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Discusses an analytical solution for the capacitance of the circular microstrip patch resonator. Shows that the electrostatic problem can be formulated as a system of dual integral equations, which is reduced to a single Fredholm integral equation of the second kind with a continuous kernel. Discusses the solution of this new integral equation in a certain range of the parameters, and derives some useful formulas for the capacitance. Finally, gives plots of the capacitance in a wide range of the relative permittivity.

In this paper some aspects concerning the finite element solution of the electromagnetic propagation in nonlinear media are studied through complementary formulations of the Maxwell equations. Nonlinear hyperbolic equations generate discontinuous solutions even if the initial and boundary conditions are regular. The numerical solution definitively breaks and the Galerkin method does not converge any more after the time at which a sharp discontinuity is developed. The sharpening of the solution is related to the loss of its uniqueness.

A new model for the evaluation of the electric field in a cable termination realized through a nonlinear stress control tube (SCT), is presented in this paper. It is based on the electro-quasistatic approximation of the Maxwell equations: the Laplace equation describes the field in the nonconducting regions whereas a diffusion-like equation gives the field dynamics in the stress control tube. A numerical model is devised by solving the Laplace equation by finite difference and diffusion equations by the Galerkin method. It is shown that even the well-known RC transmission line model can be derived from this general approach. The underlying approximations leading to the circuital model are discussed in detail. The proposed model, in contrast with the circuital one, allows us to take into account properly the nonlinear SCT characteristics and the actual boundary conditions: in this way both spatial and temporal effects of the nonlinearity are considered. The numerical results obtained by considering the general field approach and by using the transmission line model are compared.

The Galerkin equations relevant to the eddy currents induced in an iron body are considered. These equations are obtained by formulating the field problem in terms of the magnetic vector potential and by applying the Galerkin method. They are shown to have a unique steady-state solution if a certain condition on the magnetic constituitive relationship is satisfied. In particular a T-periodic source gives rise to a unique T-periodic solution to which all other solutions converge asymptotically independently from the initial conditions. Under the same condition the exponential decay of the 'transients' is shown, and an explicit lower and upper bound for its rate is given. These structural properties allow us to excluse a priori that qualitatively different asymptotic behaviours, including even chaotic solutions, may occur. Numerical simulation, when based on qualitiative information of this type, enables us to obtain the quantitative properties in an efficient manner. In order to demonstrate the practical use of these results some numerical experiments are presented.

Optical properties of plasma lenses strongly depend on the magnetic field distribution. Its measurement with conventional magnetic probes is quite critical for such application. In this paper the measurement of the magnetic field in a Z pinch discharge, based on the Faraday effect in optical fibers, is described. It is shown that it is possible, using a quite simple and relatively low cost experimental setup, to detect the field dynamics inside the discharge tube assuring low disturbance, a large bandwidth, and a high signal to noise ratio. Applications to several kinds of plasma lenses and further development are discussed. >

A wide class of electromagnetic scattering problems can be expressed as a system of dual integral equations. This kind of integral equation, occurring in boundary value problems wherein there is one equation for a certain region and another for the dual domain, is usual in diffraction problems. Considerable attention has been drawn by many researchers in the field of optics, acoustics, scattering of elastic waves, accelerator physics, and antenna theory. Wiener-Hopf techniques enable us to solve such kinds of integral equations when the two regions are contiguous and semi-infinite. Unfortunately Wiener-Hopf techniques do not apply if one of the regions is finite; this is the case for realistic scatterers, such as irises, antennas, and drift tubes in accelerators. In this article a general method for solving such dual integral equations is discussed and applied to a particular case: Hallen's equation of cylindrical antennas. This method consists of a transformation of the dual integral equations into a Fredholm integral equation of the second kind and then into a linear system of algebraic equations. Comparisons with results obtained by other methods for a wide range of frequencies show the accuracy and the robustness of the proposed one. (C) 1995 American Institute of Physics.

