Guglielmo Rubinacci

Fast Methods for Quantitative Eddy-Current Tomography of Conductive Materials

In this paper, we address the imaging of the spatial distribution of the resistivity of conductive materials by using data from eddy-current nondestructive testing. Specifically, the data consists of measurements of the impedance matrix at several frequencies acquired using a coil array. The imaging method processes the second-order term (estimated from the measured data) of the power series expansion, with respect to frequency, of the impedance matrix. This term accounts for the resistive contribution to changes of the impedance matrix, due to the presence of anomalies in the conductor under test, occurring at relatively low frequencies. The operator mapping a given resistivity distribution inside the conductor into the second-order term satisfies a proper monotonicity property. The monotonicity makes it possible to apply a fast noniterative imaging method initially developed by the authors for elliptic problems such as electrical resistance tomography. Numerical examples show the main features of the proposed method, and demonstrate the possibility of real-time imaging.

A measurement system based on magnetic sensors for nondestructive testing

The paper deals with a measurement system based on a low-cost eddy current probe for nondestructive testing (NDT) on conducting materials aimed at reconstructing the shape and position of thin cracks. The magnetic probe is characterized, highlighting good repeatability, linearity, and overall accuracy. A number of different measurement approaches are investigated, in order to choose the most appropriate for NDT applications. A numerical method is then illustrated; it proves to be able to reconstruct cracks starting from noisy measurement data.

Plasma Current, Shape, and Position Control in ITER

A linear model for feedback control of the plasma position and shape in the International Thermonuclear Experimental Reactor (ITER) is discussed. A model of the poloidal field (PF) system and of the disturbances is first derived. The main task of the control system is to avoid any contact of the hot plasma with the wall during the long duration of the burn phase. For this purpose, the control variables are specified as six gaps between the plasma separatrix and the first wall, including divertor channels. The structure model includes PF coils, vacuum vessel, first wall, backplate, and divertor fins, and it refers to the TAC-4 outline design ITER geometry. A multivariable controller is designed using the optimal linear quadratic approach. The simulation of the closed-loop system shows how the plasma shape is recovered: Step gap variations of 15 cm and poloidal beta drops of 0.2 are considered as disturbances. The performance parameters are voltages and currents in the PF coils and gap recovery time; voltage saturation of the actuators is also taken into account.

Numerical models of volumetric insulating cracks in eddy-current testing with experimental validation

This paper concerns fast electromagnetic modeling of volumetric cracks in conductive materials under eddy-current inspection. The underlying numerical method is described. The model is tested on cracks in aluminum structures employed in aeronautical manufacture. The computational results obtained with the method display satisfactory agreement with the respective experimental and numerical results obtained by representing cracks as nonconductive surfaces.

Surface integral formulations for the design of plasmonic nanostructures

Numerical formulations based on surface integral equations (SIEs) provide an accurate and efficient framework for the solution of the electromagnetic scattering problem by three-dimensional plasmonic nanostructures in the frequency domain. In this paper, we present a unified description of SIE formulations with both singular and nonsingular kernel and we study their accuracy in solving the scattering problem by metallic nanoparticles with spherical and nonspherical shape. In fact, the accuracy of the numerical solution, especially in the near zone, is of great importance in the analysis and design of plasmonic nanostructures, whose operation critically depends on the manipulation of electromagnetic hot spots. Four formulation types are considered: the N-combined region integral equations, the T-combined region integral equations, the combined field integral equations and the null field integral equations. A detailed comparison between their numerical solutions obtained for several nanoparticle shapes is performed by examining convergence rate and accuracy in both the far and near zone of the scatterer as a function of the number of degrees of freedom. A rigorous analysis of SIE formulations and their limitations can have a high impact on the engineering of numerous nano-scale optical devices such as plasmon-enhanced light emitters, biosensors, photodetectors, and nanoantennas.

A Broadband Volume Integral Formulation Based on Edge-Elements for Full-Wave Analysis of Lossy Interconnects

A new numerical fully three-dimensional (3-D) volume integral formulation for the electromagnetic analysis from static to microwave frequencies of penetrable materials (dielectric, eventually lossy, and conductors with finite conductivity) is here discussed. Its key feature is the introduction of a volumetric loop-star decomposition for treating piecewise homogeneous materials. The associated shape functions have been determined to decompose the volume current density in a solenoidal and a nonsolenoidal part, in analogy to the surface loop-star shape functions, used for modeling surface current densities on perfect electric conductors. The possibility of modeling volumetric ohmic and polarization current densities allows to compute in an accurate way the electromagnetic field in complex 3-D geometries, such as high speed interconnects, on a broad range of frequencies

Three dimensional finite elements modeling of superconductors

In this paper we present a variational formulation for the solution of eddy current problems in presence of superconductors. A suitable formulation of the macroscopic constitutive law is used so that an unconstrained minimization has to be performed. The electromagnetic problem is solved using an integral formulation, thus allowing us to discretize only the conducting regions. The method, although tested against a 1D analytical solution, is implemented for fully 3D geometries.

Analysis of a transient nonlinear 3-D eddy current problem with differential and integral methods

The paper compares the features of integral and differential formulations for the solution of of transient eddy current problems in nonlinear media. The integral method used reduces the nonlinear eddy current problem to the analysis of an equivalent network. Two dual edge element differential formulations are also used. Their field estimates automatically verify Faradays and Amperes laws and furnish the distribution of the constitutive error in the solution domain, which provides a useful tool for the refinement of the discretization. The methods are applied to analyze a massive magnetic circuit characterized by the presence of soft and hard magnetic materials with narrow gaps.

An error based approach to the solution of full Maxwell equations

Aim of this paper is to extend the error based approach to the study of general electromagnetic problems in 3D geometries in which the displacement currents may not be neglected. The unknown variables are the three-component vector potential A and W defined as the time integrals of -E and H, respectively. These potentials are constrained to satisfy initial, boundary and interface conditions. Since in this way the Maxwell equations are automatically satisfied, the solution is obtained via minimization of a global error functional which approaches zero when the constitutive equations are satisfied. >

Automatic Treatment of Multiply Connected Regions in Integral Formulations

This paper deals with the volume integral formulation of the eddy current problem in terms of the electric vector potential. Its aim is to present a simple topological algorithm for finding the additional degrees of freedom required in the discretization of a multiply connected region when using edge elements. The algorithm is completely automatic and it is based, as other previous approaches, on the application of the spanning tree technique on the graph made by the edges and nodes of the finite element mesh lying on the boundary surface of the conducting domain.