On the Transition to Turbulence in Magneto-Hydrodynamic Models of Confined Plasmas

Starting from a model of an interchange-unstable plasma in a shearless magnetic field, the successive bifurcations and the transition to turbulence of the system are studied in various approximations. Numerical calculations using the finite element method and a spectral method with mode truncation yield converging results in certain domains of parameters. In the last part of the paper it is shown that a tearing-unstable plasma in a sheared magnetic field has a formally similar description and therefore should also be investigated in terms of bifurcation theory.