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We update Ampere's theory using vector notation and derive his expression for the force between two current elements. We assume that the two elements are in different current loops and integrate over one to obtain the force on a differential element in the second. This procedure allows us to define the magnetic field in a natural manner and to derive the Lorentz force for a current segment. We equate the magnetic moments of current and permanent magnet dipoles and show that Biot and Savart could have performed their experiment using a small current loop, thus establishing the Biot-Savart law as a consequence of Ampere's theory. [DOI: 10.1119/1.3116090]

Legendre polynomials are used to approximate a smoothly varying field solution along a direction in which the geometry is invariant. The hybridization with standard finite-element (FE) shape functions defined in the cross-sectional plane leads to a discretization scheme which outperforms a standard 3-D magnetostatic FE model. Index Terms--Finite-element (FE) method, hybrid discretization, magnetostatics, spectral method.

We propose a recipe to construct a symmetric positive definite and consistent reluctance constitutive matrix to be used within discrete geometric approaches when the primal grid is generated by an enhanced subgridding of a generic hexahedral grid. We focus on a magnetostatic problem as working example. Index Terms--Cell method, discrete constitutive relations, magnetostatics, subgridding.

This paper describes a robust version to the TEAM 22 benchmark optimization problem and presents the methodology WCSA (worst case scenario approximation) to solve this problem and other similar cases. The robust multi-objective TEAM 22 model was built from its classical configuration by assuming the imprecisions in the design space. General and specific robust optimization formulas were developed to elaborate WCSA approach. WCSA adds an uncertainty parameter in the objective and constraint functions to perform the role of the system's imprecisions. A multi-objective genetic algorithm approach was chosen to deal with the robust formulation and to find out the set of robust minimizers that matches with the problem requirements. The behavior of the robust Pareto front is also examined. Index Terms--Genetic algorithms, magnetostatics, robust multi-objective optimization, robust Pareto front, TEAM 22.

Current methods to obtain fluxmetric and magnetometric demagnetizing factors assume a uniform susceptibility and solve initially the surface magnetic pole density. In this paper, a different approach is applied. This approach considers susceptibility as a function of position and finds the field distributions directly. It is proved that the magnetization distribution and the corresponding magnetic field minimize the magnetostatic energy and thus are the unique solution to the given magnetostatic problem. To verify the method, both rectangular and cylindrical magnetic media with nonlinear magnetization curves or a step change in susceptibility are considered. Index Terms--Fluxmetric demagnetizing factor, magnetization distribution, magnetometric demagnetizing factor.

This is the first report of the application of the plane wave method to the solution of the Walker equation for the magnetostatic potential in periodic magnetic composites referred to as magnonic crystals. The discussed method allows to determine the dispersion relation of magnetostatic waves in systems composed of magnetic materials as well as those comprising both magnetic and nonmagnetic materials described by the permeability tensor the elements of which are periodic functions of position. Here the method is applied to the case of one-dimensional magnonic crystals composed of alternating layers of a ferromagnet and a nonmagnetic material. The resulting band structure includes bands of backward magnetostatic waves and a band of surface magnetostatic waves, strongly dependent on the direction of propagation. The obtained results verify the applicability of the method to the considered systems, and suggest it could be used also for calculating spectra of magnetostatic and spin waves in two-dimensional magnonic crystals. Index Terms--Magnetostatic waves, magnonic crystals, superlattice.

This communication deals with a comparison between two methods of discretization: the well known finite element method and the natural element method that is a meshless method. An error estimator, based on the nonverification of the constitutive law, is used. This estimation has been applied to two examples: a device with permanent magnets and a variable reluctance machine. Index Terms--Error estimation, finite element method, magnetostatics, natural element method.

Magnetoquasistatic models commonly feature nonlinear materials. In high-energy synchrotrons, dipole magnets with aperture fields approaching 2 T are required to keep the ionized beam on a circular track. At these field magnitudes, the ferromagnetic yoke material is heavily saturated, causing a significant deterioration of the aperture field quality. In order to quantify the field quality, 3-D nonlinear finite-element simulations are carried out. The approach is tested for the SIS100 magnet of the FAIR project at the GSI, Darmstadt, Germany. Index Terms--Higher-order finite elements, magnetostatics, nonlinearity, superconductive magnets.

