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We describe an extension of the linear embedding via Green’s operators (LEGO) method to the solution of finite antenna arrays comprised of disconnected elements in a homogeneous medium. The ultimate goal is the calculation of the admittance matrix and the radiation pattern of the array. As the basic idea is the inclusion of an array element inside a LEGO electromagnetic brick, the first steptowards the solution consists of the definition and numerical calculation of hybrid scattering-admittance operators which extend the notion of scattering operators of equivalent currents introduced in the past. Then again, the combination of many bricks involves the usual transfer operators for the description of the multiple scattering between the bricks. Moreover, to reduce the size of the problem we implement the eigencurrents expansion. With the aid of a numerical example we discuss the validation of the approach and the behaviour of the total CPU time as a function of the elements forming the array.

The Adaptive Cross Approximation (ACA) algorithm has been used to compress the rank- deficient sub-blocks of the matrices that arise in the numerical solution of integral equations (IEs) with the Method of Moments. In the context of the linear embedding via Green's operator (LEGO) method — a domain decomposition technique based on IEs — an electromagnetic problem is modelled by combining "bricks" in turn described by scattering operators which, in many situations, are singular. As a result, macro basis functions defined on the boundary of a brick can be generated by applying the ACA to a scattering operator. Said functions allow compressing the weak form of the LEGO functional equations which then use up less computer memory and are faster to invert.

We describe a surface integral-equation (SIE) method suitable for computation of electromagnetic fields scattered by 2D-periodic high-permittivity and plasmonic scatterers. The method makes use of fast evaluation of the 2D-quasi-periodic Green function (2D-QPGF) and its gradient using a tabulation technique in combination with tri-linear interpolation. In particular we present a very efficient technique to create the look-up tables for the 2D-QPGF and its gradient where we use to our advantage that it is very effective to simultaneously compute the QPGF and its gradient, and tosimultaneously compute these values for the case in which the role of source and observation point are interchanged. We use the Ewald representation of the 2D-QPGF and its gradient to construct the tables with pre-computed values. Usually the expressions for the Ewald representation of the 2D-QPGFand its gradient are presented in terms of the complex complementary error function but here we give the expressions in terms of the Faddeeva function enabling efficient use of the dedicated algorithms to compute the Faddeeva function. Expressions are given for both lossy and lossless medium parametersand it is shown that the expression for the lossless case can be evaluated twice as fast as the expression for the lossy case. Two case studies are presented to validate the proposed method and to show that the time required for computing the method of moments (MoM) integrals that require evaluation of the 2D-QPGF becomes comparable to the time required for computing the MoM integrals that require evaluation of the aperiodic Green function., We describe a surface integral-equation (SIE) method suitable for computation of electromagnetic fields scattered by 2D-periodic high-permittivity and plasmonic scatterers. The method makes use of fast evaluation of the 2D-quasi-periodic Green function (2D-QPGF) and its gradient using a tabulation technique in combination with tri-linear interpolation. In particular we present a very efficient technique to create the look-up tables for the 2D-QPGF and its gradient where we use to our advantage that it is very effective to simultaneously compute the QPGF and its gradient, and to simultaneously compute these values for the case in which the role of source and observation point are interchanged. We use the Ewald representation of the 2D-QPGF and its gradient to construct the tables with pre-computed values. Usually the expressions for the Ewald representation of the 2D-QPGF and its gradient are presented in terms of the complex complementary error function but here we give the expressions in terms of the Faddeeva function enabling efficient use of the dedicated algorithms to compute the Faddeeva function. Expressions are given for both lossy and lossless medium parameters and it is shown that the expression for the lossless case can be evaluated twice as fast as the expression for the lossy case. Two case studies are presented to validate the proposed method and to show that the time required for computing the method of moments (MoM) integrals that require evaluation of the 2D-QPGF becomes comparable to the time required for computing the MoM integrals that require evaluation of the aperiodic Green function.

