Vector Potential Model Research Articles

3-D Integrated Sub-Domain Model for On-Load Magnetic Field and Force Analysis of 6-DOF Screw-Motion Permanent Magnet Synchronous Motor

This paper presents the 3-dimensional integrated sub-domain model (3-D ISM) for the 6-degree-of-freedom (DOF) screw-motion permanent-magnet synchronous motors (Sm-PMSMs). For the actively controlled and decoupled 6-DOF motion, the novel pattern of PM-array is introduced, consisting of the checker-board PMs to drive the 2-DOF screw motion and the additional tilting PMs for the other 4-DOF magnetic bearings. The armature of the proposed Sm-PMSM design contains both the linear coil sets and the rotational coil sets, where the D-Q current excitation scheme with the peak current modulation method is utilized to generate the 6-DOF forces and torques in a decoupled manner. The 3-D ISM presented in this paper accurately estimates the magnetic fields in the 3-D cylindrical space with an on-load condition, integrating the PM-induced fields from the magnetic scalar potential model and the current-induced fields from the hybrid vector potential model. The proposed 3-D ISM is validated by the equivalent 3-D finite element analysis (FEA) model, comparing the on-load magnetic fields, and the decoupled 6-DOF forces and torques. The fidelity of the proposed model is observed with an accuracy greater than 96%, while simultaneously improving the computational speed by two orders-of-magnitude as compared to the 3-D FEA.

Investigating the Impact of Diverging Spacing Factors on Array Antennas

This paper analyzed the antenna patterns for dipole array antennas of diverging spacing factor. In order to minimize the complexity of the task required in the computation, we assumed a negligible width for the dipole elements. Thus, the current flowing through the wire is assumedly constant. The Array Factor for dipole array antennas of diverging spacing factor was derived via Magnetic Vector Potential model. The required radiation patterns for the antennas were generated using the MatLab simulation tools. The generated results showed a trade-off between directivity and power loss as expected. While the diverging spacing factor results to a swift increase in the directivity of the radiation pattern, it produces many ripples for an increase in the array antenna element. Keywords: dipole, array antennas, array factor, electromagnetic fields, diverging spacing factor, Magnetic Vector Potential.

3D Hybrid Segmented Layer Modeling of On-Load Magnetic Fields and Torques for Coreless Axial-Flux Permanent Magnet Synchronous Motor

This paper presents a novel 3-dimensional hybrid segmented layer model (3D HSLM) for coreless axial-flux permanent magnet synchronous motors (AFPMSMs). In the proposed 3D HSLM, the magnetic field sources are divided into the PM array and current-driven electro-magnets, which are captured by the combination of the magnetic scalar potential and vector potential models. This paper proposes a geometry function and cylindrical harmonic index modulation functions in order to correctly capture the curvature effect by the PMs and coils with arbitrary shapes and also the radial edge effect from the finite lengths of the rotor and the stator. The proposed modeling method also enables accurate estimation of the motor characteristics on the on-load conditions using the magnetic vector potential model. The fidelity of the proposed 3D HSLM is validated against the equivalent FEM models for various cases with different PM and coil shapes, in terms of the airgap magnetic fields, motor torque, and flux linkage. The comparison results show that the proposed 3D HSLM yields a modeling accuracy of more than 98% while significantly reducing the calculation time by two orders of magnitude as compared to the FEM models.

Vector-potential finite-element formulations for two-dimensional resistive magnetohydrodynamics

Vector-potential formulations are attractive for electromagnetic problems in two dimensions, since they reduce both the number and complexity of equations, particularly in coupled systems, such as magnetohydrodynamics (MHD). In this paper, we consider the finite-element formulation of a vector-potential model of two-dimensional resistive MHD. Existence and uniqueness are considered separately for the continuum nonlinear equations and the discretized and linearized form that arises from Newton’s method applied to a modified system. Under some conditions, we prove that the solutions of the original and modified weak forms are the same, allowing us to prove convergence of the discretization and well-posedness of the nonlinear iteration near a solution.

Equivalent magnetic vector potential model for low-frequency magnetic exposure assessment

In this paper, a novel source model based on a magnetic vector potential for the assessment of induced electric field strength in a human body exposed to the low-frequency (LF) magnetic field of an electrical appliance is presented. The construction of the vector potential model requires only a single-component magnetic field to be measured close to the appliance under test, hence relieving considerable practical measurement effort—the radial basis functions (RBFs) are adopted for the interpolation of discrete measurements; the magnetic vector potential model can then be directly constructed by summing a set of simple algebraic functions of RBF parameters. The vector potentials are then incorporated into numerical calculations as the equivalent source for evaluations of the induced electric field in the human body model. The accuracy and effectiveness of the proposed model are demonstrated by comparing the induced electric field in a human model to that of the full-wave simulation. This study presents a simple and effective approach for modelling the LF magnetic source. The result of this study could simplify the compliance test procedure for assessing an electrical appliance regarding LF magnetic exposure.

Three-dimensional numerical modeling of free convection in sloping porous enclosures

Three-dimensional (3D) numerical simulations are carried out to study steady state free convection in a sloping porous enclosure heated from below. The model is based on Darcy’s law and the Boussinesq approximation. Two different approaches to solve this problem are compared: primitive variables and vector potential. Although both numerical models lead to equivalent results in terms of the Nusselt number and convective modes, the vector potential model proved to be less mesh-dependent and also a faster algorithm. A parametric study of the problem considering Rayleigh number, slope angle and aspect ratio showed that convective modes with irregular 3D geometries can develop in a wide variety of situations, including horizontal porous enclosure at relatively low Rayleigh numbers. The convective modes that have been described in previous 2D studies (multicellular and single cell) are also present in the 3D case. Nonetheless the results presented here show that the transition between these convective modes follows an irregular 3D geometry characterized by the interaction of transverse and longitudinal coils.

