Edge element formulations of eddy current problems

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms, and predicting the performance of high-temperature-superconductor (HTS) tapes, wires, and devices. This is particularly true for ac loss calculation since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, which are based on different techniques and implementations, has been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This paper presents a literature review of the methods for computing ac losses in HTS tapes, wires, and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy-current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications.

Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents

It is shown that edge elements, as vectorial finite-element approximations fields like e and h, can be used to solve scattering problems. This can be done in essentially two ways, according to which of the two fields d or b one most wishes to get in divergence-free form. Apparent drawback of edge elements (due to the increased number of degrees of freedom in comparison with nodal elements) are more than compensated by economies due to greater sparsity. Moreover, they could help get rid of unwanted spurious modes when resonance frequencies of waveguides of complicated shape are computed. >

Edge-elements for scattering problems

In [1] and [2], a variational formulation of the eddy-currents problem using the magnetic field h as state variable was introduced. We describe here two applications of the method: computation of the impedance of a probe in non-destructive testing and prediction of the characteristics of a new design of an iron-free machine. The basic idea is first exposed, leaving aside difficulties like multiple connectedness. These are treated more thoroughly in Part 3, after the description of applications in Part 2.

The "TRIFOU" Code: Solving the 3-D eddy-currents problem by using H as state variable

The theory and applications of eddy currents induced in conducting materials by time-varying magnetic fields are reviewed. The mathematical methods employed in solving the relevant problems are presented. Both analytical and numerical methods are described. Applications based on effects arising from eddy currents are discussed in detail. These applications are to magnetic levitation, electromagnetic launching, hyperthermia treatment of cancer, and nondestructive testing. >

Eddy currents: theory and applications

The numerical calculation of 3-dimensional eddy currents is complicated by the need to use vector functions to describe the interlinked flux and current distributions. The three vector components are coupled, particularly by the conditions imposed by the copper and iron surfaces, and by other changes in material properties. The range of choice of magnetic and electric vector potentials is examined, including the ℰ and H vectors as particular examples, and it is shown that the problem formulation is greatly affected by the choice of gauge, or vector-potential divergence. This introduces scalar potentials which can be used in various ways. They control the coupling conditions between the vector components. One advantage of an electric vector potential, or generalised H, formulation is that the gauge can be chosen so that the vector is zero outside the conductors, and is replaced by a scalar. Magnetic vector-potential formulations are generally less attractive, both because the vector has to be computed throughout the region of interest and because of the greater complexity of the magnetic-and electric-interface conditions.

C.J. Carpenter

Papers

Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies

Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies