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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Bibliographic Details
Published in:ESAIM: Mathematical Modelling and Numerical Analysis 1999-11, Vol.33 (6), p.1135-1148
Main Authors: Boussari, Atanda, Maschke, Erich, Saramito, Bernard
Format: Article
Language:English
Subjects:
34A47
35J45
76E25
82D10
Bifurcation
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Magnetohydrodynamics and electrohydrodynamics
Mathematical analysis
Mathematics
MHD instabilities
Ordinary differential equations
Partial differential equations
Physics
Sciences and techniques of general use
tearing modes
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Summary: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