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This paper illustrates the application of a fast SVD-based technique to the analysis of resistive wall modes in fusion devices. The computational cost scales almost linearly with the number of discrete unknowns, allowing the solution of large scale 3D problems of interest for existing or future fusion devices like the International Tokamak Experimental Reactor. Index Terms--Fast methods, integral formulations, resistive wall modes, singular value decomposition.

In this paper, we simulate the electromagnetic behavior of cable-in-conduit conductors (CICCs) and coils using a 3-D integral formulation of magneto-quasistatic Maxwell's equations, where the superconductors are represented by a power-law. The integral equation is numerically formulated using edge-elements and the nonlinear problem is discretized with a quasi-Newton algorithm. The solution of each iteration step is achieved with an iterative GMRES solver, which benefits from an singular value decomposition of the full matrix representing the integral operator. The model is applied to study the electromagnetic behavior of international thermonuclear experimental reactor (ITER) CICC and coils. Index Terms--Cable-in-conduit conductors (CICC), edge elements, fast methods, integral equations, superconducting cables.

This paper focuses on the coupling procedure between a 3-D integral formulation of the eddy currents problem and a linearized MHD model solved with a differential approach. The final aim is to develop a computational tool able to analyze the resistive wall modes of fusion plasmas, including the 3-D effects of nouaxisymmetric conducting structures surrounding the plasma. Index Terms--Integral formulation, magnetohydrodynamics, resistive wall modes.

In this paper, we use a fluid model to describe the dynamics of the conduction electrons of multiwall carbon nanotubes. A 3-D integral formulation of Maxwell's equations is used and numerically solved with a finite-elements approach based on div- conforming basis functions. The null-piny decomposition is used to avoid the low-frequency breakdown. Index Terms--Multiwall carbon nanotubes (MWCNs), surface integral equations.

The paper deals with the numerical study of the electromagnetic response of a metallic nanoparticle to an external electromagnetic field, within the framework of the classical electrodynamics. The conduction electrons of the nanoparticle are modeled as a compressible electron fluid, whose dynamics are described by means of the linearized hydrodynamic equations. The electromagnetic field scattered by the nanoparticle is evaluated by a full-wave 3-D model based on an integral equation where the unknown is the current density. The fluid quantum pressure arising from the kinetic energy of the degenerate conduction electron gas gives rise to non-local effects that strongly influence the plasmon oscillations. Index Terms--Edge elements, integral formulation, nanoparticles, non-local effects, plasmon oscillations.

The electromagnetic behavior of ITER cable-in-conduit conductors (CICCs) is simulated by using a three-dimensional integral formulation of magneto-quasistatic Maxwell's equations. This model is used for studying the electromagnetic behavior of the resistive transition in the Poloidal Field Insert Sample.

The high-energy ionized particles collected by the divertor structures in a tokamak reactor cause a localized thermal load around the strike-points, which are the intersections of the separatrix with the divertor tiles. To spread on a larger region this thermal load, it is convenient to resort to a sweeping, i.e., a periodical movement of the strike-points. This paper introduces the new model-based sweeping algorithm recently implemented on the Joint European Torus tokamak, within the eXtreme Shape Controller architecture. Index Terms--Plasma-shape control, plasma strike-point sweeping, tokamaks control.

This paper describes a set of graphic tools for the design and validation of the new plasma shape controller [eXtreme Shape Controller (XSC)], which has been recently implemented at the Joint European Torus tokamak. The XSC enables operation with high elongation and high triangularity plasmas. The software suite, which is called XSC Tools, has been developed to automate the design procedure of the XSC. These tools make use of graphic user interfaces to allow the nonspecialist users to prepare for new operative scenarios, without the help from modeling and control specialists. Once a new controller is generated, all its parameters are saved into a text file, which is used to perform the validation of the scenario via simulations. The same file is then loaded by the real-time code running on the plant, without any further processing. This feature guarantees that the controller, which is running on the plant, is exactly the same one validated through simulations. An additional effort has been made in order to make the XSC Tools machine independent, i.e., to enable their use on the different tokamaks. Index Terms--Control-system validation, software tools, tokamak control.

A three-dimensional full-wave surface integral formulation is used to predict the terminal response of unshielded twisted pairs. The proposed approach allows taking into account the skin effect, proximity effect and radiation losses. The proposed full-wave simulation is validated by comparing the results with those obtained by a software tool based on the finite integration technique, discussing advantages and limitations. The surface integral formulation results obtained on a short length of the line are used to predict the behavior of a longer line. In addition, they are used to extract equivalent circuits suitable for the time domain analysis by any commercial circuit simulator. Index Terms--Integral equations, nonuniform transmission lines, numerical analysis, unshielded twisted pairs (UTPs).

