Showing papers on "Magnetic potential published in 2012"

Relativistic magnetohydrodynamics in dynamical spacetimes: Improved electromagnetic gauge condition for adaptive mesh refinement grids

Abstract: We recently developed a new general relativistic magnetohydrodynamic code with adaptive mesh refinement that evolves the electromagnetic (EM) vector potential (A) instead of the magnetic fields directly. Evolving A enables one to use any interpolation scheme on refinement level boundaries and still guarantee that the magnetic field remains divergenceless. As in classical EM, a gauge choice must be made when evolving A, and we chose a straightforward "algebraic" gauge condition to simplify the A evolution equation. However, magnetized black hole-neutron star (BHNS) simulations in this gauge exhibit unphysical behavior, including the spurious appearance of strong magnetic fields on refinement level boundaries. This spurious behavior is exacerbated when matter crosses refinement boundaries during tidal disruption of the NS. Applying Kreiss-Oliger dissipation to the evolution of the magnetic vector potential A slightly weakens this spurious magnetic effect, but with undesired consequences. We demonstrate via an eigenvalue analysis and a numerical study that zero-speed modes in the algebraic gauge, coupled with the frequency filtering that occurs on refinement level boundaries, are responsible for the creation of spurious magnetic fields. We show that the EM Lorenz gauge exhibits no zero-speed modes, and as a consequence, spurious magnetic effects are quickly propagated away, allowing for long-term, stable magnetized BHNS evolutions. Our study demonstrates how the EM gauge degree of freedom can be chosen to one's advantage, and that for magnetized BHNS simulations the Lorenz gauge constitutes a major improvement over the algebraic gauge.

Two-Dimensional Analytical Calculation of Magnetic Field and Electromagnetic Torque for Surface-Inset Permanent-Magnet Motors

Abstract: The paper deals with a subdomain model for predicting the magnetic field distribution in surface-inset permanent-magnet (PM) motors with semi-closed slots under load conditions. Due to the presence of electrical current in the stator slots, a magnetic vector potential formulation is used. The magnetic vector potential distribution in each subdomain (air-gap, stator slots, and rotor slots with inset PMs) is obtained by solving two-dimensional Laplace's and Poisson's equations by the separation of variables method. One of the main contributions of the paper concerns the magnetic vector potential expression in the PM region. Indeed, PMs are inset into the rotor iron which leads to solve Laplace's equation with nonhomogeneous Neumann boundary conditions. Magnetic field distribution and electromagnetic torque computed with the proposed analytical method are verified with those obtained from finite-element analyses.

Uniqueness in an inverse boundary problem for a magnetic Schr\"odinger operator with a bounded magnetic potential

Abstract: We show that the knowledge of the set of the Cauchy data on the boundary of a bounded open set in $\R^n$, $n\ge 3$, for the magnetic Schrodinger operator with $L^\infty$ magnetic and electric potentials determines the magnetic field and electric potential inside the set uniquely. The proof is based on a Carleman estimate for the magnetic Schrodinger operator with a gain of two derivatives.

Vibration Analysis and Measurements Through Prediction of Electromagnetic Vibration Sources of Permanent Magnet Synchronous Motor Based on Analytical Magnetic Field Calculations

Abstract: This study is devoted to the analysis of the vibration characteristics of a permanent magnet synchronous motor (PMSM) through investigation into its electromagnetic vibration sources. For this purposed, we derive analytical solutions for the magnetic fields generated by permanent magnets (PMs) in terms of a magnetic vector potential and a two-dimensional (2-D) polar coordinate system. A 2-D permeance function is also introduced in order to consider slotting effects. The electromagnetic vibration sources such as torque ripple, cogging torque, and radial force density are analyzed using these solutions. The analytical results are validated extensively with finite element (FE) analyses. The fast Fourier transformation (FFT) analysis is employed for investigating the specific harmonic orders of the electromagnetic vibration sources that affect the vibration of the PMSM. Finally, mechanical modal analysis results and test results such as vibration measurements are obtained to confirm the validity of the analysis methods presented in this paper.

Demonstration of an inductively coupled ring trap for cold atoms

Abstract: We report the first demonstration of an inductively coupled magnetic ring trap for cold atoms. A uniform, ac magnetic field is used to induce current in a copper ring, which creates an opposing magnetic field that is time-averaged to produce a smooth cylindrically symmetric ring trap of radius 5 mm. We use a laser-cooled atomic sample to characterize the loading efficiency and adiabaticity of the magnetic potential, achieving a vacuum-limited lifetime in the trap. This technique is suitable for creating scalable toroidal waveguides for applications in matter-wave interferometry, offering long interaction times and large enclosed areas.

