Bifurcations of stationary tearing modes with a resistivity depending on a flux function Original Research Article

We consider plasma tearing mode instabilities when the resistivity depends on a flux function (ψ), for the plane slab model. This problem, represented by MHD equations, is studied as a bifurcation problem. For so doing, it is written in the form (I − T(S, ·)), 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), but it depends nonlinearly of the unknowns of the problem; this is the main difficulty, with new mathematical results. We also develop in this paper a 1-D code to compute bifurcation points from the trivial branch (equilibrium state).