Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. These bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.