Since Helicon plasma sources can efficiently couple power and generate high-density plasma, they have received interest also as spacecraft propulsive devices, among other applications. In order to maximize the power deposited into the plasma, it is necessary to assess the performance of the radiofrequency (RF) antenna that drives the discharge, as typical plasma parameters (e.g., the density) are varied. For this reason, we have conducted a comparative analysis of three Helicon sources which feature different RF antennas, namely, the single-loop, the Nagoya Type-III, and the Fractional helix. These antennas are compared in terms of input impedance and induced current density; in particular, the real part of the impedance constitutes a measure of the antenna ability to couple power into the plasma. The results presented in this work have been obtained through a full-wave approach which (being hinged on the numerical solution of a system of integral equations) allows computing the antenna current and impedance self-consistently. Our findings indicate that certain combinations of plasma parameters can indeed maximize the real part of the input impedance and, thus, the deposited power, and that one of the three antennas analyzed performs best for a given plasma. Furthermore, unlike other strategies which rely on approximate antenna models, our approach enables us to reveal that the antenna current density is not spatially uniform, and that a correlation exists between the plasma parameters and the spatial distribution of the current density.

An enhanced version of the Linear Embedding via Green's Operators (LEGO) method is introduced to analyze complex 3-D metallic structures located inside a single electromagnetic (EM) brick. For the sake of computational efficiency and memory storage requirement the surface of the entire structure is divided into smaller sub-domains and over each pair of neighboring sub-domains is defined set of characteristic basis functions (CBFs). To compress the problem all CBFs which are associated with insignificant singular values are truncated. Various comparisons between the direct solution which solves Electric Field Integral Equation (EFIE) directly over the structure and LEGO approach using CBFs are shown to prove the concept.

Gaseous plasma antennas are devices that exploit partially or fully ionized gas to transmit and receive electro-magnetic waves, in contrast with conventional antennas that are only made by metal and dielectric materials. Since plasma discharge parameters, e.g. plasma density, can be tuned, plasma antenna properties can be changed dynamically; this constitutes a promising alternative to conventional metallic antennas for applications in which reconfigurability is desired. In this work, we report on the first steps toward the realization, and the characterization in terms of radiation pattern, and magnitude of the reflection coefficient of an early prototype of a gaseous plasma antenna in the UHF frequency range. Numerical investigations have supported the design of the setup, and helped in the evaluation of the the role of plasma density profiles in affecting the antenna properties.

Gaseous plasma antennas constitute a promising alternative to conventional metallic antennas for applications in which reconfigurability is desired. By tuning the plasma discharge parameters, e.g., plasma density, antenna properties can be changed dynamically. In this work we report on recent numerical investigations into the characteristics of a plasma antenna as a function of the plasma discharge parameters, viz., plasma density, and magnetostatic field. In addition, the effect of different gasses has been examined. We have used ADAMANT (Advanced coDe for Anisotropic Media and ANTennas) — a full-wave numerical tool based on integral equations — to assess the role played by plasma discharge parameters in shaping the radiation pattern, which is mainly determined by the plasma current distribution. The experimental characterization of the plasma discharge to be used as plasma antenna is briefly presented.

Linear embedding via Green's operators (LEGO) is a diakoptics method that employs electromagnetic ``bricks'' to formulate problems of wave scattering from complex structures (e.g., penetrable bodies with inclusions). In its latest version the LEGO integral equations are solved through the Method of Moments combined with adaptive generation of Arnoldi basis functions (ABF) to compress the resulting algebraic system. In this paper we review and discuss the convergence properties of the numerical solution in relation to the number of ABFs. Besides, we address the issue of setting the threshold for stopping the generation of ABFs in conjunction with the adaptive Arnoldi algorithm.

In this paper we present the application of linear embedding via Green's operators (LEGO) to the solution of the electromagnetic scattering from clusters of arbitrary (both conducting and penetrable) bodies randomly placed in a homogeneous background medium. In the LEGO method the objects are enclosed within simple-shaped bricks described in turn via scattering operators of equivalent surface current densities. Such operators have to be computed only once for a given frequency, and hence they can be re-used to perform the study of many distributions comprising the same objects located in different positions. The surface integral equations of LEGO are solved via the Moments Method combined with Adaptive Cross Approximation (to save memory) and Arnoldi basis functions (to compress the system). By means of purposefully selected numerical experiments we discuss the time requirements with respect to the geometry of a given distribution. Besides, we derive an approximate relationship between the (near-field) accuracy of the computed solution and the number of Arnoldi basis functions used to obtain it. This result endows LEGO with a handy practical criterion for both estimating the error and keeping it in check.

