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

Atanda Boussari; Erich Maschke; Bernard Saramito

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 6, page 1135-1148
- ISSN: 0764-583X

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topBoussari, Atanda, Maschke, Erich, and Saramito, Bernard. "Steady tearing mode instabilities with a resistivity depending on a flux function ." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1135-1148. <http://eudml.org/doc/197546>.

@article{Boussari2010,

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).
},

author = {Boussari, Atanda, Maschke, Erich, Saramito, Bernard},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Bifurcation; tearing modes; MHD instabilities.; plasma tearing mode instabilities; plane slab model; MHD equations; bifurcation problem; compact operator; bifurcation parameter},

language = {eng},

month = {3},

number = {6},

pages = {1135-1148},

publisher = {EDP Sciences},

title = {Steady tearing mode instabilities with a resistivity depending on a flux function },

url = {http://eudml.org/doc/197546},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Boussari, Atanda

AU - Maschke, Erich

AU - Saramito, Bernard

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

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 6

SP - 1135

EP - 1148

AB -
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).

LA - eng

KW - Bifurcation; tearing modes; MHD instabilities.; plasma tearing mode instabilities; plane slab model; MHD equations; bifurcation problem; compact operator; bifurcation parameter

UR - http://eudml.org/doc/197546

ER -

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