrically small antennas that their isolated-resonance quality factors obtained from the ‘Q-energy’ predicts their bandwidths with greater accuracy than the ‘equivalent-circuit’ energies or the ‘electrodynamic’ energies. A generalisation is obtained for quasi-static fields of antennas that facilitate the evaluation of the expressions for the Q-energy. It is verified that the Q-energy cannot be considered stored energy in the highly dispersive lossy material. Nonetheless, using tuning elements containing highly dispersive lossy material, the bandwidth of fifty-per cent (for example) efficient electrically small dipole antennas can be designed with twice the bandwidth predicted by the Chu lower bound for the quality factor of fifty-per cent efficient antennas.

Investigation of optical properties of an overdense magnetized plasma lens in the interaction with high-intensity Gaussian laser pulses

Self-focusing of a high-intensity circularly polarized Gaussian laser pulse by an overdense magnetized thin plasma lens is numerically investigated. The quasi-static axial magnetic field can be produced by inverse Faraday effect (IFE) mechanism in laser–plasma interaction. It has been shown that the inclusion of self-transparency, ponderomotive force, and magnetic field effects significantly affect the self-focusing properties. When the strength of the magnetic field increases, the self-focusing property is enhanced for the right and is weakened for the left-handed circularly polarized laser pulse. The ponderomotive force repels electrons from the axis and drives electron cavitation and as a result further lowers the plasma frequency. When the influence of the ponderomotive force is taken into account, self-focusing for both polarizations is strongly affected. The clear difference between the effects of the right- and left-handed circularly polarized pulses may lead us to use them for different experimental applications.

Coupling between vortices and antivortices in a cross-tie wall studied by time-resolved SEMPA

Using time-resolved scanning electron microscopy with polarization analysis (TR-SEMPA) the dynamics of magnetic vortices and antivortices in a cross-tie wall is investigated. Under quasistatic external field drive both quasiparticles oscillate at opposite phase to each other (in analogy to an optical mode). An additional common motion, which stems from the finite boundary conditions in a patterned FeCoSiB rectangle, is observed (in analogy to an acoustic mode), leading in total to a stronger field-dependent displacement for the vortices compared to the antivortices. Both types of magnetic solitons are mutually coupled via the minimization of the total magnetic energy of the structure. It is shown that the TR-SEMPA results can be explained via coupling in the framework of micromagnetic simulations and that the coupling constants can be extracted. The motion is composed from the contributions of the two terminating vortices and a mutual vortex-antivortex coupling along the chain.

Super-Alfvénic translation of a field-reversed configuration into a large-bore dielectric chamber.

An experimental device to demonstrate additional heating and control methods for a field-reversed configuration (FRC) has been developed. The newly developed device, named FRC Amplification via Translation (FAT), has a field-reversed theta-pinch plasma source and a low-elongation dielectric (transparent quartz) confinement chamber with quasi-static confinement field. In the initial experiments on the FAT device, FRC translation and trapping were successfully demonstrated. Although the typical elongation of the trapped FRC in the confinement region was roughly three, no disruptive global instability, such as tilt, was observed. The FAT device increases the latitude to perform translation-related experiments, such as those concerning inductive current drive, equivalent neutral beam injection effects, and wave applications.

MODEL OF A DIPOLE WITH ATOMIC STRUCTURE

In this paper, we propose a model of a dipole with an atomic structure instead of the standard dipole model with point unlike charges and the Hertzian dipole model, which have significant drawbacks. The equations of the Hertzian dipole and the standard model operate from a distance much larger than size of the dipole, and the quasistatic Coulomb and Biot-Savart fields are the essence of the reactive near field, its own fields with a phase shift ΔφE,H = π/2, which have no restrictions on the distances to a dipole, since they are directly related to charges and their motion – currents. In the framework of the proposed dipole model, we described the physical mechanisms for the formation of near and far fields of an oscillating dipole, which are based on the use of the Coulomb and Biot-Savart fields, the quasistatic lines of force of their electric charge fields Е, and the magnetic fields of the currents Н for the analysis of energy fluxes: reactive Sr at ΔφE,H = π/2 and active Sа at ΔφE,H = 0 alike.

Spin freezing in the disordered pyrochlore magnet NaCaCo2F7 : NMR studies and Monte Carlo simulations

We present results of $^{23}$Na and $^{19}$F nuclear magnetic resonance (NMR) measurements on NaCaCo$_2$F$_7$, a frustrated pyrochlore magnet with a Curie-Weiss temperature, $T_{cw}$ ~-140 K, and intrinsic bond disorder. Below 3.6 K both the $^{23}$Na and $^{19}$F spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80 \%) of the NMR signal intensity: This proves a broad quasi-static field distribution. The $^{19}$F spin-lattice relaxation rate $^{19}(1/T_1$) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the spin freezing to the presence of bond disorder. This is corroborated by large-scale Monte-Carlo simulations of a classical bond-disordered XY model on the pyrochlore lattice. The low freezing temperature, together with the very short magnetic correlation length not captured by the simulations, suggesting that quantum effects play a decisive role in NaCaCo$_2$F$_7$.

Analysis of the Range of Applicability of Thermodynamic Calculations in the Engineering of Nitride Fuel Elements

The domains of applicability of thermodynamic calculations in the engineering of nitride fuel are analyzed. Characteristic values of the following parameters, which affect directly the concentration equilibration time, are estimated: nuclide production rate; characteristic times to local equilibrium in the considered temperature range; characteristic time needed for a stationary temperature profile to be established; characteristic time needed for a quasi-stationary concentration field to be established on a scale comparable to the size of a fuel pellet. It is demonstrated that equilibrium thermodynamic calculations are suitable for estimating the chemical and phase composition of fuel. However, a two-layer kinetic model should be developed in order to characterize the transport processes in condensed and gaseous phases. The process of diffusive transport needs to be taken into account in order to determine the composition in the hot region at the center of a fuel element.

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

Applying a quantum mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy–momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham’s symmetric energy–momentum-tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular momentum (spin) of an electro-magnetic field in the medium. Only the Minkowski tensor leads to the experimentally confirmed spin values that are multiples of ħ, providing the grounds for choosing the Minkowski representation as the proper form for the momentum density of a transverse electromagnetic field in a transparent medium, in both classical and quantum descriptions of the field. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasistatic and static fields.