A model of force balance in Jupiter's magnetodisc including hot plasma pressure anisotropy

AbstractWe present an iterative vector potential model of force balance in Jupiter's magnetodisc that includes the effects of hot plasma pressure anisotropy. The fiducial model produces results that are consistent with Galileo magnetic field and plasma data over the whole radial range of the model. The hot plasma pressure gradient and centrifugal forces dominate in the regions inward of ∼20 RJ and outward of ∼50 RJ, respectively, while for realistic values of the pressure anisotropy, the anisotropy current is either the dominant component or at least comparable with the hot plasma pressure gradient current in the region in between. With the inclusion of hot plasma pressure anisotropy, the ∼1.2 and ∼2.7° shifts in the latitudes of the main oval and Ganymede footprint, respectively, associated with variations over the observed range of the hot plasma parameter Kh, which is the product of hot pressure and unit flux tube volume, are comparable to the shifts observed in auroral images. However, the middle magnetosphere is susceptible to the firehose instability, with peak equatorial values of βh∥e−βh⊥e≃1 − 2, for Kh=2.0 − 2.5 × 107 Pa m T−1. For larger values of Kh,βh∥e−βh⊥e exceeds 2 near ∼25 RJ and the model does not converge. This suggests that small‐scale plasmoid release or “drizzle” of iogenic plasma may often occur in the middle magnetosphere, thus forming a significant mode of plasma mass loss, alongside plasmoids, at Jupiter.

Numerical Analysis of Magnetic Field Distribution of Magnetic Micro-barcodes for Suspension Assay Technology

In this study, we have investigated real-time decoding feasibility of magnetic micro-barcodes in a microfluidic channel by using numerical analysis of magnetic field distribution of the micro-barcodes. The vector potential model based on a molecular current has been used to obtain magnetic stray field distribution of ferromagnetic bars which consisting of the micro-barcodes. It reveals that the stray field distribution of the micro-barcodes strongly depends on the geometries of the ferromagnetic bar. Interestingly enough, we have found that one can avoide the miniaturization process of a magnetic sensor device needed to increase the sensitivity by optimizing the geometries of micro-barcodes. We also estimate a magnetic sensor response depending on flying height and lateral misalignment of the micro-barcodes over the sensor position and found that control of the flying height is crucial factor to enhance the detection sensitivity and reproducibility of a magnetic sensor signal in the suspension assay technology.

Particle-hole symmetric localization in two dimensions

We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states $\ensuremath{\rho}(E)$ at the band center $E=0.$ The most general system of this kind [R. Gade, Nucl. Phys. B 398, 499 (1993)] exhibits critical behavior and has $\ensuremath{\rho}(E)$ that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. [Phys. Rev. B 50, 7526 (1994)] has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder---this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ``surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is $\ensuremath{\rho}(E)\ensuremath{\sim}{E}^{\ensuremath{-}1}{e}^{\ensuremath{-}c|\mathrm{ln}E{|}^{2/3}},$ different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ``string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

Finiteness of Multi-Body Neutrino Exchange Potential Energy in Neutron Stars

The multi-body neutrino potential energy is analytically estimated for a spherical neutron star with a vector potential model for neutrinos. We show that the self-energy and the neutrino number of the neutron star coincide with the semi-classical values in the large volume limit, and confirm that there is no catastrophe in neutron stars with massless neutrinos.

On the random vector potential model in two dimensions

The random vector potential model describes massless fermions coupled to a quenched random gauge field. We study its abelian and non-abelian versions. The abelian version can be completely solved using bosonization. We analyse the non-abelian model using its supersymmetric formulation and show, by a perturbative renormalization group computation, that it is asymptotically free at large distances. We also show that all the quenched chiral current correlation functions can be computed exactly, without using the replica trick or the supersymmetric formulation, but using an exact expression for the effective action for any sample of the random gauge field. These chiral correlation functions are purely algebraic.

Cancellation of the neutron electric dipole moment in quark model calculations of Baluni's CP violating strong interaction

The neutron electric dipole moment ( D n) generated by strong CP violation is due to the anomaly plus non-perturbative U (1) effects. It should vanish in quark models, which do not incorporate these two ingredients. Calculations are presented showing how this necessary cancellation does occur in a Lorentz vector potential model, but not in a scalar potential or in a bag model; in the latter cases, it is argued that the non-zero result is a model artefact. In old perturbation theory, the cancellation when present occurs between pair and 1 2 − intermediate state contributions.

A discrete vector potential model for unsteady incompressible viscous flows

A recent approach to generate a zero divergence velocity field by operating directly on the discretized Navier-Stokes equations is used to obtain the decoupling of the pressure from the velocity field. By following the methodology suggested by Amit, Hall, and Porsching the feasibility of treating three dimensional flows and multiply connected domains is analyzed. The present model keeps the main features of the classical vector potential method in that it generates a divergence-free velocity field through an algebraic manipulation of the discrete equations. At the same time the boundary conditions are still imposed on the discrete values of the primitive variables. The accuracy of the method is tested against the exact solution for a recirculating unsteady flow both in simply and doubly connected domains. Several applications to flow fields in three-dimensional enclosures or in multiply connected domains are presented and discussed in terms of accuracy and efficiency of the method.