Center manifold approach to the reduced magnetohydrodynamic bifurcations with diffusive magnetic field lines

Bifurcations in plasmas are investigated on the basis of a reduced dissipat ive magnetohydrodynamic (MHD) model. In contrast to previous investigations , the diffusivity of magnetic field lines is taken into account. Making use of the center manifold theory for the first bifurcations, and Galerkin app roximations for higher bifurcations, it is shown that the diffusion of magn etic field lines affects the transitions in the transients. When the mode w hich resembles the so-called high confinement mode becomes unstable via a H opf bifurcation, the changes in the oscillation frequencies are calculated. It is demonstrated that over a wide range of parameter values the so calle d electrostatic approximation is quite good. The strength of the generated magnetic field fluctuations is calculated, and the influence of the latter on a possible magnetic braiding is estimated. (C) 1999 American Institute o f Physics. [S1070-664X(99)01504-9].