A novel unified method for the stable numerical solution of the time-harmonic Maxwell's equations for any frequency is presented. The method is based on an extended a--[phi] variational formulation of the full linear Maxwell's equations. This formulation avoids stability problems in the stationary limit, where it reduces to the equations of electrostatics and magnetostatics. Both capacitive and inductive effects are taken into account in a robust fashion for all frequencies. Index Terms--Finite elements, full Maxwell model, low-frequency limit, stability.

We propose a geometric reinterpretation of the Nodal Force Method in the framework of a pair of discrete formulations for magnetostatics on complementary meshes. Index Terms--Discrete approaches, forces, magnetostatics.

This paper reports on novel coilless microscanning mirrors driven by the magnetostatic force that resulted from a magnetic interaction as well as the Lorentz force that is induced by an eddy current. This eliminates complicated coil routing and insulation layer deposition and simplifies fabrication allowing easy integration with micromachining and complementary metal-oxide-semiconductor processes. Bulk micromachined one-axis and two-axis scanning mirrors are demonstrated, displaying 1-D and 2-D scanning patterns. Two-dimensional scanning patterns are easily tuned by varying the combination of driving frequencies. The results show that the diamagnetic (Cu) mirror is mainly driven by the eddy-current-induced Lorentz force, whereas the ferromagnetic (Ni) mirror is mainly driven by the magnetostatic force. [2006-0082] Index Terms--Eddy current, Lorentz force, magnetostatic force, scanning mirror.

The magnetostatic Green's function formalism is applied to study the high-frequency impedance of a planar solenoid with a thin magnetic core. The affect of the width of the magnetic stripe and the magnetic loss on the resistance and inductance of a single-turn solenoid is studied using the developed formalism.

Principle, analysis, and experimental results of a novel onchip magnetic device are presented in this paper. It provides precise contactless trapping and arraying of diamagnetic microbeads without the supply of any external energy for contamination-free biochemical applications. The trapping force modeling and computation are presented and discussed. The results demonstrate accurate modeling of the device and successful experimental achievement of precise contactless trapping of diamagnetic microbeads within a buffered paramagnetic medium. Index Terms--Bioanalytical applications, contactless handling, magnetophoresis, magnetostatic modeling, magnets.

This paper describes large-scale and fast nonlinear magnetostatic field analyses by the magnetic moment method (MMM) with the adaptive cross approximation. In order to stabilize the convergence characteristic of the Newton-Raphson method, we apply a line search technique to the MMM. Some numerical results that demonstrate the validity of the developed method are also presented. Index Terms--Adaptive cross approximation, line search, magnetic moment method (MMM), nonlinear magnetostatic field analysis.

A combined melt-spinning and electroplating techniques was used to prepare a composite magnetically hard/soft/hard trilayer ribbon with micrometric thickness. This technique to fabricate these multilayer systems could be used to tailor the magnetic permeability of a material by selective electroplating of the hard layer.

Formulas are derived giving the vector potential and the magnetic field components of a general coil of rectangular cross section and constant winding density. The solution is given in a cylindrical coordinate system in terms of trigonometric integrals. The formulas presented have been cross-checked and validated against alternative expressions giving the various field components as integrals of expressions containing Bessel and Struve functions. The trigonometric integrals for the fields can be evaluated easily to several hundred significant figures using mathematical packages such as Maple or Mathematica. Alternatively, they can be evaluated with a small FORTRAN program. Sample results and field line plots obtained with the method are given, and the field of a coil of rectangular cross section is examined in some detail. A comparison with the results of a finite-element method is also given. Index Terms--Analytical methods, axisymmetric coils, Bessel functions, elliptic integrals, Green function, Legendre functions, magnetostatics, Poisson equation.

