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This paper deals with the diffusion of rotating electromagnetic fields into hysteretic materials. A simplified vector formulation based on a parallelogram hysteresis model has been investigated, in order to significantly reduce the computational effort. Vector saturation and loss properties are discussed. The whole simulation has been done by the use of a finite-element time-domain algorithm. Index Terms--Finite-element method (FEM) simulation, parallelogram model, vector hysteresis.

This paper introduces a simplified vector model based on the Preisach approach that intrinsically satisfies loss and saturation properties. It is able to reproduce isotropic and nonisotropic behavior. The main idea is to compute the magnetization vector in two steps independently, amplitude and phase. The first one is computed by means of a scalar Preisach model with a distribution depending on the angle of the applied field with respect to a fixed direction. The phase is computed by means of a phase diagram and a simple function that take into account the history of the angle between magnetization and applied field. The proposed formulation allows fast computation of rotational and alternative vector magnetization, the computational time is of the order of two times the scalar Preisach model. Index Terms--Magnetic materials, Preisach model, vector hysteresis.

This paper discusses the numerical implementation of a new vector hysteresis model, the radial vector model, introduced as general hysteresis vector model for both isotropic and anisotropic magnetic materials. The present implementation is a 2-D one that uses ellipses as critical surfaces. The results computed by the model, applied to some basic vector hysteresis configurations, are in agreement with experimental behavior. Index Terms--Hysteron critical surfaces, magnetic vector hysteresis, modeling.

This paper deals with the characterization of dynamic loops shapes and losses in soft magnetic materials. An experimental and theoretical analysis has been done in order to describe static and dynamic hysteresis on soft ferrite cores. A parallelogram-loop-based hysteresis modeling is described and discussed. The possibility of the model to include vector hysteresis and the related properties are then discussed, with particular attention to the case of a rotating magnetic field into an isotropic and anisotropic medium. Index Terms--Dynamic modeling, magnetic hysteresis, soft materials, vector modeling.

In this paper, we present and discuss the use of a reduced Preisach vector model (RVPM) as a numerical tool for the analysis of the influence of the cut angle in the magnetic behavior of laminated Fe-Si steels. The model parameters can be deduced by measurements along the easy and hard axis, and the families of hysteresis loops and virgin curves for the same Si-Fe sheet, cut at different angles with respect to the rolling direction can be derived. In particular, we present a simplified identification procedure based on the assumption that the material is single-quadrant medium along the principal axes. Results seem to indicate that the hypothesis of factorizable Preisach function is not compatible with the real magnetic materials. Index Terms--Hysteresis, modeling, vector processing.

The characterization of the energetic magnetic behavior of hysteretic materials and the determination of the surface impedances are proposed. A numerical model in time domain is adopted for the calculations. The use of parallelogram-shaped hysteresis loops allows for simplifying the numerical formulation and for reducing the computation time with respect to more accurate models. Equivalent major loops have been defined starting from the measured ones. Comparison with the modified scalar Preisach model is presented and discussed. Index Terms--Finite-difference time domain (FDTD), magnetic hysteresis modeling, surface impedance.

In this paper we discuss the electro-thermal behavior of solid armatures in railguns. This discussion is based on a review of results obtained by a theory that takes into account the three-dimensional nature of melting and vaporizing of the contact surface between rail and armature. This theory is numerically treated by an integral approach based on a suitable decomposition of rails and armature in hexahedrons, bricks and filamentary elements. After a recall of the main points of this theory and the related numerical technique, this review paper describes the principal features about the current flow, the heat production and exchange, the presence of liquid and vapor phases at the contact face of the armature, derived by this theory. ln particular the shape of the melt front and the critical transition velocity predicted are in agreement with the experimental observations. Index Terms - Integral equations, Railguns, Skin effect, Transition metal materials.

In this paper the efficiency of equipotential and grounding systems with respect to an electrostatic discharge (ESD) event is investigated. This investigation has been made from a numerical point of view by a suitable application of Finite-Difference in Time-Domain (FDTD) algorithms to analyze different grounding system configurations, and by an experimental point of view by carrying out a measurement system for the conducted interferences in metallic objects connected to ground and stroked by ESD. Experimental measurements have been used here to validate the numerical procedure. Index terms - Electrostatic discharges, Grounding, FDTD Methods, Measurement.

This paper deals with a complete three-dimensional calculation of the magnetic vector potential and of the magnetic flux density created by disk conductors, in which an assigned current flows. The formulas presented are valid either inside or outside the conductor. The effectiveness and the time-saving possibilities of the expressions derived is shown by comparison with the numerical results obtained by direct integration of the Biot-Savart formulas and with experimental results. Index terms - Magnetic fields, integral equations, algorithms.

In this paper a numerical model for the computation of the electromagnetic field produced by an electrostatic discharge (ESD), occurring in the vicinity of a system of conducting objects, is presented. The ESD is modeled by a current flowing into a ionized channel located between two initially charged surfaces. The electromagnetic field generated by the ESD event is computed by means of a finite-difference time-domain (FDTD) algorithm based on the Yee's space-time mesh, and on the Mur's absorbing boundary conditions (ABC). A validation of the model by comparison against measured data is shown and an application to the analysis of the electromagnetic (EM) field produced by an ESD in a shielded box is presented.

