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This paper outlines a technique for predicting the residual field in magnetizable media after the source is removed. Ship builders are considering the use of dc cables, and many land-based power systems have dc links as a power feed. What will the neighboring steel's remanent field be if the cables are excited with a large current, e.g., under short circuit conditions? This paper presents a procedure for replacing the steel with a continuum of nonlinear permanent magnets. The technique consists of discretizing the magnetizable medium into subregions, as defined by a contour plot of [absolute value of [??]]. Each subregion is assigned a magnetization curve according to the characteristic B in that region. The source field is used to assign local magnetization within these regions. The technique is novel, but the real contribution is a technique that can be implemented by any user of a commercial code, and not isolated to developers. Index Terms--Computation, hysteresis, magnetization, remanence.

High-temperature superconducting trapped field magnets (TFMs) offer great potential as an alternative to second-generation YBCO wire, both in cost and performance. Attention is given to the calculation of current distribution within YBCO disks at partial and full activation and comparing this to experimental values. The best results are obtained by treating the current as a sequence of nested current rings. The fields are computed by integrating the elliptic integrals representing the fields from these rings and using variable metric optimization to choose the ring radii to best match the activation field over the unactivated material. A technique for treating the subregions of the TFM as voltage fed coils appears most expeditious for computing forces. Index Terms--Activation, bulk, high-temperature superconductor (HTS), synchronous motors, variable metric optimization.

Latin hypercube is a sampling technique for searching n dimensional space. Like Monte Carlo methods, it retains random qualities, and yet Latin hypercube is consistently more effective than Monte Carlo. Despite this fact, not a single paper has been published in IEEE TRANSACTIONS ON MAGNETICS on its use. Field analysis is a long way from delivering vectorized solutions where a vector of inputs can be processed. Stochastic algorithms are exceptionally inefficient compared to their deterministic counterparts. The best optimization tool would be a deterministic method which quickly and effectively interrogates the search space. Latin hypercube sampling, combined with pattern search solutions, comes close to achieving that objective. An improved solution for the magnetic TEAM Workshop problem 22 is presented using these tools. Index Terms--Latin hypercube, multiple minima, optimization, pattern search.

The equivalent T circuit of an induction motor is found in every engineering motors book and is becoming increasingly important with the popularity of vector control. The values used in the circuit are used to dictate the necessary gating signals for the pwm inverter. It is the de facto standard bridge between the field analyst and the motor controller. These parameters are not unique. Force, energy, voltage, and secondary power dissipation can be shown to relate to the product of synchronous reactance and the coupling coefficient of the rotor and stator. The mutual reactance, the secondary inductance, and secondary resistance are nonunique. Yet this surprising feature can be used as a solution integrity check for the field analyst. Index Terms--Coupling coefficient, equivalent circuit, induction, motor.

Power systems on naval vessels and airplanes are good examples of self-contained power systems. These types of systems are useful for testing reconfiguration, particularly ones that might be implemented continuously, not just under compromised conditions. Determining the best operating condition in real time is challenging, since it discourages stochastic approaches. A fixed grid representation of the dynamic loads is recommended, employing a phasor algorithm to update the load impedances. A new subspace approach for solving the reconfiguration is presented and compared to branch and bound algorithms. Reconfiguration is studied for a test system with 16 million switch options. Also discussed is how this information can be used in the design of the power grid a priori. Index Terms--Integer optimization, phase analysis, stochastic.

Power systems on naval vessels and airplanes are good examples of self-contained power systems. State of the art LEM modules and voltage sensors provide real time current and voltage data. This paper shows how that information can be used to construct dynamic equivalent impedance representations of the system discretized into key trunk lines. Error analysis indicates that the algorithm performing this representation can be updated in one fifth of a cycle if the signal to noise data ratio is 5% or less. The magnitude of the equivalent impedance is sufficient to determine when fault control on either end of the trunk line is required. These same equivalent impedances can be used to determine the best switch configuration to maximize load power while minimizing transmission loss subject to line load capability. The accuracy of the equivalent impedance approach is assessed for transients with active and passive loads. Index Terms--Fault detection, phase analysis, reconfiguration, transient.