An analytical model of a ferrite-cored inductor used as an eddy current probe

Abstract: An analytical model of an axisymmetric eddy current ferrite-cored probe above a multi-layered conducting half-space has been developed using a procedure in which the domain of the problem is truncated radially. This means that solutions can be expressed in the form of generalized Fourier-Bessel series. The expansion coefficients are found by matching the field across the interfaces between the subregions of the problem. Initially, the magnetic vector potential of a simple circular current filament is expanded in a series form. The solution is then modified to accommodate an infinitely long coaxial ferrite core, and the principle of superposition is invoked to derive a coil field from the filament field in the presence of the core. Next, we consider a semi-infinite core and then one of finite length. Finally, the effects of a multi-layered conductor are included. Numerical predictions of probe impedance have been compared with experimental data showing excellent agreement.

Analytical magnetic torque calculations and experimental testing of radial flux permanent magnet-type eddy current brakes

Abstract: This paper reports on analytical magnetic torque calculations and experimental tests of a radial flux permanent magnet (RFPM)-type eddy current brake (ECB). Analytical solutions for permanent magnet-generated magnetic fields that consider the eddy current reaction are obtained by using a magnetic vector potential and a two dimensional (2D) polar coordinate system. On the basis of these solutions, the analytical expressions for a magnetic torque are also derived. All analytical results are validated extensively by non-linear finite element calculations. In particular, magnetic torque measurements are obtained in tests to confirm the analyses. Finally, practical issues related to the analytical study of RFPM-type ECBs are fully discussed.

Solution to the problem of E-cored coil above a layered half-space using the method of truncated region eigenfunction expansion

Abstract: In eddy current non-destructive testing, using ferrite cores with different shapes produce interesting and very important predictions on locating underneath cracks, corrosions and flaws in conductive layers. This paper describes a method of calculating magnetic vector potential for an E-cored eddy current probe above a layered half space. The coil impedance variation with frequency and eddy currents are determined. The results of the calculations are in very good agreement with results from COMSOL.

Advanced electromagnetic modeling applied to anti-vibration systems for high precision and automotive applications

Abstract: This paper presents the application of two (semi-) analytical modeling techniques to the design of anti-vibration systems. Both methods are based on the direct solution of the Laplace and Poisson equations in terms of the scalar or magnetic vector potential. The first technique, the surface charge model, is applied to the disign of an electromagnetic gravity compensator for the high precision industry. The second tehcnique, the harmonic model, is applied to the design of an electromagnetic active suspension system for the automotive industry. These techniques facilitate the electromagnetic analysis numerical optimization and design for a broad range of topologies and configurations. Furthermore, prototypes of both anti-vibration systems are manufactured and extensive experimental test have proven the analytical analysis and design.

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings.

Abstract: State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schrodinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.

Calculation of mutual inductance from magnetic vector potential for wireless power transfer applications

Abstract: Recent renewed interest in commercial development of wireless power transfer through magnetically-coupled resonant circuits has shown the need for a computational tool that can calculate the mutual inductance of coils of arbitrary geometry and spatial orientation. This task is often performed by finite-element analysis (FEA), but this requires both access to such software and a degree of expertise on the part of the designer. This paper introduces a simple-to-use Matlab-based computational tool for calculating mutual inductance for inductors in free space based upon magnetic vector potential.

A Three Dimensional Analytical Calculation of the Air-Gap Magnetic Field and Torque of Coaxial Magnetic Gears

Abstract: In order to solve the defects that the end-efiect of magnetic fleld is ignored in two dimension (2-D) analytical method or 2-D flnite element method (FEM); meanwhile, mass computer resource and time for parametric design or optimization are wasted in three dimension (3-D) FEM, a concise and e-cient 3-D analytical approach is put forward for the calculation of the air-gap magnetic fleld and torque of coaxial magnetic gears. Based on the cylindrical coordinates where a coaxial magnetic gear is in, the equivalent current model and vector magnetic potential equation of permanent magnets in high speed permanent magnetic ring are constituted. By superposed magnetic ∞ux density of every tile permanent magnets on high speed permanent magnetic ring in cylindrical coordinates, a air-gap magnetic fleld 3-D analytical formula is set up without ferromagnetic pole-pieces; in the interest of modulated air-gap magnetic fleld 3-D analytical formula with ferromagnetic pole-pieces, three types boundary conditions using state equations of contact surfaces between ferromagnetic pole-pieces and air-gap are established by a thorough analysis of the modulate mechanism of ferromagnetic pole-pieces. Finally, magnets of the low speed permanent magnetic ring are reduced to a distribution of equivalent current, which experience the Lorentz force in modulated magnetic fleld of high speed permanent magnetic ring for torque calculation. The integrals in all aforementioned calculation are axial, so the end-efiect is embodied in above analytical model and more precise than 2-D analytical method or 2-D FEM. As the calculation results, the formula is accurate but faster than the 3-D FEM. The analytical model is suited for programmable calculation and that will make the structural and parametric design or optimization of coaxial magnetic gears simple and timesaving.

