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This paper aims to present a new iterative procedure for the 3D representation of focusing magnetic fields in TWTs generated by PPMs, by using equivalent sources and optimisation algorithms.

In the integrated optimisation strategy general models for magnetic sources are employed and local and global inverse problems are iteratively solved for the minimization of the representation error.

The results obtained show that the target accuracy is reached with a low computational effort, employing a minimum number of equivalent sources.

The procedure is robust and converges for all the examined magnetic field configurations.

Different from other approaches, the procedure presented here can be directly applied to a variety of different models for magnetic sources.

The aim of this work is to show how evolutionary computation can improve the quality of 3D‐FE mesh that is a crucial task for field evaluations using 3‐D FEM analysis.

The evolutionary approach used for optimizing 3D mesh generation is based on the bacterial chemotaxis algorithm (BCA). The objective function corresponds to the virtual bacterium best habitat, and the motion rules followed by each virtual bacterium are inspired to the natural behaviour of bacteria in real habitat.

The obtained results show that the present approach returns good accuracy performances with low‐computational costs.

The procedure is robust and converges for all the practical cases examined for validation.

The adoption of a correct optimization algorithm is fundamental to obtain good performances in terms of robustness of the results and the low‐computational costs. In this sense, the BCA is a valid instrument for improving the quality of 3D‐FE mesh.

The accurate modeling of magnetic hysteresis in electrical steels is important in several electrical and electronic applications. Numerical models have long been known that can correctly reproduce some typical behaviours of these magnetic materials. Among these, the model proposed by Jiles and Atherton must certainly be mentioned. This model is intuitive and fairly easy to implement and identify with relatively few experimental data. Also, for this reason, it has been extensively studied in different formulations. The developments and numerical tests made on this hysteresis model have indicated that it is able to accurately reproduce symmetrical cycles, especially the major loop, but often it fails to reproduce non-symmetrical cycles. This paper aims to show the positive aspects and highlight the defects of the different formulations in predicting the minor loops of electrical steels excited by non-sinusoidal currents.

The different formulations are applied to different electrical steels, and the data coming from the simulations are compared with those measured experimentally. The direct and inverse Jiles–Atherton models, including the introduction of the dissipative factor approach, are presented, and their limitations are proposed and validated using the measurements of three non-grain-oriented materials. Only the measured major loop is used to identify the parameters of the Jiles–Atherton model. Furthermore, the direct and inverse Jiles–Atherton models were used to simulate the minor loops as well as the hysteresis cycles with direct component (DC) bias excitation. Finally, the simulation results are discussed and compared to measurements for each study case.

The paper indicates that both the direct and the inverse Jiles–Atherton model formulations provide a good agreement with the experimental data for the major loop representation; nevertheless, both models can not accurately predict the minor loops even when the modification approaches proposed in the literature were implemented.

The Jiles–Atherton model and its modifications are widely discussed in the literature; however, some limitations of the model and its modification in the case of the distorted current waveform are not completely highlighted. Furthermore, this paper contains an original discussion on the accuracy of the prediction of minor loops from distorted current waveforms, including DC bias.

The purpose of this paper is to present the application of a novel hybrid algorithm, called MeTEO (Metric‐Topological‐Evolutionary‐Optimization), based on the combination of three heuristics inspired by artificial life to the solution of optimization problems of a real electronic vacuum device.

The Particle Swarm Optimization (PSO), the Flock‐of‐Starlings Optimization (FSO) and the Bacterial Chemotaxis Algorithm (BCA) were adapted to implement a novel meta‐heuristic MeTEO the FSO has been powerfully employed for exploring the whole space of solutions, whereas the PSO is used to explore local regions where FSO had found solutions, and BCA to refine the solutions found by PSO, thanks its better performances in local search.

The optimization of the focusing magnetic field of a Travelling Wave Tubes (TWT) collector is presented in order to show the effectiveness of MeTEO, in combination with COLLGUN FE simulator and equivalent source representation. The optimization of the focusing magnetic structure is obtained by using a maximum of 100 steps for each heuristic.

The paper describes the development of a novel efficient parallel method for the solution of electromagnetic device optimization problems.

The paper shows the capabilities of a novel combination of optimization methods inspired by “artificial life” which allows us to achieve effective solutions of multimodal optimization problems, typical of the electromagnetic device optimization, with an acceptable computational cost, thanks also to its natural parallel implementation.

The paper's aim is to focus on the utilization of the GRID distributed computing environment in order to reduce simulation time for parameter studies of travelling wave tube (TWT) electron guns and helix slow‐wave structures.

Two TWT finite‐element analysis modules were adapted to be run on the GRID, for this purpose scripts were written to submit a collection of independent jobs (the parameter study) to the GRID and collect the results.

A 25‐job electron gun parameter study runs on the GRID in 30‐40 min instead of 7 h locally. A 16‐job slow‐wave structure parameter study runs in 1 h on the GRID instead of 8 h locally. Turnaround time on the GRID was limited by priority levels presently set by GRID management for the various jobs submitted.

The procedures guarantee a remarkable reduction of the computing time.

For heavy‐computational cost tasks such as the above finite element electromagnetic calculations, the effective use of a heterogeneous, distributed, computing platform (the GRID computing platform) is very advantageous. The paper shows the development of new generation collaborative tools.

This paper aims the application of a novel synergy between a neural network (NN) and the finite element method (FEM) in the solution of electromagnetic problem involving hysteretic material in unbounded domain.

