Steady tearing mode instabilities with a resistivity depending on a flux function
Laboratoire de Mathématiques Appliquées,
Université Blaise Pascal de Clermont-Ferrand,
63177 Aubière Cedex, France. email@example.com.
2 C.E.N. Cadarache, 13108 Saint-Paul-Lez-Durance, France.
Revised: 11 February 1999
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).
Mathematics Subject Classification: 34A47 / 76E25 / 82D10 / 35J45
Key words: Bifurcation / tearing modes / MHD instabilities.
© EDP Sciences, SMAI, 1999