Mode-Matching Technique Applied to Three-Dimensional Magnetic Field Modeling

Abstract: A semianalytical model is derived for the description of the three-dimensional magnetic fields, generated by an array of air-cored rectangular coils above a ferromagnetic plate with cavities, or bounded slots, in the xy-plane. The magnetic fields are described with a double Fourier series and are obtained by solving the Maxwell equations using a combination of the magnetic vector and scalar potentials. Mode-matching of the double Fourier series is applied to obtain the description of the magnetic fields inside the cavities. Therefore, the mode-matching technique is extended for two dimensions. The semianalytical model is compared with three-dimensional finite element analysis and a good agreement has been found.

Design and optimization of a permanent magnet axial flux wheel motors for electric vehicle

Abstract: Axial flux motor with two flat PM rotors and one coreless stator is designed and manufactured for the propulsion of an electric vehicle supplied by a Fuel cell. The originality of the architecture consists in the stator winding which is manufactured as a printed circuit with thick copper lamination. The second originality in this paper consists on the use of the duality between magnetic vector potential and flux density in a magneto-static problem. It allows using standard 2D finite element code for the computation of the fluxes and electromotive forces of an axial flux PM motor. The model is then used to optimize the winding topology in order to increase the efficiency of the propulsion system of electric vehicle powered by a fuel cell.

Biorthogonal Shape Functions for Nonconforming Sliding Interfaces in 3-D Electrical Machine FE Models With Motion

Abstract: This paper discusses the application of Lagrange multipliers to restore field continuity across nonconforming surfaces in 3-D problems. The method makes it in particular possible to implement the relative motion of stator and rotor without remeshing in the 3-D Finite Element (FE) modeling of electrical machines. The choice of a special set of biorthogonal shape functions for the Lagrange multiplier makes it possible to preserve the positive definiteness of the FE system. It is shown that such a biorthogonal basis cannot be constructed canonically for a 3-D magnetic vector potential formulation. For a 3-D magnetic scalar potential formulation, however, the situation is different and a biorthogonal basis can be found.

Eddy Currents and Corner Singularities

Abstract: Eddy current problems are addressed in a bidimensional setting where the conducting medium is non-magnetic and has a corner singularity. For any fixed parameter δ linked to the skin depth for a plane interface, we show that the flux density |∇Aδ| is bounded near the corner unlike the perfect conducting case. Then as δ goes to zero, the first two terms of a multiscale expansion of the magnetic potential are introduced to tackle the magneto-harmonic problem. The heuristics of the method are given and numerical computations illustrate the obtained accuracy.

A transfer matrix approach to electron transport in graphene through arbitrary electric and magnetic potential barriers

Abstract: A transfer matrix method is presented for solving the scattering problem for the quasi-one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It is shown that parabolic cylindrical functions, which have previously been used in the literature, become inaccurate at high incident energies and low magnetic fields. A series expansion technique is presented to circumvent this problem. An alternate method using asymptotic expressions is also discussed and the relative merits of the two methods are compared.

Modeling and analysis of a magnetically levitated synchronous permanent magnet planar motor

Abstract: In this paper, a new magnetically levitated synchronous permanent magnet planar motor (MLSPMPM) driven by composite-current is proposed, of which the mover is made of a copper coil array and the stator are magnets and magnetic conductor. The coil pitch τt and permanent magnet pole pitch τp satisfy the following relationship 3nτt = (3n ± 1)τp. Firstly, an analytical model of the planar motor is established, flux density distribution of the two-dimensional magnet array is obtained by solving the equations of the scalar magnetic potential. Secondly, the expressions of the electromagnetic forces induced by magnetic field and composite current are derived. To verify the analytical model and the electromagnetic forces, finite element method (FEM) is used for calculating the flux density and electromagnetic forces of the MLSPMPM. And the results from FEM are in good agreement with the results from the analytical equations. This indicates that the analytical model is reasonable.