We demonstrate optical Second Harmonic Generation (SHG) in planar arrays of cylindrical Au nanoparticles arranged in periodic and deterministic aperiodic geometries. In order to understand the respective roles of near-field plasmonic coupling and long-range photonic interactions on the SHG signal, we systematically vary the interparticle separation from 60 nm to distances comparable to the incident pump wavelength. Using polarization-resolved measurements under femtosecond pumping, we demonstrate multipolar SHG signal largely tunable by the array geometry. Moreover, we show that the SHG signal intensity is maximized by arranging Au nanoparticles in aperiodic spiral arrays. The possibility to engineer multipolar SHG in planar arrays of metallic nanoparticles paves the way to the development of novel optical elements for nanophotonics, such as nonlinear optical sensors, compact frequency converters, optical mixers, and broadband harmonic generators on a chip.

A new expansion for a certain class of integrals involving Bessel functions is considered. An example is completely developed showing as an efficient series expansion can be obtained.

A model of scalar hysteresis able in describing hysteretic behavior of ferro-electric materials is presented. It is one of the easiest examples of model of hysteresis with non-local memory and enjoys all mathematical properties of the classical Preisach one. Like all black box models (i.e. all models which have not relations to the physics of the phenomenon under description) it is necessary to define a procedure of identification of model's parameters. The discussion tries to outline a methodology to define a hysteresis model pointing out the problems related to the identification procedure.

The electromagnetic scattering of a normal incident monochromatic plane wave from a ''strongly'' nonlinear dielectric slab is considered. The time dynamic of the field inside the nonlinear body is studied by means of the Galerkin method. The solutions -of the Galerkin equations are calculated using the fourth-order Runge-Kutta-Nystrom method. - Their asymptotic behaviour abruptly changes its qualitative properties by continuous variation of the system parameters and a surprising wealth of different nonlinear phenomena appears. They are: bifurcation of the periodic response, subharmonic, almost-periodic solutions and chaotic dynamics.

We used the particle swarm optimization algorithm, an evolutionary computational technique, to design metal nanoparticle arrays that produce broadband plasmonic field enhancement over the entire visible spectral range. The resulting structures turn out to be aperiodic and feature dense Fourier spectra with many closely packed particle clusters. We conclude that broadband field-enhancement effects in nanoplasmonics can be achieved by engineering aperiodic arrays with a large number of spatial frequencies that provide the necessary interplay between long-range diffractive interactions at multiple length scales and near-field quasi-static coupling within small nanoparticle clusters.

In this paper we discuss the properties of the finite dimensional nonlinear systems relative to the numerical formulations of a class of three-dimensional electromagnetic field problems. These structural properties make us more confident on the results of the numerical calculations, since problems arising from multiple or even chaotic solutions are a priori excluded. Numerical procedures for the computation of transient and steady-state solutions are presented and applied. The error introduced by the finite element discretization is estimated making use of the properties of the dual electric and magnetic formulations.

On the basis of the theory of magnetic undulator for free electron laser (FEL) we analyze the use of a large amplitude plasma wave as an electrostatic undulator. We review the original idea of the plasma undulator and consider some particular plasma undulator configurations. By using low energy electron beams we show the possibility to generate very small wavelength electromagnetic radiation. The fluid theory for the FEL with a plasma undulator, in complete analogy with the ordinary ones, is presented and the thresholds for the FEL action are discussed. An analysis for the intrinsic efficiency, with respect to the emittance and the plasma wake field effects, is presented and applied to some new configurations.

The midpoint rule time discretization technique is applied to Landau–Lifshitz–Gilbert (LLG) equation. The technique is unconditionally stable and second-order accurate. It has the important property of preserving the conservation of magnetization amplitude of LLG dynamics. In addition, for typical forms of the micromagnetic free energy, the midpoint rule preserves the main energy balance properties of LLG dynamics. In fact, it preserves LLG Lyapunov structure and, in the case of zero damping, the system free energy. All the above preservation properties are fulfilled unconditionally, namely, regardless of the choice of the time step. The proposed technique is then tested on the standard micromagnetic problem No. 4. In the numerical computations, the magnetostatic field is computed by the fast Fourier transform method, and the nonlinear system of equations connected to the implicit time-stepping algorithm is solved by special and reasonably fast quasi-Newton technique.

The high azimuthal magnetic field of a current-carrying plasma column (z-pinch) can be used to collect and focus high-energy charged particles in accelerators. The beam optics and the apparent advantages of such a linear lens compared with conventional focusing devices, such as magnets and magnetic horns, are described. When a plasma lens shall be operated in routine accelerator runs, the physics of the plasma dynamics must be largely understood and the technology has to be mastered. The results of plasma dynamics measurements and of long-term behavior tests with a plasma lens for antiproton collection are reported. The problems of the plasma dynamics control and of the plasma-wall interaction are discussed in view of the envisaged performance for antiproton collection.