We apply the linear embedding via Green's operators (LEGO) method to the scattering by large finite dielectric bodies which contain metallic or penetrable inclusions. After modelling the body by means of LEGO bricks, we formulate the problem via an integral equation for the total incident currents over the boundaries of the bricks. This equation is turned into a weak form by means of the Method of Moments (MoM) and sub-domain basis functions. Then, to handle possibly large MoM matrices, we employ an order-reduction strategy based on: i) compression of the off-diagonal sub-blocks of the system matrix by the adaptive cross approximation algorithm and ii) subsequent compression of the whole matrix by using a basis of orthonormal entire-domain functions generated through the Arnoldi iteration algorithm. The latter leads to a comparatively small upper Hessenberg matrix easily inverted by direct solvers. We validate our approach and discuss the properties of the Arnoldi basis functions through selected numerical examples.

We propose a methodology --- based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) --- for solving electromagnetic problems involving large 3-D structures comprised of ND = 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body differ from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the "ideal" structure, we follow a deterministic approach, i.e., we allow for a finite number of different realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND - 1 "fixed" bodies. Since the latter has to be computed only once, the overall procedure is indeed efficient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the offset of one element in the array.

The scattering from a large complex structure comprised of many objects may be efficiently tackled by embedding each object within a bounded domain (brick) which is described through a scattering operator. Upon electromagnetically combining the scattering operators we arrive at an equation which involves the total inverse scattering operator S-1 of the structure: We call this procedure linear embedding via Green's operators (LEGO). To solve the relevant equation we then employ the eigencurrent expansion method (EEM)-essentially the method of moments with a set of basis and test functions that are approximations to the eigenfunctions of S-1 (termed eigencurrents). We have investigated the convergence of the EEM applied to LEGO in cases when all the bricks are identical. Our findings lead us to formulate a simple and practical criterion for controlling the error of the computed solution a priori.

We present an extension of the linear embedding via Green's operators (LEGO) procedure for efficiently dealing with 3-D electromagnetic composite structures. In LEGO's notion, we enclose the objects forming a structure within arbitrarily shaped domains (bricks), which (by invoking the equivalence principle) we characterize through scattering operators. In the 2-D instance, we then combined the bricks numerically, in a cascade of successive embedding steps, to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects. In the 3-D case, however, this process becomes quite soon impracticable, in that the resulting scattering matrices are too big to be stored and handled on most computers. To circumvent this hurdle, we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure, which can be written analytically in terms of scattering operators of the bricks and transfer operators among them. We then solve this equation by the method of moments combined with the eigencurrent expansion method, which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures.

We present a full-wave numerical tool for the simulation of plasma antennas. The tool makes use of a hybrid formulation that allows treating the plasma with a Finite Element discretization, and the metallic parts with the Method of Moments. The finite element discretization is solved using a state-of-the-art sparse solver (MUMPS) in order to reduce the computational time at a minimum. The accuracy of the tool is tested by comparing the results obtained with it against those obtained with a benchmark code. Finally, a novel dual-mode plasma antenna is designed using the aforementioned tool.

We present the numerical parametric study of a reconfigurable plasma antenna array (PAA) composed of a metallic half-wavelength dipole and a set of cylindrical plasma discharges arranged in a planar square lattice. Our results, obtained with the linear embedding via Green’s operators (LEGO) method, indicate that beam-forming and beam-steering functionality can be achieved and controlled by appropriately choosing the number and position of the active plasma discharges around the dipole. Furthermore, we show that an external static magnetic field and the plasma density have a noticeable effect on the radiation pattern of the antenna.

For scattering by perfectly conducting objects in a two-dimensionally periodic setup we employ a surface-integral equation, the Ewald representation of the Green function, and the Method of Moments (MoM). For moderate-size matrices, we observe that the computation time is dominated by the computation of the matrix elements. By employing a multi-level decomposition of the Green function based on Lagrange interpolation on a Chebyshev grid, we demonstrate that the overall computation time can be reduced by 73% compared to the original MoM computation.

