Co-dimension two bifurcation analysis for two-dimensional plasma convection

The plasma flow model of resistive interchange modes in a toroidally confined plasma is similar to the well known two-dimensional hydrodynamic Bénard–Rayleigh convection paradigm. A co-dimension two bifurcation analysis of the plasma problem is presented at a marginal point where two different wavelengths become simultaneously unstable. The weakly nonlinear interaction of convection cells is observed, and the hydrodynamic and plasma physics model systems are compared. With increasing magnetic shear, the dynamics of the resistive interchange model deviates significantly from the shearless hydrodynamic Bénard–Rayleigh convection predictions. The analytical results are confirmed by numerical simulations.