Flux Field Formulation and Back-Iron Analysis of Tubular Linear Machines

Abstract: In electromagnetic machines, ferromagnetic material is one of the key components that affect the magnetic field and thus the output performance significantly. The objective of this paper is to study the influence of ferromagnetic material on magnetic field distribution of tubular electromagnetic linear machines. Generic magnetic field models are obtained for linear machines with various structure designs based on magnetic vector potential and Bessel functions. The magnetic field model is validated with numerical results from finite element calculations. The comparison between them shows that the flux model fits closely with the numerical computation. The obtained analytical model can be employed to study the flux density distribution of machine designs with single-sided, double-sided, and non back irons. It shows that the use of back iron, especially for the internal side, helps to greatly enhance the radial component of magnetic field. This component contributes to the axial force generation of tubular linear machines. The study could be useful for the design optimization of permanent-magnet linear machines.

An Extended Iterative Finite Element Model for Simulating Eddy Current Testing of Aircraft Skin Structure

Abstract: This paper presents a new finite element (FE) model for three-dimensional simulation of eddy current testing of aircraft skin structure. More specifically, scanning of ferrite-core probe over aluminum plates riveted by steel fasteners is simulated. The model uses different FE meshes to discretize the ferrite core, the aluminum plates, and the fasteners. The coil is not meshed. The reduced magnetic vector potential generated by the induced currents and/or magnetization in each domain is calculated and updated by an iterative procedure. Re-meshing due to changing probe position in conventional models is avoided. Efficiency of the model is demonstrated.

An Introduction to Waves and Oscillations in the Sun

Abstract: Chapter 1: Introduction.- 1.1: Historical Perspectives.- 1.2: The Core of the Sun.- 1.3: Radiative Zone.- 1.4: Convection Zone.- 1.5: Photosphere.- 1.6: Chromosphere.- 1.7: Corona.- 1.8: Solar Wind.- Chapter 2: Electro-Magneto Statics.- 2.1: Charge and Current Distributions.- 2.2: Coulomb's Law.- 2.3: Gauss's Law.- 2.4: Ampere's Law.- 2.5: Faraday's Law.- 2.6: Vector Magnetic Potential.- 2.7: Maxwell's Equations.- Chapter 3: MHD Equations and Concepts.- 3.1: Assumptions.- 3.2: Dimensionless Parameters.- 3.3: Mass Continuity.- 3.4: Equations of Motion.- 3.5: Energy Equation.- 3.6: MHD Equilibrium.- 3.7: Magnetic Flux Tubes.- 3.8: Current-free (Potential) fields.- 3.9: Force-Free Fields.- 3.10: Parker's Solution for Solar Wind.- Chapter 4: Waves in Uniform Media.- 4.1: Basic Equations.- 4.2: SoundWaves.- 4.3: Alfv'enWaves.- 4.4: Shear Alfv'enWaves.- 4.5: Compressional Alfv'enWaves.- 4.6: Magneto acoustic Waves.- 4.7: Internal and Magneto acoustic Gravity Waves.- 4.8: Phase-Mixing and Resonant Absorption of Waves.- Chapter 5: Waves in Non-Uniform Media- 5.1: Waves at Magnetic Interface.- 5.2: Surface and InterfacialWaves.- 5.3: Waves in a Magnetic Slab.- 5.4: Waves in Cylindrical Geometries.- 5.5: Waves in Untwisted and Twisted Tubes.- Chapter 6: Instabilities.- 6.1: Introduction.- 6.2: Rayleigh-Taylor (RT) Instability.- 6.3: Kelvin-Helmholtz (KH) Instability.- 6.4: Parametric Instability.- 6.5: Parker Instability.- Chapter 7: Waves in the Sun.- 7.1: Five minute oscillations.- 7.2: Oscillations in Sunspots.- 7.3: Chromospheric Oscillations.- 7.4: CoronalWaves.- 7.5: Coronal Seismology.- 7.6: Coronal Heating due to Waves.- 7.7: EIT and MoretonWaves.- Chapter 8: Heliosesimology.- 8.1: Equations of Motion.- 8.2: Equilibrium Structure.- 8.3: Perturbation Analysis.- 8.4: Acoustic Waves.- 8.5: Internal Gravity Waves.- 8.6: Equations of Linear Stellar Oscillations.- 8.7: Properties of Solar Oscillations (Internal).- 8.8: p and g modes.- References.- Index.