In the last years, increasing interest has grown on the synthesis of light-weight, miniaturized surfaces for light manipulation based on metamaterials. These surfaces can be easily integrated in photonic systems and they can be used as high numerical aperture lenses, light-deflection surfaces and polarization-dependent surfaces. All-dielectric nanoresonator metasurfaces are particularly promising to synthesize light manipulating devices. By simply adjusting the geometric parameters (height and diameter) of the dielectric particles, it is possible to tune the spectral positions of the electric and magnetic resonant modes. The overlap of these resonances allows to design metasurfaces exhibiting a transmission coefficient with unit-amplitude and arbitrary, spatially-variant phase distribution. Moreover, resorting to asymmetric cross-section resonators, it is possible to define metasurfaces with high-efficiency of cross-polarization. In this work, we exploit both properties of dielectric nanoresonators to design a high numerical aperture micro-lens and a thin linear-to-circular polarizer, both working in the visible range. Numerical simulations of the performances of the devices are reported.

The demand for a predictive tool to help in designing ion-cyclotron radio frequency (ICRF) antenna systems for today's fusion experiments has driven the development of codes such as ICANT, RANT3D, and the early development of TOPICA (TOrino Polytechnic Ion Cyclotron Antenna) code. This paper describes the substantive evolution of TOPICA formulation and implementation that presently allow it to handle the actual geometry of ICRF antennas (with curved, solid straps, a general-shape housing, Faraday screen, etc) as well as an accurate plasma description, accounting for density and temperature profiles and finite Larmor radius effects. The antenna is assumed to be housed in a recess-like enclosure. Both goals have been attained by formally separating the problem into two parts: the vacuum region around the antenna and the plasma region inside the toroidal chamber. Field continuity and boundary conditions allow formulating of a set of two coupled integral equations for the unknown equivalent (current) sources; then the equations are reduced to a linear system by a method of moments solution scheme employing 2D finite elements defined over a 3D non-planar surface triangular-cell mesh. In the vacuum region calculations are done in the spatial (configuration) domain, whereas in the plasma region a spectral (wavenumber) representation of fields and currents is adopted, thus permitting a description of the plasma by a surface impedance matrix. Owing to this approach, any plasma model can be used in principle, and at present the FELICE code has been employed. The natural outcomes of TOPICA are the induced currents on the conductors (antenna, housing, etc) and the electric field in front of the plasma, whence the antenna circuit parameters (impedance/scattering matrices), the radiated power and the fields (at locations other than the chamber aperture) are then obtained. An accurate model of the feeding coaxial lines is also included. The theoretical model and its TOPICA implementation have been fully validated against measured data both in vacuo and in plasma-facing conditions for real-life structures.

TOPICA is an innovative tool for the simulation of the Ion Cyclotron Radio Frequency (ICRF) antenna systems that incorporates commercial-grade graphic interfaces into a fully 3D self-consistent description of the antenna geometry and an accurate description of the plasma; it can be considered as a "Virtual Prototyping Laboratory" to assist the detailed design phase of the antenna system. Recent theoretical and computational advances of the TOPICA code has allowed to incorporate a CAD drawing capability of the antenna geometry, with fully 3D geometrical modeling, and to combine it with a 1D accurate plasma description that takes into account density and temperature profiles, and FLR effects; the profiles are inserted directly from measured data (when available), or specified analytically by the user. The coaxial feeding line is modeled as such; computation and visualization of relevant parameters (input scattering parameters, current and field distributions, etc.) complete the suite. The approach to the problem is based on an integral-equation formulation for the self-consistent evaluation of the current distribution on the conductors. The environment has been subdivided in two coupled region: the plasma region and the vacuum region. The two problems are linked self-consistently by representing the field continuity in terms of equivalent (unknown) sources. In the vacuum region all the calculations are executed in the spatial (configuration) domain, and this allows triangular-facet description of the arbitrarily shaped conductors and associated currents; in the plasma region a spectral representation of the fields is used, which allows to enter the plasma effect via a surface impedance matrix; for this reason any plasma model can be used, and at present the FELICE code has been adopted; special techniques have been adopted to increase the numerical efficiency. The TOPICA suite has been previously tested against assessed codes and against measurements of mock-ups and existing antennas. This work is devoted to an extensive set of comparisons between measured and simulated reflection coefficients (magnitude and phase), both in vacuum and with plasma during ALCATOR C-MOD operation. The comparison demonstrates a very good agreement, leading to a validation of TOPICA as a predictive tool.