An integral formulation to model, in the frequency domain, the electromagnetic response of three-dimensional (3-D) structures formed by metallic carbon nanotubes and conductors, within the framework of the classical electrodynamics, is described. The conduction electrons of the metallic nanotube are modeled as an infinitesimally thin cylindrical layer of compressible fluid, whose dynamics are described by means of the linearized hydrodynamic equations. The resulting integral equations are solved numerically by the finite element method using the facet elements and the null-piny decomposition. The proposed formulation is applied to study carbon nanotube interconnects and dipole antennas and some related results are outlined. The solutions highlight the high-frequency effects due to the electron inertia and the fluid pressure. In particular, since the kinetic inductance matrix dominates over the magnetic one, proximity effects are negligible. Index Terms--Electrodynamics, finite elements, fluid model, integral formulation, metallic carbon nanotubes.

In this paper, we analyze the initial phase of an asymmetric plasma displacement event in a tokamak. We assume a rigid model of the plasma and a three-dimensional model of the conducting structures. A volume-integral eddy current formulation is coupled to force and torque balance in the plasma. Index Terms--Eddy currents, finite-element methods, plasma stability, tokamaks.

In this paper, we use an integral formulation of the Maxwell's equations (magneto-quasi-static limit) in the presence of superconductors to analyze a resistive joint for cables of interest for controlled thermonuclear fusion. Index Terms--Edge elements, integral equations, superconducting cable joints, superconducting magnets.

A general and effective method is presented to numerically solve the electric field integral equation (EFIE) for topologically complex conducting domains by the finite element method. A new technique is proposed to decompose the surface current density into a solenoidal part and a nonsolenoidal remainder to avoid the low frequency breakdown. The surface current density field is approximated through div-conforming (facet) elements. The solenoidal part is represented through the null space of the discrete approximation D of the surface divergence operator in the subspace spanned by the facet elements, whereas the nonsolenoidal remainder is represented through its complement. The basis functions of the null space and its complement are evaluated, respectively, by the null and pseudo-inverse of the matrix D. The completeness of the null-pinv basis functions is studied. Unlike the loop-star and loop-tree basis functions, the null-pinv basis functions allow to deal with topologically complex conducting domains in a general and readily applicable way. A topological interpretation of the 'null-pinv' decomposition is given and a general and simple method to evaluate the null and pseudo-inverse of D is proposed. The computational complexity of the proposed method is discussed. Index Terms--Div-conforming (facet) elements, low frequency breakdown, multiply connected domains, null space, null-pinv decomposition, surface integral equations.

The 'standard' transmission line model describes accurately the propagation of electric signals along conducting wires, if the distance between them is much smaller than both their length and the smallest characteristic wavelength of the signals. This paper presents an 'enhanced' transmission line model that is able to describe the propagation along perfectly conducting wires in a homogeneous dielectric, and also when the distance between the wires is comparable with the smallest characteristic wave-length of the signals. The enhanced model is obtained, with suitable approximations, starting from a full-wave analysis of the problem and using an integral formulation based on the electromagnetic potentials satisfying the Lorentz gauge. It differs from the standard transmission line model, only in its constitutive relations, that is, in the relation between the per unit length (p.u.l.) magnetic flux and the current intensity, and in the relation between the electric voltage and the p.u.l. electric charge. In the standard model, these relations are of the algebraic type, and in the enhanced one they are of the convolution type, expressing nothing more than a very simple physical fact: the values of the p.u.l. flux and voltage at the generic abscissa along the wires depend on the entire distribution of the current and the p.u.l. charge, respectively. The kernels of the convolution integrals have the logarithmic singularity typical of the surface distributions and takes into account proximity effects. The solution of the enhanced model highlights the high-frequency effects due to dispersion and radiation that the standard model is unable to provide. Good agreement with the solutions obtained by a full-wave electromagnetic numerical code is achieved. Index Terms--Full-wave analysis, integral formulations, radiation losses, transmission line models, wire structures.

The adaptive fast multipole method is combined with a three-dimensional (3-D) eddy-current integral formulation using edge-element-based shape functions to reduce the computational complexity and the memory requirements from order N2 to nearly order N, where N is the number of edge-related unknowns. The effectiveness of this approach is verified with reference to the analysis of some 3-D problems of practical interest. Index Terms--Eddy currents, edge elements, fast multipole method.

