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).