This work presents a comprehensive account of the theory and implementation of a method for the self-consistent numerical analysis of plasma-facing ion-cyclotron resonance heating (ICRH) antenna arrays. The method is based on the integral-equation formulation of the boundary-value problem, solved via a weighted-residual scheme. The antenna geometry (including Faraday shield bars and a recess box) is fairly general and three-dimensional (3D), and the plasma is in the one-dimensional (1D) 'slab' approximation; finite-Larmor radius effects, as well as plasma density and temperature gradients, are considered. Feeding via the voltages in the access coaxial lines is self-consistently accounted throughout and the impedance or scattering matrix of the antenna array obtained therefrom. The problem is formulated in both the dual space (physical) and spectral (wavenumber) domains, which allows the extraction and simple handling of the terms that slow the convergence in the spectral domain usually employed. This paper includes validation tests of the developed code against measured data, both in vacuo and in the presence of plasma. An example of application to a complex geometry is also given.

We describe an extension of the Linear Embedding via Green's Operators (LEGO) approach to the solution of finite antenna arrays in which the antenna elements exist in a host dielectric material with electromagnetic properties different than those of the background medium. In this approach, each antenna element and the dielectric host medium are included inside a LEGO brick described by means of a hybrid admittance-scattering operator. The combination of LEGO bricks involves the usual transfer operators for the description of the multiple scattering phenomenon. We present an example of validation of the approach and preliminary results for an array of strap-dipoles.

We describe a surface integral-equation (SIE) method suitable for reliable computation of electromagnetic fields scattered by 2D-periodic plasmonic and dielectric structures. In particular we present an efficient technique to incorporate objects that are infinite in one or both directions of periodicity. The proposed method uses fast evaluation of the 2D quasi-periodic Green function to build the integral operators defined on the inside of the objects. In a case study the method is used to compute the reflection coefficients for a plane wave incident field impinging on a 2D-periodic array of holes in a metal layer.

A plasma antenna is a radiating device partially composed of plasma instead of metals or dielectrics, and as a result, it exhibits reconfigurable properties unlike conventional metallic antennas. By tuning the plasma discharge parameters, e.g., the plasma density, the antenna properties can be changed dynamically. In this work we report on recent numerical investigations into the characteristics of plasma antennas as a function of the plasma discharge parameters. We have used ADAMANT (Advanced coDe for Anisotropic Media and ANTennas) - a full-wave numerical tool based on integral equations - to assess the role played by plasma discharge parameters in shaping the gain function, and the antenna input impedance.

We report the numerical analysis of a plasma antenna array comprised of cylindrical plasma discharges and a conventional half-wavelength metallic dipole. In particular, the 3D radiation pattern, gain and impedance of the antenna are determined and compared for different values of the plasma density. To reduce the computational load by exploiting the translational symmetry of the structure, we have carried out the simulations with the linear embedding via Green's operators (LEGO) method. Our results suggest that the device performs better as a directive antenna at lower plasma densities, that is, when the plasma is less reflective.

We present a method for the fast generation of macro basis functions in the context of the linear embedding via Green's operators approach (LEGO) which is a domain decomposition technique based on the combination of electromagnetic bricks in turn described by means of scattering operators. We show that, when the scattering operators are rank-deficient, a reduced set of macro basis functions defined on the surface of the bricks can be obtained through the adaptive cross approximation of the scattering operator.

We describe a surface integral-equation (SIE) method suitable for reliable computation of electromagnetic fields scattered by 2D periodic gratings in homogeneous 3D space in which the gratings may consist of high permittivity dielectric materials and metals. More in particular we brie y describe the formulation, the discretization and efficient evaluation of the Quasi Periodic Green Function (QPGF) and its gradient using Ewald's method. We present a case study to illustrate the method's capability of handling high permittivity dielectric materials and a second case study to demonstrate the effectiveness and indispensability of interpolating the QPGF and its gradient using tables with precomputed values.