Variable field generation (VFG) is a newly developed inverse problem algorithm for synthesizing magnetostatic system designs. Unique to this method, the system model would be physically implemented to provide alterable magnetic field production. Within this algorithm, optimization or regularization methods must be employed to determine a useful design solution. This paper presents the process created to apply these solvers in multiple stages and the application of nesting quick linear regularization methods within more robust nonlinear optimization routines. The results of employing this process to the design of a proposed magneto-plasma-aerodynamic (MPAD) device are discussed. Index Terms--Field synthesis, inverse problem, magnetostatics, variable field generation.

This paper describes the implementation of the fast Fourier transform on multipole (FFTM) algorithm for rapid calculation of magnetostatic fields in micromagnetics. The method is based on the multipole approximation theory, in which the computation-intensive transformation operations of the multipole in local expansions are accelerated by using FFT algorithms. Hence, this algorithm has the computational efficiency of the FFT-based approach, but is not confined to use in problems with regularly spaced elements. Index Terms--Fast Fourier transform on multipole (FFTM), magnetostatic fields, micromagnetic simulations, multipole approximations.

Magnetostatic actuators exhibit bistability similarly to the Pull-In phenomena of electrostatic actuators. In this paper a methodology and model for the extraction of the magnetic Pull-In parameters of magnetostatic actuators are derived. The flux-controlled magnetostatic actuator is analyzed based on the energy representation and the magnetomotive force-controlled magnetostatic actuator is analyzed in the thermodynamic potential energy (or co-energy) representation. An algebraic equation, referred to as the magnetic Pull-In equation, for each of the two cases (flux-controlled and magnetomotive force-controlled actuators) is derived. By solving these Pull-In equations either analytically or numerically, the magnetic Pull-In parameters are obtained. Several case studies, covering displacement and torsion magnetic actuators, are presented and analyzed, illustrating the usefulness of the proposed methodology, its relative simplicity as well as the adaptability and practical usage in wide spectrum of magnetic actuators. Index Terms--Actuators, magnetic, magnetostatic, model, pull-in.

A dynamic micromagnetic algorithm is used to address systematically the contributions of magnetostatic interaction fields in magnetic systems during first-order-reversal-curve (FORC) simulations. Details of the interaction field distributions (IFD) that display a nonlinear dependency on the field history and intergrain spacing are disdcussed.

We have investigated the magnetization characteristics of rotation-symmetrical magnetic bodies in a uniform magnetic field parallel to the axis of rotation. The bodies considered here include a cylinder ([eta] = 0), a sphere ([eta] = 1), a bicone ([eta] = 2), and a rotating astroid ([eta] = 3), where [eta] is the power index. The surface magnetic charge densities [sigma] for the bodies of 0 < [eta] [less than or equal to] 3 are numerically calculated by the surface magnetic charge simulation method. The results are illustrated for the various values of [eta]. If the shape approaches the cylinder, [sigma] concentrates near the edge and takes a peak value there. If the shape approaches the bicone, [sigma] concentrates near the tip (the point cusp) and takes a peak value there. To make clear the relationship between magnetization characteristics and shape, the inclination angles of magnetization on the surface of magnetic body are numerically obtained by using [sigma]. From these results, we can investigate the local magnetization directions on the surface of the magnetic bodies in detail. Index Terms--Bicone, cylinder, magnetization characteristics, magnetostatics, rotating astroid, rotational symmetry.

The paper presents an electrodynamic analysis of tunable multiport ferrite-dielectric structures with parallel transmission lines of an arbitrary type, coupled through propagating magnetostatic modes of magnetized multilayered ferrite films. The structures are supposed to be excited at one port by an incident electromagnetic wave, and amplitudes and phases of electromagnetic waves at other ports are obtained by an analytical procedure. The model holds for an arbitrary direction of a magnetizing field and describes the interaction of magnetostatic modes in ferrite films of a finite width. The solution is obtained in a self-consistent approach, i.e., a reaction of magnetostatic waves (MSWs) on transducers, which excite them, is taken into account. Derived closed-form expressions for response functions of multiports provide the base for the modeling of a wide class of MSW devices: multichannel adjustable filters and delay lines, directional couplers, frequency-selective power dividers, tunable oscillators and active filters, and multiport resonators. The theory is also valid for the analysis of multi-element, interdigital, and meander MSW transducers. Applications of a general theory are demonstrated for numerical calculations of frequency responses of surface and forward volume MSW filters, delay lines with new types of strip-line transducers (two-port and T-type), and for the analysis of a phenomenon of mutual coupling of transducers in conventional devices. Index Terms--Ferrimagnetic films, ferrite devices, magnetostatic waves (MSWs), microwave integrated circuits.

