Steady tearing mode instabilities with a resistivity depending on a flux function

¹ Laboratoire de Mathématiques Appliquées, Université Blaise Pascal de Clermont-Ferrand, 63177 Aubière Cedex, France. saramito@ucfma.univ-bpclermont.fr.
² C.E.N. Cadarache, 13108 Saint-Paul-Lez-Durance, France.

Received: 6 May 1998
Revised: 11 February 1999

Abstract

We consider plasma tearing mode instabilities when the resistivity depends on a flux function (ψ), for the plane slab model. This problem, represented by the MHD equations, is studied as a bifurcation problem. For so doing, it is written in the form (I(.)-T(S,.)) = 0, where T(S,.) is a compact operator in a suitable space and S is the bifurcation parameter. In this work, the resistivity is not assumed to be a given quantity (as usually done in previous papers, see [1,2,5,7,8,9,10], but it depends non linearly of the unknowns of the problem; this is the main difficulty, with new mathematical results. We also develop in this paper a 1D code to compute bifurcation points from the trivial branch (equilibrium state).