In this communication we report on a combined experimental-numerical activity thas was conducted to assess the antenna-plasma interaction within a Helicon plasma source for space thrusters. The experiment is based on a versatile, re-configurable set-up which allows testing mulitiple thruster configurations under different operating condtions, featuring a high-efficiency RF antenna. The numerical results were opbtained by means of various simulation tools for both RF circuit and antenna-plasma interface analysis; these tools were validated against experimental data. The results helped to improve our understanding of antenna-plasma coupling and the assessment/prediction of the RF system performance.

We propose a methodology based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) to efficiently deal with and locally optimize 2-D electrically large electromagnetic band-gap (EBG) structures. In LEGO terminology, the composite EBG structure is broken up (diakopted) into constitutive elements called ``bricks'' that we characterize through scattering operators by invoking Love's equivalence principle, while, at the same time, the electromagnetic interaction among the bricks is captured by transfer operators. The resulting electromagnetic problem is then succinctly formulated through an integral equation involving the total inverse scattering operator S-1 of the structure. To perform local optimization, the formulation of the problem allows for variations of the electromagnetic properties and the shape of a set of objects in the EBG structure with respect to those of the others, thereby allowing us to tune a compact designated domain within a large one. Finally, the method of moments and the EEM are applied to achieve a considerable reduction in memory use for the overall problem.

A modal method for the analysis of surface relief gratings made with anisotropic material is presented. The structure is decomposed into a series of cascaded discontinuities between planar waveguides with stratified anisotropic dielectric. The basic problem is formulated by an integral equation which is solved numerically by the method of moments. The mode functions of the periodic region are assumed as basis functions to represent the unknown field on the junctions. Each junction is viewed as a waveguide junction problem and has been characterized by the generalized scattering matrix (GSM). The diffraction efficiencies of the grating are determined by combining the various GSM. In this way, the analysis method is stable and can be applied also to deep gratings.

A spectral-element type approach to determine the propagation characteristics of the bound modes of an open planar layered anisotropic waveguide is proposed. The main feature is the expansion of the electromagnetic field in each internal layer on different sets of Legendre polynomials. In the two embedding halfspaces, sets of weighted Laguerre polynomials are used. In this way, the method converges with exponential rate with increasing number of basis functions. No transcendental equation has to be solved and even modes that may exhibit coinciding or very close propagation constants are computed with great accuracy. A detailed analysis of the convergence properties of the algorithm is carried out and a way to estimate and control the error on the propagation constants is discussed.

A new numerical method to compute propagation constants and mode functions of a planar layered acoustic waveguide is described. The basic feature is the expansion of velocity and stress fields in each layer on different Legendre polynomial bases, which ensures an exponential convergence rate of the method. No transcendental equation has to be solved and also modes that have very close propagation constants (e.g., coupled Rayleigh waves) are computed with great accuracy. Convergence of the method is studied and a way to estimate and control the error on the solutions is discussed. ©1998 Acoustical Society of America.

Plasma antennas constitute a promising alternative to conventional metallic antennas for applications in which reconfigurability with respect to some property is desired. The latter feature can be achieved by tuning the plasma discharge parameters. We use a full-wave numerical tool, ADAMANT (Advanced coDe for Anisotropic Media and ANTennas), based on integral equations, to assess the role played by plasma discharge parameters in shaping the radiation pattern, which is mainly determined by the plasma current distribution. Numerical results for different discharge parameters show that the antenna radiation efficiency can be controlled by adjusting plasma density and magneto-static field.

Radiofrequency (RF) magnetized Helicon plasma sources have been proposed for the development of space thrusters, whose thrust efficiency and specific impulse depend on the power coupled into the plasma by the RF antenna that drives the discharge. In this work we report on a set of numerical experiments specifically conceived to optimize Helicon sources in terms of plasma parameters (e.g., gas species, plasma density, external magnetostatic field, neutral pressure), and the RF antenna shape. Results concerning the power coupled into the plasma and the antenna impedance for different antenna configurations and plasma parameters are presented and discussed.

