High confinement modes with radial structure

We study the radial structure of high confinement modes in a simplified, one-dimensional model of the self-consistent interaction of fluctuations, shear flow, and pressure gradient. The model describes the plasma edge with an energy flux coming from the core, which is used as a boundary condition for the pressure transport equation. As the energy flux increases, there is an L-H transition bifurcation which is described near marginal instability using a reduced Ginzburg-Landau model for the shear flow coupled to a transport equation for the pressure. For higher values of the energy flux, a second transition takes place in which the H-mode exhibits a finite-k instability. Numerical results show that this instability leads in the nonlinear regime to the spontaneous formation of a pedestal in the pressure profile, where the effective diffusivity exhibits a sharp drop. A further increase in the energy flux leads to multiple pedestals across the simulation domain.