The hysteretic nature of the material is taken into account by an original NN able to perform the modelling of any kind of quasi-static loop (saturated and non-saturated, symmetric or asymmetric). An appositely developed iterative FEM procedure is presented for the solution of this kind of problems in unbounded domains.

By starting from a small set of measured loops, the NN manages the values of the magnetic field, H, and the flux density, B, as inputs while the differential permeability is the output. In particular, the proposed NN is capable to perform the modelling of saturated and non-saturated, symmetric or asymmetric hysteresis loops.

The development of an efficient method for the solution of a complicated electromagnetic problem in unbounded domain by using an iterative approach and NNs, which can be implemented also in existing FEM code.

The paper shows that the combination of FEM, iterative procedure and NNs allows us to produce effective solutions of electromagnetic problems in unbounded domains involving also nonlinear hysteretic magnetic materials with an acceptable computational cost.

The purpose of this paper is to model one of the unsolved problems of magnetism, the reversal of hysteresis loops, in an analytical way. The mathematical models, describing the multiphase steel used in engineering practice, without any exception, are unsuited to provide a way to reverse the hysteretic process. In this paper, a proposal is put forward to model it by using analytical expressions, applying the reversal of the Langevin function. This model works with a high accuracy, giving useful answers to a long unsolved magnetic problem, the lack of reversibility of the hysteresis loop. The use of the proposal is shown by applying the reversal of Langevin function to a sinusoidal and a triangular waveform, the two most frequently used waveforms in research, test and industrial applications. Schematic representations are given for the wave reconstruction by using the proposed method.

The unsolved reversibility of the hysteresis loop is approached by a simple analytical formula, providing close approximation for most applications.

The proposed solution, applying the reversal of Langevin function, to the problem provides a good practical solution.

The simple analytical formula has been applied to a number of loops of widely different shapes and sizes with excellent results.

The proposed solution provides a missing mathematical tool to an unsolved problem for practical applications.

The solution proposed will reduce the work required and provide replacement for expensive complex test instrumentation.

To the best of the authors’ knowledge, this approach used in this study is the first successful approach in this field, irrespective of the required waveform, and is completely independent of the model used by the user.

This paper aims to present an analytical way of formulating the vital parameters of an equivalent hysteresis loop of a composite, multi-component magnetic substance. By using the hyperbolic model, the only model, which separates the constituent parts of the composite magnetic materials, an equivalent loop can be composed analytically. So far, it was only possible to superimpose the tanh functions by numerical method. With this transformation, all multi-component composite substances can be treated mathematically as a single-phase material, as in the T(x) model, and include it in mathematical operations. The transformation works with good accuracy for major and minor loops and provides an easy analytical way to arrive to the vital parameters. This also shows an analytical way to the easy solution of some of the difficult problems in magnetism for multi-component ferrous materials, such as Fourier and Laplace transforms, accommodation and energy loss, already solved for the T(x) model.

The mathematical single loop formulation of hysteresis loop of a multi-phase substance shows the way in good approximation of the sum of constituent loops, described by tanh functions. That was so far only possible by numerical methods. By doing so, it becomes equivalent to the T(x) model for mathematical operations.

The described method gives an analytical formulation [identical to the T(x) model] of multi-component hysteresis loops described by hyperbolic model, leading to simple solution of difficult problems in magnetism such as loop reversal.

Although the method is an approximation, its accuracy is good enough for use in magnetic research and practical applications in industries engaged in application of magnetic materials.

The hyperbolic model is the only one which separates the magnetic substance, used in practice, to constituent components by describing its multi-component state. Superimposing the components was only possible so far by numerical means. The transformation shown is an analytical approximation applicable in mathematical calculations. The transformation described here enables the user to apply all rules applicable to the T(x) model.

This study equally helps researchers and practical users of the hyperbolic model.

This novel analytical approach to the problem provides an acceptable mathematical solution for practical problems in research and manufacturing. It shows a way to solutions of many difficult problems in magnetism.

This paper aims the application of a novel hybrid algorithm, called MeTEO, based on the combination of three heuristics inspired by artificial life to the optimization of electrodes voltages of multistage depressed collector.

The flock-of-starlings optimization (FSO), the particle swarm optimization (PSO) and the bacterial chemotaxis algorithm (BCA) were adapted to implement a hybrid and parallel algorithm: the FSO has been powerfully employed for exploring the whole space of solutions, whereas the PSO+BCA has been used to refine the FSO-found solutions, exploiting their better performances in local search.

The optimization of the voltage of the electrodes of multistage depressed collector are efficiently handled with a moderate computational effort.

The development of an efficient method for the solution of a complicated electromagnetic optimization problem, exploiting the different characteristic of different approaches based on evolutionary computation algorithm.

The paper shows that the combination of stochastic methods having different exploration properties with appositely developed FE electromagnetic simulator allows us to produce effective solutions of multimodal electromagnetic optimization problems, with an acceptable computational cost.

The paper aims to illustrate the two kinds of analysis approach for which finite element method (FEM) can be successfully employed: the Poisson-Nernst-Planck (PNP) model and the Langevin-Lorentz-Poisson (LLP) one.

The approach of this work is to try making a survey of the use of the FEM in the modelling of charge transport/ion flow across membrane channels, in particular for the PNP analysis and for a particle based model such as LLP model.

In this paper, the two kinds of analysis approach for which FEM can be successfully employed, the PNP model and the LLP one, have been shown. In both cases the FEM is extremely useful to carry out these analysis and the simulation results obtained are in good agreement with experimental results.

The value of this paper is to demonstrate the FEM is extremely useful to carry out analysis and results which are in good agreement with experimental ones.