Bifurcations and transport barriers in the resistive-g paradigm

The so-called resistive-g (resistive pressure-gradient-driven turbulence) paradigm is a widely accepted and frequently investigated model for nonlinear plasma dynamics. The parameter dependences of the generated transport barriers as well as third order bifurcations will be discussed numerically and analytically in the present paper. First, using a Galerkin representation, bifurcating states (from the conductive states in a rectangular cell) are investigated for the cases when only one unstable mode dominates. The dependence of the bifurcation properties on the aspect ratio of the domain is discussed, leading to the conclusion that for vanishing (or small) magnetic shear the so-called low, high, and edge localized mode transitions do not occur for small aspect ratios of the domain. Including reasonable magnetic shear, the small-aspect-ratio cutoff disappears, and transport barriers may exist in a broad parameter range. Second, for small aspect ratios, interesting codimension-2 bifurcations occur. When unfolding the dynamics up to third order, e.g., a weakly nonlinear interaction of convection cells is observed. The analytical results are confirmed by numerical simulations.