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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 present an efficient formulation based on the linear embedding via Green's operators (LEGO) and the eigencurrent expansion method to optimize composite wave interaction structures, e.g., photonic-crystal based devices. In LEGO, a composite structure is broken up into "bricks" that are characterized through scattering operators and the interaction among them is captured using transfer operators. By exploiting this diakoptic nature of LEGO, we show how the optimization is accomplished using an effective operator defined over the bricks (usually few) enclosing the space where the fields are sampled. This operator encompasses the effect of the surrounding and separates the domain to be optimized from the fixed one, enabling us to carry out the optimization with little computational effort.

Linear embedding via Green's operators (LEGO) is a domain decomposition method for solving electromagnetic problems which involve composite 3-D structures. By combining the standard Method of Moments with a set of macro basis functions obtained through the Arnoldi iteration, the algebraic system of LEGO can be effectively compressed. However, under general circumstances it is not easy to choose the minimum number of macro basis functions for a given level of accuracy, since many physical and geometrical factors come into play. To shed light on this topic, we discuss a few examples with a focus on the convergence of the numerical solution.

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.

Linear embedding via Green's operators (LEGO) [1, 2] is a domain decomposition method in which the electromagnetic scattering by an aggregate of N D bodies (immersed in a homogeneous background medium) is tackled by enclosing each object within an arbitrarily-shaped bounded domain D k (brick), k = 1, …, N D (e.g., see Fig. 1). The bricks are characterized electromagnetically by means of scattering operators S kk , which are subsequently combined to form the total inverse scattering operator S−1 of the structure [1]. Finally, we use the eigencurrent expansion method (EEM) [1,3] to solve the relevant equation involving S−1, viz.

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].

This paper describes recent upgrades of TOPICA (Torino Politecnico Ion Cyclotron Antennas) formulation and implementation. TOPICA is a code capable of handling both the actual geometry of ion cyclotron (IC) antennas and an accurate plasma description; it can predict the performances of IC launchers with an unprecedented accuracy and numerical efficiency, validated against data measured in plasma operation conditions. In the reported upgrade, a new multi-cavity approach is introduced, producing significant savings in terms of CPU and memory requirements and allowing the analysis of large antennas even with limited computational resources. In fact, by formally separating the structure's cavities with a number of mathematical surfaces called ‘apertures’, the method of moments interaction matrix is block-wise sparse and, as a consequence, can be manipulated with a far higher numerical efficiency; this also allows an out-of-core solution.

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.

The Tore Supra (CEA) antenna for the ion cyclotron range of frequencies (ICRF) is a so-called resonant double loop antenna with internal matching capacitors. The required capacitance range is crucial for antenna and the tuning-and-matching network design. The capacitance value for a given discharge is also important for antenna operation. We discuss a method to accurately predict the tuning capacitance values in the presence of plasma operation and for efficiently accounting for the capacitors in the performance analysis. The presented method relies on the use of the TOPICA code, a numerical suite developed for prediction and analysis of modern ICRF antenna systems; it is able to handle antennas with a realistic 3D geometry and an accurate 1D plasma model. Very good agreement with the experimental capacitance values is found using TOPICA, providing further experimental validation of the computational algorithm and physics model.

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.

The demand for a predictive tool to help designing ICRH antennas for fusion experiments has driven the development of codes like ICANT, RANT3D, and the early developments and further upgrades of TOPICA code. Currently, TOPICA handles the actual geometry of ICRH antennas (with their housing, etc.) as well as a realistic plasma model, including density and temperature profiles and FLR effects. Both goals have been attained by formally splitting 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 writing a set of coupled integral equations for the unknown equivalent (current) sources; finite elements are used on a triangular-cell mesh and a linear system is obtained on application of the weighted-residual solution scheme. In the vacuum region calculations are done in the spatial domain, whereas in the plasma region a spectral (wavenumber) representation of fields and currents is adopted, thus allowing a description of the plasma by a surface impedance matrix. Thanks to this approach, any plasma model can be used in principle, and at present Brambilla's FELICE code has been employed. The natural outputs of TOPICA are the induced currents on the conductors 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. This paper is precisely devoted to the description of TOPICA, whereas examples of results for real-life antennas are reported in a companion paper [1] in this proceedings. ©2005 American Institute of Physics

In the past twenty years plasma-based propulsion systems have found increasing aerospace interest; although they were initially conceived as rockets for interplanetary missions, more recent advances in plasma-based concepts have led to the identification of radio-frequency (RF) generation and acceleration systems as capable of providing not only continuous thrust, but also controllable exhaust velocities, as required in maneuvering applications. The most interesting such studies for plasma propulsion are those focused on the possibility of coupling radio frequency power to plasma, exploiting the possibility of having very efficient devices to generate and heat the plasma, magnetically confining it in a trap in the heating region, so that ion can escape the magnetic trap only when they are energetic enough to be converted into direct out-going flow which provides the thrust. The structure of this system is therefore based on of three stages where plasma is respectively generated, heated and expanded in a magnetic nozzle. The heating stage acts as an amplifier; here plasma is heated by the radio frequency waves by the process of ion cyclotron resonance. It has been developed and tested a numerical tool for the electromagnetic modeling of the ICRF antenna, of the RF booster unit of plasma thrusters, and of the RF-plasma interactions. The latter is studied in the critical ICRF acceleration region by setting up a convenient Electromagnetic (EM) analytical and numerical model based on the Moment-Method solution of a suitable set of integral equations. Solution of the relevant integral equation directly provides the electric surface current density induced on antenna conductors, but the ultimate quantity to be computed is the circuit characterization (e.g. admittance matrix) at the input ports. ©2005 American Institute of Physics

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.