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.
Abstract-This paper describes in detail different formulations of the inverse-source problem, whereby equivalent sources and/or fields are to be computed on an arbitrary 3-D closed surface from the knowledge of complex vector electric field data at a specified (exterior) surface. The starting point is the analysis of the formulation in terms of the Equivalence Principle, of the possible choices for the internal fields, and of their practical impact. Love's (zero interior field) equivalence is the only equivalence form that yields currents directly related to the fields on the reconstruction surface; its enforcement results in a pair of coupled integral equations. Formulations resulting in a single integral equation are also analyzed. The first is the single-equation, two-current formulation which is most common in current literature, in which no interior field condition is enforced. The single-current (electric or magnetic) formulation deriving from continuity enforcement of one field is also introduced and analyzed. Single-equation formulations result in a simpler implementation and a lower computational load than the dual-equation formulation, but numerical tests with synthetic data support the benefits of the latter. The spectrum of the involved (discretized) operators clearly shows a relation with the theoretical Degrees of Freedom (DoF) of the measured field for the dual-equation formulation that guarantees extraction of these DoF; this is absent in the single-equation formulation. Examples confirm that singleequation formulations do not yield Love's currents, as observed both with comparison with reference data and via energetic considerations. The presentation is concluded with a test on measured data which shows the stability and usefulness of the dual-equation formulation in a situation of practical relevance.
We propose a method to significantly improve the spectral properties of the EFIE MoM matrix for broad-band analysis of structures with fine details, non-uniform meshes, and large overall sizes. A multilevel approach allows to overlay fine meshes and quasi-Nyquist sampled meshes; the fine-mesh conditioning is solved via hierarchical basis functions, and the quasi-Nyquist sampled part is treated by an algebraic incomplete LU preconditioner. Numerical results show the effectiveness of the approach for several realistic structures with overall sizes of ten/twenty wavelengths and levels of detail from very moderate to extending over the whole structure.
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