Although the beneficial and detrimental effects of human cells electic field (EF) exposure are well investigated, the interactions mechanisms between the cell and the EF are still a matter of research. In this work we present a numerical approach to investigate the induced cell-cell EF gradients at different regions of multi-layered spherical cells. Based on a symbolic scattering-matrix approach, the induced EF in a single cell is obtained using the equivalent electrical network for the multilayered sphere. Cell-cell EF interactions are obtained for a group of 60 randomly positioned cells exposed to an EF of 100 V/m. Two cases were analyzed by setting the EF frequency to 50 Hz and 2.45 GHz. Numerical results show cellular electrical responses that are in agreement with experimental observations. Quantitative results show that cell-cell EF interactions might be enough to trigger electrically mediated biological responses in the cells. Therefore, the model can be used to investigate possible interactions mechanism between cells and EFs.

We present a full-wave numerical tool, dubbed ADAMANT (Advanced coDe for Anisotropic Media and ANTennas), devised for the analysis and design of radiofrequency antennas which drive the discharge in helicon plasma sources. ADAMANT relies on a set of coupled surface and volume integral equations in which the unknowns are the surface electric current density on the antenna conductors and the volume polarization current within the plasma. The latter can be inhomogeneous and anisotropic whereas the antenna can have arbitrary shape. The set of integral equations is solved numerically through the Method of Moments with sub-sectional surface and volume vector basis functions. This approach allows the accurate evaluation of the current distribution on the antenna and in the plasma as well as the antenna input impedance, a parameter crucial for the design of the feeding and matching network. We report several numerical examples which serve to validate ADAMANT against other well-established numerical approaches as well as experimental data. The numerical accuracy of the computed solution versus the number of basis functions in the plasma is also assessed. Finally, we employ ADAMANT to characterize the antenna of a real-life helicon plasma source.

We describe a domain decomposition strategy based on the combination of linear embedding via Green's operators (LEGO) and an electric-field integral equation (EFIE) for solving radiating conducting elements in the presence of anisotropic media. Furthermore, in order to facilitate the inversion of the LEGO surface integral equation we employ the eigencurrents expansion method (EEM) to generate local entire-domain basis functions on the boundary of each LEGO sub-domain. Through a few selected numerical examples we discuss the accuracy of the overall approach and the convergence properties of the EEM.

Linear embedding via Green’s operators (LEGO) is a domain decomposition method particularly well suited for the solution of scattering and radiation problems comprised of many objects. The latter are enclosed in simple-shaped subdomains (electromagnetic bricks) which are in turn described by means of scattering operators. In this paper we outline the extension of the LEGO approach to the case of penetrable objects with dyadic permittivity or permeability. Since a volume integral equation is only required to solve the scattering problem inside a brick and the scattering operators are inherently surface operators, the LEGO procedureper secan afford a reduction of the number of unknowns in the numerical solution with the Method of Moments and subsectional basis functions. Further substantial reduction is achieved with the eigencurrents expansion method (EEM) which employs the eigenvectors of the scattering operator as local entire-domain basis functions over a brick’s surface. Through a few selected numerical examples we discuss the validation and the efficiency of the LEGO-EEM technique applied to clusters of anisotropic bodies.

Radiofrequency (RF) magnetized Helicon plasma sources have been proposed for the development of space thrusters, whose thrust efficiency and specific impulse depend on the power coupled into the plasma by the RF antenna. To date emphasis has been on the absorption of wave energy by nonuniform plasmas but not much on the role played by the antenna. To fill this gap, we propose a full-wave numerical tool, ADAMANT (Advanced coDe for Anisotropic Media and ANTennas), devised for the analysis and design of RF antennas which drive the discharge in Helicon plasma sources. Results concerning the antenna current distribution and power coupled into the plasma for different antenna configurations and plasma parameters are presented.

The exposure of biological cells to an incident electric field (EF) affects cellular behaviour. However, the interaction mechanisms are still a matter of discussion. Although most of the evidence comes from experimental trials, numerical simulations are helpful to obviate the lack of reproducible experimental results and to resolve contradictory conclusions. In this work we present a numerical framework for computing the intracellular EF in arbitrary-shaped biological cells with nucleus. As an example, up to four inhomogeneous cells exposed to an incident EF of 1 V/m at 2.45 GHz are studied. The solution is obtained by implementing the electric flux volume integral equation (VIE) and the Method of Moments (MoM) with SchaubertWilton-Glisson (SWG) basis functions. Qualitative results show that the intracellular EF is related to the neighboring cells in terms of number and position. Quantitative analysis shows intracellular variations in the order of 20-30 mV/mm, which might be enough to trigger biological responses in cells. Therefore, this approach may be suitable to further investigate the cell-cell EF interactions, especially in non-canonical shaped cells with non-concentric nucleus.