In this paper an approach to the numerical analysis of the electromagnetic interferences (EMI) radiated by metallic grids, like Faraday's cages, hit by a lightning stroke is proposed. This approach is based on a hybrid differential-integral mathematical formulation in which a Finite-Difference Time-Domain scheme is used to evaluate the current density distribution inside the conductors, while the Kirchhoff's integral expressions are used for the computation of the transient electric and magnetic fields generated by the current flow into the grid. The introduction of a suitable scalar potential defined on the surface of the conductor allows to determine a complete set of boundary conditions for the problem of the magnetic diffusion of the current into the conductor and to reduce the region to be numerically treated by the differential formulation to the only conducting materials. Examples of application of the method to the numerical analysis of the EMI radiated by a Faraday's cage struck by lightning are given.

This paper deals with the numerical analysis of the behavior of diffracting perforated shields, and in particular of honeycomb structures. For the numerical computation a Yee's finite difference algorithm with Mur's absorbing boundary conditions is employed. A particular technique allows to limit the spatial dimension of the simulating grid, suitably taking into account the external field source. The computed results show the effectiveness and the accuracy of the method.

In this paper, the problem of the electromagnetic diffusion of electrostatic discharge (ESD) currents, interfering directly on the metallic enclosures of electronic equipments, and of the electromagnetic interferences (EMI) produced, is modeled and computed via a suitable finite-difference time-domain numerical approach. The levels of the radiated fields produced by standard ESD current waveforms in grounded metallic shells are evaluated, and the effects of the different arrangements of the grounding wires of the enclosure on the resulting EMI levels are discussed.

This paper deals with a numerical modelling of the interferences produced by electrostatic discharges that reach the surface of metallic boxes containing electronic circuits and flow toward the ground connections. The wave-form of the interfering current assumed is taken from the draft of the CENELEC ESD Standard. The distribution of the current density into the enclosure during the electrostatic discharge event is deduced by means of a scalar magnetic potential approach in the frequency domain, and by a consequent finite difference discretization. The passages from the frequency domain to the time domain and forward are made using the discrete Fourier transform. This formulation of the problem allows the simulation grid to be reduced to only the metallic enclosure, saving time either in preparation of the input data or in the numerical computation. The electromagnetic interferences radiated by the enclosure during the electrostatic discharge event are directly computed by multipole expansion of the resulting current density distribution.

The coupled problem of the three-dimensional diffusion of current and heat in railguns with solid armature is formulated by means of a circuital approach. Rails and projectile are divided in a high number of small-size parallelepipeds, so that temperature and current density may be imagined uniform in every parallelepiped. Integrating the Ohm's law over each parallelepiped an equivalent R-L electrical network is obtained, whose resistive and inductive parameters are evaluated by means of explicit analytical expressions, possible in the case of discretization in parallelepipeds. The use of current filamentary parallelepipeds in the zone of the rails where only current directed in the sense of motion may be hyphotized, avoid to remesh in time the grid. The voltage fall in the boundary layers between rail and moving armature are taken into account by means of suitable driven generators. The integration of the Fourier's law over each parallelepiped leads to an R-C equivalent thermal network, whose external nodes are suitably connected to take into account the heat exchange by radiation and convection. The position of the projectile is deduced by the application of the virtual displacement principle, where the discretization in parallelepipeds allows to express the Lorentz's force again by means of explicit analytical relations. The non linear differential equations system so obtained fully simulates the behaviour of a solid armature railgun, and is solved in time, updating at each time-step the coefficients variable with current density, temperature, and projectile displacement. The proposed model has demonstrated good capability to simulate experimental railguns shots, as long as the frictional heat is negligible in comparison to the Joule heat and did not occur melting and arcing.

The three-dimensional integration of the Biot-Savart's law for conductors in annular sector shape, in which only a constant distributed, theta-directed current flows, is reported. The obtained expressions allow a quick and accurate evaluation of the components of the vector potential of the stationary magnetic field and of the magnetic induction due to this type of conductor, in iron free-media. The relations presented in this paper, together with similar expressions, valid for other shapes of conductors and current distributions, can be usefully employed to evaluate the magnetic fields in complex, linear and iron-free structures, when the examined geometry can be well approximated with a series of current elements of elementary shape, of which solution of Laplace's equation is known in closed form.

This paper deals with a magnetic modeling for the estimation of the dynamic losses in soft ferrite cores. A time-domain MSPM based algorithm for the hysteresis losses evaluation, added to a simplified, one-dimensional modeling of the eddy current losses, are used to predict the total specific losses in cores subjected to a.c. and distorted wave-forms. Experimental analysis show satisfactory capability of prediction of the modeling proposed, used as a CAD tool. Index Terms--Eddy current losses, hysteresis losses, modeling, soft ferrites.

We present here a novel technique for the identification of the parameters of the probability function used in the Preisach-based modeling. This technique seems to overpass the problems linked with the use of a product of two single-valued functions as a probability function that in the case of soft magnetic materials may cause an unacceptable lack in accuracy of the model. Experimental tests are presented in the final section of the paper indicating the satisfactory improvement of the predictive capacity of the model due to the proposed identification technique. Index Terms--Hysteresis, measurements, modeling, soft magnetic materials.