Andrea Stella

An integral formulation for eddy current analyses in axisymmetric configurations

A method for solving problems of electromagnetic field diffusion in axisymmetric configurations with linear conducting media is presented. The approach, which is based on lumped-parameter circuit modeling, has a number of theoretical and practical advantages in comparison with other methods currently used, particularly in dealing with problems where the coupling between the magnet system and the external feed network is important. The authors describe in detail the analytical basis and the numerical approach of the method and present its most interesting aspects together with a discussion on a number of critical problems faced during numerical implementation. In order to show the methods capabilities and performance, some numerical results are given. >

The RFX magnet system

Abstract The reversed field pinch (RFP) magnetic confinement requires both toroidal and poloidal components for the magnetic field induction. As in tokamaks, the former is provided by the toroidal and poloidal components for the the ohmic heating (OH) winding and the equilibrium field (EF) winding. The two induction field components have similar amplitudes, so that the toroidal component required in a RFP is about one order of magnitude lower than that in a tokamak with equal plasma current and aspect ratio. Owing to the local stability properties, the TF coils have to be located as close as possible to the plasma but, at the same time, the magnetic field ripple from TF coils (as well as any kinds of stray fields) must be kept to a minimum. Another peculiarity of the TF winding is that it is required to operate with a time-varying current and at high voltage levels. From these points of view, the design of RFP TF windings presents much less technological problems than a tokamak of similar size. The RFP requires a high toroidal loop voltage during fast current rise and a relatively high toroidal loop voltage during the flat top. The main consequences for the RFX PF magnet systems are as follows: • - large flux and energy to be inductively stored; • - very high voltage across the OH and EF winding terminals, giving rise to substantial insulation problems; • - the very fast rate required for current rise may produce remarkable skin effects within the OH conductors, so that large cross-section conductors have to be avoided; • - the electrodynamic forces acting on the OH winding are large and comparable with those in tokamaks; • - in case of any fault, currents in the coils can rise beyond safety limits at a very high rate, leading to extremely critical conditions for the machine integrity . From a mechanical point of view, both the OH and the EF windings are subject to working conditions similar to those experienced in tokamaks. Thus, RFX windings were manufactured with a similar technology. To detect the TF and PF winding faults a very fast, hard-wired system has been developed, which is able to elaborate signals from specific probes and to decide on necessary protective actions. The present contribution deals with the whole magnet system of RFX, including all TF and PF magnets, mechanical structure, magnetic and electric measurement instrumentation, as well as the fast fault detection system. After a review of the basic concepts representing the theoretical background behind the main choices, all aspects and features concerning the magnet design are presented in detail and deeply discussed. The manufacturing technology is then presented together with the main problems met during manufacture, development and acceptance tests and the methods adopted in order to solve them are explained. On-site assembly procedures, testing and the first integrated RFX operation are finally described.

Automated optimal design techniques for inverse electromagnetic problems

Two methods are considered for the solution of automated digital optimal design problems. The computer procedures based on these methods have been implemented and tested. The first method, based on a deterministic approach, considers a quadratic approximation of the cost function. The second, based on a stochastic approach, is derived from the simulated annealing algorithm. Both methods, implemented as computer codes, have been applied to the solution of a test synthesis problem where the magnetic field is generated by discrete coils. The deterministic method is substantially faster, especially when the calculation of the cost function is time consuming. On the other hand, the stochastic method gives good approximation of the global minimum independently of the initial conditions: as far as CPU time is concerned, the method is more expensive, but can be profitably used when the cost function can be calculated quickly and the number of design variables is large. >

Confinement studies on RFX

The results of the first year of operation of the experiment RFX are reported. Profiles of electron density, electron and ion temperature and impurity emission have been measured at plasma current I<0.7 MA. The energy confinement parameters at different density are reported, the best values ( tau E approximately 1ms, beta theta approximately 8%) being obtained operating at higher density. The role of the impurity content in determining the present performance of the experiment is discussed.

A procedure for axisymmetric winding design under parametric constraints: An application to the RFX poloidal transformer

The problem of winding design to perform a specified field synthesis is usually carried out as analytic determination of current distribution within a given region. This approach may be useful for conceptual or preliminary design, but presents severe technical difficulties from a construction point of view. A construction oriented procedure for axisymmetric air core windings for fusion devices has been developed, to account for parametric constraints such as current per turn, current density, number of turns and diagnostic accessibility. Starting from a preliminary tentative design, presenting suitable electrical parameters, each coil position is automatically adjusted, within specified limits, to achieve the required field synthesis. A package has been implemented and succesfully applied to the RFX [1] Poloidal Field Transformer design and the main results are reported in the paper together with a number of numerical examples.

A Proper Generalized Decomposition Approach for Fuel Cell Polymeric Membrane Modeling

Modeling polymeric proton-exchange membranes (PEM) at the heart of fuel cells requires the solution of highly nonlinear partial differential equations in very thin and flat domains. Recently, the Proper Generalized Decomposition methods have emerged as particularly promising methods for these types of problems. This paper introduces the basics of this novel class of approaches to PEM modeling and highlights their potential benefits.

Solving 3-D Eddy Currents in Thin Shells of Any Shape and Topology

A novel 3-D integral formulation for solving eddy currents in thin conductors of any shape and topology is presented. The field problem is formulated with the cell method in terms of mesh currents in order to minimize the number of unknowns and, thus, computing requirements. We prove that additional degrees of freedom, globally defined, are required with complex topologies.

A method for the identification of the plasma magnetic boundary in machines for fusion research

The paper deals with a method for the identification of the plasma magnetic contour in machines for fusion research using magnetic measurements. The method is based on the integration of an electromagnetic model of the passive structures surrounding the plasma and of an equivalent plasma representation able to reproduce the magnetic configuration measured at the probe locations. No physical equilibrium is considered for the plasma and therefore the results of the identification are meaningful outside the plasma contour only.

The RFX toroidal field winding design

The RFX toroidal field winding consists of 48 coils, which can be connected in many series/parallel configurations according to the toroidal field programming required for plasma operation. For ease of maintenance each coil consists of two identical half-coils connected at the equatorial plane of the machine. To be in alignment, the half coils are placed into grooves machined in an aluminum shell, which also has the function of withstanding the overturning moment caused by to the interaction between the current and the poloidal field. Stainless-steel clamping belts are provided around the coils to withstand their electromagnetic expansion forces and to keep them in the grooves. Thermal expansion of the half coils takes place freely along the grooves, due to thin layers of low-friction material placed on the coil surfaces. The demountable joints which connect the conductors of the half coils are designed to allow thermal expansion. Two basic alternative solutions considered for the electric contacts are discussed: the first based on a multicontact plug-in system, the second on bolted joints. >

Current diffusion in the RFX magnetizing winding

RFX is a fusion Reversed Field Pinch (RFP) experiment under construction in Padua, Italy. Its air-core magnetizing winding is part of the poloidal-field winding and is devoted to inducing the toroidal plasma current by transformer action. This is obtained by slowly charging the winding to a specified current which is then forced to deca quickly. During this fast decay, the current density distribution inside each conductor behaves according to diffusion equations and this causes the transient stray magnetic field in the plasma region to rise well above the static value. A numerical approach, based on the volume integral formulation, is developed to study these diffusion phenomena. After a brief description of the mathematical basis of the method, the numerical analysis performed is presented and the stray-field evolution of a number of technical solutions considered to comply with the RFX design specifications are compared. >