Ideal MHD stability calculations in presence of magnetic separatricesReport as inadecuate

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1 Associazione EURATOM-ENEA 2 Toulouse - ONERA - The French Aerospace Lab

Abstract : The use of magnetic coordinates, in which field lines are straight, defines the simplest approach to the numerical study of the ideal MHD stability of magnetoplasma equilibria: it allows the use of 1-dimensional radial Finite Elements, while adopting a Fourier decomposition in the poloidal angle. However the magnetic coordinates become singular in presence of magnetic separatrices. This difficulty becomes particularly relevant in the stability analysis of a simply connected axisymmetric plasmas Flux-Core-Spheromak or Chandrasekhar-Kendall-Furth configurations, which embed a magnetic separatrix with regular X-points B!=0 and are bounded by an edge magnetic separatrix that includes a part of the symmetry axis R=0 and is limited by two singular X-points B=0. The approach taken in the present paper is that of maintaining the 1-dimensional radial Finite Elements, while using an asymptotic analysis of the perturbed plasma displacement near the separatrices. The permissible asymptotic limits for the perturbed displacement are derived: they have simple analytical expressions in Boozer magnetic coordinates. An intensified numerical radial mesh following Boozer magnetic coordinates is set up near the magnetic separatrices; it requires: a logarithmic fit to the rotational transform near the embedded magnetic separatrix; a minimum distance between the radial mesh and both separatrices; finally an extended spectrum of poloidal mode numbers in the Boozer angle. The numerical results are compared -a posteriori- with the permissible asymptotic limits for the perturbed displacement. The radial displacement variable radial contravariant component of the perturbed displacement is found to be always near to its most unstable asymptotic limit, while the full range of permissible asymptotic behaviours can be obtained for the binormal and parallel displacement variables which are combinations of the poloidal and toroidal contravariant components of the perturbed displacement.

Author: Franco Alladio - Alessandro Mancuso - Paolo Micozzi - François Rogier -



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