High rotation speed is the key to enhanced power density in rotating machines. High speed, shock, and construction considerations argue for solid rotors. However, output transient voltage requirements cause concern that changes in the field current will not be registered quickly in the stator. This paper examines different techniques for estimating the machine time constant, including an analytic solution of a smooth air gap machine and a transfer relation solution based on time harmonic solutions. It discusses an empirical solution and an equivalent surface current approach for predicting the loss in the rotor. These solutions compare favorably to rotational transient finite-element solutions. Index Terms--Harmonic, power dissipation, rotating machine, transfer relation, transient, wound rotor.

Transcranial magnetic stimulation (TMS) is used commonly as both a diagnostic tool and as an alternative to electric shock therapy for the treatment of clinical depression. Among the clinical issues encountered in its use is the mitigation of accompanying pain. The objective becomes one of minimizing the induced surface field while still achieving the target field objective. Three techniques discussed for realizing this end are 1) placing a conducting shield over a portion of the central target region, 2) using supplementary coils of opposite polarity in tandem with the primary field, and 3) opening the core angle to distribute the field. Option (3) shows the greatest promise for reducing the ratio of the maximum surface field to the induced target field Index Terms--Electric field, iron core, magnetic, stimulation, suppression.

High power density applications require special treatment in design optimization. Among the critical questions is how the working torque angle will change through an optimization analysis. We present a new method for computing and using the synchronous reactance that accounts for the torque angle in the midst of complex parameter changes. The challenge is to tally this effect along with the load power factor into a variable metric optimization. Our new technique both computes this reactance under heavy saturation and integrates it into the machine design. The technique also covers appropriate stator current excitation densities in transient and steady-state excitation. Index Terms--Deterministic, optimization, reactance, superconducting, synchronous.

The classical approach to solving transient problems is a finite difference-based time-stepping procedure. A powerful alternative when motion is not involved is to use time harmonic solutions to build the transfer function of the system, appropriate for a spectrum of source excitations. This paper shows how nonlinear problems are approached with this method, and how the transfer function is derived using variable metrics and multivariate splines. Index Terms--Eddy current, Laplace, time harmonic, transient.

Variational Metrics and other direct search techniques have proved useful in magnetic optimization. At least one technique used in magnetic optimization is to first fit the data of the desired optimization parameter to the data. If this fit is smoothly differentiable, a number of powerful techniques become available for the optimization. The author shows the usefulness of tensor product splines in accomplishing this end. Proper choice of augmented knot placement not only makes the fit very accurate, but allows for differentiation. Thus the gradients required with direct optimization in divariate and trivariate applications are robustly generated. Index Terms - Direct optimization, magnet, Spline, Maglev

The calculus of stationary points or indirect optimization is noted for rapid speed. It's speed is realized in an analytical representation of the Hessian and a polynomial fit of both the objective function and the constraints. Constraints are treated as active using Lagrangian multipliers. Because the algorithm's speed is so rapid, the problem can be repeated multiple times with random starting guesses to circumvent the possibility of encountering local wells. Both an analytic and an actual field problem are considered by way of providing examples of the technique. Index terms - optimization, functional approximations, gradients

The analysis of single and multiphase induction motors continues to represent a challenge to researchers in computational electromagnetics due to the presence of [Tau][Omega] x B electric fields. This contribution cannot be inserted into the Green's function for boundary element codes; finite difference and finite element approaches are forced to hard code these effects, compensating at high speeds with upwinding techniques. The direct computation of these affects using transfer relations in a linear environment offers an analytical backdrop both for benchmark testing numerical codes and for design assessment criteria. In addition to torque-speed predictions, the terminal relations and total power dissipation in the rotor are computed for an exposed winding three-phase and single-phase machine. Index Terms - Eddy currents, induction motor, torque.

Null flux were suggested by Danby and Powell in the late 1960's as a useful means for realizing induced lift with little drag. As an array of alternating magnets is translated past a set of null flux coils, the currents induced in these coils act to vertically center the magnets on those coils. At present, one Japanese MAGLEV system company and two American-based companies are employing either null flux or flux eliminating coils in their design for high speed magnetically levitated transportation. The principle question addressed in paper is: what is the proper choice of coil length to magnet length in a null flux system? A generic analysis in the time and frequency domain is laid out with the intent of showing the optimal design specification in terms of coil parameters. Index Terms - Computation theory, magnetic levitation, magnets.

Quasi-permanent magnets constructed from melt textured yttrium barium copper oxide superconductors can trap multi-Tesla fields and retain that field semi-indefinitely. These magnets can be employed in lieu of permanent magnets because the fields so trapped attain near zero creepage decay. The fields produced by these magnets, their prediction and design expectations when they are integrated in large scale arrays are studied.

