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

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 opera...

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Veröffentlicht in:ESAIM: Mathematical Modelling and Numerical Analysis 1999-11, Vol.33 (6), p.1135-1148
Hauptverfasser: Boussari, Atanda, Maschke, Erich, Saramito, Bernard
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Sprache:eng
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Zusammenfassung: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).
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an:1999138