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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.

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.

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 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.

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.

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.

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 discuss the application of linear embedding via Green's operators (LEGO) to the solution of the scattering of electromagnetic waves from random distributions of different objects. The latter are enclosed in simple-shaped bricks described via scattering operators that have to be computed only once for a given frequency. Therefore, the study of many distributions made of the very same objects but located in different positions can be efficiently carried out by re-using the scattering operators. Besides, the equation of LEGO is solved via the Moment Methods combined with Arnoldi basis functions - which allows the corresponding algebraic system to be effectively compressed. We investigate the properties of LEGO through a few numerical examples.

We tackle the scattering from a finite dielectric host medium containing a regular arrangement of (metallic or penetrable) inclusions by using the linear embedding via Green's operators method. After “dicing” the structure into “bricks”, we state an integral equation which we turn into a weak form via the Method of Moments (MoM) with subdomain basis functions. Then, to proceed i) we compress the off-diagonal blocks of the MoM matrix via adaptive cross approximation, and ii) we reduce the size of the whole MoM matrix by expanding the unknown on a set of orthonormal basis functions generated through the Arnoldi iteration. We elaborate on the properties of this approach through a few numerical examples.

We propose a methodology - based on Linear Embedding via Green's Operators (LEGO) and the eigencurrent expansion method - for solving large 3-D structures comprised of ND >> 1 objects. The problem is formulated through an integral equation involving the total inverse scattering operator S -1 of the structure. Upon analyzing an electromagnetic band-gap open cavity, as an example of application, we show that hundreds of thousands of unknowns can be effortlessly handled and that the CPU times scale just linearly with ND. © 2009 IEEE.

Linear embedding via Green's operators (LEGO) is a computational method in which the multiple scattering between adjacent objects — forming a large composite structure — is determined through the interaction of simple-shaped building domains, whose electromagnetic (EM) behavior is accounted for by means of scattering operators. This method has been successfully demonstrated for 2-D electromagnetic band-gaps (EBG) and other structures [1], and for very simple 3-D configurations [2]. In this communication we briefly report on the full extension of LEGO to large complex 3-D structures, which may be EBG-based but may also include finite antenna arrays as well as frequency selective surfaces, to name but a few applications. In particular, we shall outline two modifications that were crucial for scaling up the LEGO method, namely, the introduction of a total inverse scattering operator S−1 and the eigencurrent expansion method (EEM) [3].

Recent advances in plasma-based propulsion systems have led to the development of electromagnetic (RF) generation and acceleration systems, capable of providing highly controllable and wide-ranging exhaust velocities, and potentially enabling a wide range of missions from KWs to MWs levels. In this paper we report on the development of a system-level modelling of a three-stage helicon plasma thruster composed of a helicon plasma source, a confining magnetic field structure enclosing a plasma heating section, and a magnetic nozzle. This modelling can help to optimize the design parameters (antenna shape, matching circuits and generators, and the ensuing evaluation of the required power, mass and other physical parameters, including magnetic field for confinement), and estimate the system feasibility: in particular our activity focuses on the most critical RF issues and on the RF-plasma interactions. We have divided the study into two different and linked parts: 1) RF system modelling, which provides an "interface" between the RF power generation and the power deposition into the plasma and relies on the TOPICA code, and 2) plasma device modelling of the sub-systems and of their connection, which yields the global, system-level description of the engine.

Progress is reviewed on the simulation of wave-particle interactions in the ion cyclotron range of frequencies (ICRF). Two important aspects of this problem are described. First, mode conversion from a long wavelength fast magnetosonic wave to short wavelength ion Bernstein waves (IBW) and ion cyclotron waves (ICW) is simulated and validation tests of the simulations against experiment are presented. Second, simulations of the quasilinear evolution of nonthermal ion tails during the minority heating are reviewed and experimental validation tests are also discussed. In this paper we describe how access to teraflop computing capability has made it possible to advance the state of the art in this area. We also discuss two aspects of the wave-particle interaction where future work is needed and where in particular access to sub-petaflop and petaflop computing capability would be highly desirable. This work involves the interaction of ICRF waves with energetic neutral beam ions at high ion cyclotron harmonic number and addresses the inclusion of finite ion drift orbit effects in the nonthermal ion tail evolution and the inclusion of nonlinear effects such as RF sheaths in the antenna – edge plasma coupling.

An innovative tool has been realized for the 3D/1D simulation of Ion Cyclotron Radio Frequency (ICRF), i.e. accounting for antennas in a realistic 3D geometry and with an accurate 1D plasma model. 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 by means of a magnetic current (electric field) distribution on the aperture between the two regions. In the vacuum region all the calculations are executed in the spatial domain while in the plasma region an extraction in the spectral domain and an analytical evaluation of some integrals are employed that permit to significantly reduce the integration support and to obtain a high numerical efficiency leading to the practical possibility of using a large number of sub‐domain basis functions on each solid conductor of the system. The p...

An innovative tool has been realized for the 3D/1D simulation of Ion Cyclotron Radio Frequency (ICRF), i.e. accounting for antennas in a realistic 3D geometry and with an accurate 1D plasma model. 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 by means of a magnetic current (electric field) distribution on the aperture between the two regions. In the vacuum region all the calculations are executed in the spatial domain while in the plasma region an extraction in the spectral domain of some integrals is employed that permits to significantly reduce the integration support and to obtain a high numerical efficiency leading to the practical possibility of using a large number of sub-domain (rectangular or triangular) basis functions on each solid conductor of the system. The plasma enters the formalism of the plasma region via a surface impedance matrix; for this reason any plasma model can be used; at present the FELICE code has been adopted, that affords density and temperature profiles, and FLR effects. The source term directly models the TEM mode of the coax feeding the antenna and the current in the coax is determined self-consistently, giving the input impedance/admittance of the antenna itself. Calculation of field distributions (both magnetic and electric), useful for sheath considerations, is included. This tool has been implemented in a suite, called TOPICA, that is modular and applicable to ICRF antenna structures of arbitrary shape. This new simulation tool can assist during the detailed design phase and for this reason can be considered a "Virtual Prototyping Laboratory" (VPL). The TOPICA suite has been tested against assessed codes and against measurements and data of mock-ups and existing antennas. The VPL is being used in the design of various ICRF antennas and also for the performance prediction of the ALCATOR C-MOD D antenna.