In this paper, we solve the eddy-current problem in presence of superconductors in three-dimensional geometries, fed through electrodes and possibly carrying transport current. An integral formulation of the electromagnetic part of the problem is complemented by a variational form of the macroscopic constitutive relationship of a superconductor, obtained by the use of a suitable power-law characteristic. This formulation allows us to solve the problem as an unconstrained minimization of a functional that is convex under suitable assumptions. Index Terms--Edge elements, integral equations, superconducting devices.

In this paper, we analyze the electromagnetic fields in the Joint European Torus (JET) tokamak taking into account the effects of its three-dimensional (3-D) metallic structures. The systems considered here that interact with the plasma are basically the vacuum vessel, the magnetic circuit, and the active poloidal field (PF) coils. The first two have important 3-D effects that may cause significant deviations from purely axisymmetric estimates. The numerical results will be compared to the experimental data and will give indications for the tuning of approximate equivalent axisymmetric models. Index Terms--Eddy currents, electromagnetic devices, finite-element calculations.

In this paper, we present a unified approach for treating both the coupling between circuits and electromagnetic fields and multiply connected domains. The eddy-currents equations are solved using an integral formulation exploiting nonlocal basis functions. Index Terms--Circuit-fields coupling, eddy currents, edge elements, integral formulations, multiply connected domains.

A quadratic approach is used to find the unknown resistivity of a conducting body. The resistivity variation are supposed to be spatially localized. The multiresolution analysis is discussed in order to obtain a good estimate of the resistivity profile with a limited number of unknown parameters. The method allows to identify the regions where the perturbations may be localized and to retrieve the unknowns parameters only in those regions. Some numerical results show the main features of the proposed approach. Index terms - Non-destructive evaluation, wavelets, eddy currents.

A wavelet-based approach is presented for solving Maxwell equations. Full benefit is gained from the wavelets in terms of self-adaptativity of the resolution. Using interpolating wavelets allows for a simpler treatment of any operation involving the function, including the imposition of boundary conditions. Index terms - Wave propagation, wavelets, time domain, finite differences, multiresolution.

The aim of this paper is to present a Lagrangian unified approach to shape-dependent electromagnetic problems (equilibrium, dynamic coupled, shape inverse, trajectory inverse problems). The main features of this approach are illustrated, and a comparison with the usual Eulerian point of view is made, from both the analytical and the numerical side, showing several advantages of the Lagrangian approach. A simple analytical example is presented in order to help comprehension and to show the effectiveness of the method. In addition, some practical applications are described. Index Terms - Coupled problems, electromagnetic analysis, finite element methods, inverse problems, mechanical systems, numerical analysis, optimization methods, velocity effects.

The aim of this paper is to show how SMES devices, if arranged with more than two magnetic dipoles, can perform better. The analysis is carried out either considering or not the presence of a ferromagnetic shield. In the latter case a shape optimization of the iron shield is performed using a combined stochastic/deterministic method. The paper shows how advantages can be taken by evaluating the sensitivity matrix of the iron shape optimization by means of a Lagrangian formulation of the Maxwell's equations.

The aim of this paper is to present a completely Lagrangian approach to solve a plasma z-pinch problem, described by the MHD model. Some considerations will be done about the general advantages of using a Lagrangian approach in solving mechanically coupled problems. The results obtained will be compared with some experimental data, showing a good agreement.

This paper presents a completely lagrangian approach able to solve shape inverse (optimization and identification) electromagnetic problems. A first order deterministic minimization technique combined with a lagrangian finite element approach is used. Theoretical and numerical advantages and drawbacks of such a method are discussed, and some applications are presented.

In this paper we analyse the time evolution of a tokamak plasma after the failure of the vertical control system. In this case, the plasma eventually touches the conducting wall and gives rise to currents which flow partly in the wall, partly in the plasma. We show how, under simplifying assumptions, the problem can be analysed by means of pure electromagnetic formulations. After a brief review of the state of the art in the analysis of this phenomenon, we propose and discuss three alternative Eulerian approaches: an evolutionary equilibrium formulation, a convection-diffusion model and a 3D error-based approach.

In this paper some aspects concerning the finite element solution of the electromagnetic propagation in nonlinear media are studied through complementary formulations of the Maxwell equations. Nonlinear hyperbolic equations generate discontinuous solutions even if the initial and boundary conditions are regular. The numerical solution definitively breaks and the Galerkin method does not converge any more after the time at which a sharp discontinuity is developed. The sharpening of the solution is related to the loss of its uniqueness.

The aim of this paper is to present an efficient technique for the fast solution of three-dimensional eddy currents problems. The method combines Fast Fourier Transform (FFT) on a regular grid for the calculation of long-range interaction, and the standard method for evaluating the short range interaction. Index Terms--Eddy currents, fast algorithms, finite element methods, integral equations.