Optimization of radiofrequency helicon plasma sources for the development of space plasma thrusters (whose thrust efficiency and specific impulse depend on the power coupled into the plasma) has focused on the absorption of wave energy by cold collisional plasmas, but not much on the role played by the antenna that drives the discharge. To overcome these limitations and to optimize the power deposited by the antenna into the plasma, we propose a full-wave approach based on integral equations to compute the current distribution on the antenna conductors self-consistently, i.e., also keeping into account the effect that the plasma in turn has on the antenna. Preliminary results of antenna current distribution and antenna impedance versus frequency and plasma parameters are presented.

We describe the application of the linear embedding via Green's operator (LEGO) technique to the solution of scattering problems that involve objects with anisotropic electromagnetic properties. Thanks to this approach, the usage of volume integral equations is restricted to the calculation of the scattering operators of a small number of LEGO sub-domains. Since the scattering operators are surface operators, they constitute a means to reduce the computational burden. Further reduction is accomplished by applying the eigencurrent expansion method. We elaborate on the overall procedure by discussing a fewnumerical examples.

Electrotaxis is the cell migration induced by the presence of an external electric field (EF). It has been found that electrotaxis directs cell migration parallel to the EF and towards a preferential electrode. However, the internal cellular mechanisms affected by the external EF are not well understood. The goal of this work is to introduce a numerical framework for modelling electrotaxis by calculating the EF distribution inside the cells. The key assumption is that the cells (due to their dielectric nature) behave approximately as dipoles when exposed to an impressed EF. Besides, cell dynamics is described using two reaction-diffusion equations. Numerical results—obtained for osteogenic cell migration by electrotaxis—are in agreement with experimental reports and provide an insight into the cell-to-cell interactions in the presence of an external EF. Therefore, our model may constitute a methodological basis for the study of causal relations between EF and cells.

We present a spectral approach to effectively estimate radiation losses from 2-D slab photonic crystals. The method is based on a plane wave decomposition of the incident propagating mode inside the slab and the construction of a self-consistent Kirchhoff equivalent source (on the slab surface) which accounts for the actual radiation modes excited in the crystal. The proposed modelling strategy is combined with a domain decomposition method, viz, linear embedding via Green's operators.

The domain decomposition strategy known as linear embedding via Green's operators (LEGO) is applied to the solution of 3-D radiation problems in which the sources are localized inside complex structures. Accordingly, the structure is formally “diced” into small sub-domains (bricks) whose electromagnetic behavior is accounted for by scattering operators. Unlike the conventional LEGO, though, some bricks may contain a source, and hence play the role of “generators” in the equivalent model. In this communication we introduce the functional equation that describes a generator brick. We then show how the set of integral equations of LEGO are modified. Finally, we provide numerical results which demonstrate the validity of this approach.

The calculation of electromagnetic (EM) fields and waves inside finite-sized structures comprised of different media can benefit from a diakoptics method such as linear embedding via Green's operators (LEGO). Unlike scattering problems, the excitation of EM waves within the bulk dielectric requires introducing sources inside the structure itself. To handle such occurrence, we have expanded the set of LEGO sub-domains - employed to formulate an EM problem - to deal with the inclusion of elementary sources. The corresponding subdomains (bricks) play the role of ``generators'' in the equivalent model. Moreover, if a source is ``turned off'', as it were, the enclosing brick can be utilized as a numerical ``probe'' to sample the EM field. In this paper, we present the integral equations of LEGO modified so as to accommodate generator/probe bricks. Numerical results are provided which demonstrate the validity and the efficiency of the approach.

We present the extension of the linear embedding via Green's operators (LEGO) scheme to problems that involve elementary sources localized inside complex structures made of different dielectric media with inclusions. We show how this new feature allows solving problems of wave propagation within, e.g., devices based on electromagnetic band-gap structures.