Computing magnetic field distributions is important for a range of practical applications. In the past, integral-equation-based schemes for such analysis have primarily relied on scalar formulations. In this paper, we introduce a novel integral equation that is cast in terms of the magnetic flux density and construct a method of moments solver by representing the flux with a set of basis functions whose normal component is continuous. This solver is then augmented with a recently introduced version of the fast multipole method that lowers the computational complexity and the memory requirements from O([N.sup.2]) to O(N), where hr is the number of basis functions used for the analysis. We validate magnetic field distributions computed by the proposed scheme by comparing them with those obtained analytically. Finally, we demonstrate the efficacy of this scheme by applying it to the analysis of practical problems in the nonlinear regime. Index Terms--Fast algorithms, fast multipole method, magnetostatic, volume integral equations.

A numerical code has been developed for the full-wave determination of the resonant frequencies and quality factors of microstrip patches with right-angle corners of arbitrary shape in the case in which the substrate of the patches is a magnetized ferrite with arbitrarily oriented bias magnetic field. The code is based on the solution of an electric-field integral equation by means of Galerkin's method in the spectral domain. The evaluation of the infinite integrals arising from the application of the numerical method is efficiently carried out by means of a technique based on the interpolation of the spectral dyadic Green's function. The numerical results obtained indicate that microstrip patches fabricated on ferrite substrates present cutoff frequency regions in which resonances cannot occur owing to the excitation of magnetostatic modes. The limits of these cutoff regions are shown to be dependent on the orientation and the magnitude of the bias magnetic field, on the shape of the patches, and even on the nature of every particular resonant mode. The numerical results also show that the resonant frequencies of microstrip patches on magnetized ferrites can always be tuned over a wide frequency range provided the orientation of the bias magnetic field is suitably chosen. Index Terms--Magnetic tuning, magnetostatic modes, microstrip resonators, microwave ferrites, spectral-domain approach.

This paper presents a generalized sensitivity formula that is applicable to any objective function of the optimization problems in two-dimensional (2-D) linear magnetostatic systems. For the objective function defined on an interface boundary as well as in a region, the shape design sensitivity expression is derived in a closed form from the augmented Lagrangian method, the material derivative concept and the adjoint variable method. The resultant sensitivity formula is expressed as a line integral along the interface boundary undergoing shape modification. Three shape design problems, whose objective functions are defined on an interface boundary or in a region, are tested to validate the derived sensitivity formula. Index Terms--Adjoint variable method, augmented Lagrangian method, continuum approach, design sensitivity analysis, magnetostatic system, shape optimization.

Discrete formulations based on the consistent finite integration technique for magneto-quasi-static problems involve the solution of either singular or very ill-conditioned algebraic systems of equations. For these formulations a regularization based on an augmentation with discrete grad-div-operators is proposed, extending the ideas in Hahne and Weiland (1992) and Bossavit (2000). Possible effects on the spectra of the algebraic systems are discussed and confirmed in numerical experiments. Index Terms--Algorithms, eddy currents, finite integration technique (FIT), gauging, regularization.

We present a mixed formulation for magnetostatics in unbounded domains. The magnetic flux density B is the principal unknown and it is interpolated with facet finite elements. The reduced scalar potential [psi]!, which is considered as a Lagrange multiplier, is an auxiliary unknown; it is taken as constant over each tetrahedron. We compare it with a previously presented H-oriented mixed formulation. Index Terms--Facet finite elements, magnetostatics, mixed formulation.