Error bounding has been a subject of keen interest for field theoreticians over the last decade. This paper details the technique for not only specifying and indexing field uncertainty at any given point, but force and torque errors as well. The technique allows one to specify the force or torque on an object to a given value plus or minus another value. With single-layer or boundary formulations, continuity of the normal B field is implicitly insured; the discontinuity in tangential H is shown to imply an error in surface current which can be linked directly to the calculation of the uncertainty of forces and torques. With nonlinear problems additional errors result from internal magnetization current which is used to handle internal saturation. The theoretical formulations predicting errors with three cases are presented: static-linear, static- and nonlinear, and time harmonic. Any error predictions in the field and global quantities such as force, torque, or inductance result from equivalent surface and volume currents.

Magnetic Shielding or degaussing is a special subclass of inverse magnetic fiel problems targeted at minimizing the signature of a magnetizable object placed i an external field. This is usually accomplished by placing an appropriate 'skin of current around or just inside the object. The problem is more demanding than the typical inverse problem in that the goal is to reduce the induced field everywhere outside the object, thus making the target cost function difficult t construct. Boundary Element Methods (BEM) can be formulated in terms of equivalent surface currents which are representative of the pattern of surface current necessary to minimize the signature. This paper investigates how and under what conditions this is so. In addition the paper examines the applicatio of the Method of Fundamental Solutions (MFS) to the same problem. With MFS, the object cost function is integral to the formulation. Both methods are applied t simple two dimensional box structures placed in the Earth's field.

This paper considers the prediction of induced electric fields for nerve stimulation. Although functional electric stimulators have been in existence fo many years, functional (site specific) magnetic stimulation is virgin territory The problem of predicting localized electric fields from potential magnetic stimulators falls into a special class of eddy current problems. In this class, the currents do not themselves effect the primary magnetic field responsible fo the induced current; the medium conductivity is far too small for this secondar coupling. A two stage static magnetic analysis is used to compute the induced electric fields accurately for a number of problems falling within this category. The computations accurately reflect the influence conductivity jumps at interfaces, induced charges, and voltages between points, but use conventional magnetic scalar potential boundary element solvers. The problems are solved as if they were magneto-quasistatic using duality. Comparisons to experiment validate the accuracy of this technique. The analysis is addressed t the induced bioelectric fields during magnetic stimulation, but the theory applies equally well to any problem where the induced eddy current has little bearing on the field because of its small amplitude.

With the recent progress in the parallel processing technology, there comes the need to reinvestigate various techniques employed in computational electromagnetics. The Monte Carlo technique discussed is one alternative that has the attractive feature of requiring very little set up time. Because no grid or volume discretization is involved, a smaller demand on storage capacity is required. The approach proposed is based on the random walk idea of a particle moving about in a medium, and registering information upon contact with a boundary. The standard Helmholtz type equation encountered in eddy current problems is solved by letting one particle becomes multiple particles in its walk through the problem. Application to a simple 2-D eddy current problem is presented. The solution was calculated at every point in a grid by two methods, once by a direct finite difference approach, and also by the Monte Carlo method. The results indicate that on a data parallel system such as Maspar MP-1, the Monte Carlo method becomes competitive in CPU time as a total solution approach for problems involving more than 300 unknowns.

Often the true strength of a field formulation is found in the efficiency and accuracy of its post processing capability. Any method of replacing derivatives with integrals is desirable numerically. The method outlined here is especially advantageous with eddy current problems, because it allows the interfaces of all conducting regions to be replaced with equivalent magnetic surface charge and surface current. These equivalent sources are an immediate result of the field computation, and require virtually no additional computation. In terms of these equivalent sources, external fields are found quite accurately from surface integrations. With boundary element method (BEM) techniques, this ability is especially valuable in terms of its accuracy and speed in finding global quantities such as force. The equivalent sources are directly related to the second order vector potential which has separability advantages in a number of coordinate systems.

