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Steady tearing mode instabilitieswith a resistivity depending on a flux function

Published online by Cambridge University Press:  15 August 2002

Atanda Boussari ,
Erich Maschke  and
Bernard Saramito
Atanda Boussari
Affiliation:
Laboratoire de Mathématiques Appliquées, Université Blaise Pascal de Clermont-Ferrand, 63177 Aubière Cedex, France. [email protected].
Erich Maschke
Affiliation:
C.E.N. Cadarache, 13108 Saint-Paul-Lez-Durance, France.
Bernard Saramito
Affiliation:
Laboratoire de Mathématiques Appliquées, Université Blaise Pascal de Clermont-Ferrand, 63177 Aubière Cedex, France. [email protected].
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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. Forso doing, it is written in the form (I(.)-T(S,.)) = 0, whereT(S,.) is a compact operator in a suitable space and S is the bifurcationparameter.In this work, the resistivity is not assumed to be a given quantity (as usuallydone in previous papers, see [1,2,5,7,8,9,10], but it depends nonlinearly of the unknowns of the problem; this is the main difficulty, with newmathematical results.We also develop in this paper a 1D code to compute bifurcation points from the trivialbranch (equilibrium state).

Keywords

Bifurcationtearing modesMHD instabilities.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 6 , November 1999 , pp. 1135 - 1148
Copyright
© EDP Sciences, SMAI, 1999

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