Linearly perturbed MHD equilibria and 3D eddy current coupling via the control surface method

Abstract

In this paper, a coupling strategy based on the control surface concept is used to self-consistently couple linear MHD solvers to 3D codes for the eddy current computation of eddy currents in the metallic structures surrounding the plasma. The coupling is performed by assuming that the plasma inertia (and, with it, all Alfven wave-like phenomena) can be neglected on the time scale of interest, which is dictated by the relevant electromagnetic time of the metallic structures. As is shown, plasma coupling with the metallic structures results in perturbations to the inductance matrix operator. In particular, by adopting the Fourier decomposition in poloidal and toroidal modes, it turns out that each toroidal mode can be associated with a matrix (additively) perturbing the inductance matrix that commonly describes the magnetic coupling of currents in vacuum. In this way, the treatment of resistive wall modes instabilities of various toroidal mode numbers and their possible cross-talk through the currents induced in the metallic structures can be easily studied.

Electromagnetic disruption analysis in IGNITOR

“…Several modelling approaches are available for the analysis of the electromagnetic interactions between the plasma and the conductors [3][4][5][6][7][8][9][10][11][12][13], ranging from simple linearized axisymmetric codes, to nonlinear axisymmetric evolutionary equilibrium modes, to three-dimensional MHD linearized and nonlinear models. Such codes are widely and extensively used for the numerical analysis of future devices; however, none of them can be applied to all cases of interest, due to specific limitations and ranges of applicability.…”

Three-dimensional Cauchy-condition surface method to identify the shape of the last closed magnetic surface in the Large Helical Device

“…On the other hand, 3-D analyses are required for non-axisymmtric plasma, e.g., in a helical type device such as the Large Helical Device (LHD) of the National Institute for Fusion Science (NIFS), Japan. Even in tokamaks, 3-D considerations are required in some situations caused by perturbations during their operation [8,9].…”

A fast technique applied to the analysis of Resistive Wall Modes with 3D conducting structures

“…The CarMa computational tool is described in details in [13,14]. Here we simply report the main points.…”

“…Doing so, we compute the plasma response, which is static thanks to the fact that we have neglected plasma mass. For each of these M solutions, we evaluate the quantity (9), hence giving rise to a N Â M matrix S. Typically, it results M ( N due to the fact that S is a (regular) surface; moreover, M does not depend on N. The expression of the elements of matrix S is given in [14].…”

“…Of course, the inclusion of fine geometrical details may easily lead to huge memory and computational time requirements. To this purpose, in this paper we present the development of ''fast" techniques, for the treatment of large computational models, within the formulation behind the CarMa code, which is able to perform a 3D analysis of RWMs [13][14][15] and has also been validated with experimental results [16].…”