Much of what has been learned about the physiology of the brain has come from animal studies, in which stimulating electrodes may be surgically implanted into the brain itself. Such studies can not, of course, be ethically performed in humans. However, in the 1980s, a technique was developed that permits the direct stimulation of the human cerebral cortex. The technique is not invasive and is apparently harmless. It uses high power electromagnetic coils to generate a strong magnetic pulse at the surface of the scalp. This strong pulse generates electrical currents within the brain, and these currents stimulate the nerve cells. Little is known, however, about the actual brain structures that are being stimulated by these magnetic pulses. Researchers have narrowed down the stimulated area by the simple and time-honored technique of triangulation. They developed a special magnet which consists of two coils slightly off-axis. The magnetic fields generated the same electrical field at only one point. Using a specific finger movement as the indicator of the desired brain stimulation, the magnets were moved to determined the position for best stimulation. Plotting the intersection of the electric field graphs against a brain image obtained by magnetic resonance imaging, the investigators determined that the magnetic stimulation of the brain is acting at the boundary between the grey and the white matter in the cerebral cortex. The point of stimulation was always at the crown of a gyrus, that is, at the top of a fold of the cerebral cortex, and not within a sulcus, or groove. Although the precision of the localization remains crude, the results suggest that magnetic stimulation acts directly upon layer VI of the human cerebral cortex. (Consumer Summary produced by Reliance Medical Information, Inc.)

Electrodynamic Maglev systems are distinguished from electromagnetic systems in that the currents yielding lift and guidance forces are induced by the movement of the vehicle. Above a threshold speed, such a system is inherently stable, and has the additional benefit of having greater flexibility to system construction tolerances in that the magnet vertical position can change by as much as 5 cm. A stacked magnet design is considered which couples into a set of interleave coils which are interconnected in such a way as to yield both lift and guidance forces. A mutual coupling analysis is embraced wherein the mutual inductance between the permanent magnets on board the vehicle and the coils are computed using closed form analytical expressions for filaments. The derivatives of these expressions are then averaged to compute both the induced current and the forces on the coils as a function of the system geometry and speed. A full transient analysis must be performed to accurately account for entry and exit effects. The results are compared to those experimentally measured on a test track and extrapolations are offered to suggest future design considerations.

The analysis of thin iron shells has classically been problematic due to cancellation errors across the thickness of the shells. A boundary element formulation is developed which eliminates the volume of the shell. The collapsed interface is assumed to contain both single and double layer surface currents to represent their field contribution in all of space. The double layer currents accurately simulate the channeling of flux into the shell. The single layer surface currents accurately reflect the thin shell's perturbation to the field far from the shell. A thin shell cylinder and sphere serve as the test body against which the formulation's predictions are compared for a variety of element densities.

Describes a method designed for engineering application in which high accuracy is secondary to modest computational requirements for three-dimensional eddy current fields. Information on the second-order vector potential formulation; Functions of the null field integral technique; Analysis of the importance of additional eigenvalues.

The field and current induced in a trapped field magnet during a transient current excitation is complicated by the fact that the conductivity of the material changes wildly depending on both the magnitude of the induced current and the local B field. A mutual inductance approach is presented for solving this coupled problem; it involves discretizing the bulk superconductor into cells and precomputing the inductance coupling matrix of all cells with one another and with the excitation coils. The benefits of this approach are that the numerical simulation is rapid and flexible. The latter is important because the conductivity of the individual cells is dependent on the current density, the magnetic field density magnitude, and the temperature. The proposed approach allows the modeling of a very sharp J\-E relationship which has proved problematic using conventional finite element approaches. In addition, a phenomenological model relating the critical current density to the field is introduced for these tests in place of the Kim model. The field simulation is tested with a challenging dwell time experiment in which the trapped field above a bulk superconductor is predicted for various excitation current hold times. [ABSTRACT FROM AUTHOR]

Presents a study that examined various techniques for the acceleration of multivariable optimization problems. Characterization of magnetic field optimization problems with three or more variables; Comparison of radial basis functions, multivariable splines and a class of representative functions for accuracy and speed; Result and conclusion of the study.

Presents information on a study which examined the boundary element methods for modeling voltage driven magnetoquasistatic devices. Circuit and current constraints; Experimental results; Conclusions.

Presents a study on the calculus of stationary points or indirect optimization for rapid speed. How its speed is realized in an analytical representation of the Hessian and a polynomial fit of both the objective function and constraints; Examples and techniques in solving actual field problems.

Presents a boundary element method for determining the impedance matrix in an eddy-current problem. Background for the boundary element method; Numerical results; Phasor interpretation for determining impedance matrix results; Conclusions.