Basic features of the one-dimensional diffusion of the electromagnetic field in a linear, homogeneous, isotropic, time-invariant, and infinitely large conducting region are described. As the initial condition for the magnetic field, a spatial pattern suggested by the elementary Fourier function (Gaussian distribution) is assumed; a simple development follows which introduces in a straightforward manner some basic features of the diffusion phenomena. The suggested procedure is intended for use in classroom instruction about the basic concepts on electromagnetic diffusion and is especially suited to students with no previous knowledge about the solution of partial differential equations. >

The paper describes how a finite element technique has been applied to the dynamic analysis of magnetic field configurations produced by a passive conducting shell in a fusion device. The relevance of the problem in the design of Reverse Field Pinch (RFP) magnetic fusion experiments is firstly pointed out, then the numerical method developed for this kind of applications is described. The technique has been applied to the design of the poloidal field system of RFX, a large RFP device now under construction [1]. The most significant results of the analysis and a discussion on the field control possibilities are finally reported.

The calculation of three-dimensional eddy currents is of primary interest for many applications. Several formulations of the electromagnetic problem have been proposed. In this paper the Galerkin method is applied to the integral formulation in terms of current density so as to consider only two scalar functions as unknowns instead of four (the current density vector \underline{J} and the electrical scalar potentials φ). These simplifications can be achieved by exploiting the definition of an auxiliary vector potential \underline{T} so that the shape functions for the current density intrinsically verify both solenoidality and boundary conditions.

Cet article presente une methodologie generate pour l’etude des structures electromagnetiques imprimees. Les structures canoniques a microbandes peuvent etre decrites au moyen d’un systeme d’equations integrates couplees, qui peut facilement etre transforme en un systeme d’equations algebriques en utilisant une serie de Neumann, c’est-a-dire une serie de fonctions de Bessel. Une analyse numerique attentive montre que des matrices effectives petites sont necessaires dans le but d’obtenir une precision raisonnable des champs ou des potentiels. Des cas statiques et dynamiques sont etudies.

This paper deals with the evaluation of the longitudinal coupling impedance due to a charged particle traveling along the axis of an iris in a circular waveguide. The solution of the electromagnetic problem is given in terms of a dual series expansion, and some interesting developments of this technique are presented in this paper. [S1098-4402(99)00032-4]

The convolution method is applied to analyse lossy multiconductor lines with non-linear loads. The line is described as a time-domain m-port, through the input and transfer impulse responses. A new method is used to evaluate analytically the principal parts of these responses, i.e., the parts containing all the irregular terms, such as Dirac pulses. Once the irregular parts are known, the regular remainders are easily calculated by numerical inversion. The convolution integrals have been evaluated using two different methods, one based on crude trapezoidal rule and the other based on a fast recursive algorithm. The latter is obtained by an exponential fitting of the regular parts of the impulse responses. A comparison between the computation times of these two methods is presented.

In this paper an effective analytical-numerical approach to study the electromagnetic interaction between a bunch of particles and the drift tube of the vacuum chamber of a particle accelerator is presented. Particular attention is dedicated to the longitudinal coupling impedance, which is expanded as a Neumann series. Numerical calculations can be easily performed in a wide range of frequency.

We examine the two port representations of a lossy line in the time domain. We give a closed form expression for the canonical responses defining the adopted representation. These expressions are arranged into two contributions: an impulsive term and a regular part. The extension to the multi-conductors case described by Toeplitz, symmetric, and tridiagonal matrices is also discussed.