A Transfer Matrix Approach to Electron Transport in Graphene through Arbitrary Electric and Magnetic Potential Barriers

Abstract: A transfer matrix method is presented for solving the scattering problem for the quasi one-dimensional massless Dirac equation applied to graphene in the presence of an arbitrary inhomogeneous electric and perpendicular magnetic field. It is shown that parabolic cylindrical functions, which have previously been used in literature, become inaccurate at high incident energies and low magnetic fields. A series expansion technique is presented to circumvent this problem. An alternate method using asymptotic expressions is also discussed and the relative merits of the two methods are compared.

The watt-balance operation: magnetic force and induced electric potential on a conductor in a magnetic field

Abstract: In a watt balance experiment, separate measurements of magnetic force and induced electric potential in a conductor in a magnetic field allow for a virtual comparison between mechanical and electrical powers, which leads to and an accurate measurement of the Planck constant. In this paper, the macroscopic equations for the magnetic force and the induced electric potential are re-examined from a microscopic point of view and the corrective terms due to a non-uniform density of the conduction electrons induced by their interaction with the magnetic field are investigated. The results indicate that these corrections are irrelevant to the watt balance operation.

Impact of radial external magnetic field on plasma deformation during contact opening in SF6 circuit breakers

Abstract: A three-dimensional (3D) transient model is developed to investigate plasma current deformation driven by internal and external magnetic fields and their influences on arc stability in a circuit breaker The 3D distribution of electric current density is obtained by solving the current continuity equation along with the generalized Ohm's law in the presence of an external magnetic field, while the magnetic field induced by the current flowing through the arc column is calculated by the magnetic vector potential equation The applied external field imposes a rotational electromagnetic force on the arc and influences the plasma current deformation, which is discussed in this paper In SF6 circuit breakers when gas interacts with the arc column, the fundamental equations such as Ampere's law, Ohm's law, turbulence model, transport equations of mass, momentum, and energy of plasma flow have to be coupled for analysing the phenomenon The coupled interactions between the arc and the plasma flow are described within the framework of magnetohydrodynamic equations in conjunction with a K?? turbulence model Simulations are focused on sausage and kink instabilities in the plasma (these phenomena are related to the electromagnetic field distribution and define the plasma deformations) The 3D simulation reveals the relation between plasma current deformation and instability phenomena, which affects the arc stability during the operation Plasma current deformation is a consequence of coupling between electromagnetic forces (resulting from internal and radial external magnetic fields) and the plasma flow that are described in the simulations

Electronic Energy Band and Transport Properties in Monolayer Graphene with Periodically Modulated Magnetic Vector Potential and Electrostatic Potential

Abstract: We investigated the electronic energy band and transport features of graphene superlattice with periodically modulated magnetic vector potential and electrostatic potential. It is found that both parallel magnetic vector potential and electrostatic potential can decisively shift Dirac point in a different way, which may be an efficient way to achieve electron or hole filter. We also find that applying modulated parallel and anti-parallel magnetic vector potential to the electrons can efficiently change electronic states between pass and stop states, which can be useful in designing electron or hole switches and lead to large magneto-resistance.

Eigenvalue bounds for radial magnetic bottles on the disk

Abstract: We consider a Schrodinger operator H with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator Under some assumptions on an additional radial potential V the operator H + V has a discrete negative spectrum and we obtain an upper bound on the number of negative eigenvalues As a consequence we get an upperbound of the number of eigenvalues of H smaller than any positive value, which involves the minimum of B and the square of the L^2 -norm of A(r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centerde in the origin

Mixing excitation generating set for electric automobile

Abstract: Provided is a mixing excitation generating set for an electric automobile, belonging to the automobile motor electric appliance technology field. The mixing excitation generating set comprises a rotor, a stator, a front end cap, a rear end cap, and an electronic controller. The mixing excitation generating set is characterized in that: a brushless electric excitation rotor and a tangential permanent magnetism rotor are installed upon one shaft, with the brushless electric excitation rotor and the tangential permanent magnetism rotor sharing one armature winding and the generated magnetic potential combined in magnetic circuit. When in operation, the mixing excitation generating set enables the magnetic field of the superposed electric excitation field and the permanent magnetism magnetic field to be adjustable by adjusting the size and direction of the electrifying current of the electric excitation rotor and ensures that the generating unit outputs direct current having stable voltage within width loading range. The excitation generating set of the utility model features compact structure, convenient installation, safe usage, and reliability.