R. Fresa

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. >

Optimization of the power supply demand for plasma shape control in a tokamak

We focus on the estimation of the minimum poloidal field coil voltages for the plasma shape control in a tokamak. For given coil locations and for a class of disturbances we propose a procedure for the evaluation of the minimum voltages needed to guarantee that the plasma boundary displacement remains within specified limits. The impact of this problem on the minimization of the power supply cost is discussed for the case of the International Thermonuclear Experimental Reactor (ITER).

Accuracy Assessment of Numerical Tracing of Three-Dimensional Magnetic Field Lines in Tokamaks with Analytical Invariants

Abstract We consider the problem of the accurate tracing of long magnetic field lines in tokamaks, which is in general crucial for the determination of the plasma boundary as well as for the magnetic properties of the scrape-off layer. Accurate field line tracing is strictly related to basic properties of ordinary differential equation (ODE) integrators, in terms of preservation of invariant properties and local accuracy for long-term analysis. We introduce and discuss some assessment criteria and a procedure for the specific problem, using them to compare standard ODE solvers with a volume-preserving algorithm for given accuracy requirements. In particular, after the validation for an axisymmetric plasma, a three-dimensional (3-D) configuration is described by means of Clebsch potentials, which provide analytical invariants for assessing the accuracy of the numerical integration. A standard fourth-order Runge-Kutta routine at fixed step is well suited to the problem in terms of reduced computational burden, with extremely good results for accuracy and volume preservation. Then we tackle the problem of field line tracing in the determination of plasma-wall gaps for a 3-D configuration, demonstrating the effective feasibility of the plasma boundary evaluation in tokamaks by tracing field lines with standard tools.

Analysis of resistive joints for superconducting cables for fusion applications

In this paper, we use an integral formulation of the Maxwells equations (magneto-quasi-static limit) in the presence of superconductors to analyze a resistive joint for cables of interest for controlled thermonuclear fusion

Three-dimensional defect localization from time-of-flight/eddy current testing data

This paper deals with the inverse problem of defect detection in a conductive material using eddy current nondestructive evaluation (NDE) methods. We consider a full three-dimensional time-domain problem in the quasistatic regime. The inversion method exploits the properties of the Q-transform, an integral operator capable of mapping wave propagation fields into diffusive fields. This one-to-one operator allows one to define the concept of time-of-flight (TOF) for diffusive fields. Specifically, we show that by properly choosing the waveform of the driving current, the distance between probe and defect can be easily extracted from eddy current measurements, as in TOF measurements employed in wave propagation NDE methods.

Identification of the B–H curve from external measurements using complementary formulations

This paper deals with theoretical and numerical problems related with the inverse problem of the reconstruction of the first piece of the piecewise affine approximation of the B–H nonlinear characteristic starting from the knowledge of measured flux–current relationship. The reconstruction of the first piece of the characteristic is critical, as highlighted in novel approaches reconstructing the whole characteristic without relying on the common assumption that the driving system produces a uniformly distributed magnetic field inside the specimen. In this paper a proof will be given of the uniqueness of the solution of the inverse problem based on elementary analysis arguments and a numerical procedure that, by means of the use of complementary formulations, allows one to compute and control the reconstruction error due to the numerical formulation. The paper is organized as follows: a brief discussion of the problem is reported in Section 1, the numerical formulation and the error bounds are reported in Section 2, the uniqueness of the inverse problem is addressed in Section 3 and numerical examples are reported in Section 4.

An integrated approach to the control of magnetically confined plasmas

Abstract In this paper, a short review of the work done in the framework of a nation-wide research programme on ‘Models and Methods for Plasma Control in Magnetically Confined Fusion Experiments’ is presented. The broad aim of the overall programme is to develop and propose a new effective and reliable approach to the on-line plasma control for future fusion experiments, starting from the todays theoretical background, validated by experimental evidence from a number of tests performed on existing experiments. The proposed formulation to approach the control problem is a linearized model in terms of suitable state variables and input/output relationships. The basic project has been subdivided into four major areas of investigation: the linearized response plasma model, the three-dimensional electromagnetic model, the identification techniques and finally the plasma control requirements. The most remarkable results, achieved so far in each area above, are presented in the paper.

Use of compensation theorem for the robustness assessment of electromagnetic devices optimal design

Purpose – The purpose of this paper is to present the use of the compensation theorem (CT), well known in the analysis of linear electric networks, to compute sensitivity of the performance functions used in the robust design or tolerance analysis of electromagnetic devices. Design/methodology/approach – The CT is first illustrated in the case of a simple field analysis problem. Then, using numerical simulations, the effectiveness of compensation approach for assessing impact of the small modification of material properties is shown. The numerical simulations are performed with a finite elements code based on an integral formulation. Findings – The complexity of additional computations to assess the effect of small variations involved in sensitivity analysis can be reduced. Research limitations/implications – The method can be applied only to linear systems; in addition, although compensation applies to any variations, the reduction of computational complexity is achieved only for small variations, giving...