Using a micro magnetic algorithm based on the finite element combined with the boundary method, hysteresis loops and magnetization states of magneto statically coupled Nickel nanowires can be simulated without making use of simplifying assumptions. The most pronounced influence of the magneto static coupling on the shape of the hysteresis loops of an ensemble of wires is the reduction of the coercive field with an increasing number of interacting wires and only if the magneto static interaction of several wires is considered, the coercive field of the array approaches the experimental value well.anl

Results demonstrate that at low incident energies significant intermixing of nickel on copper occurs and correlates with interfacial roughness and incident atom angle. Data also indicate that high quality interfaces with minimal interfacial roughness and mixing can be produced by energy modulation during multilayer growth.

In order to solve the nonlinear equation system arising when solving magnetic fields with the finite element method, very often the Newton-Raphson method is applied. Sometimes it is advantageous or necessary to apply relaxation factors in order to improve the convergence. In this paper reasons and workarounds for the convergence problem are discussed. Index terms - Convergence of numerical methods, Newton-Raphson method, magnetostatics, nonlinear equations, nonlinear magnetics

In this paper we study different approaches to introduce the source terms due to the inductors crossed by a uniform current density [J.sub.0] in 3D FEM. Two equivalent methods are developed to decompose the current density J in the facet element space with divergence free close to [J.sub.0]. This decomposition is used in a-formulation without gauge condition. Moreover from the flux facet the source field [H.sub.s] can be calculated in the edge element space and introduced in [Phi]-formulation. As examples of applications we have studied a coil with a complex geometry and a iron core coil. Index-Terms- Finite element method, magnetostatics, magnetic field, inductor, current.

Hybrid b- and h-formulations for the solution of the 2D magnetostatic problem are presented. These formulations can be written in such a way that the resulting system matrices are identical up to the coefficient related to the material properties. Thus after the evaluation of the required matrix terms two complementary solutions of the problem are obtained easily with the total computational cost of almost one. The complementarity of the solutions gives a good basis for the adaptive mesh refinement. In the derivation of the formulations differential forms, which best describe the underlying idea, have been used. Index terms - magnetostatics, integrodifferential equations, finite element method, differential forms, adaptive mesh refinement

In this paper we analyze a three - dimensional method for the computation of the magnetic fields, produced by thin ferromagnetic shells. Integrodifferential equation is used to define the scalar potential distribution inside magnetized region. Magnetic field inside a thin shell is calculated using FEM. This method is shown to give accurate results for the field inside thin spherical shells in the wide range of the shielding factor. Index terms - magnetic fields, magnetostatics, magnetic shielding, integrodifferential equations, finite element methods, error analysis.

The magnetization distributions in recorded transitions in thin film disk media are shown to consist of simple longitudinal magnetization transitions along with flux closure patterns. Together they give rise to the familiar sawtooth patterns but also indicate why arctangent and other approximations used in record theory have proved so successful even when sawteeth are known to be present. Index Terms - Disk media, magnetic recording, magnetization distributions.

The theoretical formation and propagation properties of microwave magnetic envelope solitons were modeled from the nonlinear Schrodinger equation without damping. based on soliton threshold input amplitude criteria from inverse scattering theory, input amplitudes were set midpoint between the one-and two-soliton threshold values. The soliton formation time [T.sub.S] was defined as the time required for the pulse amplitude to stabilize after launch. This [T.sub.S] was found to be independent of the nonlinear response coefficient N and to vary as the inverse of the dispersion coefficient D. One possible way to model these [T.sub.S] dependencies is through the relation [T.sub.S] [approximately equal to] [[[T.sub.d] [T.sub.nl]].sup.1/2], where [T.sub.d] and [T.sub.nl] are characteristic dispersion and nonlinear response times, respectively. This result suggests a simple geometric mean relation between these characteristic times. Index Terms - Delay, delay estimation, dispersive media, ferrimagnetic films, magnetostatic volume wave, magnetostatic wave, nonlinear differential equations, nonlinear magnetics, nonlinear wave propagation, solitons, yttrium iron garnet.

