A discrete geometric formulation for eddy-current problems in fusion devices

All thermonuclear controlled fusion devices under construction or design have such high performances to require a special care in the dimensioning of various components, specically from the electromagnetic point of view. To this purpose, it is fundamental to develop models which are both accurate (i.e. able to describe the physical phenomena) and predictive (i.e. useful not only to explain what happens in running experiments, but also to reliably extrapolate to other range of parameters). The dynamics of fusion plasmas is often conveniently described by Magneto-Hydro-Dynamics (MHD) equations, which predict that some unstable evolution modes may exist. On the other hand, the complexity of the intrinsically 3D model of the interactions between a realistic unstable plasma, the surrounding passive structures (important to guarantee a good MHD stability) and the active conductors (coils) require the numerical solution of challenging electromagnetic problems. In this work a discrete geometric formulation for eddy-current problems in the frequency domain is developed; the magnetic elds produced by a typical active coil system is calculated in the presence of 3D conductive structures.