Purpose - Nowadays, nano-antennas or nanoscale absorbers made by innovative materials such as carbon nanotubes are gaining more and more interest, because of their outstanding features. The purpose of this paper is to investigate the scattering properties of carbon nanotubes, either isolated or arranged in arrays. The peculiar behaviour of such innovative materials is studied, taking also into account the finite length of the structure and the dependence of the scattering field from the operating temperature. Design/methodology/approach - First a model is presented for the electrical transport along the carbon nanotubes, based on Boltzmann quasi-classical transport theory. The model includes quantistic and inertial phenomena observed in the carbon nanotube electrodynamics. The model also includes the effects of temperature. Using this electrodynamical model, the electromagnetic formulation of the scattering problem is cast in terms of a Pocklington-like equation. The numerical solution is obtained by means of the Galerkin method, with special care in handling the logarithmic singularity of the kernel. Case studies are carried out, either referred to isolated single-wall carbon nanotubes (SWCNTs) and array of SWCNTs. Findings - The scattering properties of SWCNT are strongly influenced by the temperature and by the distance between the tubes. As temperature increases, the amplitude of the resonance peaks decreases, at a rate which is double the rate of changes of temperature. The resonance frequencies are insensitive to temperature. As for the distance between the tubes in an array, it influence the scattering resonance introducing a shift in the resonance frequencies which is appreciable for distances lower than the semi-length of the CNT. For higher distances the CNT scattered field may be regarded as the sum of the fields emitted by each CNT, as if they were isolated. Research limitations/implications - As far as now only SWCNTs have been studied. The multi-wall carbon nanotubes would show a richer behaviour with temperature, due to the joint effect of reduction of the mean free path and increase of the number of conducting channels, as temperature increases. Practical implications - Possible use of carbon nanotubes as absorbing material or scatterers. Originality/value - The model presented here is based on a self-consistent and physically meaningful description of the CNT electrodynamics, which takes rigorously into account the effect of temperature, size and chirality of each CNT.

The aim of this note is to demonstrate that the electromagnetic field, in the time domain, sustained by a point charge moving at a constant velocity along the axis of a circular waveguide can be expanded by means of a Fourier-Bessel series. This expansion is rapidly convergent in the complementary range of the classical integral representations, namely for large values of \z' - vt'\. Quickly convergent expansions are necessary for tracking codes to simulate beam dynamics in accelerators.

In this paper the diffusion of the magnetic field in a hysteretic iron core slab is considered. The dynamics of the field is described by means of a finite dimensional nonlinear dynamic system obtained by applying the Galerkin method. Two different models have been used to describe the magnetic hysteresis: the Preisach's scalar model and a new scaler model based on a sequential algorithm. Good agreement has been found between the simulations obtained by using the two models. >

Two different numerical methods for the finite element solution of nonlinear Maxwell equations in the time domain are discussed: the Galerkin formulation and the constitutive error based approach. The scattering of a plane wave from a nonlinear dielectric slab is analysed. A general analytical solution for this class of problems is derived and compared with the numerical solutions.

It is shown that resonant excitation of large amplitude (>or approximately=10^4 V cm^(-1) ) plasma waves is possible through the beating of two microwaves of nearly equal frequencies in an 'open' resonator filled with plasma of subcritical density. Detailed calculation are presented of the configuration, growth and saturation of the pump and plasma waves in the resonant cavity.

In an underdense plasma a large‐amplitude plasma oscillation may be produced by the beating of two electromagnetic waves with a frequency difference approximately equal to the plasma frequency. In the spatially one‐dimensional, cold, and collisionless plasma the large‐amplitude plasma oscillation is limited by the nonlinearity caused by relativistic effects. In this paper a simple nonlinear equation, resembling the original equation of Rosenbluth and Liu [Phys. Rev. Lett. 29, 701 (1972)], is derived in the weak beat power limit from the fully relativistic fluid model proposed by Sprangle, Sudan, and Tang [Appl. Phys. Lett. 45, 375 (1984); Phys. Fluids 28, 1974 (1985)]. This equation also contains the effects of the relativistic transverse motion. Its analytical solution, describing the plasma oscillation dynamics, is given in a closed form by using Jacobian elliptic functions. The analytical computations are compared with numerical computations. Finally the fully relativistic equation, describing free pla...

In this paper the nonlinear problem of the free boundary equilibrium of a plasma inside a conducting circular shell has been solved analytically in the high beta limit. The unknown function describing the plasma shape has been expanded in a Volterra functional series, the functional analogous to the Taylor series. The hierarchy of the linear integral equations obtained from the expansion is, at least in principle, analytically solvable, so that the solution of each equation can be given in a closed form. The analytical computations have been carried out up to the fourth order and the results compared with numerical computations.