The surface magnetic charge distributions with edge singularities are studied for a half-infinite circular cylinder with uniform permeability. The cylinder is placed in an axially uniform magnetic field. The subject of this study is the charge densities around the edges on both side and end surfaces. The charge densities over a certain distance from the edge on the side surface are regarded as constant. It is shown that an integral equation can be found for the charge density around the edge on the side surface. The unknown quantity in the integral equation is expressed as a product of a bounded function and an edge-singular power function depending on the relative permeability. The charge density on the end surface is expressed as a function of the charge densities on the side surface. Numerical calculations are carried out for various values of the relative permeability and are illustrated to clarify the surface magnetic charge densities. The charge densities around the edge are proportional to a certain inverse power of a distance from the edge. It is clarified for the first time that the edge singularity power factor increases with the relative permeability [Mu] and is equal to the same on the right-angled wedge of the same [Mu]. Index Terms - Cylinders, magnetic fields, magnetostatics, numerical analysis.

The cross-track profile of media noise is measured on a precision spinstand for oriented and nonoriented media. These data are correlated with magnetic force microscopy (MFM) images to determine the location of track-edge noise with high spatial resolution. A significant component of track-edge noise is located in a narrow band at the edge of bits recorded in opposition to the previously saturation-erased direction. This reverse erase-edge noise (REEN) increases as orientation ratio increases. The magnitude and distribution of REEN is consistent with a reverse-dc-erase mechanism. [Delta]M data indicate a greater influence of magnetostatic and/or exchange coupling for the oriented media. Together with larger on-track reverse-dc-erase noise and higher supralinear transition noise, these results suggest enhanced collective magnetization reversal for the oriented media relative to the nonoriented media. MFM images also reveal the presence of narrow magnetic-dipolar strips at the track edges. These dipolar strips are generated by cross-track components of the head field. The track-edge dipole moment decreases as orientation ratio increases due to preferential alignment of easy axes along the down-track direction. These dipoles contribute to base line shift and are not a significant source of media noise. Index Terms - Magnetic force microscopy, media noise, oriented media, oriented ratio, signal-to-noise ratio.

We have proposed a delay line of microstrip type consisting of a microstrip line fabricated on a composite substrate of two yttrium iron garnet films separated by a gadolinium gallium garnet layer. The dispersion relations are derived assuming magnetic walls at the edges of the strip. Experiments are carried out at S band with nonuniform magnetic field. Insertion loss less than 25 dB with large delay time more than 800 ns is observed experimentally. The experimental results on delay line characteristics are briefly discussed with theory. Index Terms - Delay line, magnetostatic wave, microstrip line, YIG film.

Low temperature characteristics are studied for the linear and nonlinear magnetostatic wave (MSW) propagation in yttrium iron garnet (YIG) films theoretically and experimentally. It is confirmed that the saturation magnetization is the only factor which governs the propagation characteristics at low temperatures. Moreover, the ferromagnetic resonance (FMR) linewidth [Delta]H of a YIG film is measured from the propagation loss and delay of MSW, and it is found that the A H becomes larger at low temperatures. Index Terms - Low temperature, magnetostatic wave, nonlinear.

Nonlinear magnetostatic analysis generally involves an iterative approach such as direct iteration, the Newton-Raphson method, or a combination of both. However, those techniques always require the solution of a new linear system at each iteration that is CPU time consuming. Some acceleration can be carried out in order to partially overcome this drawback, but this may lead to a loss of convergence. In this paper, it is shown that the 2-D nonlinear magnetostatic problem may be solved by using the transmission-line modeling (TLM) method that is usually exploited for the solution of electrical networks. The fundamental mechanism of this method is the modeling of the nonlinearity as fictitious sources so that the stiffness matrix of the problem remains unchanged at all iterations. Substantial reduction in execution time is obtained with excellent convergence properties. Numerical results are presented, and a comparison to the classical Newton-Raphson algorithm points out the efficiency of our method.